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1. Figure 120 The arguments ddraw_color Used to specify a color for the Path ddraw_color is a reference to a Color Colors are described in Chapter 16 Color Reference page 88 The most basic Colors are predefined in 3DLDF in the namespace Colors and users may create new Colors and specify their red green blue values The Path p could be drawn in red by calling p draw Colors red This manual isn t intended to be printed in color so there s no figure to demon strate this However gray values can be printed on non color printers using namespace Colors p draw gray pencircle scaled 25mm Figure 121 Chapter 26 Path Reference 182 ddashed A string representing a dash pattern as defined in MetaPost Dash patterns have no meaning in 3DLDF they are simply strings that are written unchanged to out_stream p draw black evenly Figure 122 ppen A string representing a pen as defined in Metafont and MetaPost Pens have no meaning in 3DLDF they are simply strings that are writ ten unchanged to out_stream p draw black pensquare xscaled 3mm yscaled 25mm scaled 5mm Figure 123 picture Indicates the Picture on which the Path should be drawn The two versions of draw differ in the position of the picture argument In the first version it s the last argument while in the second version it s the first argument If a picture argument is used it s
2. 1 Path q2 p0 draw p1 cout lt lt q2 get_line_switch Path q3 false amp p1 amp p2 p0 0 cout lt lt q3 get_line_switch Figure 109 Some Path functions only work on linear Paths so it s necessary to be able to dis tinguish them from non linear ones The function is_linear should be enough to ensure that all of these functions work so I plan to make line_switch obsolete soon However at the moment it s still needed See Section 26 15 Path Reference Querying page 194 Chapter 26 Path Reference 166 bool cycle_switch Protected variable true if the Path is cyclical otherwise false bool on_free_store Protected variable true if the Path was dynamically allocated on the free store Otherwise false Set to true only in create_new lt Path gt which should be the only way Paths are ever dynamically allocated See Section 26 2 Path Constructors and Setting Functions page 167 bool do_output Protected variable Used in Picture output Set to false if the Path isn t projectable using the arguments passed to Picture output See Section 21 8 Picture Reference Out putting page 114 signed short fill_draw_value Protected variable Set in the drawing and filling functions and used in Path output to determine what MetaPost code to write to out_stream See Section 26 12 Path Reference Drawing and Filling page 180 and Section 26 16 Path Reference Outputting
3. 122 22 4 Constructors and Setting Functions 122 220 Destruct r nerin A da ai a 123 22 06 Operator iia o aaa 124 DAT COPY Aaa AE 126 ZA Querying a a di 126 22 9 Returning Coordinates o o oocoooocccococccnoocccco 127 22 10 Returning Informati0N 00ooococoooccccocncc oo 129 2211 MOM id A da So 129 22 12 Affine Transformations 0 0000 cece cece ee ooo 130 22 13 Applying Transformations 00000 eee 135 2214 7 PEOJCCUNE noria each he tea tase te Sears 135 22 15 Vector Operations 0 0 cece eee eee ee 135 22 16 Points and Lines 0 ccc ccc cece eens 140 22 17 WitETSeChIONS h mai a SES aoe ody ds ot aol glans 143 2218 DRAWINGS e resisae 8 a eee aaa ai eis ote eta ben pale 144 22 19 Labelling 00 eee cette eens 147 22 20 OHOWING mA Awe Woe ees artes a Sect 149 22 21 Oubputting ti de atte does 149 23 Focus Reference ooooooooooooooo 151 23 1 Data Members ice ick ted Ga di ate see ages 151 23 27 Global Variabl s o xi oracion aa deus sith bbe Se Stee tie 151 23 3 Constructors and Setting Functions 152 23 4 Operators is wit ita tel ee PAL he wae ies Bes 152 23 0 Modifying its gine ia os dete ae bee hae ie 152 23 05 UY tat hol Lisi ht tad oleate Ee 153 23 1 Showin rat ee eae Gs cee ka pat pe eal aes 153 vi 24 Line Reference oo oooooooo ooo 154 24 1 Data MembersS o oooocococororcnc cee eee
4. Chapter 31 Ellipse Reference 229 4 1 Point D A D shift 2 0 4 e location D WARNING In Ellipse location Point doesn t lie in plane of Ellipse Returning 2 e scale 1 5 0 1 5 e location A WARNING In Ellipse do_transform const Transforms This transformation has made this non elliptical ERROR In Ellipse location Ellipse is non elliptical Returning 3 Figure 164 Point angle_point real angle const function Returns a point on the Ellipse given an angle A Point pis set to the zeroth Point on the Ellipse and rotated about the line from the center of the Ellipse in the direction of the normal to the plane of the Ellipse Then the intersection of the ray from the center through p and the perimeter of the Ellipse is returned Ellipse e origin 6 4 Point P e angle_point 135 current_picture output Projections PARALLEL_X_Z Chapter 31 Ellipse Reference 230 Figure 165 Fig 166 demonstrates that the rotation is unfortunately not always in the direction one would prefer I don t have a solution to this problem yet Ellipse e origin 6 4 90 Point P e angle_point 135 Point Q e angle_point 135 Figure 166 31 9 Intersections bool_point_pair intersection_points const Point amp const virtual function pO const Point amp p1 bool_point_pair intersection_points const Path amp p const virtual function These functions return
5. Figure 1 16 Chapter 3 Transforming Points 17 3 4 Rotating The function rotate rotates a Point about one or more of the main axes It takes three real arguments specifying the angles of rotation in degrees about the x y and z axes respectively Only the first argument is required the other two are 0 by default If rotation about the y axis or the y and z axes only are required then 0 must be used as a placeholder for the first and possibly the second argument Point p 0 1 p rotate 90 p show p po 0 0 1 p rotate 0 90 p show p J p 41 0 0 p rotate 0 0 90 p show p p 0 1 0 The rotations are performed successively about the x y and z axes However rotation is not a commutative operation so if rotation about the main axes in a different order is required then rotate must be invoked more than once Point A 2 3 4 Point B A A rotate 30 60 90 A show A 4 A 4 59808 0 700962 2 7141 B rotate 0 0 90 B rotate 0 60 B rotate 30 B show B 4 B 4 9641 1 43301 1 51795 Rotation need not be about the main axes it can also be performed about a line defined by two Points The function rotate with two Point arguments and a real argument for the angle of rotation in degrees about the axis The real argument is optional with 180 as the default Point pO 1 06066 O 1 06066 Point p1 1 06066 0 1 06066 pl p
6. 2 75865 cout lt lt bp second gt de bp q get_distance C cout lt lt bp first 340 cout lt lt bp second 340 Figure 106 Chapter 25 Plane Reference 161 25 6 Intersections bool_point intersection_point const Point amp p0 const const function Point amp p1 bool_point intersection_point const Path amp p const function These functions find the intersection point of the Plane and a line In the first version the line is defined by the two Point arguments In the second version the Path p must be linear i e p is_linear must be true Both versions of intersection_point return a bool_point bp where bp pt is the intersection point or INVALID_POINT if there is none If an intersection point is found bp b will be true otherwise false Returning a bool_point makes it possible to test for success without comparing the Point returned against INVALID_POINT Point center 2 2 3 5 Reg_Polygon h center 6 4 80 30 10 Plane q h get_plane Point PO center mediate h get_point 2 PO shift 5 N center Point P1 PO P1 rotate h get_point 1 h get_point 4 P1 3 P1 PO P1 shift P0 P1 shift 3 5 2 bool_point bp q intersection_point PO P1 Point i_P bp pt Point P4 h get_point 3 mediate h get_point 0 75 P4 shift N center Point P5 P4 P5 rotate h get_point 3 h get_point 0 P4 shift 1 2 Path theta P4 P5
7. Figure 141 vector lt Point gt intersection_points const Polygon amp r const function Finds the intersection points of two Polygons Let v be the vector lt Point gt returned by intersection_points If the Polygons are coplanar v will contain the inter section points of the edges of the Polygons as in Fig 142 Rectangle r origin 4 4 Reg_Polygon rp origin 5 5 0 36 rp shift 0 0 25 vector lt Point gt v r intersection_points rp Chapter 27 Polygon Reference 203 Figure 142 If the Polygons lie in parallel planes there can be no intersection points If they lie in non parallel non coplanar planes intersection_points first finds the intersec tion line of the two planes Then it finds the intersection points of this line with the two Polygons if they exist There can no more than four intersection points in this case v 0 and v 1 will be the intersection points of the line with this while v 2 and v 3 will be the intersection points of the line with r If one or more of the intersection points doesn t exist the corresponding member of v will contain INVALID_POINT as a placeholder Point A 1 1 1 Rectangle r A 4 4 Reg_Polygon p A 5 5 p rotate 90 30 p shift 2 0 3 vector lt Point gt v r intersection_points p Figure 143 In Fig 144 the Rectangle r and the Reg_Polygon p don t overlap at all nor does the intersection line of the
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9. Chapter 26 Path Reference 197 26 16 Outputting bool project const Focus amp f const unsigned short proj real Function factor Calls Point project f proj factor on the Points on the Path If Point project fails i e returns false for any of the Points this function returns false Otherwise it returns true vector lt Shape gt extract const Focus amp f const unsigned short Function proj real factor Checks that the Points on points can be projected using the values for f proj and factor If they can a vector lt Shape gt containing only this is returned Called in Picture output bool set_extremes void Virtual function Sets the appropriate elements in projective_extremes to the minimum and max imum values of the x y and z coordinates of the Points on the Path Used in Picture output for determining whether a Path can be output using the argu ments passed to Picture output const valarray lt real gt get_extremes void Inline const virtual function Returns projective_extremes Used in Picture output real get_minimum_z void const virtual function real get_mean_z void const virtual function real get_maximum_z void const virtual function These functions return the minimum mean or maximum value respectively of the z coordinates of the Points on the Path Used in the surface hiding algorithm in Picture output void suppress_output void Virtual functio
10. Chapter 27 Polygon Reference 201 When the Point arguments and the Reg_Polygon are coplanar as in Fig 139 two intersection points are possible In this case only intersection points of the line with an edge of the Reg_Polygon are returned in the bool_point_pair Point A 1 1 1 Reg_Polygon r origin 5 3 Transform t t rotate 15 12 11 t shift A Point P 2 0 1 Point Q 2 0 1 P Q r t bool_point_pair bpp r intersection_points P Q bpp first pt dotlabel f rt bpp second pt dotlabel s Figure 139 In Fig 140 the lines BC and PQ are not coplanar with the Reg_Polygon r In each case only one intersection point is possible and it can be either an intersection with an edge of the Reg_Polygon or lie within its perimeter Point B r get_point 3 mediate r get_point 4 Point C B B shift 0 2 5 C shift 0 2 5 Point P 1 2 1 Point Q 0 2 1 B C P Q r t bool_point_pair bpp r intersection_points B C bpp first pt dotlabel i_0 rt bpp r intersection_points P Q bpp first pt dotlabel i_1 rt Chapter 27 Polygon Reference 202 Figure 140 In Fig 141 the intersection point of r with the line PO does not lie on the line segment PQ bpp r intersection_points P Q bpp first pt dotlabel i rt cout lt lt bpp first b lt lt bpp first b lt lt endl lt lt flush bpp first b
11. Point p0 2 2 3 Ellipse e p0 3 4 30 60 5 2 Point p1 pO mediate e get_point 11 5 Point A e get_normal A 2 5 A shift p1 Point B A mediate p1 2 bool_point_pair bpp e intersection_points A B Point C O 2 0 Point D O 3 5 0 C D rotate 2 0 5 C D shift e get_point 4 bpp e intersection_points C D Figure 154 In Fig 155 q and e are coplanar In this case only the intersections of q with the perimeter of e are returned by intersection_points A pO mediate e get_point 3 1 5 B p0 mediate e get_point 11 1 5 Path q A B bpp e intersection_points q Chapter 30 Regular Closed Plane Curve Reference 219 Figure 155 30 4 Segments Path segment unsigned int factor real angle 0 bool const function closed true Returns a Path representing a segment of the Reg_C1_Plane_Curve factor must be gt 1 and lt number_of_points If it is not an error message is issued and an empty Path is returned If angle is non zero the segment Path is rotated by angle about a line from center in the direction of the normal to the plane of the Reg_C1_Plane_Curve Please note that a Reg_C1_Plane_Curve must have a meaningful center in order for rotation to work If the absolute value of angle gt 360 a warning is issued and fmod angle 360 is used If closed is true the Path will be a cycle with the ends of the curved segment joined us
12. 19 295 I identity matike satata eiea RARO 20 ImageMagick sei lt we hoe end 77 78 ImageMagick convert 00000000 77 ImageMagick display 005 78 input routines o rene paa a ete hae a 10 intersection ano rias EE o eee 73 intersection points o oooocooocooccoooomo 73 intersection the0ry oooooococccccccccccoo 73 invariance projective o ooooooooooomoo 276 A cts eben 21 K kl dge inane te tdi 271 L linear Paths i iaa ge Leche pata we eed 165 lines drawing 0 cece eee eee eee eee 24 local variable listS o oooooooooooo 92 M Matrix NVETSION orinal seesaw es gets oT aces 21 matrix operationS 0 cece ee eee 20 Matrix Identity 35 ie a eee tees SS 20 measurement unitS eee eee eee 10 member function 00 e ee ee eee eee 3 Metatont o eraai ae dat le aie a ese the Eanes dees 6 MietaBost cnica tea plas dates iaa ae etait 6 multi threading 000000 277 multiple inheritance oooo oooooo ooo 275 N non arbitrary Path 000000 0 73 non uniform rational B splines NURBS 276 NURBS non uniform rational B splines 276 operations Matrix 00 eee eee eee 20 output file gt neces ieee ee at 54 73 144 output les cinco id ee cd bee o hae 54 P painter s algorithm 000 00 68 A A as 276 Path connectors 0 0c eee ee eee eee eee
13. cout lt lt n_mag 4 11 3137 n_mag ut lt lt n magnitude 4 1 Chapter 22 Point Reference 138 0 70 5288 Figure 88 If 9 0 or 180 sin will be 0 and P x Q will be 0 0 0 The cross product thus provides a test for parallel vectors Point P 1 2 1 Point Q P Point R R Q shift 3 1 1 Point s Q R Point n P cross_product s n show n 4 n 0 0 0 wl origin Figure 89 real magnitude void const function Returns the magnitude of the Point This is its distance from origin and is equal to 4 12 y 2 Point P 13 15 7 22 cout lt lt P magnitude 4 29 9915 Chapter 22 Point Reference 139 real angle Point p const function Returns the angle in degrees between two Points Point P 3 75 1 25 6 25 Point Q 5 2 5 6 25 real angle P angle Q cout lt lt angle 4 73 9084 Point n origin get_normal P Q n show n 4 n 0 393377 0 91788 0 0524503 MaS Figure 90 Point unit_vector const bool assign const bool silent false Function Point unit_vector void const function These functions return a Point with the x y and z coordinates of world_ coordinates divided by the magnitude of the Point The magnitude of the resulting Point is thus 1 The first version assigns the result to this and should only ever be called with assign true Calling it with the argument
14. real radius Private variable The radius of the surrounding circle for a Reg_Polygon Umkreis unsigned short sides Private variable The number of sides of a Reg_Polygon bool on_free_store Private variable true if the Reg_Polygon was dynamically allocated on the free store otherwise false Dynamic allocation of Reg Polygons should only be performed by create_ new lt Reg_Polygon gt which sets on_free_store to true 28 2 Constructors and Setting Functions void Reg_Polygon void Default constructor Creates an empty Reg_Polygon void Reg_Polygon const Point amp ccenter const unsigned short Constructor ssides const real ddiameter const real angle_x 0 const real angle_y 0 const real angle_z 0 Creates a Reg_Polygon in the x z plane centered at the origin with the number of sides specified by ssides and with radius ddiameter 2 The Reg Polygon is rotated about the x y and z axes in that order by the angles given by angle_x angle_y and angle_z respectively if any one of them is non zero Finally the Reg_Polygon is shifted such that its center is located at ccenter Reg_Polygon r origin 3 2 75 10 15 12 5 r draw Chapter 28 Regular Polygon Reference 206 WK he Figure 145 void set const Point amp ccenter const unsigned short ssides Setting function const real ddiameter const real angle_x 0 const real angle_y 0 const real angle_z 0 Corresponds to the co
15. subpersp mp by initialize_io see Section 17 2 I O Func tions page 92 ofstream tex_stream Variable TeX code can be written to a file through tex_stream if desired 3DLDF makes no use of it itself Currently attached to subpersp tex by initialize_io see Section 17 2 I O Functions page 92 17 2 I O Functions void initialize_io string in_stream_name string out_stream_name Function string tex_stream_name char program_name Opens files with names specified by the first three arguments and attaches them to the file streams in_stream out_stream and tex_stream respectively Comments are written at the beginning of the files containing their names a datestamp and the name of the program used to generate them void write_footers void Function Writes code at the end of the files attached to in_stream out_stream and tex_ stream before the streams are closed Currently they write comments containing local variable lists for use in Emacs void beginfig unsigned short i Inline function Writes beginfig i to out_stream void endfig unsigned short i 0 Inline function Writes endfig to out_stream The argument i is syntactic sugar it s ignored by endfig but may help the user keep track of what figure is being ended Chapter 18 Shape Reference 93 18 Shape Reference Class Shape is defined in shapes web Shape is an abstract class which means that all o
16. Corresponds to the constructor above 4 Where possible I prefer to use the C data type string rather than char however it was necessary to use char here because 0 is not a valid string even though string may be implemented as char and 0 must be a valid argument since it is needed to indicate the end of the argument list Chapter 26 Path Reference 171 void Path const Path amp p Copy constructor Creates a new Path making it a copy of p Path create_new lt Path gt const Pathx p Template specializations Path create_new lt Path gt const Path amp p Pseudo constructors for dynamic allocation of Paths They create a Path on the free store and allocate memory for it using new Path They return a pointer to the new Path If p is a non zero pointer or a reference the new Path will be a copy of p If the new object is not meant to be a copy of an existing one 0 must be passed to create_new lt Path gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information create_new lt Path gt is used in the drawing and filling functions for copying a Path and putting the copy onto a Picture See Section 26 12 Path Reference Drawing and Filling page 180 26 3 Destructor void Path void virtual Destructor All of the Points on a Path are created by create_new lt Point gt which allo cates them dynamically on the free store Therefore the destructor calls delete on all
17. Even where objects don t intersect their projections may In order to handle these cases properly it is necessary to break up the Shapes on a Picture into smaller Shapes until there are none that intersect or whose projections intersect Then any of the three methods of sorting described above can be used to sort the Shapes and they can be output Before this can be done 3DLDF must be able to find the intersections of all of the different kinds of Shapes If 3DLDF converted solids to polyhedra and curves to sequences of line segments this would reduce to the problem of finding the intersections of lines and planes however it does not yet do this Even if it did a fully functional hidden surface algorithm must compare each Shape on a Picture with every other Shape Therefore for n Shapes there will be n n r r possibly time consuming comparisons The following table shows how many comparisons are needed for n Shapes for several values of n Shapes Comparisons 10 45 100 4950 1000 499 500 10 000 49 995 000 100 000 4 99995 x 10 Figure 71 Clearly such a hidden surface algorithm would considerably increase run time Currently all of the Shapes on a Picture are output as long as they lie completely within the boundaries passed as arguments to Picture output See Section 21 8 Pictures Outputting page 114 It would be more efficient to suppress output for them if they are completely
18. Point center 2 0 3 for int i 0 i lt 5 i f set pos dir 10 15 i Rectangle r center 3 3 r draw current_picture output f current_picture clear pos shift 1 1 0 Chapter 9 Pictures 66 dir rotate 0 0 10 endfig 1 Figure 63 In Fig 63 current_picture is output 5 times within a single MetaPost figure Since the file passed to MetaPost is called persp mp the file of Encapsulated PostScript EPS code containing Fig 63 is called persp 1 To use this technique for making an animation it s necessary to output the Picture into multiple MetaPost figures Point pos 2 10 3 Point dir 2 10 3 Focus f Point center 2 0 3 for int i 0 i lt 5 i f set pos dir 10 15 i Rectangle r center 3 3 r draw beginfig i 1 current_picture output f endfig current_picture clear pos shift 1 1 0 dir rotate 0 0 10 Now running MetaPost on persp mp generates the EPS files persp 1 persp 2 persp 3 persp 4 and persp 5 containing the five separate drawings of r Chapter 9 Pictures 67 9 3 Surface Hiding In Fig 64 Circle c lies in front of Rectangle r Since c is drawn and not filled r is visible behind c default_focus set 1 3 5 0 3 5 10 Point p 0 2 5 Rectangle r p 3 4 90 r draw Point q 2 2 3 Circle c q 3 90 c draw current_pi
19. bp q intersection_point theta Point i_theta bp pt draw_axes Chapter 25 Plane Reference 162 Figure 107 Line intersection_line const Plane amp p const function Returns a Line representing the line of intersection of two Planes See Chapter 24 Line Reference page 154 In Fig 108 intersection_line is used to find the line of intersection of the Planes derived from the Rectangles ry and r using get_plane see Section 26 15 Paths Reference Querying page 194 Please note that there is no guarantee that l position will be in a convenient place for your drawing A bit of fiddling was needed to find the Points P and P I plan to add functions for finding the intersection lines of plane figures but haven t done so yet Rectangle r0 origin 5 5 10 15 6 Rectangle ri origin 5 5 90 50 10 ri r0 rotate 30 30 30 ri r0 shift 1 1 3 Plane q0 r0 get_plane Plane qi r1 get_plane Line 1 q0 intersection_line q1 1 show 1 A position 0 11 2193 20 0759 direction 0 0466595 0 570146 0 796753 Point PO 1 direction PO shift 1 position PO show PO 4 PO 0 0466595 10 6491 19 2791 Point P1 1 direction P1 shift l position Point P2 PO P1 P2 12 5 Chapter 25 Plane Reference 163 P2 shift PO cout lt lt P2 is_on_plane q0 J 1 cout lt lt P2 is_on_plane q1 li Point P3 PO P1 P3 7 P3 shift PO
20. cd 3DLDF 1 1 5 1 configure prefix usr local mydir 3DLDF 1 1 5 1 configure generates a Makefile from the Makefile in in 3DLDF 1 1 5 1 and in each of the subdirectories 3DLDF 1 1 5 1 CWEB 3DLDF 1 1 5 1 DOC and 3DLDF 1 1 5 1 DOC TEXINFO Now make install causes the 3DLDF to be built The executable is called 3d1df See the files README and INSTALL in the 3DLDF distribution for more information 11 1 1 Template Functions 3DLDF 1 1 5 is the first release that contains template functions namely template lt class C gt C create_new which is defined in creatnew web and template lt class Real gt Real get_second_largest which is defined in gs1tmp1t web See Chapter 14 Dynamic Allocation of Shapes page 84 and Section 15 3 Get Second Largest Real page 87 In order for template functions to be instantiated correctly their definitions must be available in each compilation unit where specializations are declared or used For non template functions it suffices for their declarations to be available and their definitions are found at link time For this reason the definitions of create_new and get_second_ largest are in their own CWEB files and are written to their own header files The latter are included in the other CWEB files that need them In addition AM_CXXFLAGS frepo has been added to the file Makefile am in 3DLDF 1 1 5 CWEB so th
21. const real angle 180 Function Rotation around an arbitrary axis The Point arguments represent the end points of the axis and angle is the angle of rotation Since 180 rotation is needed so often 180 is the default for angle Transform rotate const Path amp p const real angle 180 Function Rotation around an arbitrary axis Path argument The Path p must be linear i e p is_linear must return true See Section 26 15 Path Reference Querying page 194 19 11 Alignment with an Axis Transform align_with_axis Point p0 Point p1 char axis z Function Returns the Transform that would align the line through p0 and p1 with the major axis denoted by the axis argument The default is the z axis This function is used in the functions that find intersections Point PO 1 1 1 Point P1 2 3 4 PO draw P1 PO dotlabel P_0 P1 dotlabel P_1 Transform t t align_with_axis PO P1 z PO P1 t t show t ate 0 949 0 169 0 267 0 0 0 845 0 535 0 Chapter 19 Transform Reference 106 0 316 0 507 0 802 0 0 632 0 169 1 6 1 PO show PO 4 PO 0 0 0 P1 show P1 4 Pi 0 0 3 74 The following example shows how align_with_axis can be used for putting plane figures into a major plane default_focus set 2 3 10 2 3 10 10 Circle c origin 3 75 25 6 c shift 2 3 c draw Point n c get_normal n shift c get_center Transfor
22. const real r see above but with r placed first Point pO 10 11 12 real r 2 5 Point p1 r po pi show Point 25 27 5 30 Point operator void const operator Unary minus prefix Returns a Point with x y and z coordinates world_ coordinates equal to the the x y and z coordinates world_coordinates of this multiplied by 1 void operator const real r Operator Divides the updated x y and z coordinates world_coordinates of the Point by r Point operator const real r const operator Returns a Point with x y and z coordinates world_coordinates equal to the updated x y and z coordinates of this divided by r bool operator Point p Operator bool operator const Point amp p const operator Equality comparison for Points These functions return true if the updated values of the world_coordinates of the two Points differ by less than the value returned by Chapter 22 Point Reference 126 Point epsilon otherwise false See Section 22 10 Point Reference Returning Information page 129 bool operator const Point amp p const operator Inequality comparison for Points Returns false if this p otherwise true 22 7 Copying Shape get_copy void const function Creates a copy of the Point and allocates memory for it on the free store using create_new lt Point gt It returns a pointer to Shape that points to the new Point This function is used in the
23. from world_coordinates these values will all be the same These functions are pure virtual functions in Shape and are called on Points through pointers to Shape Therefore they must be consistent with the versions for other types derived from Shape See Section 18 10 Outputting Shapes page 95 Chapter 23 Focus Reference 23 Focus Reference 151 Class Focus is defined in points web Focuses are used when creating a perspective projection They represent the center of projection and can be thought of like a camera viewing the scene 23 1 Data Members Point position The location of the Focus in the world coordinate system Point direction The direction of view from position into the scene Point up The direction that will be at the top of the projected drawing real distance The distance of the Focus from the plane of projection real angle Used for determining the up direction char axis Private variable Private variable Private variable Private variable Private variable Private variable The main axis onto which the Focus is transformed in order to perform the perspective projection z by default It will normally not matter which axis is used but it might be advantageous to use a particular axis in some special situations Transform transform Private variable The Transform which will be applied to the Shapes on the Picture when the latter is output The effect of this
24. o o oo o o o 118 unsuppress_output 95 197 254 V VOL sard ree A e Ps A 150 Concept Index Concept Index A ammatin title cti Fe Ae 65 66 arbitrary Path bite See es Seo earns 73 B B SplineS cane oe sts eee yn ed 276 B zi r Curves niceties we cee Gs e Meee OG 276 DUgS al a teas dt 18 CD R Compact Disk Recordable 78 Compact Disk Recordable CD R 78 Comprehensive TeX Archive Network CTAN 2 connecting Points o o ooooooooo 24 CONECTO on 4 sad aa E a eae a 28 73 contributing to 83DLDF 73 control points evoca arre 28 COMES ae HR eld tito 28 convert ImageMagick oooooocccccccccco 77 CTAN Comprehensive TEX Archive Network 2 CU Deeper ahaha eer ane a ae Noahs 28 derivation ses eie a r a o ae 275 derived classes 0oooooooooooomoomooo 275 display ImageMagick ooooooooomooooo 78 drawing and filling ooo o ooooooooo 24 O at Se eae 92 EmacsDiSPDiici oli On oa eee 79 Encapsulated PostScript EPS 4 6 77 79 EPS Encapsulated PostScript 4 6 77 79 F FDL GNU Free Documentation License 282 fil Output s reres a ta 144 function templates 0 eee eee 74 function member ooooccocoocccoooo o 3 future pla a cn td ala 73 H help lines citant dr 146 hidden surface algorithm ooo 68 homogeneous coordinates oooooooooooo
25. page 197 const Color draw _color Protected variable Pointer to the Color used if the Path is drawn const Color fill_color Protected variable Pointer to the Color used if the Path is filled string dashed Protected variable String written to out_stream for the dash pattern in a MetaPost draw or undraw command If and only if dashed is not the empty string dashed lt dash pattern gt is written to out_stream Dash patterns have no meaning inside 3DLDF dashed if non empty is written un changed to out_stream I may change this in the future string pen Protected variable String written to out_stream for the pen to be used in a MetaPost draw undraw filldraw or unfilldraw command If and only if pen is not the empty string withpen lt gt is written to out_stream Pens have no meaning inside 3DLDF pen if non empty is written unchanged to out_stream I may change this in the future bool arrow Protected variable Indicates whether an arrow should be drawn when outputting a Path Set to true on a Path created on the free store and put onto a Picture by drawarrow valarray lt real gt projective_extremes Protected variable Contains the maxima and minima of the x y and z coordinates of the projections of Points on a Path using a particular Focus Set in set_extremes and used in Picture output for surface hiding Chapter 26 Path Reference 167 vector lt Point gt points Protected
26. real yx 0 real yz 0 Function real zx 0 real zy 0 Calls transform shear with the same arguments and returns its return value namely a Transform representing the shearing operation only Shearing modifies each coordinate of a Point proportionately to the values of the other two coordinates Let o Yo and zg stand for the coordinates of a Point P before P shear a B y e C and 21 y1 and z for its coordinates afterwards my Mtayrt Bz Y Y yt 0z A z er EY Fig 84 demonstrates the effect of shearing the four Points of a 3 x 3 Rectangle e a square r in the x y plane using only an xy argument making it non rectangular Point PO Point P1 3 Point P2 3 3 Point P3 0 3 Rectangle r p0 pl p2 p3 r draw r shear 1 5 r draw black evenly Chapter 22 Point Reference 134 Pz 0 3 P gt 3 3 Q 4 5 3 Q2 7 5 3 e DAD A ee gt P a Po Qo 0 0 Pi Q1 3 0 Figure 84 Transform shift real x real y 0 real z 0 Function Transform shift const Point amp p Function Each of these functions calls the corresponding version of Transform shift on transform and returns its return value namely a Transform representing the shift ing operation only The Point is shifted x units in the direction of the positive x axis y units in the direction of the positive y axis and z units in the direction of the positive
27. 0 45 p 5 p 6 p 7 rotate 0 0 45 pl6 p 7 rotate 0 0 45 p 7 rotate 0 0 45 Path r0 true amp p 0 amp p 1 amp pl2l ro ro ro ro scale 25 3 ro ro filldraw ro amp p 3 amp p 4 amp p 5 amp p 6 amp p 7 0 filldraw black light_gray scale 2 5 shift 0 0 2 5 filldraw black gray shift 0 0 2 5 Chapter 26 Path Reference 189 a gt Figure 131 void undraw string ddashed string ppen Picture amp Function picture current_picture void undraw Picture amp picture string ddashed string ppen Function Allocates a copy of the Path on the free store puts a pointer to it on picture shapes sets its fi11_draw_value to UNDRAW and the values of its dashed and pen according to the arguments The second version is convenient for passing a Picture argument without having to specify all of the other arguments This function undraws a Path This is equivalent to drawing the Path using the background color Colors background_color Undrawing is useful for removing a portion of a Path Point PO 1 1 Point P1 2 1 Point P2 2 3 Point P3 1 1 Path p false amp origin amp PO amp P1 amp P2 amp P3 0 p draw black pencircle scaled 3mm p undraw pencircle scaled 1mm Figure 132 Chapter 26 Path Reference 190 void unfill Picture amp picture
28. 00 cece eee eee eee eee 249 3407 Querying wee dae alg Pete een cea ee 250 34 8 Returning Elements and Information 250 Getting Shape Centers 00 0 c eee een eee 250 Getting Shapes 0 6 0 0 cect e tee cere cence eee 251 349 SHOWING tid aid AN Da Na wold abe e ee 8 253 34 10 Affine Transformations 000 00 cc cece eee 253 34 11 Applying Transformations 000 00000 254 34212 Opus ats eee hc Manica es 254 34 13 Drawing and Filling 0 0 eee eee eee 255 SALA Ola OE rra A ida 256 35 Faced Solid Reference 257 35 1 Data Members 0 0 0 ccc cece nee teenies 257 36 Cuboid Reference 24 258 36 1 Data Members 00 0 a E a ene a E E 258 36 2 Constructors and Setting Functions 258 36 3 Operators cence es ia ia dias 259 37 Polyhedron Reference 260 37 1 Data Members 0 c cece ccc cnet teen enes 260 37 2 Regular Platonic Polyhedra 02000 260 37 2 1 Tetrahedron 0 0 c eet ene e nes 260 37 2 1 1 Data Members oooooooooo 260 37 2 1 2 Constructors and Setting Functions 260 AN oe ne 262 37 2 2 Dodecahedron 00 0 cece cece eee 264 37 2 2 1 Data Members 2005 264 37 2 2 2 Constructors and Setting Functions 264 A N tsiect wit nwtioh ee tiden ge ead 265 37 2 3 Icosahedron 0 00 c cece cee ee
29. 2 5 cout lt lt P angle Q 112 002 cout lt lt P dot_product Q 4 4 real P_Q_angle 180 0 PI acos P dot_product Q P magnitude Q magnitude cout lt lt P_Q_angle 4 112 002 3 2 5 0 112 002 7 Pe Q 4 Figure 86 If the angle O between two vectors P and Q is 90 then cos 0 is 0 so Pe Q will also be 0 Therefore dot_product can be used as a test for the orthogonality of vectors Chapter 22 Point Reference 137 Point P 2 Point Q P Point QO PO QO Q rotate 0 0 90 P x Q rotate 0 45 45 P Q rotate 45 cout lt lt P angle Q 90 cout lt lt P dot_product Q 4 0 P 1 1 70711 0 292893 1 41421 1 1 Figure 87 Point cross_product Point p const function Returns the cross or vector product of this and p If P and Q are Points P x Q yrzo 2PYq 2P2Q UP2Q Pyg YPLQ P Q sin 0 where P and Q are the magnitudes of P and Q respectively 0 is the angle between P and Q and 7 is a unit vector perpendicular to both P and Q in the direction of a right hand screw from P towards Q Therefore cross_product can be used to find the normals to planes Point P 2 2 2 Point Q 2 2 2 Point n P cross_product Q n show n n 0 8 8 real theta PI 180 0 P angle Q cout lt lt theta 4 1 23096 real n_mag P magnitude Q magnitude sin theta
30. GNU Free Documentation License 284 that you add no other conditions whatsoever to those of this License You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute However you may accept compensation in exchange for copies If you distribute a large enough number of copies you must also follow the conditions in section 3 You may also lend copies under the same conditions stated above and you may publicly display copies 3 COPYING IN QUANTITY If you publish printed copies or copies in media that commonly have printed covers of the Document numbering more than 100 and the Document s license notice requires Cover Texts you must enclose the copies in covers that carry clearly and legibly all these Cover Texts Front Cover Texts on the front cover and Back Cover Texts on the back cover Both covers must also clearly and legibly identify you as the publisher of these copies The front cover must present the full title with all words of the title equally prominent and visible You may add other material on the covers in addition Copying with changes limited to the covers as long as they preserve the title of the Document and satisfy these conditions can be treated as verbatim copying in other respects If the required texts for either cover are too voluminous to fit legibly you should put the first ones listed as many as fit reasonably on the actual cover and conti
31. See Section 22 4 Point Reference Constructors and Setting Functions page 123 and Section 22 11 Point Reference Modifying page 130 Chapter 22 Point Reference 120 signed short drawdot_value Private variable Used to tell Point output what MetaPost drawing command drawdot or undrawdot to write to out_stream when outputting a Point When drawdot or undrawdot is called on a Point the Point is copied and put onto the Picture which was passed to drawdot or undrawdot as an argument current_picture by default drawdot_value is either set to Shape DRAWDOT or Shape UNDRAWDOT on the copy this gt drawdot is not set const Color drawdot_color Private variable Used to tell Point output what string to write to out_stream for the color when outputting a Point string pen Private variable Used to tell Point output what string to write to out_stream for the pen when outputting a Point valarray lt real gt projective_extremes Protected variable A set of 6 real values indicating the maximum and minumum x y and z coordinates of the Point Used for determining whether a Point is projectable with the param eters of a particular invocation of Picture output See Section 21 8 Picture Reference Outputting page 114 Obviously the maxima and minima will always be the same for a Point namely the x y and z coordinates However set_extremes and get_extremes the functions that access proj
32. The length of the horizon line leftwards of the center of vision real horizon_rt Default 0 The length of the horizon line rightwards of the center of vision real gl_lft Default 0 The length of the ground line leftwards of the line from the focus to the center of vision real gl_rt Default 0 The length of the ground line rightwards of the line from the focus to the center of vision Example persp_0 3 2 10 5 47 5 7 5 8 5 9 5 8 5 9 5 VP 42 591 gt horizon ground line De center of vision vanishing point measuring point left right Figure 199 Chapter 39 Adding a File 273 39 Adding a File Version 1 1 1 was the first version of 3DLDF since it became a GNU package the cur rent version is 1 1 5 1 In previous versions recompilation was controlled by an auxilliary program which I wrote in C using CWEB However in the course of making 3DLDF conformant to the GNU Coding Standards this has been changed Recompilation is now controlled by make as is customary The chapter Compiling in previous editions of this manual is therefore no longer needed Nonetheless using CWEB still has consequences for the way recompilation must be handled and it was fairly tricky getting make to work for 3DLDF Users who only put code in main web and or change code in existing files won t have to worry about this for others this chapter explains how to add files to 3DLDF Let s say you
33. const Point amp p0 const Point amp p1 const const function Point amp p2 bool verbose false bool test_points true Returns true if this lies within the triangle determined by the three Point argu ments otherwise false If the code calling is_in_triangle has ensured that po p and po determine a plane i e that they are not colinear and that this lies in that plane then false can be passed to is_in_triangle as its test_points argument If the verbose argument is true information resulting from the execution of the function are printed to standard output or standard error This function is needed for determining whether a line intersects with a polygon 22 9 Returning Coordinates The functions in this section return either a single coordinate or a set of coordinates Each has a const and a non const version The arguments are the same with one exception char c Only in get_coord Indicates which coordinate should be returned Valid values are x X y Y z Z w and W char coords Indicates the set of coordinates which should be returned or from which the coordinate to be returned should be chosen from Valid values are w for world_coordinates the default p for projective_coordinates u for user_coordinates and v for view_coordinates const bool do_persp Only relevant if projective_coordinates or one of its elements is to be re turned If t
34. current_picture Function Allocates a copy of the Path on the free store puts a pointer to it on picture shapes and sets its fill_draw_value to UNFILL This function is useful for removing a portion of a filled region Point pt 4 pt 0 set 2 2 pt 1 set 2 2 pt 2 set 2 2 pt 3 set 2 2 Path p true amp pt 0 amp pt 1 amp pt 2 amp pt 3 0 p draw p dotlabel p filldraw black gray p scale 5 5 p unfill Figure 133 void unfilldraw const Color amp ddraw_color Function Colors background_color string ddashed string ppen Picture amp picture current_picture void unfilldraw Picture amp picture const Color amp ddraw_color Function Colors background_color string ddashed string ppen Allocates a copy of the Path on the free store puts a pointer to it on picture shapes sets its fill_draw_value to UNFILLDRAW and the values of its draw_color dashed and pen according to the arguments While the default for ddraw_color is Colors background_color any other Color can be used so that unfilldraw can unfill a Path and draw an outline around it The second version is convenient for passing a Picture argument without having to specify all of the other arguments This function is similar to unfill see Section 26 12 Path Reference Drawing and Filling page 180 except that the outline of the Path will
35. false Also the defaults for ddraw_color and ddashed differ from those for draw void drawarrow const Color ddraw_color const virtual function Colors default_color string ddashed string ppen Picture amp picture current_picture void drawarrow Picture amp picture const Color amp const virtual function ddraw_color Colors default_color string ddashed string ppen Like draw except that the MetaPost command drawarrow is written to out_stream when picture is output The second version is convenient for passing a Picture argument without having to specify all of the other arguments Point m Chapter 26 Path Reference 184 Point n 2 2 m dotlabel m bot n dotlabel n m drawarrow n Figure 125 void draw_axes real dist 2 5 string pos_x Non member function bot string pos_y 1ft string pos_z bot const Color amp ddraw_color Colors default_color const string ddashed const string ppen const Point amp shift_x origin const Point amp shift_y origin const Point amp shift_z origin Picture amp picture current picture void draw_axes const Color amp ddraw_color real dist Non member function 2 5 string pos_x bot string pos_y 1ft string pos_z bot const string ddashed const string ppen const Point amp shift_x origin const Point amp shift_y origin const Point
36. if the Picture it s on is output again vector lt Shape gt extract const Focusg f const unsigned Virtual function short proj real factor Tests whether all of the Shapes belonging to the Solid are projectable using the arguments passed to output If it is this function returns a vector of pointers to Shape containing a single pointer to the Solid If not an empty vector is returned bool set_extremes void Virtual function Sets projective_extremes to contain the maximum and minimum values for the x y and z coordinates of the Points on the Shape Used for determining projectability of a Solid using a particular set of arguments Chapter 34 Solid Reference 255 const valarray lt real gt get_extremes void const inline virtual function Returns projective_extremes real get_minimum_z void const virtual functions real get_maximum_z void real get_mean_z void Returns the minimum maximum or mean z value respectively of the Points be longing to the Solid Used for surface hiding See Section 9 3 Surface Hiding page 67 34 13 Drawing and Filling void draw const vector lt const Color gt v const virtual function Colors default_color_vector const string ddashed const string ppen Picture amp picture current_picture Draws the Solid This function allocates a new Solid makes it a copy of this and puts a pointer to the copy onto picture shapes The data members of the
37. 0 707 0 0 383 0 924 0 0 1 0 0 383 0 924 0 0 707 0 707 0 0 924 0 383 0 1 0 0 0 924 0 383 0 0 707 0 707 0 0 383 0 924 0 0 1 0 0 383 0 924 0 0 707 0 707 0 0 924 0 383 0 cycle Figure 119 26 11 Applying Transformations void apply_transform void Virtual function Calls Point apply_transform on all of the Points on points See Section 22 13 Point Reference Applying Transformations page 135 26 12 Drawing and Filling void draw const Color amp ddraw_color const virtual function Colors default_color const string ddashed const string ppen Pictureg picture current_picturel l void draw Picture amp picture const Colorg const Virtual function ddraw_color Colors default_color string ddashed string ppen Allocates a copy of the Path on the free store puts a pointer to the copy on picture shapes sets its fill_draw_value to DRAW and the values of its draw_color dashed and pen according to the arguments The second version is convenient for passing a Picture argument without having to specify all of the other arguments Chapter 26 Path Reference 181 All of the arguments to draw are optional so it can be invoked as follows Point A Point B 2 Point C 3 3 Point D 1 2 Point E 1 1 Path p true amp A amp B amp C amp D amp E 0 p draw
38. 123 void clear void Function Sets all of the coordinates in all of the sets of coordinates i e world_coordinates user_coordinates view_coordinates and projective_coordinates to 0 and resets transform void clean int factor 1 Function Calls apply_transform and sets the values of world_coordinates to 0 whose absolute values are less than epsilon x factor void reset_transform void Function Sets Transform to the identity Transform Performed in apply_transform after the latter updates world_coordinates Section 22 13 Point Reference Applying Transformations page 135 22 12 Affine Transformations Transform rotate const real x const real y 0 const real z Function o Transform rotate const Point amp p0 const Point amp p1 const real Function angle 180 Transform rotate const Path amp p const real angle 180 Function Each of these functions calls the corresponding version of Transform rotate and returns its return value namely a Transform representing the rotation only In the first version taking three real arguments the Point is rotated x degrees around the x axis y degrees around the y axis and z degrees around the z axis in that order Point p0 1 0 2 pO rotate 90 p0 show p0 4 pO 1 2 0 Point pi 1 1 1 pi rotate 90 90 90 p1 show pt1 J pi 1 1 1 Chapter 22 Point Reference 131 Figure 81 Please note that
39. 3 Net vector lt Reg_Polygon gt get_net const real Static function triangle_diameter Returns the net of the Tetrahedron i e the two dimensional pattern of triangles that can be folded into a model of a tetrahedron The net lies in the x z plane The triangles have enclosing circles of diameter triangle_diameter The center of the middle triangle is at the origin vector lt Reg_Polygon gt vrp Tetrahedron get_net 2 for vector lt Reg_Polygon gt iterator iter vrp begin iter vrp end iter xxiter draw 1 Albrecht D rer invented this method of constructing polyhedra Chapter 37 Polyhedron Reference 263 Z Vv Figure 189 This function is used in the non default constructor See Section 37 2 1 2 Polyhedron Reference Regular Platonic Polyhedra Tetrahedron Constructors and Setting Func tions page 261 The constructor starts with the net and rotates three of the triangles about the adjacent vertices of the middle triangle Currently all of the Polyhedron constructors work this way However this is not ideal because rotation uses the sine and cosine functions which cause inaccuracies to creep in I think there must be a better way of constructing Polyhedra but I haven t found one yet The Polyhedron constructors are also especially sensitive to changes made to Transform align_with_axis I have already had to rewrite them twice and since Transform align_with_axis may need t
40. MetaPost and CWEB are available from the Comprehensive T X Archive Network CTAN See one of the following web sites for more information Germany http dante ctan org http ftp dante de http www dante de United Kingdom http www cam ctan org http ftp tex ac uk USA http www tug ctan org http www ctan tug org 1 2 About This Manual This manual has been created using Texinfo a documentation system which is part of the GNU Project whose main sponsor is the Free Software Foundation Texinfo can be used to generate online and printed documentation from the same input files For more information about Texinfo see Stallmann Richard M and Robert J Chassell Texinfo The GNU Documentation Format The Free Software Foundation Boston 1999 For more information about the GNU Project and the Free Software Foundation see the following web site http www gnu org The edition of this manual is 1 1 5 1 and it documents version 1 1 5 1 of 3DLDF The edition number of the manual and the version number of the program are the same as of 16 January 2004 but may diverge at a later date Note that I me etc in this manual refers to Laurence D Finston so far the sole author of both 3DLDF and this manual Currently and similar formulations refer to version 1 1 5 1 of 3DLDF as of 16 January 2004 This manual is intended for both beginning and advanced users of 3DLDF So if there s something you don
41. Point P O 1 1 Reg Polygon h P 7 4 80 2 5 h draw black evenly h draw_out_circle Figure 150 Chapter 29 Rectangle Reference 211 29 Rectangle Reference Class Rectangle is defined in rectangs web and is derived from Polygon using public derivation As noted above in Section 27 4 Polygon Reference Affine Transformations page 200 class Rectangle like class Reg_Polygon currently inherits its transformation functions and operator const Transform amp from Polygon Consequently the data members of a Rectangle except for center are not recalculated when it s transformed I plan to change this soon It will also be necessary to add the function Rectangle is_rectangular in order to test whether a Rectangle is still rectangular 29 1 Data Members real axis_h Private variables real axis_v The lengths of the horizontal and vertical axes respectively of the Rectangle Ac tually they are merely the horizontal and vertical axes by convention since there are no restrictions on the orientation of an Rectangle Please note that axis_h and axis_v are currently not recalculated when a Rectangle is transformed I plan to do something about this soon bool on_free_store Private variable true if the Rectangle was dynamically allocated on the free store otherwise false Dynamic allocation of Rectangles should only be performed by create_new lt Rectangle gt which sets on_free_store to tru
42. Point normal Public variable Represents the normal to the plane real distance Public variable The distance of the plane from the origin 25 2 Global Constants const Plane INVALID_PLANE Constant A Plane with point normal and distance INVALID_REAL INVALID_PLANE is returned from Path get_plane if the Path is not planar See Section 26 15 Path Reference Querying page 194 25 3 Constructors void Plane void Default constructor Creates a degenerate Plane with point normal origin and distance 0 Planes constructed using this constructor will probably be set using the assignment operator or Path get_plane immediately or very soon after being declared See Section 25 4 Planes Reference Operators page 158 and Section 26 15 Paths Ref erence Querying page 194 void Plane const Plane amp p Copy constructor Creates a new Plane making it a copy of p Chapter 25 Plane Reference 158 void Plane const Point amp p const Point amp n Constructor If p is not equal to n this constructor creates a Plane and sets point to p normal is set to n and made a unit vector distance is calculated according to the following formula Let n stand for normal p for point and d for distance d p n If d 0 origin lies in the Plane If d gt 0 origin lies on the side of the Plane that normal points to considered to be outside If d lt 0 origin lies on the side of the Plane that normal do
43. Protected variable The radius of the circle enclosing a pentagonal face of the Dodecahedron 37 2 2 2 Constructors and Setting Functions void Dodecahedron void Default constructor Creates an empty Dodecahedron void Dodecahedron const Point amp p const real Constructor pentagon_diameter real angle_x 0 real angle_y 0 real angle_z 0 Creates a Dodecahedron with its center at the origin where the pentagonal faces have enclosing circles of diameter pentagon_diameter If any of angle_x angle_y or angle_z is non zero the Dodecahedron is rotated by the amounts specified around the corresponding axes Finally if p is not the origin the Dodecahedron is shifted such that center comes to lie at p Point P 1 2 4 Dodecahedron d P 3 12 5 16 2 d draw Chapter 37 Polyhedron Reference 265 Figure 191 d filldravO Figure 192 37 2 2 3 Net vector lt Reg_Polygon gt get_net const real Static function pentagon_diameter bool do_half false Returns the net i e the two dimensional pattern of pentagons that can be folded into a model of a dodecahedron The net lies in the x z plane The pentagons have enclosing circles of diameter pentagon_diameter The center of the center pentagon of the first half of the net is at the origin If the argument do_half is true only the first half of the net is created This is used in the non default constructor See Section 37 2 2 2 Polyhedron Referen
44. Run convert 3DLDF 1 ps 3DLDFmp 1 png ImageMagick supplies a display utility which can be used to display the PNG image display 3DLDFmp 1 png It can be included in an HTML document as follows lt img src 3DLDFmp 1 png alt Fig 1 Please note The PNG files for this manual are now called filename 3DLDF1 png 3DLDF2 png 3DLDF199 png because I wasn t able to write files with names like 3DLDFmp lt number gt png to a CD R Compact Disk Recordable when number had more than one digit 3 Rokicki Dvips A DVI to PostScript Translator p 24 Chapter 11 Installing and Running 3DLDF 79 11 2 1 1 Emacs Lisp Functions The file 3DLDF 1 1 5 1 CWEB cnepspng el contains definitions of two Emacs Lisp functions that can be used to convert Encapsulated PostScript EPS files to structured PostScript PS and Portable Network Graphics PNG files convert eps filename do not delete files Emacs Lisp function Converts an EPS image file to the PS and PNG formats If called interactively convert eps prompts for the filename including the extension of an EPS image file It follows the procedure described above in Section 11 2 1 Converting EPS Files page 77 to create filename ps and filename png If do not delete files is nil the tex dvi and log files will be deleted This is the case when convert eps is called interactively with no prefix ar
45. Shapes belonging to the copy are set appropriately so that they can be drawn when Picture output is called The Colors used for drawing the various Paths Circles Ellipses etc belonging to the Solid are passed in v If the Solid contains more Shapes than v contains pointers to Color the Color pointed to by the last pointer on v is used to draw the remaining Shapes Currently a Solid can only be drawn with a single dash pattern ddashed and pen ppen void fill const vector lt const Color gt v const virtual function Colors default_color_vector Picture amp picture current_picture Fills the Solid This function allocates a new Solid makes it a copy of this and puts a pointer to it onto picture shapes The data members of the Shapes belonging to the copy are set appropriately so that they can be filled when Picture output is called The Colors used for filling the various Paths Circles Ellipses etc belonging to the Solid are passed in v If the Solid contains more Shapes than v contains pointers to Color the Color pointed to by the last pointer on v is used to fill the remaining Shapes void filldraw const vector lt const Color gt draw_colors const virtual function Colors default_color_vector const vector lt const Color gt fill_colors Colors background_color_vector const string ddashed const string ppen Picture amp picture current_picture Filldraws th
46. Transforms transform and persp 23 6 Querying const Point amp get_position void Inline const function Returns position const Point amp get_direction void Inline const function Returns direction const real amp get_distance void Inline const function Returns distance const Point amp get_up void Inline const function Returns up const Transform amp get_transform void Inline const function Returns transform const real amp get_transform_element const unsigned Inline const function int row const unsigned int column Returns an element of transform given two unsigned ints for the row and the column const Transform amp get_persp void Inline const function Returns persp const real amp get_persp_element const unsigned int Inline const function row const unsigned int column Returns an element of persp given two unsigned ints for the row and the column 23 7 Showing void show const string text_str Focus const bool const function show_transforms false Prints text_str to standard output stdout then calls Point show on position direction and up Then the values of distance axis and angle are printed to stdout If show_transforms is true transform and persp are shown as well Chapter 24 Line Reference 154 24 Line Reference The struct Line is defined in lines web Lines are not Shapes They are used for performing vector operations A Line is defined by a
47. a copy of an existing one 0 must be passed to create_ new lt Solid gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information 34 3 Destructor void Solid void virtual Destructor This function currently has an empty definition but its existence prevents GCC 3 3 from issuing the following warning class Solid has virtual functions but non virtual destructor 34 4 Operators const Solid amp operator const Solid s Virtual function Assignment operator Makes this a copy of s discarding the old contents of this Transform operator const Transformg t Virtual function Multiplication by a Transform All of the Shapes that make up the Solid are trans formed by t 34 5 Copying Shape get_copy void const virtual function Dynamically allocates a new Solid on the free store using create_new lt Solid gt and makes it a copy of this Then a pointer to Shape is pointed at the copy and returned Used for putting Solids onto Picture shapes in the drawing and filling functions for Solid See Section 34 13 Solid Reference Drawing and Filling page 255 Chapter 34 Solid Reference 250 34 6 Setting Members bool set_on_free_store bool b true Virtual function Sets on_free_store to b This function is called in the template function create_new See Section 34 2 Solid Reference Constructors and Setting Functions page 249 34 7 Querying
48. a machine readable copy represented in a format whose specification is available to the general public that is suitable for revising the document straightforwardly with generic text editors or for images com posed of pixels generic paint programs or for drawings some widely available drawing editor and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters A copy made in an otherwise Transparent file format whose markup or absence of markup has been arranged to thwart or discourage subsequent modification by readers is not Transparent An image format is not Transparent if used for any substantial amount of text A copy that is not Transparent is called Opaque Examples of suitable formats for Transparent copies include plain ASCII without markup Texinfo input format LaT X input format SGML or XML using a publicly available DTD and standard conforming simple HTML PostScript or PDF designed for human modification Examples of transparent image formats include PNG XCF and JPG Opaque formats include proprietary formats that can be read and edited only by proprietary word processors SGML or XML for which the DTD and or processing tools are not generally available and the machine generated HTML PostScript or PDF produced by some word processors for output purposes only The Title Page means for a printed book the title page itself plu
49. amp shift_z origin Picture amp picture current_picturel These functions draw lines centered on the origin and ending in arrows in the direc tions of the positive x y and z axes and labels them with the appropriate letters draw_axes is used in many of the figures in this handbook It can be helpful in determining whether a Focus has a good up direction See Section 23 1 Focus Reference Data Members page 151 In the first version all of the arguments are optional In the second version ddraw_color is required and has been moved to the front of the argument list This version is often convenient when a Color other than the default is desired The arguments dist The length of the lines drawn The default is 2 5 The value 0 can be used as a dummy argument if the default for dist is desired but other arguments must be specified pos x pos y pos_z The position arguments for the labelling commands for each of the axes The defaults are bot for the x and z axes and 1ft for the y axis The usual strings for the position of labels can be used namely top bot lft rt ulft urt 11 t lrt and If is used that axis is not drawn This can be useful for parallel projections Chapter 26 Path Reference 185 onto one of the major planes In addition d can be used to indicate that the default should be used for that label This can be useful if one needs a placeholder but doe
50. arguments to shear Point p x y z Transform t t shear a b c d e f p t gt p x ay bz y cx dz z ex fy Transform t t shear 2 3 4 5 6 7 t show t E 1 4 6 0 2 1 T 0 3 5 1 0 0 0 0 1 Transform shift real x real y 0 real z 0 Function Transform shift const Point amp p Function These functions create a Transform t representing the shifting operation locally mul tiplies this by t and returns t The version with the argument const Point amp p passes the updated x y and z coordinates of p from world_coordinates to the version with three real argu ments When a Transform representing a single shifting operation only is applied to a Point the x y and z arguments are added to the corresponding coordinates of the Point Point p x y z Transform t t shift a b c p t Chapter 19 Transform Reference 103 gt p 2 0 Yy bz 0CG Transform shift_times real x real y 1 real z 1 Function Multiplies the corresponding elements of matrix by the real arguments i e matrix 3 0 is multiplied by x matrix 3 1 is multiplied by y and matrix 3 2 is multiplied by z Returns this Ordinary shifting is additive so a special function is needed to multiply the ele ments of matrix responsible for shifting The effect of shift_times is to modify a Transform representing a shifting operation such that the direction of the shift is maintain
51. as a placeholder in the call to drawdot The following example undraws a dot at the same location using a smaller pen undraw does not take a Color argument p undrawdot pencircle scaled 2mm P O Figure 4 For complete descriptions of drawdot and undrawdot see Section 22 18 Point Refer ence Drawing page 144 Drawing and undrawing dots is not very exciting In order to make a proper drawing it is necessary to connect the Points The most basic way of doing this is to use the Point member function draw with a Point argument Point pO Point p1 2 2 p0 draw p1 l Pens are a concept from Metafont In 3DLDF there is currently no type Pen Pen arguments to functions are simply strings and are written unaltered to out_stream For more information about Metafont s pens see Knuth The Metafontbook Chapter 4 2 Colors are declared in the namespace Colors so if you have a using declaration in the function where you use drawdot you can write black instead of Colors black For more information about namespaces see Stroustrup The C Programming Language Chapter 8 Chapter 5 Drawing and Labeling Points 25 Figure 5 p0 draw p1 is equivalent in its effect to p1 draw p0 The function Point draw takes a required Point amp argument a reference to a Point an optional Color argument and optional string arguments for the dash pattern and the pen The string arguments if
52. avoid the use of preprocessor macros as much as possible for the reasons given by Stroustrup in the The C Programming Language 7 8 pp 160 163 and Design and Evolution of C Chapter 18 pp 423 426 However conditional compilation is one of the tasks that only the preprocessor can perform Chapter 3 Transforming Points 14 shift takes three real arguments whereby the second and third are optional To shift a Point in the direction of the positive or negative y axis and or the positive or negative z axis only then a 0 argument for the x direction and possibly one for the y direction must be used as placeholders as in the example above shift can be invoked with a Point argument instead of real arguments In this case the x y and z coordinates of the argument are used for shifting the Point Point a 10 10 10 Point b 1 2 3 a shift b a show a 4 a 11 12 13 Another way of shifting Points is to use the binary operator Point operator with a Point argument Point a0 1 1 1 Point ai 2 2 2 a0 al a0 show a0 4 a0 3 3 3 3 2 Scaling The function scale takes three real arguments The x y and z coordinates of the Point are multiplied by the first second and third arguments respectively Only the first argument is required the default for the others is 1 If one wants to perform scaling in either the y dimension only or the y and z dimensions only a dummy argument o
53. be undrawn using the pen specified with the ppen argument or MetaPost s currentpen if no ppen argument is specified In addition the Path will be drawn using the Color specified Chapter 26 Path Reference 191 in the ddraw_color argument Since the default is Colors background_color the Path will be undrawn unless a different Color is specified Point pt 6 pt 01 set C2 2 pt 1 set 0 3 ptl2 set 2 2 pt 3 set 2 2 pt 4 set 0 3 pt 5 set 2 2 Path p true amp pt 0 amp ptli amp pt 2 amp pt 3 amp pt 4 amp pt 5 0 p fill gray p scale 5 5 p unfilldraw black pensquare xscaled 3mm Figure 134 26 13 Labelling void label unsigned int i 0 string position_string const function top short text_short 0 bool dot false Picture amp picture current_picturel void label Picture amp picture unsigned int i 0 string const function position_string top short text_short 0 bool dot false Calls Point label O on all of the Points on points They are numbered con secutively starting with i The other arguments are used for all of the Points so it s not possible to specify different positions for the labels for different Points dot will normally not be specified unless a picture argument is used in the first version dotlabel calls label O with dot true Chapter 26 Path Reference 192 The
54. bpq otherwise INVALID_POINT Ifa Point is found the b element of the bool_point will be true otherwise false The step argument is used when the Ellipses are coplanar and either have different centers or the vertical axis of one Ellipse is colinear with the horizontal axis of the other and vice versa In these cases the intersection points must be found by an Chapter 31 Ellipse Reference 232 iterative routine A Point p travels around the perimeter of this and its location with respect to e is tested step is the angle of rotation used for stepping around the perimeter of this The default value 3 should be adequate unless the Ellipses differ greatly in size If the verbose argument is true intersection_points will print information about the intersection points to standard output In Fig 168 the Ellipses e and f both lie in the x z plane are centered at the origin and intersect at four points Ellipse e origin 5 2 Ellipse f origin 2 5 bool_point_quadruple bpq e intersection_points f bpq first pt dotlabel 1 111ft bpq second pt dotlabel 2 urt bpq third pt dotlabel 3 ulft bpq fourth pt dotlabel 4 lrt Figure 168 In Fig 169 e and f are coplanar but don t lie in a major plane have different centers and only intersect at two points Ellipse e origin 4 2 Ellipse f origin 2 5 shift 0 O 1 rotate 0 15 shift 1 0 1 f shift 25 1 1 x f r
55. constructor Creates an empty Ellipse void Ellipse const Point amp ccenter const real aaxis_h const Constructor real aaxis_v const real angle_x 0 const real angle_y 0 const real angle_z 0 const unsigned short nnumber_of_points DEFAULT_NUMBER_OF_POINTS Creates an Ellipse in the x z plane centered at the origin with its horizontal axis aaxis_h and its vertical axis aaxis_v If any of the arguments angle_x angle y Chapter 31 Ellipse Reference 223 or angle_z is non zero the Ellipse is rotated about the x y and z axis in that order by the amounts indicated by the corresponding arguments Finally the Ellipse is shifted such that its center comes to lie at ccenter Ellipse e origin 6 4 CIN NU Figure 159 Point P 1 1 1 Ellipse e P 6 4 15 12 11 e draw Figure 160 Chapter 31 Ellipse Reference 224 void set const Point ccenter const real aaxis_h const Setting function real aaxis_v const real angle_x 0 const real angle_y 0 const real angle_z 0 const unsigned short nnumber_of_points DEFAULT_NUMBER_OF_POINTS Corresponds to the constructor above Ellipse create_new lt Ellipse gt const Ellipsex e Template specializations Ellipse create_new lt Ellipse gt const Ellipse amp e Pseudo constructors for dynamic allocation of Ellipses They create a Ellipse on the free store and allocate memory for it using new Ellipse They return a pointer to t
56. coordinate values and the values they should have So far I haven t found a solution for this problem On the other hand it hasn t yet affected the usability of 3DLDF 1 5 2 No Input Routine 3DLDF does not yet include a routine for reading input files This means that user code must be written in C compiled and linked with the rest of the program I admit this is not ideal and writing an input routine for user code is one of the next things I plan to add to 3DLDF I plan to use Flex and Bison to write the input routine The syntax of the input code should be as close as possible to that of MetaPost while taking account of the differences between MetaPost and 3DLDF For the present however the use of 3DLDF is limited to those who feel comfortable using C and compiling and relinking programs Please don t be put off by this It s not so difficult and make does most of the work of recompiling and running 3DLDF See Chapter 11 Installing and Running 3DLDF page 74 for more information 1 6 Ports I originally developed 3DLDF on a DECalpha Personal Workstation with two processors running under the operating system Tru64 Unix 5 1 using the DEC C compiler I then ported it to a PC Pentium 4 running under Linux 2 4 using the GNU C compiler GCC 2 95 3 and a PC Pentium II XEON under Linux 2 4 using GCC 3 3 I am currently only maintaining the last version I do not believe that it s worthwhile to maintain a version fo
57. defined All other Shapes are derived from one of these classes These output O functions then write the MetaPost code to the output file through the output file stream out_stream beginfig 1 default_focus set 0 0 10 0 O 10 10 Circle c origin 3 90 c draw c shift 1 5 c draw current_picture output endfig 1 Figure 50 The C code for Fig 50 starts with the command beginfig 1 and ends with the command endfig 1 They simply write beginfig arg and endfigQ to out_ stream The optional unsigned int argument to endfig is not written to out_stream it s merely syntactic sugar for the user Chapter 9 Pictures 55 In MetaPost the endfig command causes output and then clears currentpicture This is not the case in 3DLDF where Picture output and Picture clear must be invoked explicitly beginfig 1 Point pO Point p1 1 2 3 pO draw p1 current_picture output endfig 1 beginfig 2 current_picture clear Circle C origin 3 c fi110 current_picture output endfig 2 In Fig 51 two Pictures are used within a single figure beginfig 1 Picture my_picture default_focus set 0 0 10 0 O 10 10 Circle c origin 3 90 c draw my_picture my_picture output c shift 1 5 c fill light_gray current_picture output endfig 1 Figure 51 Multiple objects or complex objects made up of sub objects can be stored in a Pictu
58. empty string the default it is printed on a line of its own to standard output Otherwise Line is printed Following this Point show is called on position and direction Point p 1 2 3 Point d 12 3 21 36 002 Line LO p d LO show LO LO position 1 2 3 direction 12 3 21 36 002 Line L1 p get_line d L1 show L1 Chapter 24 Line Reference 4 Lt position 1 2 3 direction 13 3 23 33 002 Path q L1 get_path q show q 3 q fill_draw_value 1 2 3 12 3 21 36 002 156 Chapter 25 Plane Reference 157 25 Plane Reference The struct Plane is defined in planes web Planes are not Shapes They are used for performing vector operations A Plane is defined by a Point representing a point on the plane a Point representing the normal to the plane and the distance of the plane from the origin The most common use of Planes is to represent the plane in which an existing plane figure lies Therefore they most likely to be created by using Path get_plane See Section 26 15 Path Reference Querying page 194 However class Plane does have constructors for creating Planes directly if desired See Section 25 3 Planes Reference Constructors page 157 25 1 Data Members Because the main purpose of Plane is to provide information about Shapes its data mem bers are all public Point point Public variable Represents a point on the plane
59. gt c is compared to the old lt filename gt cxx using diff Whitespace comments and line preprocessor commands are ignored The lt filename gt c is only renamed to lt filename gt cxx and compiled if they differ This way changes to the T X text only in a CWEB file no longer cause recompilation and relinking The main Texinfo file is now called 3DLDF texi It was formerly called 3DLDFman texi This is because Automake expects this name For this reason the CWEB file passed as an argument to cweave has been renamed 3DLDFprg web It was formerly called 3DLDF web Bibliography 280 Bibliography Cundy H Martyn and A P Rollet Mathematical Models Oxford 1961 Oxford University Press Unfortunately out of print Finston Laurence D 3DLDF The Program Gottingen 2003 Fischer Gerd Ebene algebraische Kurven Vieweg Studium Aufbaukurs Mathematik Friedr Vieweg amp Sohn Verlagsgesellschaft mbH Braunschweig Wiesbaden 1994 Gill Robert W Creative Perspective London 1975 Thames and Hudson Ltd ISBN 0 500 27056 2 Harbison Samuel P and Guy L Steele Jr C A Reference Manual Pren tice Hall Englewood Cliffs New Jersey 1995 ISBN 0 13 326232 4 Case ISBN 0 13 326224 3 Paperback Hobby John D Smooth Easy to Compute Interpolating Splines Discrete and Computa tional Geometery 1 2 Springer Verlag New York 1986 Hobby John D A User s Manual for Meta
60. label should be located relative to the Point The valid values are the strings used in MetaPost for this purpose i e top bot 1ft rt 11ft lower left Lrt lower right ulft upper left and urt upper right The default is top 3DLDF does not catch the error if an Chapter 22 Point Reference 149 invalid position argument is used the string is written to the output file and an error will occur when MetaPost is run The dot argument is used to determine whether the label should be dotted or not The default is false The function dotlabel calls label O passing true as the latter s dot argument void dotlabel const string text_str const string const function position_str top Picture amp picture current_picture void dotlabel const short text_short const string const function position_str top Picture amp picture current_picture These functions are like label except that they always produces a dot Point p0 2 3 p0 dotlabel p_0 Po Figure 103 22 20 Showing void show string text char coords w const bool const function do_persp true const bool do_apply true Focus f 0 const unsigned short proj Projections persp const real factor 1 Prints text followed by the values of a set of coordinates to standard output stdout The other arguments are similar to those used in the function
61. more convenient because this is the location of the CWEB TEX and MetaPost files that you ll be editing Alternatively call ldfr which is merely a shell script that calls make run This takes care of running 3dldf MetaPost TEX and dvips producing a PostScript file containing your drawings You can display the latter on your terminal using Ghostview or some other PostScript viewer print it out and whatever else you like to do with PostScript files However you can also perform the actions performed by make run by hand by writing your own shell scripts by defining Emacs Lisp commands or in other ways Even if you choose to use make run it s important to understand what it does The following explains how to do this by hand The CWEB source files for 3DLDF are in the subdirectory 3DLDF 1 1 5 1 CWEB They must be ctangled and the resulting C files must be compiled and linked in order to create the executable file 3d1ldf The C files and header files generated by ctangle the object files generated by the compiler and the executable 3d1df all reside in 3DLDF 1 1 5 1 CWEB Therefore the latter must be your working directory Since 3DLDF has no input routine as yet as explained in Section 1 5 2 No Input Rou tine page 8 it is necessary to add C code to the function main in main web and or in a separate function in another file In the latter case the function containing the user code must be i
62. not always have the same number of sides Point p 0 3 Reg_Polygon polygon for int i 3 i lt 9 i polygon set p i 3 polygon draw p shift 0 1 Figure 26 Chapter 7 Plane Figures 40 7 2 Rectangles A Rectangle can be constructed in the x z plane by specifying a center Point the width and the height Rectangle r origin 2 3 r draw YA a ar i Figure 27 Three additional arguments can be used to specify rotation about the x y and z axes respectively Rectangle r origin 2 3 30 45 15 r draw T P Figure 28 If a Point p other than the origin is specified as the center of the Rectangle the latter is first created in the x z plane centered about the origin as above Then any rotations specified are performed Finally the Rectangle is shifted such that its center comes to lie at p Chapter 7 Plane Figures 41 Point p0 5 1 3 Rectangle r p0 4 2 30 30 30 r draw Figure 29 This constructor has a corresponding setting function Rectangle r for int i 0 i lt 180 i 30 r set origin 4 2 i r draw Figure 30 Rectangles can also be specified using four Points as arguments whereby they must be ordered so that they are contiguous in the resulting Rectangle Chapter 7 Plane Figures 42 Point pt 4 pt 0 shift 1 2 pt 2 pt 1 pt 0 pt 1 rotate 180 pt
63. of the label with respect to the Point The label text is formatted using TRX so it can contain math mode material between dollar signs Please note that double backslashes must be used where a single backslash would suffice in a file of MetaPost code for example for TEX control sequences Alternatively a short argument can be used for the label The position argument is optional with top as the default If the empty string is used the label will centered about the Point itself This will usually only make sense for label O because it would otherwise interfere with the dot Valid arguments for the position are the same as in MetaPost top bot bottom 1 t left rt right ulft upper left urt upper right 11 t lower left and 1rt lower right Point p0 Point p1 1 Point p2 2 Point p3 p0 Point p4 p1 Point p5 p2 p3 p4 p5 shift 0 1 p0 draw p1 pi draw p2 p2 draw p5 p5 draw p4 p4 draw p3 p3 draw p0 p0 label p_0 pi dotlabel 1 p2 dotlabel p2 bot p3 dotlabel This is p_3 lft p4 label 4 p5 label leftarrow p_5 rt This is p3 4 P5 a p2 Figure 8 Chapter 5 Drawing and Labeling Points For complete descriptions of Point label Section 22 19 Points Labelling page 147 and Point dotlabel 27 see Chapter 6 Paths 28 6 Paths Points alone are not enough for making useful draw
64. page 273 and Chapter 41 Changes page 278 for more information The CWEB files in the directory 3DLDF 1 1 5 1 CWEB contain the source code for 3DLDF The file 3DLDFprg web in this directory is only ever used for cweaving it is never ctangled and contains no C code for compilation It does however include all of the other CWEB files so that cweave 3DLDFprg web generates the T X file containing the complete documentation of the source code of 3DLDF The files 83DLDF 1 1 5 1 CWEB 3DLDFprg tex 3DLDF 1 1 5 1 CWEB 3DLDFprg dvi and 3DLDF 1 1 5 1 CWEB 3DLDFprg ps are included in the distribution of 3DLDF as a convenience However users may generate them themselves should there be some reason for doing so by entering make ps from the command line of a shell from the working directory 3DLDF 1 1 5 1 or 3DLDF 1 1 5 1 CWEB Alternatively the user may generate them by hand from the working directory 3DLDF 1 1 5 1 CWEB in the following way 1 cweave 3DLDFprg web generates 3DLDFprg tex 2 tex 3DLDFprg or tex 3DLDFprg tex generates 3DLDFprg dvi 3 dvips o 3DLDFprg ps 3DLDFprg possibly with additional options generates 3DLDFprg ps 4 lpr P lt print queue gt 3DLDFprg ps sends 3DLDFprg ps to a printer on a UNIX or UNIX like system The individual commands may differ depending on the system you re using 1 4 Metafont and MetaPost Metafont is a system crea
65. pictures tim points tim lines tim planes tim paths tim curves tim polygons tim rectangs tim widgets cxx ellipses o loader tim pspglb tim io tim colors tim transfor tim shapes tim pictures tim points tim lines tim planes tim paths tim curves tim polygons tim rectangs tim widgets tim ellipses cxx In addition widgets tim must be added to the list of prerequisites in all of the following targets up to and including examples o Chapter 40 Future Plans 275 40 Future Plans 3DLDF is a work in progress In fact it can never be finished because the supply of interesting geometric constructions is inexhaustible However presently 3DLDF still has a number of major gaps If you re interesting in contributing to 3DLDF with respect to one of the topics below and in the following sections or if you have ideas of your own see Section 1 7 Contributing to 3DLDF page 9 e Input routine The lack of one is the most significant defect in 3DLDF as mentioned in Section 1 5 2 No Input Routine page 8 e Port to other platforms See Section 1 6 Ports page 8 40 1 Geometry 3DLDF currently provides a set of basic plane and solid geometrical figures However some important ones are still missing There are many useful geometrical data types and functions whose implementation would require no more than elementary geometry e Add constructors with a normal vector argument rather than angles of rotation about the main a
66. present are passed unchanged to the output file The empty string following the argument p1 is a placeholder for the dash pattern argument which isn t used here p0 draw p1 Colors gray pensquare scaled 5cm rotated 45 epi Poe Figure 6 The function Point undraw takes a required Point amp argument and optional string arguments for the dash pattern and the pen Unlike Point draw a Color argument would have no meaning for Point undraw The string arguments are passed unchanged to the output file undraw can be used to hollow out the region drawn in Fig 6 Since a dash pattern is used portions of the middle of the region are not undrawn p0 undraw p1 evenly scaled 6 pencircle scaled 2cm Figure 7 3 A reference is an alternative name for an object The main use of references is for specifying arguments and return values for functions in general and for overloaded operators Chapter 11 in particular Stroustrup The C Programming Language 5 5 p 97 Chapter 5 Drawing and Labeling Points 26 For complete descriptions of draw and undraw see Section 22 18 Point Reference Drawing page 144 5 2 Labeling Points The labels in the previous examples were made by using the functions Point label and Point dotlabel which make it possible to include T X text in a drawing label and dotlabel take string arguments for the text of the label and the po sition
67. rotations are not commutative operations Nor are they commutative with other transformations So if you want to rotate a Point about the x y and z axes in that order you can do so with a single invocation of rotate as in the previous example However if you want to rotate a Point first about the y axis and then about the x axis you must invoke rotate twice Point ptO 1 1 1 pt0 rotate 0 45 ptO rotate 45 ptO show pt0 pto 0 1 70711 0 292893 In the version taking two Point arguments p0 and pl and a real argument angle the Point is rotated angle degrees around the axis determined by p0 and p1 180 by default Point P 2 0 0 Point A Point B 2 2 2 P rotate A B 180 Chapter 22 Point Reference 132 Protatedy 0 666667 1 33333 1 33333 A CR D gt initial 2 0 0 Figure 82 Transform scale real x real y 1 real z 1 Function Calls transform scale x y z and returns its return value namely a Transform representing the scaling operation only Scaling causes the x coordinate of the Point to be multiplied by x the y coordinate of the Point to be multiplied by y and the z coordinate of the Point to be multiplied by z Point pO 1 0 3 p0 scale 4 p0 show p0 al pO 4 0 3 Point p1 2 1 2 pi scale 2 3 4 pi show p1 4 pi 4 3 8 Chapter 22 Point Reference 133 Figure 83 Transform shear real xy real xz 0
68. scale 1 3 1 p2 p3 a 10 a rotate p0 p1 75 11 p4 a 12 p2 show p2 4 p2 18 51 36 13 p3 show p3 4 p3 27 159 103 14 p4 show p4 p4 24 4647 46 2869 81 5353 CONANT RWNE In this example a is shifted and scaled and a is applied to both in line 9 This works because the binary operation operator const Transforms t returns t making it pos sible to chain invocations of Following this a is rotated 75 about the line through py and p Finally all three transformations which are stored in a are applied to pa 4 2 Inverting Transforms Inversion is another operation that can be performed on Transforms This makes it possible to reverse the effect of a Transform which may represent multiple transformations Chapter 4 Transforms 22 Point p Transform t t shift 1 2 3 t scale 2 3 4 t rotate 45 45 30 t show t 4 t 1 22 0 707 1 41 0 0 238 2 59 1 5 0 3 15 1 45 2 0 7 74 10 2 4 41 1 p t p show p 4 p 7 74 10 2 4 41 Transform u u t inverse u show u 4 u 0 306 0 0265 0 197 2 85e 09 0 177 0 287 0 0906 1 12e 09 0 354 0 167 0 125 0 1 2 3 1 p u p show p p 0 0 0 u t u show u J u 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 If inverse is called with no argument or with the argument false it returns a Transform representing its inverse and remains unchanged If it is called with th
69. second version is convenient for passing a Picture argument without having to specify all of the other arguments void dotlabel unsigned int i 0 string position_string const function top short text_short 0 Picture amp picture current_picturel void dotlabel Picture amp picture unsigned int i 0 string const function position_string top short text_short 0 Like label O except that the Points are dotted 26 14 Showing void show string text char coords w const bool const function do_persp true const bool do_apply true Focus f 0 const unsigned short proj Projections PERSP const real factor 1 Prints information about the Path to standard output stdout text is simply printed out unless it s the empty string in which case Path is printed out coords indi cates which set of coordinates should be shown Valid values are w for the world_ coordinates p for the projective_coordinates u for the user_coordinates and v for the view_coordinates whereby the latter two are currently not in use see Section 22 1 Point Reference Data Members page 119 If do_apply is true apply_transform is called on each Point updating its world_coordinates and resetting its transform Otherwise it s not The arguments do_persp f proj and factor are only relevant when showing projective_coordinates If do_persp is true the Points are
70. short shrift I hope to correct these defects in future editions 1 2 1 Conventions Data types are formatted like this int Point Path Plurals are formatted in the same way ints Points Paths It is poor typographical practice to typeset a single word using more than one font e g ints Points Paths This applies to data types whose plurals do not end in s as well e g the plural of the C class Polyhedron is Polyhedra When C functions are discussed in this manual I always include a pair of parentheses to make it clear that the item in question is a function and not a variable but I generally do not include the arguments For example if I mention the function foo this doesn t imply that foo takes no arguments If it were appropriate I would include the argument type foo int or the argument type and a placeholder name foo int arg or I would write foo void to indicate that foo takes no arguments Also I generally don t indicate the return type unless it is relevant If it is a member function of a class I may indicate this e g bar_ class foo or not depending on whether this information is relevant This convention differs from that used in the Function Index page 292 which is generated automatically by Texinfo There only the name of the function appears without parentheses parameters or return values The class type of member functions may appear in the Function Index e g bar_cl
71. sources of information about spline curves 4 Jones Huw Computer Graphics through Key Mathematics p 282 3 Knuth Donald Ervin The METAFONTbook p 130 and Hobby John D Smooth Easy to Compute Interpolating Splines Discrete and Computational Geometery 1 2 Chapter 40 Future Plans 277 existing rendering software If I decide to do the latter there are again two possibilities having 3DLDF write output in a format that a renderer can input or linking to a library supplied by a rendering package I haven t yet decided which course to pursue However in the long run Id like it to be possible to use 3DLDF for fancier graphics than is currently possible using MetaPost and PostScript alone 40 4 Multi Threading When 3DLDF is run there is only one thread of execution However it could benefit from the use of multiple threads In particular it may be faster and more efficient to have Picture output run in its own thread In this case it will no longer be possible to share current_picture among figures It may also be worthwhile to execute the code for figures i e the code between beginfig and endfig inclusive in their own threads This will require some changes in the way data are handled For example if non constant objects are shared among figures there may be no advantage to multi threading because of the need to coordinate the access of the threads to the objects If threads are used then no
72. stored in the static variable Point measurement_units which is a string Its default value is cm for centimeters At present it is best to stick with one unit of measurement for a drawing After I ve defined an input routine 3DLDF should handle units of measurement in the same way that Metafont does Another difference is that the Points pt0 pti and pt2 have three coordinates x y and z whereas z0 has only two x and y Actually the difference goes deeper than this In Metafont a pair has two parts xpart and ypart which can be examined by the user In 3DLDF a Point contains the following sets of coordinates world_coordinates user_coordinates view_coordinates projective_coordinates These are sets of 3 dimensional homogeneous coordinates which means that they contain four coordinates x y z and w Homogeneous coordinates are used in the affine and perspective transformations see Chapter 4 Transforms page 19 Currently only world_coordinates and projective_coordinates are used in 3DLDF The world_coordinates refer to the position of a Point in 3DLDF s basic unchanging co ordinate system The projective_coordinates are the coordinates of the two dimensional projection of the Point onto a plane This projection is what is ultimately printed out or displayed on the computer screen Please note that when the coordinates of a Point are referred to in this manual the world_coordinates are meant unless otherwise st
73. t understand it s probably best to skip it and come back to it later Some of the more difficult points or ones that presuppose familiarity with features not yet described are in the footnotes I firmly believe that an adequate program with good documentation is more useful than a great program with poor or no documentation The ideal case of course is a great program with great documentation I m sorry to say that this manual is not yet as good as Id like it to be I apologize for the number of typos and other errors I hope they don t detract too much from its usefulness I would have liked to have proofread and corrected it again before publication but for reasons external to 3DLDF it is necessary for me to publish now I plan to set up an errata list on the official 3DLDF website http www gnu org software 3dldf and or my own website http wwwuser gwdg de 1finstol1 Chapter 1 Introduction 3 Unless I ve left anything out by mistake this manual documents all of the data types constants and variables namespaces and functions defined in 3DLDF However some of the descriptions are terser than I would like and I d like to have more examples and illustrations There is also more to be said on a number of topics touched on in this manual and some topics I haven t touched on at all In general while I ve tried to give complete information on the what and how the why and wherefore has sometimes gotten
74. that will be drawn Draws a pattern in the x z plane consisting of hexagons The outer hexagons form a tessellation The middle and inner hexagons fit within the outer hexagons The hexagons are drawn in double rows The tessellation can be repeated by copying a double row and shifting the copy to lie directly behind the first double row If the Picture with the pattern is projected with the Focus in front of the pattern looking in the direction of the back of the pattern the first row of hexagons will appear Chapter 33 Pattern Reference 244 larger than the rows behind it Therefore in order for the perspective projection of the pattern to fill a rectangular area on the plane of projection it will generally be necessary to increase the number of sets of hexagons in each double row On the other hand if the same number of sets of hexagons were used in the front double row as will be needed for the back double row many of them would probably be unprojectable The return value of this function is the number of hexagons drawn default_focus set 0 10 10 O 10 25 10 hex_pattern_1 1 0 0 5 5 Figure 178 default_focus set 5 5 10 0 10 25 10 hex_pattern_1 2 1 5 1 2 5 2 black gray black light_gray black Figure 179 33 2 Roulettes and Involutes A roulette is the curve generated by a point which is carried by a curve which rolls on a fixed curve The locus of a point carried by a circle ro
75. the function representing the appropriate transformation Then this is multiplied by t and t is returned Returning t instead of this makes it possible to put the affine transformation function at the end of a chain of invocations of Transform operator Transform t0 ti t2 t3 tO t1 x t2 t3 scale 2 3 5 9 tO t1 and t2 are all multiplied by the Transform with 2 0 00 matrix Mra Y 0 0 9 O 0 0 0 1 representing the scaling operation not t3 which may represent a combination of transfor mations Transform scale real x real y 1 real z 1 Function Creates a Transform t representing the scaling operation locally multiplies this by t and returns t A Transform representing scaling only when applied to a Point p will cause its x coordinate to be multiplied by x its y coordinate to be multiplied by y and its z coordinate to be multiplied by z Transform t t scale x y Z gt t matrix oox o Ox 00 RhOoo a Chapter 19 Transform Reference 102 Transform t t scale 12 5 20 1 3 t show t dE 12 5 0 0 0 0 20 0 0 0 0 1 3 0 0 0 0 1 Transform shear real xy real xz 0 real yx 0 real yz 0 Function real zx 0 real zy 0 Creates a Transform t representing the shearing operation locally multiplies this by t and returns t When applied to a Point shearing causes each coordinate to be modified according to the values of the other coordinates and the
76. the ground plane with the picture plane and the left side with length 5cm at an angle of 90 40 50 to the ground line 2 There are many books on linear perspective for artists I ve found Gwen White s Perspective A Guide for Artists Architects and Designers to be particularly good Vredeman de Vries Perspective contains beautiful examples of perspective constructions Chapter 9 Pictures 61 MP CV A o its horizon MP 50 VP A0 r ground line center of vision vanishing point measuring point left right Figure 56 While it s possible to use 3DLDF to make a perspective construction in the traditional way as Fig 56 shows the code for Fig 57 achieves the same result more efficiently default_focus set 0 4 6 0 4 6 6 Rectangle r origin 2 5 0 40 Point p 2 0 1 5 r shift p r get_point 0 r draw 72 Figure 57 In Fig 56 it was convenient to start with the corner point ro if we needed the center of R it would have to be found from the corner points However in 3DLDF Rectangles are most often constructed about the center Therefore in Fig 58 R is first constructed about the origin with the rotation about the y axis passed as an argument to the constructor It is then shifted such that R points 0 the first or zeroth if you will Point on R comes to lie at 2 0 1 5 Unlike the other transformations currently used in 3DLDF the perspective
77. the maximum z values of the projective_coordinates of the Points belonging to the Shapes r is filled and drawn first because it has the Point with the positive z coordinate of greatest magnitude When subsequently r is drawn it covers part of the top of r which lies in front of r and should be visible current_picture output default_focus PERSP 1 MAX_Z Chapter 9 Pictures 71 ri To Figure 68 In Fig 69 the Shapes on current_picture are sorted according to the minimum z values of the projective_coordinates of the Points belonging to the Shapes r1 is drawn and filled last because it has the Point with the negative z coordinate of greatest magnitude It thereby covers the bottom part of rO which lies in front of r1 and should be visible current_picture output default_focus PERSP 1 MIN_Z r1 TO Figure 69 Neither sorting by the mean z value in the projective_coordinates nor suppressing sorting does any good In each case one Rectangle is always drawn and filled last covering parts of the other that lie in front of the first 3DLDF s hidden surface algorithm will fail wherever objects intersect not just where one extends past the other in both the positive and negative z directions Rectangle r origin 3 4 45 Circle c origin 2 45 r filldraw c filldraw black gray current_picture output default_focus PERSP 1 NO_SORT Chapter 9 Pictures 72 Figure 70
78. transfor mation is non affine Affine transformations maintain parallelity of lines while the rules of Chapter 9 Pictures 62 perspective state that parallel lines with one exception appear to recede toward a vanishing point In Fig 56 the lines 7977 and 7373 appear to vanish toward the right hand 40 vanishing point while 7973 and rir appear to vanish toward the left hand 50 vanishing point The lower the angle of a vanishing point the further away it is from the center of vision as Fig 58 shows VP 802 VP a 60 VP 70 VP 50 VP 40 VP 30 VP 20 e horizon __ VP 10 x 28 3564cm VP 5 x 57 1503cm ground line gt VP 0 5 a 572 943cm Figure 58 In Fig 58 the 0 5 vanishing point is nearly 53 meters away from the CV and a line receding to it will be very nearly horizontal However the distance from the focus to the CV is only 5cm As this distance increases the distance from the CV to a given vanishing point increases proportionately If the distance is 30cm a more reasonable value for a drawing then the x coordinate of VP 10 is 170 138 cm that of VP 5 is 342 902 cm and that of VP 0 5 is 3437 66 cm This is the reason why perspective drawings done by hand rarely contain lines receding to the horizon at low angles This problem doesn t arise when the perspective transformation is used In this case any angle can be calculated as easily as any othe
79. transformations affine and perspective possible in three dimensional space Any combination of transformations can be represented by a single transformation matrix This means that consecutive transformations of a Point can be saved up and applied to its coordinates all at once when needed rather than updating them for each transformation Transforms work by performing matrix multiplication of Matrix with the homogeneous world_coordinates of Points If a set of homogeneous coordinates a x y z w and Matrix M a oa m n O a TO 0 Jo P then the set of homogeneous coordinates 8 resulting from multiplying a and M is calculated as follows B axM xa yb z2c wd xe yf 29 wh 1i4 yj zk wl 1m yn z0 wp Please note that each coordinate of 8 can be influenced by all of the coordinates of a Operations on matrices are very important in computer graphics applications and are described in many books about computer graphics and geometry For 3DLDF I ve mostly used Huw Jones Computer Graphics through Key Mathematics and David Salomon s Com puter Graphics and Geometric Modeling It is often useful to declare and use Transform objects in 3DLDF just as it is for transforms in Metafont Transformations can be stored in Transforms and then be used to transform Points by means of Point operator const Transform amp 1 Transform t 2 t shift 0 1 3 Point p 1 0 0 4 p t 1 It is un
80. two or more Shapes intersect they must be broken up into smaller objects until there are no more intersections I don t expect to have a proper solution soon but I expect that I will be able to make some improvements See Section 9 3 Surface Hiding page 67 const bool do_warnings Default true If true output issues warnings to stderr standard error output if a Shape cannot be output because it lies outside the limits set by the following arguments Sometimes a user may only want to project a portion of a Picture in which case such warnings would not be helpful In this case do_warnings should be false const real min_x_proj Default 40 The minimum x coordinate of the projection of a Shape such that the Shape can be output If projective_coordinates 0 of any Point on a Shape is less than min_x_proj the Shape will not be projected at all const real max_x_proj Default 40 The maximum x coordinate of the projection of a Shape such that the Shape can be output If projective_coordinates 0 of Chapter 21 Picture Reference 117 void any Point on a Shape is greater than max_x_proj the Shape will not be projected at all const real min_y_proj Default 40 The minimum y coordinate of the projection of a Shape such that the Shape can be output If projective_coordinates 1 of any Point on a Shape is less than min_y_proj the Shape will not be projected at all const real max_y_proj Default 40 The maximum y coordin
81. use it for making three dimensional graphics except in a very limited way One insuperable problem is the severe limitation on the magnitude of user defined numerical variables in Metafont and MetaPost This made sense for Metafont s and MetaPost s original purposes but they make it impossible to perform the calculations needed for 3D graphics Another problem is the data types defined in Metafont Points are represented as pairs of real values and affine transformations as sets of 6 real values This corresponds to the representation of points and affine transformations in the plane as a two element vector on the one hand and a six element matrix on the other While it is possible to work around the limitation imposed by having points be represented by only two values it is impracticable in the case of the transformations For these reasons I decided to write a program that would behave more or less like Metafont but with suitable extensions and the ability to handle three dimensional data namely 3DLDF It stores the data and performs the transformations and other necessary calculations and is not subject to the limitations of MetaPost and its data types Upon output it performs a perspective transformation converting the 3D image into a 2D one The latter can now be expressed as an ordinary MetaPost program so 3DLDF writes its output as MetaPost code to a file In the following it may be a little unclear why I sometimes refer to Metafo
82. variable Pointers to the Points on the Path vector lt string gt connectors Protected variable The connectors between the Points on the Path Connectors are simply strings in 3DLDF they are written unchanged to out_stream const Color help_color Public static variable Pointer to a const Color which becomes the default for draw_help See Sec tion 26 12 Path Reference Drawing and Filling page 180 Please note that help_color is a pointer to a const Color not a const pointer to a Color or a const pointer to a const Color It s easy to get confused by the syntax for these types of pointers string help_dash_pattern Public static variable The default dash pattern for draw_help bool do_help_lines Public static variable true if help lines should be output otherwise false If false a call to draw_ help does not cause a copy of the Path to be created and put onto a Picture See Section 26 12 Path Reference Drawing and Filling page 180 26 2 Constructors and Setting Functions void Path void Default constructor Creates an empty Path with no Points and no connectors void Path const Point amp p0 const Point amp p1 Constructor Creates a line more precisely a line segment between p0 and p1 The single con nector between the two Points is set to and the data member line_switch of type bool is set to true There are certain operations on Paths that are only applicable to lines so it s necessa
83. vector lt Ellipse gt ellipses vector lt Reg_Polygon gt reg_polygons vector lt Rectangle gt rectangles Vectors of pointers to the Paths Circles Ellipses Reg_Polygons and Rectangles respectively belonging to the Solid if any exist valarray lt real gt projective_extremes Protected variable The maximum and minimum values for the x y and z coordinates of the Points belonging to the Solid Used in Picture output for testing whether a Solid is projectable using a particular set of arguments unsigned short CIRCLE Public static const variables unsigned short ELLIPSE unsigned short PATH unsigned short RECTANGLE unsigned short REG_POLYGON Used as arguments in the functions get_shape_ptr and get_shape_center see Section 34 8 Returning Elements and Information page 250 Chapter 34 Solid Reference 249 34 2 Constructors and Setting Functions void Solid void Default constructor Creates an empty Solid void Solid const Solid amp s Copy constructor Creates a new Solid and makes it a copy of s Solid create_new lt Solid gt const Solid s Template specializations Solid create_new lt Solid gt const Solid amp s Pseudo constructors for dynamic allocation of Solids They create a Solid on the free store and allocate memory for it using new Solid They return a pointer to the new Solid If s is a non zero pointer or a reference the new Solid will be a copy of s If the new object is not meant to be
84. version that finds the intersection point of the traces of the lines on the major planes is used See Section 22 17 Point Reference Intersections page 143 Point A 1 1 1 Point B 1 1 1 Path pO A B Point C 2 1 1 Point D 1 75 0 25 0 25 Path p1 C D bool_point bp p0 intersection_point p1 bp pt dotlabel i bp pt show bp pt 4 bp pt 0 5 0 5 0 5 Figure 138 Chapter 27 Polygon Reference 199 27 Polygon Reference Class Polygon is defined in polygons web and is derived from Path using public deriva tion Polygon is mainly intended for use as a base class for more specialized kinds of polygons Currently the classes Reg_Polygon regular polygon and Rectangle are defined See Chapter 28 Regular Polygon Reference page 205 and Chapter 29 Rectangle Reference page 211 27 1 Data Members Point center Private variable The center of the Polygon if it has one However a Polygon need not have a center If it doesn t center should be set to INVALID_POINT 27 2 Operators Transform operator const Transformg t Virtual operator Multiplies a Polygon by the Transform t Similar to Path operator const Transform amp t except that center is transformed as well See Section 26 4 Path Reference Operators page 171 27 3 Querying const Point amp get_center void Virtual function Point get_center void const function These functions return cent
85. want to add a file widgets web that defines a class Widget and that the latter needs access to class Rectangle and is in turn required by class Ellipse Code must be added to 3DLDF 1 1 5 1 CWEB Makefile for ctangling widgets web compiling widgets cxx and linking widgets o with the other object files to make the executable 3dldf The best way to do this is to change 3DLDF 1 1 5 1 CWEB Makefile am and use Au tomake to generate a new Makefile in Then configure can be used to generate a new Makefile It would be possible to modify Makefile by hand but I don t recommend it The following assumes that the user has access to Automake If he or she is using a GNU Linux system this is probably true widgets web must be added between rectangs web and ellipses web in the fol lowing variable declaration in 3DLDF 1 1 5 1 CWEB Makefile am 3dldf_SOME_CWEBS pspglb web io web colors web transfor web shapes web pictures web points web lines web planes web paths web curves web polygons web rectangs web ellipses web circles web patterns web solids web solfaced web cuboid web polyhed web utility web parser web examples web Now add widgets o between ellipses o and rectangs o in the following variable declaration 3dldf_OBS_REVERSED main o examples o parser o utility o polyhed o cuboid o solfaced o solids o patterns o circles o ellips
86. way output of Shapes that couldn t be output when Picture output was called with a particular set of arguments won t necessarily be suppressed when Picture output is called again with different arguments Chapter 19 Transform Reference 96 19 Transform Reference Class Transform is defined in transfor web Point is a friend of Transform 19 1 Data Members Matrix matrix Private variable A 4 x 4 matrix of real representing the actual transformation matrix 19 2 Global Variables and Constants Transform user_transform Variable Currently has no function It is intended to be used for transforming the coordinates of Points between the world coordinate system WCS and a user coordinate system UCS when routines for managing user coordinate systems are implemented const Transform INVALID_TRANSFORM Constant Every member of matrix in INVALID_TRANSFORM is equal to INVALID_REAL const Transform IDENTITY_TRANSFORM Constant Homogeneous coordinates and Transforms are unchanged by multiplication with IDENTITY_TRANSFORM matrix is an identity matrix 1 0 0 0 0 1 0 0 0 01 0 0 0 0 1 See Chapter 4 Transforms page 19 19 3 Constructors void Transform void Default constructor Creates a Transform containing the identity matrix void Transform real r Constructor Creates a Transform and sets all of the elements of matrix to r Currently this constructor is never used but who knows Maybe someday it will b
87. z axis p0 1 2 3 pO shift 2 3 5 p0 show p0 J p0 3 5 8 Transform shift_times real x real y 1 real z 1 Function Transform shift_times const Point amp p Function Each of these functions calls the corresponding version of Transform shift_ times on transform and returns its return value namely the new value of transform shift_times makes it possible to increase the magnitude of a shift applied to a Point while maintaining its direction Please note that shift_times will only have an effect if it s called after a call to shift and before transform is reset This is performed by reset_transform which is called in apply_transform and can also be called directly See Section 19 12 Transform Reference Resetting page 107 and Section 22 13 Point Reference Applying Transformations page 135 Point P drawdot shift 1 1 1 drawdot shift_times 2 2 2 drawdot shift_times 2 2 2 drawdot shift_times 2 2 2 drawdot uu VU UU UU UO Chapter 22 Point Reference 135 Figure 85 22 13 Applying Transformations void apply_transform void Function Updates world_coordinates by multiplying it by transform which is subsequently reset to the identity Transform 22 14 Projecting bool project const Focus f const unsigned short proj Function Projections PERSP real factor 1 bool project const unsigned short amp pr
88. 0 2 5 10 10 epicycloid_pattern_1 5 3 3 1 36 current_picture output Chapter 33 Pattern Reference 247 Figure 181 Chapter 34 Solid Reference 248 34 Solid Reference Class Solid is defined in solids web It s derived from Shape using public derivation It is intended to be used as a base class for more specialized classes representing solid figures e g cuboids polyhedra solids of rotation etc 34 1 Data Members bool on_free_store Protected variable true if the Solid was dynamically allocated on the free store otherwise false Solids should only be allocated on the free store by create_new lt Solid gt or anal ogous functions for derived classes See Section 34 2 Solid Reference Constructors and Setting Functions page 249 Point center Protected variable The center of the Solid An object of a type derived from Solid need not have a meaningful center However many do so it s convenient to be able to access it using the member functions of Solid bool do_output Protected variable Set to false in Picture output if the Solid cannot be projected using the arguments of that particular invocation of output Reset to true at the end of Picture output so that the Solid will be tested for projectability again if output is called on the Picture again vector lt Path gt paths Protected variables vector lt Circle gt circles
89. 0 PACE Si rn E N a cals bo ake 257 O E E RO 93 fill color beso oe es Gate eed ED 166 fill_draw_value o 166 PILLDRAW amp 4 aan oa eiii dd 93 LOCUS rr ido Lad was ato 63 FOCUS AS a e A t et 151 TOCUSO o tata tte lts 222 E 222 G PL AS A Seas AA 91 PLC ir a a das EE Pea 91 grean partoo mia Dee AO 88 Breen A senemi a Sty dae tes Wao 91 H A Gio eed Se wlabro es eee 258 hel px Color it ge tice Sakae 91 167 help Color _ Vector 45 eek 28S eee be hans 91 help_dash_pattern 00000 167 hexagon_radius cee cece eee 269 I MALETA side Me age Bi aes 51 266 IDENTITY_TRANSFORM o oooooooooooo 96 AEB A A o i 92 internal Mia acota pta 205 INVALID_BOOL_PO0INT eoccoisirar cs o 122 INVALID_BOOL_POINT_PAIR 122 INVALID_BOOL_POINT_QUADRUPLE 122 Data Type and Variable Index INVALID_BOOL_REAL_POINT 122 INVALID ETNE cda o la ae 154 INVALID PLANE gt i Arona aa ia ze 157 INVALID POINT ern an ake Re ee eee 122 INVALID REAL coe nko oko Se eh eS eS ee 82 INVALID REAL PAIR Sain sie eee 82 INVALID_REAL_SHORT 04 82 INVALID_TRANSFORM o ooooooocococoooooo 96 A O ibe haat 114 L Label td da O nated dll a le 108 A O pe teed 111 ldtureal double iii ars o ate 82 laf Teal float os ccs A A ee 82 lightgray orn E E wie els shone aaiene 4 91 Din S25 A aaa Sy soba patna ad 154 EINE SWIC CHL ai Sas da dar
90. 00 pixels per inch 6 Chapter 1 Introduction 8 projection are generated by means of the algorithms MetaPost inherited from Metafont These algorithms however are designed to find the most pleasing curve given one or more two dimensional points and connectors they do not account for the the fact that the two dimensional points are projections of three dimensional ones This can lead to unsatisfactory results especially where extreme foreshortening occurs In particular curl dir tension and control points should be used cautiously or avoided altogether when specifying connectors 3DLDF operates on the assumption that given an adequate number of points MetaPost will produce an adequate approximation to the desired curve in perspective since the greater the number of points given for a curve the less choice MetaPost has for the path through them My experience with 3DLDF bears this out Generally the curves look quite good Where problems arise it usually helps to increase the number of points in a curve A more serious problem is the imprecision resulting from the operation of rotation Rotations use the trigonometric functions which return approximate values This has the result that points that should have identical coordinate values sometimes do not This has consequences for the functions that compare points The more rotations are applied to points the greater the divergence between their actual
91. 1 1 5 1 41421 1 41421 cycle r0 show r0 p 4 ro fill_draw_value Perspective coordinates 5 05646 4 59333 0 040577 2 10249 4 86501 0 102123 1 18226 1 33752 0 156559 3 51276 1 2796 0 193084 cycle ri show ri 4 ri fill_draw_value 1 2 12132 2 12132 1 2 12132 2 12132 1 2 12132 2 12132 1 2 12132 2 12132 cycle ri show r1 p 4 rl Chapter 9 Pictures 70 fill_draw_value Perspective coordinates 5 09222 0 995681 0 133156 2 98342 1 03775 0 181037 1 39791 4 05125 0 208945 2 87319 3 93975 0 230717 cycle y 2 12132 2 12132 4142 1 41421 x 2 12132 2 12132 1 41421 1 41421 Figure 67 In Fig 67 the Rectangles r and r intersect along the x axis The z values of the world_coordinates of ry are 1 41421 and 1 41421 two Points each while those of r are 2 12132 and 2 12132 So r has two Points with z coordinates greater than the z coordinate of any Point on ro and two Points with z coordinates less than the z coordinate of any Point on rg The Points on rp and r all have different z values in their projective_ coordinates but r still has a Point with a z coordinate greater than that of any of the Points on rg and one with a z coordinate less than that of any of the Points on rp In Fig 68 the Shapes on current_picture are sorted according to
92. 1 Data Members aR ccc A AEE E RE 222 31 2 Constructors and Setting Functions 222 31 3 Performing Transformati0DS o ooooooococoooccoo 224 SLA Operators oia e A AA 224 310 Labels Aa aan 224 31 6 Affine Transformations 0 00 00 cece eee eee 226 IL Querying su fea ea cae ee eas eas Phe ade os 226 31 8 Returning Elements and Information 227 31 9 IntersectionS 0 cece ene teenie enes 230 Oils VOY 21 hiat aT E Sica nc hate eg EN ech Pee en he hg 235 31 11 Rectangles a cece cece tenes 236 Circle Reference oo oo ooooooooo o 238 32 1 Data Members 00 cece ccc nett oo 238 32 2 Constructors and Setting Functions 238 32 3 Operators ia elite Len othe ma nek 238 IL Olieryin A eesti teat ate 239 32 0 Intersections s asad daa a a eA ape hae A ERO LS 240 Pattern Reference o o ooooooooo o o 242 33 1 Plane Tesselati0OS o oooooocoooorrorrmoo 242 33 2 Roulettes and Involutes o oooooooooooooo 244 33 2 1 Epicycloids 00 cece cee eee 245 viii 34 Solid Reference o oooooo oo 248 34 1 Data Members 0 ccc cece nent enn a 248 34 2 Constructors and Setting Functions 248 34 3 Destructo ya s sacs RE arias ali 249 34A O E Adis Dee falda a thai EA da ede S 249 34 5 COPYING a aes tee ieee de aN ea eae 249 34 6 Setting Members
93. 196 set_dash_pattern 0 eee 174 Set draw COLO italia Tove Ss 174 set SLlemeNnt rns ees na inaia rn New ee poca di 99 set_extremes hiret bese ees 95 150 197 254 Seti color rc eden bank Row ee ia 174 set_fill_draw_value 174 set green PUT lr eres eed 90 A cists y Bees ba a 89 294 set_on_free_store 93 130 173 250 SSE POM sie OR carted ti Gly Senet se ion 174 set red part A ee ote Se ae Ss 90 set tra nsform iia a da 114 set_use_name ccc eee 89 shear is 94 102 133 175 200 226 254 shift 94 102 113 134 176 177 200 226 254 shift_times 103 134 178 200 226 show 90 94 100 114 149 153 155 163 192 253 SNOW COLOS ci eles eNi 193 ShoW_tIanS 0TM oooooooo o 114 149 SIZE NA aaa Bo A ese le Tes 194 SLP iii da a ias 140 194 polid A RO 249 SOL ce TUSE adds 217 235 solve quadratica oil es y te as 271 S bpat he odia e noto fas 194 suppress_labelsS o ooo oooommoo om 117 suppress_output 95 150 197 254 T A 4 i thie aia ee oda ee 261 Transform cese ee ste Ie ste a ORs Nee 96 GUN Ceo ade tr hea one secs oe Mtge ete 271 Trunc_Octahedron 0 cece een eens 269 U WNL AW a E A eke ama 146 189 256 u d avd t co siete casa esl dike Said ns Bde Dade e s 145 A A ey ee ea 189 256 nfilldr ibs teed otk eae ne ole oe ee eee 190 256 unit VE CEO iria a eo 139 unsuppress_labelS
94. 2 5 0 0 0 0 1 dm is unchanged Chapter 19 Transform Reference 99 Transform operator const Transform t const operator Multiplication of a Transform by another Transform without assignment The return value is a Transform whose matrix contains values that are the result of the matrix multiplication of matrix and t matrix 19 5 Matrix Inversion Transform inverse void const function Transform inverse bool assign false Function Returns a Transform T with a T matrix that is the inverse of matrix If assign true then matrix is set to its inverse In the const version matrix remains unchanged The second should only ever be called with true as its assign argument If you re tempted call inverse false you might as well just leave out the argument which issues a warning message and calls the const version 19 6 Setting Values void set_element const unsigned short row const unsigned short Function col real r Sets the element of matrix indicated by the arguments to r Transform t t set_element 0 2 3 45569 t show t dt 1 0 3 46 0 0 1 0 0 0 0 1 0 0 0 0 1 19 7 Querying bool is_identity void Function Returns true if this is the identity Transform otherwise false This function has both a const and a non const version In the non const version clean is called on this before comparing the elements of matrix with 1 for the main diagonal and 0 for the other elements In the const ver
95. 262 265 268 270 EST MOTMAL iii id iia td 195 get_numerical_eccentricity 228 get path se hia tdt iia den ii 155 got path Ptc o as 253 gat A es ee ee 153 get_persp_element o o ooocoocmmo m oo 153 PSC PLANS in rt a 195 POUMPOIN Gai nid at tetera ha teeta erat 194 PSC rPOSIE TOM ten cine wnat Nears Greate teeta ee 153 g t radis sxc ies cage eet 207 240 get_rectangle_center 44 251 get_rectangle_ptI o oooooocoo o oo 253 get Ted Pai ide a ts 90 get_reg_polygon_centel 251 get_reg_polygon_ptr 0 0000 253 get_register_width o o oo o oo 86 get_second_largest o oooooccooocooo 87 get_shape_center 0 ccc cece eee 250 Pet shape ptr instala 252 Pet SIZ shi caste eee te ee kh ea eet 195 get transformo seen ae Med ee tai 126 153 get_transform_element 153 get Upare A deeb tee tae 153 get use namens se en hee hi 90 Bet Wits set Bitte e ie 129 PORE eee mo es Be nee ees Ja bed 128 Pty ws tas fe Sie aban oon teams ee R 129 BE eee Bee td Tad thes naan hie A beeen dali hd 129 I Tcosahedron i i iaig cei eed bce neds 267 TN SCLE Ci hak bs et Ee a 207 in ella pseert i feet ats tar ae ee eae 214 in rectangle iii e ews Y 236 initiallize color Socios ta nE 90 TNitialiZe i ma ii tae aes 92 intersection_line 162 intersection_point 143 161 198 intersection_points
96. 3 pt 1 pt 2 pt 3 rotate 0 180 Rectangle r pt 0 pt 2 pt 3 pt 1 r draw Figure 31 This constructor checks whether the Point arguments are coplanar however it does not check whether they are really the corners of a valid rectangle the user or the code that calls this function must ensure that they are In the following example r although not rectangular is a Rectangle as far as 3DLDF is concerned pt 0 shift 0 1 pt 3 shift 0 1 Rectangle q pt 0 pt 2 pt 3 pt 1 q draw Chapter 7 Plane Figures 43 Figure 32 This constructor is not really intended to be used directly but should mostly be called from within other functions that should ensure that the arguments produce a rectangular Rectangle There is also no guarantee that transformations or other functions called on Rectangle Circle or other classes representing geometric figures won t cause them to become non rectangular non circular or otherwise irregular Sometimes this might even be desirable I plan to add the function Rectangle is_rectangular soon so that users can test Rectangles for rectangularity 7 3 Ellipses Ellipse has a constructor similar to those for Reg_Polygon and Rectangle The first argument is the center of the Ellipse and the following two specify the lengths of the horizontal and vertical axes respectively The Ellipse is first created in the x z plane centered about the origin T
97. 30 c1 filldraw Chapter 8 Solid Figures 48 Figure 38 8 2 Polyhedron The class Polyhedron is meant for use only as a base class no objects of type Polyhedron should be declared Instead there is a class for each of the different drawable polyhedra Currently 3DLDF defines only three Tetrahedron Dodecahedron and Icosahedron There s no need for a Cube class because cubes can be drawn using Cuboid see Section 8 1 Cuboid Getstart page 47 Polyhedra have a high priority in my plans for 3DLDF I intend to add Octahedron soon which will complete the set of regular Platonic polyhedra Then I will begin adding the semi regular Archimedean polyhedra and their duals The constructors for the classes derived from Polyhedron follow the pattern familiar from the classes already described The constructors for the classes described below have identical arguments First a Point specifying the center then a real for the diameter of the surrounding circle Umkreis in German of one of its polygonal faces followed by three real arguments for the angles of rotation about the main axes 8 2 1 Tetrahedron The center of a tetrahedron is the intersection of the lines from a vertex to the center of the opposite side At least in 3DLDF this is the center of a Tetrahedron I m not 100 certain that this is mathematically correct Tetrahedron t origin 4 t draw t get_center dotlabel c Chapter 8 Solid F
98. 3DLDF User and Reference Manual 3 dimensional drawing with MetaPost output Manual edition 1 1 5 1 for 3DLDF Version 1 1 5 1 January 2004 Laurence D Finston This is the 3DLDF User and Reference Manual edition 1 1 5 1 for 3DLDF 1 1 5 1 This manual was last updated on 16 January 2004 3DLDF is a GNU package for three dimensional drawing with MetaPost output The author is Laurence D Finston Copyright c 2003 2004 Laurence D Finston Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 2 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back Cover Texts A copy of the license is included in the section entitled GNU Free Documentation License Short Contents O ooN na A WN E WWwWwWwWWNNNNNYNNNYN NY N FBR BRR RB rR Fe oP WN Fr OU AN OTK WNYNF DO AN DT FP WN FF CO Fe UU Oak m oie NI O 1 Points veda ca Se DT A A ee BS ee abi sew oe Ss aS 10 Transiorming Points sesia ae eu A alent a are 13 AA a oo ea eS wes 19 Drawing and Labeling Points soo ae scan Swe ee eee 24 PPAR os sho od Bea aah are a Shai Sas EE pars SG aa a bao ae a ee 28 Plane Pitt pisado ar See te ke 36 Solid Figures vana ee ae ees 47 Pict res eos saris E co dal ca A oe ara ea aN ALA a th Pe 54 A O A RN 73 Installing and Running 3DLDF Ss 016 200 dal a io ida ad 74 Typedefs and Utility StEUCTULES Sd
99. 3dldf again 2 Call CWEB 3dldf at the command line It writes a file of MetaPost code called 3DLDFput mp 3 Run MetaPost on the file 3DLDFmp mp which inputs 3DLDFput mp mpost 3DLDFput The result is an Encapsulated PostScript file 3DLDFput lt integer gt for each figure in your drawing Chapter 11 Installing and Running 3DLDF 77 4 The file 3DLDFtex tex should contain code for including the 3DLDFput lt integer gt files This is an example taken from the 3DLDFtex tex included in the distribution You may change it to suit your purposes vbox to vsize vskip 2cm line hskip 2cm Figure 1 hss vfil line hskip 2cm epsffile 3DLDFmp 1 hss vss 5 Run TFX on 3DLDFtex tex to produce the DVI file 3DLDFtex dvi tex 3DLDFtex 6 Run dvips on the DVI file to produce the PostScript file 3DLDFtex ps dvips o 3DLDFtex ps 3DLDFtex 7 3DLDFtex ps can be viewed using Ghostview it can be printed using lpr on a Unix like system you can convert it to PDF with ps2pdf or to some other format using the appropriate program I sincerely hope that it worked If it didn t ask your local computer wizard for help On the computer I m using I found that special arguments for setting landscape and papersize in TEX files for DIN A3 landscape didn t work Ghostview cut off the right sides of the drawings Nor did it work to call dvips t landscape t a3 This caused an e
100. 73 Path intersections 0 0 2 e eee ee eee 73 Pathsrits ont al cd Kee da eta eae 28 Concept Index Pen expressi0O ooccococcoccocconcoccc e 144 A RN 24 PNG Portable Network Graphics 4 77 79 278 Points connecting 0 cece ee ee eee 24 Portable Network Graphics PNG 4 77 79 278 PostScript PS coins eae 4 77 79 PostScript structured 77 79 projective invariance 0 cee eee ee 276 PS PostScript ree atia i 4 77 79 R raw MetaPost code annann eee eee 58 reflectionS n on nnana naaar cece cece e ae 276 RGB red green blue 0 00020005 88 S Sad daba 276 296 Shadows ii a ee ea ted ek te ta 276 Spline Curves 4 58 ieee Le eee ale RS at 276 SPINES 925 6a hee Lake eet a ee es 276 structured PostScript 000 77 79 surface hiding cite pc 68 surface patches 0 cee eee eee eee 276 symbols pio ii 4 system dependencies 0000000 82 T template functions 0 0 eee eee 74 Templates ci papada 74 CONSION in ii ade 28 theory of intersection oooooooooccccccco 73 TODOS HS a ad ee 58 83 U units of measurement ooo oooooccooroco om 10
101. 8 Regular Polygon Reference 208 Circle c h in_circle c unfilldraw black Figure 147 Circle draw_in_circle const Color amp ddraw_color const function Colors default_color const string ddashed const string ppen Picture amp picture current_picturel Circle draw_in_circle Picture amp picture current_picture const function const Color amp ddraw_color Colors default_color const string ddashed const string ppen Draws and returns the enclosed Circle of the Reg_Polygon Point P O 1 1 Reg Polygon h P 7 4 80 2 5 h draw black evenly h draw_in_circle Chapter 28 Regular Polygon Reference 209 Figure 148 Circle out_circle void const function Returns the surrounding Circle of the Reg_Polygon Point P O 1 1 Reg_Polygon h P 6 4 15 12 11 5 Circle c h out_circle c filldraw black gray h unfilldraw black Figure 149 Chapter 28 Regular Polygon Reference 210 Circle draw_out_circle const Color amp ddraw_color const function Colors default_color const string ddashed const string ppen Picture amp picture current_picturel Circle draw_out circle Picture amp picture const function current_picture const Color amp ddraw_color Colors default_color const string ddashed const string ppen Draws and returns the surrounding Circle of the Reg_Polygon
102. 9 6 Setting Values 0 cece eee eee eee eee eee 99 LOTA QUEME soso it is li 99 19 8 Returning Informati0N 0ooooocooocccccocccco o 100 19 9 SHO WIDE sesane ea enito Sad DEANA Pea Ae 100 19 10 Affine Transformations 0 0000 c cece eee eee 101 19 11 Alignment with an Axis 0 cece eee eee eee 105 19 12 Resetting ea aioa E ean ee ee E E e as 107 19 137 Clean ii a AA epi ees 107 20 Label Reference oooooooooo oo 108 20 1 Data Members ai ha ies eee oa ade 108 20 2 COPE Stata ap EN a aoe ele ee 109 20 3 Out Putting it pee ae Ge a ee Ok yeh a a 109 21 Picture Reference o ooo ooo 111 21 1 Data Members 0 0 cc cece cee eens 111 21 22 Global Variables iras esc eS Siecle aie es eee 111 213 COnStructOrs cocoa ia otk 111 214 Operators ts ui dae dda phd da dada 112 21 5 Affine Transformations 00 0000 cece cee cence 113 2126 Modifying scotia eta sak exe Lites 113 DAT SHOWING A 2 toad eet 114 21 8 Outputting ices epininni ia bebe A a een 114 21 8 1 NamespaceS esr cece AA ee aes 114 21 8 1 1 Namespace Projections 114 21 8 1 2 Namespace Sorting 114 21 8 2 Output Functions oo ooooooooooo 115 22 Point Reference ss carre 119 22 1 Data Members 0 0 c ccc cece cece cee eee eees 119 22 2 Typedefs and Utility Structures o oooooooccoooooo 121 22 3 Global Constants and Variables
103. Bjarne The C Programming Language Special Edition Reading Mas sachusetts 2000 Addison Wesley ISBN 0 201 70073 5 Stroustrup Bjarne The Design and Evolution of C Reading Massachusetts 1994 Addison Wesley Publishing Company ISBN 0 201 54330 3 Vredeman de Vries Jan Perspective New York 1968 Dover Publications Inc Standard Book Number 486 21086 4 The beautiful perspective constructions in this volume are taken from the original work first published by Henricus Hondius in Leiden in 1604 and 1605 White Gwen Perspective A Guide for Artists Architects and Designers London 1968 and 1982 B T Batsford Ltd ISBN 0 7134 3412 0 Appendix A GNU Free Documentation License 282 Appendix A GNU Free Documentation License Version 1 2 November 2002 Copyright c 2000 2001 2002 Free Software Foundation Inc 59 Temple Place Suite 330 Boston MA 02111 1307 USA Everyone is permitted to copy and distribute verbatim copies of this license document but changing it is not allowed 0 PREAMBLE The purpose of this License is to make a manual textbook or other functional and useful document free in the sense of freedom to assure everyone the effective freedom to copy and redistribute it with or without modifying it either commercially or non commercially Secondarily this License preserves for the author and publisher a way to get credit for their work while not being considered responsible for modifications made b
104. Figure 76 string position Private variable The position of the text with respect to pt Valid values are as in MetaPost top bot bottom lft left rt right ulft upper left Ift lower left urt upper right Irt lower right bool DO_LABELS Public static variable Enables or disables creation of Labels If true label and dotlabel cause Labels to be created and put onto a Picture If false they are not Note that it is also possible to suppress output of existing Labels when outputting a Picture 20 2 Copying Label get_copy void const Function Creates a copy of the Label and returns a pointer to the copy Called in Picture operator and Picture operator where Pictures are copied Users should never need to call this function directly See Section 21 4 Picture Reference Operators page 112 This function dynamically allocates a new Label and a new Point within the Label and copies the strings from this to the new Label The standard library functions for strings take care of the allocation for the string members of Label 20 3 Outputting void output const Focus amp f const unsigned short proj real Function factor const Transform t Writes MetaPost code for the labels to out_stream It is called in Picture output see Section 21 8 Picture Reference Outputting page 114 Users should never need to call this function directly When Pi
105. G 2 oie a ea aan Risa aa oo needs 192 26 15 QUEDE coc sag Bes teed rr aa dies GOs BNE 194 26 16 Outpltting da pd AAA 196 26 17 IntersectionS 0 ccc ccc a eie E ae a ade 197 27 Polygon Reference o o o o ooooo o 199 27 1 Data MemberS oooooooororon cece ene eens 199 27 2 Operators cacin ede cke aa a eed a ae a s 199 27 3 QUCTYING An a AD ARA AEA N A 199 27 4 Affine Transformations 000 ccc ccc eee eee 199 20D Intersections iaa A daa Sa taa 200 vil 28 29 30 31 32 33 Regular Polygon Reference 205 28 1 Data Members irie a a e a a rr 205 28 2 Constructors and Setting Functions 205 28 3 OPErat TS roana vag ecise aaa 207 284 UEM a A tia dd 207 28 9 Circle it a dada 207 Rectangle Reference o o ooooo o 211 29 1 Data Members 0 00 eee eee eee eee 211 29 2 Constructors and Setting Functions 211 293 Operators iii dade tne bane ead eee ee 212 29 4 Returning Pointsec e e rianan i eee eee eee nee 212 29 5 gt Querying saiia n eee Wee pa eae ee bees 213 29 6 Ellipsesis cos nasls a tee eae ba Po ea aa 213 Regular Closed Plane Curve Reference 216 30 1 Data Members 0 ccc eet tenn enes 216 30 2 Querying ca ee ia bebe eae a 216 30 3 IntersectionS 00 cece ncn cnet teenies 217 S04 Sepments Tirei ah dorset te fens 219 Ellipse Reference o ooooooooooooo 222 31
106. LDBL_MAX However I doubt that this amount of precision would be worthwhile If it ever were required 3DLDF would have to be changed in other ways too In particular it would have to use more precise trigonometric functions for rotations See Section 1 5 1 Accuracy page 7 Chapter 16 Color Reference 88 16 Color Reference Class Color is defined in colors web 16 1 Data Members string name Variable The name of the Color bool use_name Variable If true name is written to out_stream when the Color is used for drawing or filling Otherwise the RGB red green blue values are written to out_stream bool on_free_store Variable true if the Color has been created by create_new lt Color gt which allocates mem ory for the Color on the free store Otherwise false Colors should only ever be dynamically allocated by using create_new lt Color gt See Section 16 2 Color Reference Constructors and Setting Functions page 88 real red_part Variable real green_part Variable real blue_part Variable The RGB red green blue values of the Color A real value r is valid for these variables if and only if0 lt r lt 1 16 2 Constructors and Setting Functions void Color void Default constructor Creates a Color and initializes its red_part green_part and blue_part to 0 use_ name and on_free_store are set to false void Color const Color amp c const string n const Copy constructor bool u t
107. Members Point focusO Protected variables Point focusl The foci of the Ellipse They are located on the major axis of the Ellipse at a distance of linear_eccentricity from center on opposite sides of the minor axis real linear_eccentricity Protected variable The linear eccentricity of the Ellipse e such that e a b where a and b are half the lengths of the major and minor axes respectively Let h stand for axis_h and v for axis_v If h gt v then a h 2 and b v 2 If v gt h then a v 2 and b h 2 If h v then the Ellipse is circular but not an object of type Circle and a b v 2 h 2 The linear eccentricity is the distance along the major axis of the Ellipse from center to focus0 and focus1 real numerical_eccentricity Protected variable The numerical eccentricity e of the Ellipse such that e e a lt 1 where e is the linear eccentricity of the Ellipse and a is half the length of the major axis of the Ellipse real axis_h Protected variables real axis_v The horizontal and vertical axes respectively of the Ellipse Actually they are only or vertical horizontal by convention since there are no restric tions on the orientation of an Ellipse unsigned short Protected static variable DEFAULT_NUMBER_OF_POINTS The number of Points on an Ellipse unless another number is specified when an Ellipse constructor is invoked 31 2 Constructors and Setting Functions void Ellipse void Default
108. NVALID_BOOL_REAL_POINT Constant b is false r is INVALID_REAL and pt is INVALID_POINT bool_point_quadruple Constant INVALID_BOOL_POINT_QUADRUPLE first second third and fourth are all INVALID_BOOL_POINT Chapter 22 Point Reference 123 22 4 Constructors and Setting Functions void Point void Default constructor Creates a Point and initializes its x y and z coordinates to 0 void Point const real x const real y CURR_Y const real z Constructor CURR_Z Creates a Point and initializes its x y and z coordinates to the values of the argu ments x y and z The arguments y and z are optional If they are not specified the values of CURR_Y and CURR_Z are used They are 0 by default but can be changed by the user This can be convenient if all of the Points being drawn in a particular section of a program have the same z or y and z values void set const real x const real y CURR_Y const real z Setting function CURR_Z Corresponds to the constructor above but is used for resetting the coordinates of an existing Point void Point const Point amp p Copy constructor Creates a Point and copies the values for its x y and z coordinates from p void set const Point amp p Setting function Corresponds to the copy constructor above but is used for resetting the coordinates of an existing Point This function exists purely as a convenience the operator operator see Section 22 6 Point Refer
109. O rotate 0 30 30 p0 show p0 pO 1 25477 0 724444 0 388228 pi show pi 4 pl 1 25477 0 724444 0 388228 p0 draw p1 Point p2 1 06066 0 1 06066 p2 show p2 4 p2 1 06066 0 1 06066 Chapter 3 Transforming Points 18 Point p3 p2 p3 rotate p1 pO 45 p3 show p3 4 p3 1 09721 1 15036 1 17879 Point p4 p2 p4 rotate p1 p0 90 p4 show p4 p4 0 882625 2 05122 0 485242 Point p5 p2 p5 rotate p1 pO 135 p5 show p5 4 p5 0 542606 2 17488 0 613716 Point p6 p2 p6 rotate p1 pO p6 show p6 4 p6 0 276332 1 44889 1 47433 y j gt Figure 2 I have sometimes gotten erroneous results using rotate for rotation about two Points It s usually worked to reverse the order of the Point arguments or to change sign of the angle argument I think I ve fixed the problem though Chapter 4 Transforms 19 4 Transforms When Points are transformed using shift shear or one of the other transforma tion functions the world_coordinates are not modified directly Instead another data member of class Point is used to store the information about the transformation namely transform of type class Transform A Transform object has a single data element of type Matrix and a number of member functions A Matrix is simply a 4 x 4 array of reals defined using typedef real Matrix 4 4 Such a matrix suffices for performing all of the
110. Point representing a position vector and a Point representing a direction vector See also the descriptions of Point get_line in Section 22 16 Points and Lines page 140 and Path get_line in Section 26 15 Path Reference Querying page 194 24 1 Data Members Point position Public variable Represents the position vector of the Line Point direction Public variable Represents the direction vector of the Line 24 2 Global Constants const Line INVALID_LINE Constant position and direction are both INVALID_POINT 24 3 Constructors void Line const Point amp pos origin const Point amp dir Default constructor origin Creates a Line setting position to pos and direction to dir If this function is called with no arguments it creates a Line at the origin with no direction Point p 2 1 2 Point d 3 3 3 5 Line LO p d Line L1 p get_line d Chapter 24 Line Reference 155 d Ly direction 3 3 3 5 L direction 5 2 1 5 Figure 104 void Line const Line amp 1 Copy constructor Creates a Line making it a copy of I 24 4 Operators void operator const Line amp 1 Assignment operator Sets this to l 24 5 Get Path Path get_path void const function Returns a linear Path with two Points on the Line The first Point will be position and the second will be position direction 24 6 Showing void show string text Function If text is not the
111. Post AT amp T Bell Laboratories Murray Hill NJ No date Jones Huw Computer Graphics through Key Mathematics Springer Verlag London Lim ited 2001 ISBN 1 85233 422 3 Knuth Donald Ervin Metafont The Program Computers and Typesetting D Addison Wesley Publishing Company Inc Reading Massachusetts 1986 ISBN 0 201 13438 1 Knuth Donald Ervin The METAFONTbook Computers and Typesetting C Addison Wesley Publishing Company Inc Reading Massachusetts 1986 Knuth Donald Ervin TeX The Program Computers and Typesetting B Addison Wesley Publishing Company Inc Reading Massachusetts 1986 ISBN 0 201 13437 3 Knuth Donald E The TpXbook Computers and Typesetting A Addison Wesley Publish ing Company Inc Reading Massachusetts 1986 Knuth Donald E and Silvio Levy The CWEB System of Structured Documentation Version 3 64 February 2002 Rokicki Tomas Dvips A DVEto PostScript Translator for version 5 66a February 1997 http dante ctan org CTAN dviware dvips Salomon David Computer Graphics and Geometric Modeling Berlin 1999 Springer Verlag ISBN 0 387 98682 0 Stallman Richard M and Roland McGrath GNU Make A Program for Directing Recompilation make Version 3 79 Boston 2000 Free Software Foundation Inc ISBN 1 882114 80 9 Bibliography 281 Stallman Richard M Using and Porting the GNU Compiler Collection For GCC Version 3 3 2 Boston 2003 Free Software Foundation Inc Stroustrup
112. Section 22 12 Point Reference Affine Transformations page 130 Point operator Point p const operator Returns a Point with world_coordinates representing the difference between the updated values of this gt world_coordinates and p world_coordinates void operator Point p Operator Subtracts the updated values of p world_coordinates from those of this gt world_ coordinates Chapter 22 Point Reference 125 real operator const real r Operator Multiplies the updated x y and z coordinates world_coordinates of the Point by r and returns r This makes it possible to chain invocations of this function If P is a Point then P r is equivalent in its effect to P scale r r r except that P world_coordinates is modified directly and immediately without changing P transform This is possible because this function calls apply_transform to up date the world_coordinates before multiplying them r so transform is the identity Transform Point P 1 2 3 P x 7 P show P 4 P 7 14 21 Point Q 1 5 2 7 13 82 Q P 1 28 P show P 4 P 8 96 17 92 26 88 Q show Q 4 Q 1 92 3 456 17 6896 Point operator const real r const operator Returns a Point with x y and z coordinates world_coordinates equal to the updated x y and z coordinates of this multiplied by r Point operator const real r const Point amp p Non member operator Equivalent to Point operator
113. The following values of r are possible for a call to P is_on_line A B where the Point P lies on the line AB P A r 0 P B r 1 P lies on the opposite side of A from B gt r lt 0 P lies between A and B 0 lt r lt 1 P lies on the opposite side of A from B gt r gt 1 Point A 1 2 Point B 2 3 Point C B mediate A 1 25 bool_real br C is_on_line A B Chapter 22 Point Reference 142 Point D A mediate B br D is_on_line A B Point E A mediate B 1 25 br E is_on_line A B Point F D F shift 1 1 br F is_on_line A B F r INVALID REAL Figure 92 Point mediate Point p const real r 5 const function Returns a Point r of the way from this to p Point p0 1 0 1 Point p1 10 0 10 Point p2 5 5 5 Point p3 p0 mediate p1 1 5 p3 show p3 4 p3 15 5 0 15 5 Point p4 p0 mediate p2 1 3 0 p4 show p4 p4 1 1 66667 1 Chapter 22 Point Reference 143 Figure 93 22 17 Intersections bool_point intersection_point Point p0 Point p1 Point Static function q0 Point q1 bool_point intersection_point Point p0 Point p1 Point Static function q0 Point q1 const bool trace These functions find the intersection point if any of the lines determined by p0 and pl on the one hand and q0 and ql on the other Let bp be the bool_point returned by intersection_point If an intersection point is found th
114. The return value is void because there is no guarantee that all of the Points on a Path will have identical transform members although it s likely Please note that shift_times will only have an effect on the Points on a Path if it s called after a call to shift and before an operation is applied that causes Point apply_transform to be called Transform rotate const Point amp p0 const Point amp p1 const Virtual function real angle 180 Creates a Transform t locally and calls t rotate p0 p1 angle t is then applied to all of the Points on points The return value is t Transform rotate const Path amp p const real angle 180 Function If p is_linear returns true this function creates a Transform t locally and calls t rotate p angle t is then applied to all of the Points on points The return value is t Otherwise it issues an error message and returns INVALID_TRANSFORM 26 10 Aligning with an Axis Transform align_with_axis const char axis z const function Transform align_with_axis bool assign const char axis z Function Transform align_with_axis const Point amp p0 const Point amp pl Function const char axis These functions return the Transform which if applied to the Path would align it with the major axis indicated by the axis argument The first and second versions can only be called for Paths where line_switch is true The first version is const so the Path rem
115. WiCures 20 tc ci aid 36 7 1 Regular Polygons oooooooocooococooooococ 36 7 2 Rectangles eo cli o id Pes a 39 A ELSES yooh ios hit acta it eek ee eas Bie oa haa a 43 AY A OO EN 45 10 11 12 13 14 15 16 Solid Figures AAA 4T Bol CUBOS A E E E E T EAE TEN 47 8 2 Polyhedrone i cn c ecnca cria ana AE ad a A 48 8 21 Tetrahedron Ver aorta aa 48 8 2 2 Dodecahedrod oocoooccccococcccocccc 49 8 2 3 Icosahedron oooooccooccccccoccc ee eens 51 PICCULES vin es Wes Sas EA AAA 54 O21 PrOJeCUIONS ii oe ena eae ek 58 9 1 1 Parallel Projections 0 0c cence 58 9 1 2 The Perspective Projection 60 9 27 FOCUSES sir ula ts a ds ati 63 93 Surface Hiding cota da cn a Ra eaa ERA 66 Tntersecti as israel aos 73 Installing and Running 3DLDF 74 11 1 gt mstalling IDELDE 000 ti aes 74 11 1 1 Template FunctioNS 0ooooocooocccoooo 74 11 2 Running 3DLDF ineine e eA eee 75 11 2 1 Converting EPS Files 000 77 11 2 1 1 Emacs Lisp Functions 78 11 2 2 Command Line Arguments 79 Typedefs and Utility Structures 81 Global Constants and Variables 82 Dynamic Allocation of Shapes 84 System Informati0N o o oooooo 85 151 Edie tuerca e ea 85 15 2 Register Width 0 cece eect eee eA e ia 86 15 3 Get Second Largest Real 0 0 c eee eee
116. _REAL_FLOAT and LDF_REAL_DOUBLE e Transform epsilon and Point epsilon now return different values depending on the values of the preprocessor macros LDF_REAL_FLOAT and LDF_REAL_DOUBLE I have not yet tested whether good values are returned when real is double e MAX_REAL and MAX_REAL_SQRT are no longer constants Their values are set at the beginning of main However users should not change their values MAX_REAL is the second largest float or double on a given machine This now works for all common architectures e Added namespace System containing the following functions get_endianness is_ big_endian is_little_endian get_register_width is_32_bit is_64_ bit and the template function get_second_largest namespace System and its functions are documented in system texi which is new in edition 1 1 5 1 e Replaced the various create_new_ lt type gt functions with the template function create_new The latter is documented in creatnew texi which is new in edition 1 1 5 1 e Added the file S3DLDF 1 1 5 1 CWEB cnepspng el to the distribution It contains the definitions of the Emacs Lisp functions convert eps and convert eps loop See Sec tion 11 2 1 1 Running 3DLDF Converting EPS Files Emacs Lisp Functions page 79 Chapter 41 Changes 279 e Added the files 3DLDF 1 1 5 1 CWEB exampman web and 3DLDF 1 1 5 1 CWEB examples mp to the distribution They contain the C and MetaPost co
117. a TO T1 T2 r Now 900 5bo Co 5do 901 5b 9C1 5d Mo Seo Sfo 5go Sho M 5er 5f 591 hy si bio 5d 5ko 5lo i 5i 55 5k 5h 5Mo 3Mo 900 Po omy omy 901 Op 5a9 5bo 5c 5de 5 2 5f2 59 5She 5i 52 5ko Sg 5M2 5M2 503 Spo Chapter 19 Transform Reference 98 This function is not currently used anywhere but it may turn out to be useful for something Transform operator const real r const operator Multiplication of a Transform by a scalar without assignment The return value is a Transform A If this matrix has elements Er then A matrix has elements Ea such that E4 r x Er for all E Transform operator const Transformk t Operator Performs matrix multiplication on matrix and t matrix The result is assigned to matrix tis returned not this This makes it possible to chain invocations of this function Transform a a shift 1 1 1 Transform b b rotate 0 90 Transform c c shear 5 4 Transform d d scale 3 4 5 Let am bm and Cm stand for a matrix b matrix c matrix and d matrix respec tively 1 0 0 0 0 5 0 5 0 707 0 1 10100 b 0 146 0 854 0 5 0 m jo 010 0 854 0 146 05 0 1 1 1 1 0 0 0 1 1 12 14 0 3000 10 1 15 0 ce 0 4 0 0 eat Set m 10 gt A 0 0 0 0 1 000 1 a b c d a b and c are transformed by d which remains unchanged Now 3000 1 5 2 3 54 0 10400 ioe 0 439 3 41 25 0 m jo o 5 0 2 56 0 586 25 0 34 5 1 0 0 0 1 3 48 70 0 ia 30 4 75 0 33 5
118. ains unchanged The second version should only be called with assign true so that the Transform is applied to the Chapter 26 Path Reference 179 Path actually aligning it with the axis indicated If the second version is called with assign false a warning message is issued to the standard error output stderr since one might as well use the first version in this case but it won t do any harm The third version creates a Transform t locally that would align the line from p0 to pl with the axis indicated and applies t to the Path Point A 2 3 2 Point B 1 1 3 Path p A B Transform t p align_with_axis true z t show t Ait 0 316 0 507 0 802 0 O 0 845 0 535 0 0 949 0 169 0 267 0 2 53 1 86 2 67 1 p t p show p A p 2 53 1 86 2 67 1 02 1 23 3 67 Point C 1 C t inverse Path q q rae q C for int i 0 i lt 15 i C rotate A B 360 0 16 q C q set_cycle true q show q 4 q 1 68 3 1 05 1 9 2 68 1 06 2 13 2 4 1 21 2 35 2 22 1 48 2 51 2 15 1 83 2 59 2 22 2 21 2 58 2 4 2 55 2 49 2 68 2 81 2 32 3 2 95 2 1 3 32 2 94 1 87 3 6 2 79 1 65 3 78 2 52 1 49 3 85 2 17 1 41 3 78 1 79 1 42 3 6 1 45 1 51 3 32 1 19 cycle q align_with_axis A B z q show q 4d q Chapter 26 Path Reference 180 1 0 0 0 924 0 383 0 0 707
119. al void unsuppress_output void Virtual function Resets do_output to true so that a Point can potentially be output if Picture output is called again for the Picture the Point is on This function is called in Picture output See Section 21 8 Picture Reference Outputting page 114 vector lt shape gt extract const Focusg f const unsigned short Function proj real factor Attempts to project the Point using the arguments passed to Picture output which calls this function If extract succeeds it returns a vector lt shape gt con taining only the Point Otherwise it returns an empty vector lt shape gt bool set_extremes void Virtual function Sets extreme values for x y and z in projective_coordinates This is of course trivial for Points because they only have one x y and z coordinate So the maxima and minima for each coordinate are always the same valarray lt real gt get_extremes void Virtual inline const function Returns projective_extremes real get_minimum_z void Virtual const function real get_maximum_z void Virtual const function real get_mean_z void Virtual const function These functions return the minimum maximum and mean z value of the Point get_minimum_z returns projective_extremes 4 get_maximum_z returns projective_extremes 5 and get_mean_z returns projective_extremes 4 projective_extremes 5 2 However since a Point has only one z coordinate
120. alue is t Shifts each of the Points on the Path according to the arguments default_focus set 5 10 10 0 10 10 10 Point pt 6 pt 0 set 2 2 pt 1 set 0 3 pt 2 set 2 2 pt 3 set 2 2 pt 4 set 0 3 pt 5 set 2 2 Path p true amp pt 0 amp pt 1 amp pt 2 amp pt 3 amp pt 4 amp pt 5 0 p draw p shift 3 3 3 p draw Chapter 26 Path Reference Figure 117 Transform shift const Point amp p Creates a Transform t locally and calls t shift p t is then applied to all of the Points on points The return value is t 177 Function This version of shift uses the x y and z coordinates of the Point p to shift the Path default_focus set 5 10 10 0 10 10 10 Point pt 6 pt 0 set 2 2 pt 1 set 0 3 pt 2 set 2 2 pt 3 set 2 2 pt 4 set 0 3 pt 5 set 2 2 Path p true amp ptl0 amp pt 1 amp pt 2 amp pt 3 amp ptl4 amp pt 5 0 p draw Point s 1 1 1 p shift s p draw Chapter 26 Path Reference 178 Figure 118 void shift_times real x real y 1 real z 1 Virtual function void shift_times const Point amp p Virtual function Each of these functions calls the corresponding version of Point shift_times on all of the Points on points See Section 22 12 Point Reference Affine Transforma tions page 130
121. ansform t Function Sets transform to t and returns t void kill_labels void Function Removes the Labels from the Picture 21 7 Showing void show string text bool stop false Function Prints information about the Picture to standard output show first prints the string Showing Picture to standard output followed by text if the latter is not the empty string Then it calls transform show prints the size of shapes and labels and the value of do_labels Then it calls show on each of the Shapes on shapes Since show is a virtual function in class Shape the appropriate show is called for each Shape i e Point show for a Point Path show for a Path etc If stop is true execution stops and the user is requested to type lt RETURN gt to continue Finally the string Done showing picture is printed to standard output void show_transform string text Transform from Picture Function Calls transform show passing text as the argument to the latter function 21 8 Outputting 21 8 1 Namespaces 21 8 1 1 Namespace Projections The namespace Projections is defined in pictures web const unsigned short PERSP Constant const unsigned short PARALLEL_X_Y Constant const unsigned short PARALLEL_X_Z Constant const unsigned short PARALLEL_Z_Y Constant const unsigned short AXON Constant const unsigned short ISO Constant These constants can be used for the projection ar
122. ansform t See Section 31 3 Ellipse Reference Performing Transformations page 224 Rotating and shifting an Ellipse neither change the size of an Ellipse nor cause it to become non elliptical However scaling and shearing can have these effects For this reason in scale and shear O do_transform is called with true as its check argument while it is false in rotate shift and shift_times If scaling or shearing is performed on an Ellipse and it is still elliptical after the transformation focus0 focusi axis_h axis_v linear_eccentricity and numerical_eccentricity are all recalculated If the Ellipse is non elliptical af ter the transformation axis_h axis_v linear_eccentricity and numerical_ eccentricity are all set to INVALID_REAL center focus0 and focus1 are not set to INVALID_POINT Although they are no longer the center and foci of an elliptical Ellipse they may still have some use for the user or programmer Chapter 31 Ellipse Reference 227 31 7 Querying bool is_elliptical void const function Returns true if the Ellipse is elliptical otherwise false Certain transformations such as shearing and scaling can cause Ellipses to become non elliptical bool is_quadratic void Inline const function Returns true because the equation for an ellipse in the x y plane with its center at the origin is the quadratic equation x a y b 1 where a is half the horizontal axis and b is half the ver
123. ansformk t Operator Multiplies transform by t By multiplying a Point successively by one or more Transforms the effect of the transformations is saved up in transform Only when an operation that needs updated values for the world_coordinates is called on a Point or the Point is passed as an argument to such an operation is the transfor mation stored in transform applied to world_coordinates by apply_transform which subsequently resets transform to the identity Transform See Section 22 13 Point Reference Applying Transformations page 135 Point operator Point p const operator Returns a Point with world_coordinates that are the sums of the corresponding world_coordinates of this and p after they ve been updated this remains unchanged as in many other functions with Point arguments p is passed by value because apply_transform must be called on it in order to update its world_ coordinates If p were a const Point amp it would have to copied within the function anyway because apply_transform is a non const operation Point p0 2 6 28 Point p1 3 14 92 Point p2 p0 p1 p2 show p2 4 p2 1 8 64 void operator Point p Operator Adds the updated world_coordinates of p to those of this Equivalent in effect to shift p In fact this function merely calls p apply_transform and Point shift real real real with p s x y and z coordinates from world_coordinates as its arguments See
124. are described in subsequent chapters bool Idf_real_float Constants bool Idf_real_double Set to 0 or 1 to match the values of the preprocessor macros LDF_REAL_FLOAT and LDF_REAL_DOUBLE The latter are used for conditional compilation and determine whether real is typedeffed to float or double i e whether real is made to bea synonym of float or double using typedef ldf_real_float and l1df_real_double can be used to control conditional expressions in non conditionally compiled code real PI Constant The value of PI 7 is calculated as 4 0 x arctan 1 0 I believe that a preprocessor macro PI was available when I compiled 3DLDF using the DEC C compiler and that it wasn t when I used GNU CC under Linux but I m no longer sure valarray lt real gt null_coordinates Variable Contains four elements all 0 Used for resetting the sets of coordinates belonging to Points but only when the DEC C compiler is used This doesn t work when GCC is used real INVALID_REAL Constant Actually INVALID_REAL is the largest possible real value i e float or double on a given machine So from the point of view of the compiler it s not invalid at all However 3DLDF uses it to indicate failure of some kind For example the return value of a function returning real can be compared with INVALID_REAL to check whether the function succeeded or failed An alternative approach would be to use the exception handling facilities o
125. arguments are used or not It is not currently possible to adjust the positions of the labels on the two dimensional projection itself This would probably be more useful but would require changing the way Picture output functions picture The Picture onto which the Paths and Labels are put Chapter 26 Path Reference 187 void fill const Color amp ffill_color const function Colors default_color Picture amp picture current_picture void fill Picture amp picture const Color amp ffill_color Function Colors default_color Allocates a copy of the Path on the free store puts a pointer to it onto picture shapes sets its fill_draw_value to FILL and its fill_color to ffill_color The second version is convenient for passing a Picture argument without having to specify all of the other arguments The arguments are similar to those of draw except that the Color argument is called ffill_color instead of ddraw_color p fill gray Figure 129 void filldraw const Color amp ddraw_color const function Colors default_color const Color amp ffill_color Colors background_color string ddashed string ppen Picture amp picture current_picturel l void filldraw Picture amp picture const Color amp ddraw_color const function Colors default_color const Color amp ffill_color Colors background_color string ddashed string ppen Allocate
126. arties remain in full compliance FUTURE REVISIONS OF THIS LICENSE The Free Software Foundation may publish new revised versions of the GNU Free Documentation License from time to time Such new versions will be similar in spirit to the present version but may differ in detail to address new problems or concerns See http www gnu org copyleft Each version of the License is given a distinguishing version number If the Document specifies that a particular numbered version of this License or any later version applies to it you have the option of following the terms and conditions either of that specified version or of any later version that has been published not as a draft by the Free Software Foundation If the Document does not specify a version number of this License you may choose any version ever published not as a draft by the Free Software Foundation Appendix A GNU Free Documentation License 288 A 0 1 ADDENDUM How to use this License for your documents To use this License in a document you have written include a copy of the License in the document and put the following copyright and license notices just after the title page Copyright C year your name Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documentation License Version 1 2 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back C
127. ass foo but only in index entries that have been entered explicitly by the author such entries are not generated by Texinfo automatically Examples are formatted as follows Point p0 1 2 3 Point p1 5 6 7 9 Path pa p0 p1 p0 show p0 4 p0 1 2 3 Examples can contain the following symbols Indicates output to the terminal when 3DLDF is run gt Indicates a result of some sort It may precede a illustration generated by the code in the example Indicates that the following text is an error message Chapter 1 Introduction 4 This manual does not use all of the symbols provided by Texinfo If you find a symbol you don t understand in this manual which shouldn happen see page 103 of the Texinfo manual Symbols N The set of the natural numbers 0 1 2 3 4 Z The set of the integers 3 2 1 0 1 2 3 4 R The set of the real numbers 1 2 2 Illustrations The illustrations in this manual have been created using 3DLDF The code that generates them is in the Texinfo files themselves that contain the text of the manual Texinfo is based on TX so it s possible to make use of the latter s facility for writing ASCII text to files using TRX s write command The file 3DLDF 1 1 5 1 CWEB exampman web contains the C code and the file 3DLDF 1 1 5 1 CWEB examples mp contains the MetaPost code for generating the illustrations 3DLDF was built using GCC 2 95 when the illustration
128. at the C compiler is called using the frepo option The manual Using and Porting the GNU Compiler Collection explains this as follows Chapter 11 Installing and Running 3DLDF 75 Compile your template using code with frepo The compiler will generate files with the extension rpo listing all of the template instantiations used in the corresponding object files which could be instantiated there the link wrapper collect2 will then update the rpo files to tell the compiler where to place those instantiations and rebuild any affected object files The link time overhead is negligible after the first pass as the compiler will continue to place the instantiations in the same files 1 The first time the executable 3dldf is built the files that use the template functions are recompiled one or more times and the linker is also called several times This doesn t happen anymore once the rpo files exist Template instantiation differs from compiler to compiler so using template functions will tend to make 3DLDF less portable I am no longer able to compile it on the DECalpha Personal Workstation I had been using with the DEC C compiler See Section 1 6 Ports page 8 for more information 11 2 Running 3DLDF To use 3DLDF call make run from the command line in the shell The working directory should be 3DLDF 1 1 5 1 or 3DLDF 1 1 5 1 CWEB Either will work but the latter may be
129. ata types and operations are modelled on those of Metafont and Meta Post and while the only form of output 3DLDF currently produces is MetaPost code it is nonetheless not in principle tied to MetaPost It could be modified to produce PostScript code directly or output in other formats It would also be possible to modify 3DLDF so that it could be used for creating graphics interactively on a terminal by means of an appropriate interface to the computer s graphics hardware The name 3DLDF 3D plus the author s initials was chosen because while not pretty it s unlikely to conflict with any of the other programs called 3D something 1 1 Sources of Information This handbook and the use of 3DLDF itself presuppose at least some familiarity on the part of the reader with Metafont MetaPost CWEB and C If you are not familiar with any or all of them I recommend the following sources of information Knuth Donald Ervin The METAFONTbook Computers and Typesetting C Addison Wesley Publishing Company Inc Reading Massachusetts 1986 Hobby John D A User s Manual for MetaPost AT amp T Bell Laboratories Murray Hill NJ No date Knuth Donald E and Silvio Levy The CWEB System of Structured Documentation Version 3 64 February 2002 Chapter 1 Introduction 2 Stroustrup Bjarne The C Programming Language Special Edition Reading Mas sachusetts 2000 Addison Wesley ISBN 0 201 70073 5 The manuals for
130. ate of the projection of a Shape such that the Shape can be output If projective_coordinates 1 of any Point on a Shape is greater than max_y_proj the Shape will not be projected at all const real min_z_proj Default 40 The minimum z coordinate of the projection of a Shape such that the Shape can be output If projective_coordinates 2 of any Point on a Shape is less than min_z_proj the Shape will not be projected at all const real max_z_proj Default 40 The maximum z coordinate of the projection of a Shape such that the Shape can be output If projective_coordinates 2 of any Point on a Shape is greater than max_z_proj the Shape will not be projected at all suppress _labels void Function Suppresses output of the Labels on a Picture when output is called This can be useful when a Picture is output transformed and output again one or more times in a single figure Usually it will not be desirable to have the Labels output more than once In Fig 79 current_picture is output three times but the Labels on it are only output once Ellipse e origin 3 5 e label e draw Point pto 3 Point pt1 3 pt0 draw pt1 Point pt2 0 0 4 Point pt3 0 0 4 pt2 draw pt3 ptO dotlabel 0 lft pt1 dotlabel 1 rt pt2 dotlabel 2 bot pt3 dotlabel 3 current_picture output Projections PARALLEL_X_Z current_picture rotate 0 60 Chapter 21 Picture Reference current_p
131. ated Chapter 2 Points 11 Points can be declared and their values can be set in different ways Point pto Point pt1 1 Point pt2 2 3 52 Point pt3 4 5 7 13 205 pto is declared without any arguments i e using the default constructor so the values of its x y and z coordinates are all 0 pt1 is declared and initialized with one argument for the x coordinate so its y and z coordinates are initialized with the values of CURR_Y and CURR_Z respectively The latter are static constant data members of class Point whose values are 0 by default They can be reset by the user who should make sure that they have sensible values pt2 is declared and initialized with two arguments for its x and y coordinates so its z coordinate is initialized to the value of CURR_Z Finally pt3 has an argument for each of its coordinates Please note that pt0 is constructed using a the default constructor whereas the other Points are constructed using a constructor with one required argument for the x coordinate and two optional arguments for the y and z coordinates The default constructor always sets all the coordinates to 0 irrespective of the values of CURR_Y and CURR_Z 2 2 Setting and Assigning to Points It is possible to change the value of the coordinates of Points by using the assignment operator Point operator or the function Point set with appropriate argu ments Point pt0 2 3 3 7 Point pt1 pti p
132. bjects In particular if any one of them cannot be projected using the arguments passed to Picture output this will have no effect on whether the others are outputted or not Currently there are no Shapes without an output function either belonging to the class or inherited However it s useful to be able to define Shapes in this way so that they can be tested without having to define an output function first bool set_extremes void Pure virtual function Sets the values of projective_extremes for the Shape This is needed in Picture output for determining the order in which objects are output real get_minimum_z void const pure virtual functions real get_maximum_z void real get_mean_z void These functions return the minimum maximum and mean z value respectively of the projected Points belonging to the Shape i e from projective_extremes The values for the Shapes on the Picture are used for determining the order in which they are output const valarray lt real gt get_extremes void const pure virtual function Returns projective_extremes void suppress_output void Pure virtual function Sets do_output to false This function is called in Picture output if a Shape on a Picture cannot be output using the arguments passed to Picture output void unsuppress_output void Pure virtual function Sets do_output to true Called in Picture output after output is called on the Shapes This
133. bool is_on_free_store void const virtual function Returns the value of on_free_store true if the Solid was dynamically allocated on the free store otherwise false Solids and objects of classes derived from Solid should only ever be allocated on the free store by a specialization of the template function create_new See Section 34 2 Solid Reference Constructors and Setting Functions page 249 34 8 Returning Elements and Information const Point amp get_center void const virtual function Returns center If the Solid doesn t have a meaningful center the return value will probably be INVALID_POINT Getting Shape Centers const Point amp get_shape_center const unsigned short const virtual function shape_type const unsigned short s Returns the center of a Shape belonging to the Solid Currently the object can be a Circle Ellipse Rectangle or Reg_Polygon and it is accessed through a pointer on one of the following vectors of pointers to Shape circles ellipses rectangles or reg_polygons The type of object is specified using the shape_type argument The following public static const data members of Solid can and probably should be passed as the shape_type argument CIRCLE ELLIPSE RECTANGLE and REG_POLYGON The argument s is used to index the vector This function is called within the more specialized functions in this section namely get_circle_center get_ellipse_center get_rectangle_center and get_
134. c projections soon real factor Default 1 Passed from output to extract and from there to project The world_coordinates of the Points that are projected are multiplied by factor which enlarges or shrinks the projected image without altering the Picture itself factor is probably most useful for parallel projections where the Focus f isn t used with a perspective projection the parameters of the Focus can be used to influence the size of the projected image const unsigned short sort_value Default Sorting MAX_Z The value used should be one of the con stants defined in namespace Sorting See Section 21 8 1 2 Namespace Sorting page 115 above If MAX_Z the default is used the Shapes on the Picture are sorted according to the maximum z value of the projective_extremes of the Points belonging to the Shape If MIN_Z is used they are sorted according to the minimum z value and if MEAN_Z is used they are sorted according to the mean of the maximum and min imum z values If NO_SORT is used the Shapes are output in the order in which they were put onto the Picture The surface hiding algorithm implemented in 3DLDF is quite primitive and doesn t always work right For Shapes that intersect it can t work right I plan to work on improving the surface hiding algorithm soon This is not a trivial problem To solve it properly each Shape on a Picture must be tested for intersection with every other Shape on the Picture If
135. ce Regular Platonic Polyhedra Dodecahedron Constructors and Setting Functions page 264 vector lt Reg_Polygon gt vrp Dodecahedron get_net 1 for vector lt Reg_Polygon gt iterator iter vrp begin iter vrp end iter iter draw Chapter 37 Polyhedron Reference 266 Figure 193 void draw_net const real pentagon_diameter bool portrait Static function true bool make_tabs true Draws the net for a Dodecahedron in the x z plane The pentagons have enclosing circles of diameter pentagon_diameter The origin is used as the center of the middle pentagon of the first half of the net The centers of the pentagons are numbered If the argument portrait is true the default the net is arranged for printing in portrait format If it s false it s arranged for printing in landscape format The argument make_tabs currently has no effect When I get around to programming this it will be used for specifying whether tabs for gluing and or sewing a cardboard model should be drawn too Dodecahedron draw_net 1 false Figure 194 37 2 3 Icosahedron Class Icosahedron is defined in polyhed web It is derived from Polyhedron using public derivation Icosahedra have 20 regular triangular faces 37 2 3 1 Data Members real dihedral_angle Protected static const variable The angle between the faces of the Icosahedron namely 138 11 a arcsin 2 3 real tria
136. configure script generates a config h file which is now included in loader web Some of the preprocessor macros defined in config h are used to conditionally include library header files but so far there is no error handling code for the case that a file can t be included I hope to improve the way 3DLDF works together with Autoconf and Automake in the near future 3DLDF 1 1 5 is the first release that contains template functions Template instantiation differs from compiler to compiler so using template functions will tend to make 3DLDF less portable See Section 11 1 1 Template Functions page 74 for more information I am no longer able to build 3DLDF on the DECalpha Personal Workstation I m fairly sure that it would be possible to port it but I don t plan to do this since Tru64 Unix 5 1 and the DEC C compiler are non free software 1 7 Contributing to 3DLDF So far I ve been the sole author and user of 3DLDF I would be very interested in having other programmers contribute to it I would be particularly interested in help in making 3DLDF conform as closely as possible to the GNU Coding Standards I would be grateful if someone would write proper Automake and Autoconf files since I haven t yet learned how to do so I m working on it See Chapter 1 Introduction page 1 for information on how to contact the author Using 3DLDF Since 3DLDF does not yet have an input routine user code must be writ
137. const string pos top const bool dot const function false Picture amp picture current_picturel Labels the Points on points using lowercase letters pos is used to position all of the labels It is currently not possible to have different positions for the labels Chapter 31 Ellipse Reference 225 Ellipse e origin 6 4 e draw e label Figure 161 void dotlabel string pos top Picture amp picture Inline const function current_picture Like label O except that the Points are dotted Ellipse e origin 6 4 e draw e dotlabel Chapter 31 Ellipse Reference 226 Figure 162 31 6 Affine Transformations Transform rotate const real x const real y 0 const real z 0 Transform rotate const Point amp p0 const Point amp p1 const real angle 180 Transform rotate const Path amp p const real angle 180 Transform scale real x real y 1 real z 1 Transform shear real xy real xz 0 real yx 0 real yz 0 real zx 0 real zy O Transform shift real x real y 0 real z 0 Transform shift const Point amp p void shift_times real x real y 1 real z 1 void shift_times const Point amp p Virtual function Virtual function Virtual function Virtual function Virtual function Virtual function Virtual function Virtual function Virtual function These create a Transform t locally and call do_tr
138. cout lt lt P3 is_on_plane q0 lp Le cout lt lt P3 is_on_plane q1 ln gk Figure 108 25 7 Showing void show string text const function Prints information about the Plane to standard output If text is not the empty string it is printed to the standard output Otherwise Plane is printed Following this if the Plane is equal to INVALID_PLANE see Section 25 2 Planes Reference Global Constants page 157 a message to this effect is printed to standard output Otherwise normal and point are shown using Point show see Section 22 20 Point Reference Showing page 149 Finally distance is printed Point A 1 3 2 5 Rectangle r0 A 5 5 10 15 6 Plane p r0 get_plane 3 p normal 0 0582432 0 984111 0 167731 Chapter 25 Plane Reference 164 point 0 722481 2 38245 0 525176 distance 2 47476 Chapter 26 Path Reference 165 26 Path Reference Class Path is defined in paths web It is derived from Shape using protected derivation 26 1 Data Members bool line_switch Protected variable true if the Path was created using the constructor Path const Point amp p0 const Point amp p1 directly or indirectly See Section 26 2 Path Reference Constructors and Setting Functions page 167 Point p0 Point p1 1 1 Point p2 2 3 Path q0 p0 p1 cout lt lt q0 get_line_switch REN Path ql qi q0 cout lt lt q1 get_line_switch
139. covered by other objects This also requires comparisions and could be implemented together with a fully functional hidden surface algorithm Shadows reflections highlights and shading are all effects requiring comparing each Shape with every other Shape and could greatly increase run time Chapter 10 Intersections 73 10 Intersections There are no functions for finding the intersection points of two or more arbitrary Paths This is impossible so long as 3DLDF outputs MetaPost code 3DLDF only knows about the Points on a Path it doesn t actually generate the curve or other figure that passes through the Points and consequently doesn t know how it does this In addition an arbitrary Path can contain connectors In 3DLDF the connectors are merely strings and are written verbatim to the output file however in MetaPost they influence the form of a Path 3DLDF can however find the intersection points of some non arbitrary Paths So far it can find the intersection point of the following combinations of Paths 1 Two linear Paths i e Paths for which Path is_linear returns true see Sec tion 26 15 Path Reference Querying page 194 In addition the static Point member function Point intersection_points can be called with four Point ar guments The first and second arguments are treated as the end points of one line and the third and fourth arguments as the end points of the other 2 A line and a Poly
140. ctions of derived classes pair lt real real gt solve char axis_unknown real const inline virtual function known Returns a pair lt real real gt with first second INVALID_REAL Intended to be overloaded by member functions of derived classes signed short location Point ref_pt Point p const virtual function Returns a signed short indicating the location of p with respect to the Reg_C1_ Plane_Curve which must be planar The Reg_C1_Plane_Curve constructors should ensure that Reg_C1_Plane_Curves are but there is no guarantee that they will not have been manipulated into a non planar state by shearing for example The argument ref_pt is used within the function for shifting a copy of the Reg_C1_ Plane_Curve to a convenient position It need not be the center of the Reg_C1_ Plane_Curve however classes derived from Reg_C1_Plane_Curve will probably have their own versions of location which will pass center as the ref_pt argument to this function Reg_C1_Plane_Curves need not have a meaningful center location returns the following values 1 p and this are coplanar and p lies outside the perimeter of this 0 p and this are coplanar and p lies on the perimeter of this 1 p and this are coplanar and p lies inside the perimeter of this 2 p and this are not coplanar 3 Something has gone terribly wrong 4 The normal to this has 0 magnitude i e the Points on this are colinear 5 An error occurred in p
141. ctive projection is non affine so w can take on other values valarray lt real gt user_coordinates Private variable A set of four homogeneous coordinates x y z and w user_coordinates currently has no function It is intended for use in user defined coordinate systems For example a coordinate system could be defined with respect to a plane surface that isn t parallel to one of the major planes Such a coordinate system would be convenient for drawing on the plane A Transform would make it possible to convert between user_coordinates and world_coordinates valarray lt real gt view_coordinates Private variable A set of four homogeneous coordinates x y z and w view_coordinates currently has no function It may be useful for displaying multiple views in an interactive graphical user interface or for some other purpose Transform transform Private variable Contains the product of the transformations applied to the Point When apply_ transform is called for the Point directly or indirectly the world_coordinates are updated and transform is reset to the identity Transform See Section 22 13 Point Reference Applying Transformations page 135 bool on_free_store Private variable Returns on_free_store This should only be true if the Point was dynamically allo cated on the free store Points should only ever be dynamically allocated by create_ new lt Point gt which uses set_on_free_store to set on_free_store to true
142. ctors and Setting Functions page 267 vector lt Reg_Polygon gt vrp Icosahedron get_net 1 5 for vector lt Reg_Polygon gt iterator iter vrp begin iter vrp end iter iter draw Figure 197 void draw_net const real triangle_diameter bool portrait Static function true bool make_tabs true Draws the net for an Icosahedron in the x z plane The triangles have enclosing circles of diameter triangle_diameter If the argument portrait is true the default the net will be arranged for printing in portrait format If it s false it will be arranged for printing in landscape format In portrait format the center of the bottom right triangle is at the origin In landscape format the center of the bottom left triangle is at the origin The triangles are numbered The argument make_tabs currently has no effect When I get around to programming this it will be used for specifying whether tabs for gluing and or sewing a cardboard model should be drawn too Icosahedron draw_net 2 false Chapter 37 Polyhedron Reference 269 SE Figure 198 37 3 Semi Regular Archimedean Polyhedra Once I ve added class Octahedron the only Platonic polyhedron I haven t programmed yet I plan to start adding classes for the semi regular Archimedean polyhedra 37 3 1 Truncated Octahedron Class Trunc_Octahedron is defined in polyhed web It is derived from Polyhedron using public derivatio
143. ctors for dynamic allocation of Circles They create a Circle on the free store and allocate memory for it using new Circle They return a pointer to the new Circle If c is a non zero pointer or a reference the new Circle will be a copy of c If the new object is not meant to be a copy of an existing one 0 must be passed to create_ new lt Circle gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information Chapter 32 Circle Reference 239 32 3 Operators Circleg operator const Circle amp c Assignment operator Makes the Circle a copy of c Circleg operator const Ellipse amp e Assignment operator Makes the Circle a copy of e if e is circular radius is set to e axis_v 2 and this is returned If e is not circular this function issues an error message and returns this 32 4 Querying bool is_circular void const function Returns true if the Circle is circular otherwise false Certain transformations such as shearing and scaling can cause Circles to become non circular Circle c origin 3 90 cout lt lt c is_circular 4 1 Circle d c d shift 2 5 d scale 2 3 cout lt lt d is_circular 4 0 Chapter 32 Circle Reference 240 Figure 176 real get_radius void Inline function Returns radius real get_diameter void Inline function Returns 2xradius 32 5 Intersections bool_point_quadruple intersection_points const Virtual const fu
144. cture output is invoked the MetaPost code for Labels is written to out_stream after the code for the drawing and filling commands This prevents the Labels from being covered up However they can still be covered by other Labels or Chapter 20 Label Reference 110 by Shapes or Labels from subsequent invocations of Picture output within the same figure see Section 17 2 I O Functions page 92 for descriptions of beginfig and endfig Chapter 21 Picture Reference 111 21 Picture Reference Class Picture is defined in pictures web 21 1 Data Members Transform transform Private variable Applied to the Shapes on the Picture when the latter is output It is initialized as the identity Transform and can be modified by the transformation functions by Picture operator const Transform amp see Section 21 4 Picture Reference Operators page 112 and by Picture set_transform see Section 21 6 Picture Reference Modifying page 113 vector lt Shape gt shapes Private variable Contains pointers to the Shapes on the Picture When a drawing or filling function is invoked for a Shape a copy is dynamically allocated and a pointer to the copy is placed onto shapes vector lt Label gt labels Private variable Contains pointers to the Labels on the Picture When a Point is labelled either directly or through a call to label or dotlabel for another type of Shape a Label is dynamically allocat
145. cture output Figure 64 If instead c is filled or filldrawn only the parts of r that are not covered by c should be visible r draw c filldrawO Chapter 9 Pictures 68 Figure 65 What parts of r are covered depend on the point of view i e the position and direction of the Focus used for outputting the Picture default_focus set 8 0 5 5 3 5 10 Figure 66 Determining what objects cover other objects in a program for 3D graphics is called surface hiding and is performed by a hidden surface algorithm 3DLDF currently has a very primitive hidden surface algorithm that only works for the most simple cases The hidden surface algorithm used in 3DLDF is a painter s algorithm which means that the objects that are furthest away from the Focus are drawn first followed by the objects that are closer which may thereby cover them In order to make this possible the Shapes on a Picture must be sorted before they are output They are sorted according to the z values in the projective_coordinates of the Points belonging to the Shape This may seem strange since the projection is two dimensional and only the x and y values from projective_coordinates are written to out_stream However the perspective transfor mation also produces a z coordinate which indicates the distance of the Points from the Focus in the z dimension The problem is that all Shapes except Points themselves consist of multipl
146. d const function Returns true if the Rectangle is rectangular otherwise false Transformations such as shearing can cause Rectangles to become non rectangular 29 6 Ellipses Ellipse out_ellipse void const function Returns the smallest Ellipse that surrounds the Rectangle Point P 1 1 3 Rectangle r P 3 4 60 30 15 Ellipse e r out_ellipse e filldraw black gray r unfilldraw black Chapter 29 Rectangle Reference 214 Figure 152 Ellipse in ellipse void const function Returns the Ellipse enclosed by the Rectangle Point P 1 1 3 Rectangle r P 3 4 60 30 15 Ellipse e r in_ellipse r filldraw black gray e unfilldraw black Figure 153 Chapter 29 Rectangle Reference 215 Ellipse draw_out_ellipse const Color amp ddraw_color const function Colors default_color string ddashed string ppen Picture amp picture current_picture Draws the smallest Ellipse that surrounds the Rectangle The arguments are like those of Path draw see Section 26 12 Path Reference Drawing and Filling page 180 The return value is the surrounding Ellipse Ellipse draw_in_ellipse const Color amp ddraw_color const function Colors default_color string ddashed string ppen Picture amp picture current_picture Draws the Ellipse enclosed by the Rectangle The arguments are like those of Path draw see Section 26 12 Path Refere
147. d In this example it s rotated 90 about the x axis so that it comes to lie in the x y plane Reg_Polygon p origin 5 3 90 Chapter 7 Plane Figures 37 p draw Figure 21 In this example it s rotated 36 about the y axis so that it appears to point in the opposite direction from the first example Reg Polygon p origin 5 3 0 36 p draw Figure 22 In this example it s rotated 90 about the z axis so that it lies in the z y plane Reg Polygon p origin 5 3 0 0 90 p draw Chapter 7 Plane Figures 38 Figure 23 In this example it s rotated 45 about the x y and z axes in that order Reg_Polygon p origin 5 3 45 45 45 p draw Figure 24 Reg Polygons need not be centered about the origin If another Point pt is used as the first argument the Reg_Polygon is first created with its center at the origin then the specified rotations if any are performed Finally the Reg_Polygon is shifted such that its center comes to lie on pt Point P 2 1 1 Reg Polygon hex P 6 4 60 30 30 hex draw Chapter 7 Plane Figures 39 Figure 25 In the following example the Reg_Polygon polygon is first declared using the de fault constructor which creates an empty Reg_Polygon Then the polygon is repeatedly changed using the setting function corresponding to the constructor used in the previous examples Fig 26 demonstrates that a given Reg_Polygon need
148. d NO 144 E Ellipses 34035 dd eae eos Bene 222 endf igei a eee eh et 92 epicycloid_pattern_1l o o ooo 245 OPS ia 100 129 extract a2 erie oils pas 95 150 197 254 F e AN AO RS eb 186 187 255 filldraw ria tad 187 255 FOCUS iaa ne oes 152 G getall coords Loc te os 128 Petcaxis Mres orse sd tates ehh ex 213 228 LA US View whee ice Bebe 213 228 get blue part sous a aes pels Rela 90 get_center poe eraat p cece eee 199 227 250 get_circle_center i 2 cs8i ies eee de esis 251 pot circle pero dence sade al te dee a fut 252 get_coefficients 217 235 BOC Mas ues Sa a ra 128 get topy heck oe eg oes Hee 93 109 126 173 249 Betidiameter i cise he Gia ci eee O 240 Get direction tira es Wek ney eee 153 get distance nia oia td aid dais 153 159 Get elements ci eta iy eee ea a eS 99 get_ellipse_center cee eee 251 get_ellipse_ptI o oocooocoocmo oo 253 g et_endianness ooccinonco rs 85 get_extremes 95 150 197 255 BCU LOCUS oc tang eae Mew eis a kA a ales 227 getugreen part veterans ogee eee Sete 90 get last 2point cds An 195 O A a EE G ERAT 140 195 get_line_sWitch oooooooooommoo o 194 get_linear_eccentricity 228 get_maximum_z 95 150 197 255 get Mean Zi ae Heck ahd 95 150 197 255 get_minimum_z 95 150 197 255 Function Index LN CA A NN 90 ZO CIDO E iran as oe ead s
149. d and drawn using the function filldraw This func tion draws the Path using the pen specified or MetaPost s currentpen by default A Color for drawing the Path can also be specified otherwise the default color currently Colors black is used In addition the Path is filled using a second Color which can be specified or the background color Colors background_color by default Filling a Path using the background color causes it to hide objects that lie behind it See Section 9 3 Surface Hiding page 67 for a description of the surface hiding algorithm and examples Currently this algorithm is quite primitive and only works for simple cases Point p0 3 0 1 Point p1 3 1 1 p0 draw p1 pa filldraw Figure 14 Chapter 6 Paths 33 The following example uses arguments for the Colors used for drawing and filling and the pen The empty string argument before the pen argument is a placeholder for the dash pattern argument pa filldraw black gray pensquare xscaled 3mm yscaled 1mm rotated 60 Figure 15 Paths can also be undrawn unfilled and unfilldrawn using the corresponding functions pa fill gray p0 undraw p1 pencircle scaled 3mm Figure 16 pa fill gray Chapter 6 Paths 34 Path q q pa q scale 5 5 q unfill Figure 17 The function unfilldraw takes a Color argument for drawing the Path which is Colors backg
150. de respectively for generating the illustrations in this manual 41 3 3DLDF 1 1 4 2 e The illustrations in the HTML output are now scaled to magstep3 41 4 3DLDF 1 1 4 1 e The HTML output now includes illustrations 41 5 3DLDF 1 1 4 e MAX_REAL is now the second largest float value However the calculation is system dependent and will only work on 32 bit little endian architectures I will start working on porting this soon e Fixed bug in tsthdweb that caused files to be compiled more often than necessary It will be necessary to keep an eye on this e Added Rectangle is_rectangular e Made mediate a member function of Point e It is now possible to generate this manual in the Info and HTML formats 41 6 3DLDF 1 1 1 3DLDF 1 1 1 was the first version of 3DLDF since it became a GNU package the current version is 1 1 5 1 Tt is now conformant to the GNU Coding Standards except that a functioning 3DLDF info cannot be generated from 3DLDF texi The distribution now includes a configure script Makefile in files and other files generated by Autoconf and Automake Recompilation is now handled by make rather than the auxilliary program 3DLDFcpl The files 3DLDFcp1 web and 3DLDFprc web have been removed from the distribution The extension of the C files generated by ctangle is changed from c to cxx before they are compiled After ctangle is run on a CWEB file lt filename
151. default construc tor with no arguments In this case the x y and z coordinates will all be 0 See Section 22 4 Point Reference Constructors and Setting Functions page 123 Point A 1 A show A 4 A 1 0 0 CURR_Y 5 A set 2 A show A J A 2 5 0 CURR_Z 12 Point B 3 B show B 4 B 3 5 12 Point C C show C 4 C 0 O 0 22 2 Typedefs and Utility Structures point_pair first second typedef Synonymous with pair lt Point Point gt bool_point b pt struct b is a bool and pt is a Point bool_point also contains two constructors and an assignment operator described below void bool_point void Default constructor Creates a bool_point and sets b to false and pt to INVALID_POINT void bool_point bool bb const Point amp ppt Default constructor Creates a bool_point and sets b to bb and pt to ppt void bool_point operator const bool_point amp bp Assignment operator Sets b to bp b and pt to bp pt bool_point_pair first second typedef Synonymous with pair lt bool_point bool_point gt bool_point_quadruple first second third fourth struct This structure contains four bool_points It also has two constructors and an as signment operator described below void bool_point_quadruple void Default constructor Creates a bool_point_quadruple and sets first second third and fourth all to INVALID_BOOL_POINT Chapter 22 Point Reference 122 void bool_p
152. does not yet exist When it does it will return the net i e the two dimensional pattern of hexagons and squares that can be folded into a model of a truncated octahedron The net will lie in the x z plane The hexagons and squares will have enclosing circles of diameter hexagon_diameter If the argument do_half is true only the first half of the net will be created This will be used in the non default constructor See Section 37 3 1 2 Polyhedron Reference Regular Platonic Polyhedra Truncated Octahedron Constructors and Setting Functions page 269 Chapter 38 Utility Functions 271 38 Utility Functions double trunc double d Function Defined in pspglb web For some reason when I compile 3DLDF using GNU CC on a PC Pentium II XEON under Linux 2 4 4 i686 the standard library function trunc is not available Therefore I ve had to write one This is a kludge Someday I ll have to try to find a better solution to this problem pair lt real real gt solve_quadratic real a real b real c Function Defined in pspglb web This function tries to find the solutions Sy and S to the quadratic equation ax bx c according to the formulae Sy b 1 b 4ac 2a and S b b 4ac 2a Let r stand for the return value If Sy cannot be found r first will be INVALID_REAL otherwise Sy If S cannot be found r second will be INVALID_REAL otherwise S4 x 4 a 2 r 62 8 0 real_pai
153. drawing commands for putting Points onto Pictures See Section 22 18 Point Reference Drawing page 144 22 8 Querying bool is_identity void inline function Returns true if transform is the identity Transform Transform get_transform void const inline function Returns transform bool is_on_free_store void const function Returns true if memory for the Point has been dynamically allocated on the free store i e if the Point has been created using create_new lt Point gt See Sec tion 22 4 Point Reference Constructors and Setting Functions page 123 bool is_on_plane const Plane amp p const function Returns true if the Point lies on the Plane p otherwise false Planes are conceived of as having infinite extension so while the Point C in Fig 80 does not lie within the Rectangle r it does lie on g so C is_on_plane q returns true Point P 1 1 1 Rectangle r P 4 4 20 45 35 Plane q r get_plane Point A 2 0 2 Point B 2 1 64143 2 Point C 0 355028 2 2185 6 48628 cout lt lt A is_on_plane q 30 cout lt lt B is_on_plane g 41 cout lt lt C is_on_plane q 1 Tus unlikely that Points will lie on a Plane unless the user constructs the case specially In Fig 80 the coordinates for B and C were found by using Plane intersection_point See Section 25 6 Planes Intersections page 161 Chapter 22 Point Reference 127 Figure 80 bool is_in_triangle
154. due e cae al a 81 Global Constants and Variables is eee 82 Dynamic Allocation of Shapes corria ler ds 84 System Informati n ss sesse a e a E 85 Color ROTTEN ama aa a a oa ee a 88 Inputand Outputs De tie a ie IR ed alee ee ees 92 Shape Reference a a es da as Se eS Sera ow 93 Transform Reference cas a s A aw a oe 96 Label Referentes lt i arate i ad a ID AA A A a 108 Pict re Reference al e a ADA A AAA 111 Point Referehce sses a orou wen ee a A eae 119 Focus References da O E a es a a aa are 151 inte Reference seac as e a Be aa 154 Plane References ads mama a e ed ba ike Wn Ot 157 Path Referente ee a oh ca ea aan Se ie ec aaa aw i oh 165 Polygon Reference 1 es pi ie a we ae SS ee 199 Regular Polygon Reference es sare dia eto sw ad 205 Rectangle Reference acre ot 211 Regular Closed Plane Curve Reference o o oo o o o o 216 Ellipse Reterentes Yasna a ete ede 222 Cifrele Referenc socs de AR oe ERA DE AAA A 238 Pattern Reference omiso o A Sw Se wa DA 242 re A NS EN 248 Paced Solid Referentes daros e taa BS aa SOS 257 36 C bold Meter en a e Sica wwe EA EA AA A AAA 258 37 Polyhedron Referencias 260 Oo Utility PODES da e n od wn A ee She eS 271 39 o A AN 273 40 Future Plans i e es AAA A AAA G 275 A a AAA NO 278 Bibhographij A A 280 A GNU Free Documentation License 282 Data Type and Variable decis di ER AAA 289 Pimetion ides s ws eee ESTER A AAA AAA 292 Concept Midex sesse aesa a a o ee ous ee S
155. e 121 bool real ch a a tad Mac bh eas 81 bool2real pointy ice ee eked 122 C CONG CT ae rd 199 216 248 Circlen dicing dics Mien one Sa eee E 36 238 CIRCLE ah ily ra be doe oe eee ot 248 CALC Si si ei ie esd ban SO esa ee a 248 COLOR Rated oe cece tee Lata a Bobby eae ba tee at 88 connectors hho fey eek t eS 167 CUD OTA AA aape tase ate es 47 258 CURR Y rarem aa A NAS S 120 CURR Zerain ae oaae aaa tae Tee ae ed ee de 120 CM E p EE KE O ate ant 91 AS eos ree meide E A 166 D dashed ies dia ta ited dd 166 default_backgroudd oo ooooooccooocoooo 91 G6FauLt COLOL id tia p 91 default_color_vectol oooooooooo o 91 default Locus sabes eed Sees 152 DEFAULT_NUMBER_OF_POINTS 222 depths A 258 dihedral_angle 260 264 266 direction eein oye tee ie Meehan oe 151 154 GISTAN A Str c deeb rada Des idea 151 157 do Help ines is ice cto bee le hee o 167 Oe TABS Ss see s aae geet tanned se ad dsd 111 DOULABELS a 22 oan eee hey eto ed Beg es 109 289 do output Acts yt ee heey yet 120 166 248 Dodecahedron i i8 ae te Sh aes 49 264 fe Ko EIE a a Re late 108 DRA Wins aa as EA ni 93 draw COLO o a ia Rete 166 DRAWDO Tiida ic ta 93 Grawdot_ color iia aid is 120 drawdot_vValue oooooooooooooooo 120 E ls A E 260 CASES il A da 257 ELLI pse rrn a A io Tas 36 222 ELLIPSE petias aa EI 248 ClITPSES ci ao dad 248 F PFACELTVAALUS 2 di ta La OWS at 26
156. e 29 2 Constructors and Setting Functions void Rectangle void Default constructor Creates an empty Rectangle void Rectangle const Point amp ccenter const real aaxis_h Constructor const real aaxis_v const real angle_x 0 const real angle_y 0 const real angle_z 0 Creates a Rectangle in the x z plane centered at the origin with width aaxis_h in the 2 direction and height aaxis_v in the 2 direction If one or more of the arguments angle_x angle_y or angle_z are used it is rotated by those amounts around the appropriate axes Finally the Rectangle is shifted such that its center lies at ccenter Point C 1 1 1 Rectangle r C 3 4 30 30 30 Chapter 29 Rectangle Reference 212 X Figure 151 void set const Point amp ccenter const real aaxis_h const Setting function real aaxis_v const real angle_x 0 const real angle_y 0 const real angle_z 0 Corresponds to the constructor described above void Rectangle const Point amp p0 const Point amp p1 const Point amp Constructor p2 const Point amp p3 Creates Rectangle using four Point arguments The order of the arguments must correspond with a path around the Rectangle This function does not currently check that the arguments yield a valid Rectangle therefore all code using it must ensure that they do void set const Point amp pt0 const Point amp pt1 const Point amp Setting function p
157. e Points that may have different z coordinates 3DLDF currently does not yet have a satisfactory Chapter 9 Pictures 69 way of dealing with this situtation In order to try to cope with it the user can specify four different ways of sorting the Shapes They can be sorted according to the maxi mum z coordinate the minimum z coordinate the mean of the maximum and minimum z coordinate max min 2 and not sorted In the last case the Shapes are output in the order of the drawing and filling commands in the user code The z coordinates referred to are those in projective_coordinates and will have been calculated for a particular Focus The function Picture output takes a const unsigned short sort_value argument that specifies which style of sorting should be used The namespace Sorting contains the following constants which should be used for sort_value MAX_Z MIN_Z MEAN_Z and NO_SORT The default is MAX_Z 3DLDF s primitive hidden surface algorithm cannot work for objects that intersect The following examples demonstrate why not using namespace Sorting using namespace Colors using namespace Projections default_focus set 5 3 10 3 1 1 10 180 Rectangle rO origin 3 4 45 Rectangle ri origin 2 6 45 r0 draw ri drawQ current_picture output default_focus PERSP 1 MAX_Z r0 show r0 4 ro fill_draw_value 1 5 1 41421 1 41421 1 5 1 41421 1 41421 1 5 1 41421 1 4142
158. e Solid This function allocates a new Solid makes it a copy of this and puts a pointer to it onto picture shapes The data members of the Shapes belonging to the copy are set appropriately so that they can be filldrawn when Picture output is called Chapter 34 Solid Reference 256 void void void void The Colors used for drawing and filling the various Paths Circles Ellipses etc belonging to the Solid are passed in draw_colors and fill_colors If the Solid contains more Shapes than draw_colors contains pointers to Color the Color pointed to by the last pointer on draw_colors is used to draw the remaining Shapes The same applies to fill_colors Currently a Solid can only be filldrawn with a single dash pattern ddashed and pen ppen undraw const string ddashed const const virtual function string ppen Picture amp picture current_picture Undraws the Solid This function allocates a new Solid makes it a copy of this and puts a pointer to it onto picture shapes The data members of the Shapes belonging to the copy are set appropriately so that they can be undrawn when Picture output is called A Solid can currently only be undrawn using a single dash pattern ddashed and pen ppen unfill Picture amp picture current_picture const virtual function Unfills the Solid This function allocates a new Solid makes it a copy of this and puts a pointer to it onto p
159. e argument true it is set to its inverse Complete reversal of the transformations applied to a Point as in the previous example probably won t make much sense However partial reversal is a valuable technique For example it is used in rotate for rotation about a line defined by two Points The following example merely demonstrates the basic principle an example that does something useful would be too complicated Chapter 4 Transforms Transform t t shift 3 4 5 t rotate 45 t scale 2 2 2 Point p p t p show p 4 p 6 12 7279 1 41421 t inverse true p rotate 90 90 p t p show p 4 p 3 36396 5 62132 2 37868 23 Chapter 5 Drawing and Labeling Points 24 5 Drawing and Labeling Points 5 1 Drawing Points It s all very well to declare Points place them at particular locations print their locations to standard output and transform them but none of these operations produce any MetaPost output In order to do this the first step is to use drawing and filling commands The drawing and filling commands in 3DLDF are modelled on those in Metafont The following example demonstrates how to draw a dot specifying a Color see Chap ter 16 Color Reference page 88 and a pen Point P 0 1 P drawdot Colors black pencircle scaled 3mm P O Figure 3 In drawdot a Color argument precedes the string argument for the pen so Colors black must be specified
160. e corresponding Point will be stored in bp pt otherwise bp pt will be set to INVALID_POINT If the intersection point lies on both of the line segments bp b will be true otherwise false The two versions use different methods of finding the intersection point The first uses a vector calculation the second looks for the intersections of the traces of the lines on the major planes If the trace argument is used the second version will be called whether trace is true or false Ordinarily there should be no need to use the trace version Point A 1 1 Point B 1 1 Point C 1 1 Point D 1 1 bool_point bp Point intersection_point A B C D bp pt dotlabel i cout lt lt bp b lt lt bp b lt lt endl lt lt flush 4 bp b Chapter 22 Point Reference 144 Figure 94 Point A 5 5 Point B 1 5 1 5 Point C 1 1 Point D 1 1 bool_point bp Point intersection_point A B C D true bp pt dotlabel i cout lt lt bp b lt lt bp b lt lt endl lt lt flush 4 bp b Figure 95 22 18 Drawing There are two versions for each of the drawing functions The second one has the Picture argument picture at the beginning of the argument list rather than at the end This is convenient when passing a picture argument Where picture is optional the default is always current_picture void drawdot const Color amp ddrawdot_color const func
161. e i dca a nee es 124 Operators vii 2 E a el ee betes 125 Operator sios bie heed We Rl eee 125 Operator lt lt i ti dos sore eel ee eee 89 150 operator 89 97 112 124 152 155 158 207 212 224 239 249 259 operator for Points 00 11 operatora o 89 125 159 out cirolas ayh hae ey eh a Eee 209 out ellipse oe ire es ii a a 213 out rectangle icc sie hands Meee eee een 236 OUTPUT av rhe a blocks 95 109 115 150 197 254 Function Index P Path vsti pit ioa EA TE adahes 167 168 170 171 POS 20 na wen hashed eae eet as ay Vice aes Sad 271 PICture A OE 111 112 PVA exis a tt ad 157 158 DOME da ii neice daa it 123 Point intersection_pointsS 73 Point operator s ica a 11 Pointi Seth httice diana lo deta te DoE E iia pa 11 Project siri r elas 22 oe EEAS 135 197 Q QUA tas le E fas 220 R Teal CLUS il ci it DS See ir 81 Rectangle std ets ed did 211 212 Reg Polygon cil io ib 205 COSO did tada la th Ec Tee dali ai 107 r s t amplia a lia 153 reset_transform 114 130 LOVE a Pll scat ind tian a ias A 196 rotate 94 105 113 130 174 178 200 226 254 S scale 94 101 113 132 174 200 226 254 SERMENT t E A 219 set 88 89 123 152 168 169 170 206 212 223 238 262 set for Points 3 1 ga cs te ea 11 Set bl part il trestle a eee 90 Set_CONNECtOLTS eee eee 174 SOPH CY cla dida ad tata gael dla ias dele eon
162. e sese diarios 111 119 151 Transformeri noe ie kee ee ek eae ee 19 96 triangle radius o ainda 260 266 Trunc_Dctahedron ooooooooo 269 Truncated Dctahedro0d o ooooooooo o 269 U UNDRAW da a Shy Gk b is a Sa ee ed 93 UNDRAWDOT intenta ARG Hae AE eee Ee 93 UN PIEL feos ad ots Ba wis Sa ee eee 93 UNFILLDRAVW ones wey oa e be Yee a wth od de Cet 93 UP A Berea rat aba at 151 SE Damen osae ash E A ri N 88 USET_COOLdiMates ooo ooo 119 user_coordinates Point 10 user transform ceci SER oh oe a 96 291 V vertex radis ia 260 VELELCES id tir A 257 view_Co0rdinates o ooooooo ooo 119 view_coordinates Point 10 Vil a a dude E 91 Violet red a 91 W PAICE a ia a ae AER 91 Width id dla ia di 258 world_coordinatesS o ooooooooo ooo 119 world_coordinates Point 10 Function Index Function Index ACUDA rd a tata 259 PA A A Bes 171 O O ides eb ip D 124 aR Os Cd ste ss De cde O ES 249 A align With axis iiien Sree pd 105 178 TN Sse are dl Tare ees hades tts erate et Ayes 139 angle O 217 229 append o eae eee ee ae baie ag wares biel 172 apply_transform 94 135 180 254 B be gant pe tact seh A ta ta 92 bool point pce eesti aha ed lett s 121 bool_point operator 4 121 bool_point_quadruple 121 122 bool_point_quadruple operator 122 bool_real_p
163. e the bool part is true if the Point lies on the line segment between p0 and pl otherwise false If the Point lies on the line segment the real part is a value r such that 0 lt r lt 1 indicating how far the Point is along the way from pO to p1 For example if the Point is half of the way from p0 to pl r will be 5 If the Point does not lie on the line segment but on the line passing through p0 and pl r will be lt 0 or gt 1 If the Point doesn t lie on the line passing through p0 and pl r will be INVALID_REAL Point pO 1 2 1 Point p1 3 2 5 Point p2 p0 mediate p1 75 Point p3 p0 mediate p1 1 5 Point p4 p2 p4 shift 2 1 1 bool_real br p2 is_on_segment p0 p1 cout lt lt br first 41 cout lt lt br second 4 0 75 bool_real br p3 is_on_segment p0 p1 cout lt lt br first Chapter 22 Point Reference 141 4 0 cout lt lt br second 4 1 5 bool_real br p4 is_on_segment p0 p1 cout lt lt br first 4 0 cout lt lt br second 3 40282e 38 cout lt lt br second INVALID_REAL 2 P3 Pa P P2 Po Figure 91 bool_real is_on_line const Point amp p0 const Point amp p1 const function Returns a bool_real where the bool part is true if the Point lies on the line passing through p0 and pl otherwise false If the Point lies on the line the real part is a value r indicating how how far the Point is along the way from pO to pl otherwise INVALID_REAL
164. e useful for something void Transform real r0_0 real r0_1 real r2 real r0_2 real Constructor r0_3 real r1_0 real r1_1 real r1_2 real r1_3 real r2_0 real r2 1 real r2_2 real r2_3 real r3_0 real r3_1 real r3_2 real 3 9 Each of the sixteen real arguments is assigned to the corresponding element of ma trix matrix 0 0 r0_0 matrix 0 1 r0_1 etc Useful for specifying a trans formation matrix completely Chapter 19 Transform Reference 97 19 4 Operators Transform operator const Transform t Assignment operator Sets this to t and returns t Returning this would of course have exactly the same effect real operator real r Operator Multiplication with assignment by a scalar This operator multiplies each element E of matrix by the scalar r The return value is r This makes it possible to chain invocations of this function For az bz Cz D2e ER TEN Transform TO a_0 b_0 c_0 d_0 e_0 f_0 g_0 h_O i_0O j_0 k_0 1_0 m_0 n_0 o_0 p_0 Transform Ti a_1 b_1 c_1 d_1 e_1 f_1 gi h_1 i_1 j_1 k_1 1_1 m_1 n_1 o_1 p_1 Transform T2 a_2 b_2 c_2 d_2 e_2 2 g 2 h_2 i_2 j_2 k_2 1_2 m_2 n_2 0_2 p_2 real r 5 Let Mo M and Ma stand for TO matrix T1 matrix and T2 matrix respectively ao bo Co do ay by C1 d o fo Y ho i fi gn hi Mo Mi a si to jo ko bo 1 ti j k h Mo Mo 09 Po M M Oi Pi a2 by amp da 2 fo Y he la ja ko l
165. e_name const bool b Function Sets use_name to b Chapter 16 Color Reference 90 void modify const real r const real g 0 const real b 0 Function Adds r g and b to red_part green_part and blue_part respectively Following the addition if red_part green_part and or blue_part is greater than 1 it is reduced to 1 If it is less than 0 it is increased to 0 void set_red_part const real q Function void set_green_part const real q Function void set_blue_part const real q Function Let p stand for red_part green_part or blue_part depending upon which function is used If 0 lt q lt 1 pis set to q If q lt 0 pis set to 0 If q gt 1 pis set to 1 16 5 Showing void show string text const function Prints information about the Color to standard output If text is not the empty string prints text on a line of its own Otherwise it prints Color Then it prints name use_name red_part green_part and blue_part 16 6 Querying bool is_on_free_store void const function Returns on_free_store This will only be true if the Color was created by create_ new lt Color gt See Section 16 2 Color Reference Constructors and Setting Func tions page 88 real get_red_part bool decimal false Inline const function real get_green_part bool decimal false Inline const function real get_blue_part bool decimal false Inline const function These functions return t
166. ective_extremes are pure virtual functions in class Shape so the Point versions must be consistent with the versions for other types derived from Shape bool do_output Protected variable true by default Set to false by suppress_output which is called on a Shape by Picture output if the Shape is not projectable See Section 21 8 Picture Reference Outputting page 114 string measurement units Public static variable The unit of measurement for all distances within a Picture cm for centimeters by default The x and y coordinates of the projected Points are always followed by measurement_units when they re written to out_stream Unlike Metafont units of measurement cannot be indicated for individual coordinates Nor can measurement _ unit be changed within a Picture When I write an input routine I plan to make it behave the way Metafont does however 3DLDF will probably also convert all of the input values to a standard unit as Metafont does real CURR_Y Public static variable real CURR_Z Public static variable Default values for the y and z coordinate of Points when the x coordinate or the x and y coordinates only are specified Both are 0 by default Chapter 22 Point Reference 121 These values only used in the constructor and setting function taking one required real value for the x coordinate and two optional real values for the y and z coordinates They are not used when a Point is declared using the
167. ed the Point is copied to Label pt and a pointer to the Label is placed onto labels bool do_labels Private variable Used for enabling or disabling output of Labels when outputting a Picture The default value is true It is set to false by using suppress_labels and can be reset to true by using unsuppress_labels See Section 21 8 2 Picture Reference Output Functions page 115 Often when a Picture is copied transformed and output again in a single figure it s undesirable to have the Labels output again in their new positions To avoid this use suppress_labels after outputting the Picture the first time 21 2 Global Variables Variable Picture current_picture Variable The Picture used as the default by the drawing and filling functions 21 3 Constructors void Picture void Default constructor Creates an empty Picture 1 jabel and dotlabel are currently only defined for Point and Path and the latter s derived classes i e not for Solid and its derived classes Chapter 21 Picture Reference 112 void Picture const Picture amp p Copy constructor Creates a copy of Picture p Circle c origin 3 c draw current_picture output Projections PARALLEL_X_Z Picture new_picture current_picture new_picture shift 2 new_picture output Projections PARALLEL_X_Z current_picture new_picture Figure 77 21 4 Operators void operator const Picture amp p Assignment operator Makes t
168. ed while changing the distance If the Transform represents other operations in addition to shifting e g scaling and or shearing the effect of shift_times may be unpredictable Transform t t shift 1 2 3 1 0 0 0 10100 gt t matrix 0010 123 1 t shift_times 2 2 2 1000 10100 gt t matrix 0010 2 4 6 1 Rectangle r 4 r 0 set origin 1 1 90 r 3 r 2 r 1 rlo0 Transform t t shift 1 5 1 5 r o t r 0 draw t shift_times 1 5 1 5 r 1 t r 1 draw t shift_times 1 5 1 5 r 2 t r 2 draw t shift_times 1 5 1 5 r 3 t r 3 draw 2 Fora person not in the sense of the program behaving unpredictably Chapter 19 Transform Reference o Figure 73 Cuboid c origin 1 1 1 C draw Transform t t rotate 30 30 30 00 t00 toO a EO E S A R shift 1 O 1 t draw shift_times 1 5 t draw shift_times 1 5 t draw shift_times 1 5 t draw shift_times 1 5 t draw 1 5 1 5 1 5 1 5 104 Chapter 19 Transform Reference 105 A E KS E Figure 74 Transform rotate real x real y 0 real z 0 Function Rotation around the main axes Creates a Transform t representing the rotation multiplies this by t and returns t Transform rotate Point p0 Point p1
169. ee 295 ii Table of Contents 1 Introduction s 6020004 c0cdeen hve ter ses ee bs 1 1 1 Sources of Information 0000 c cece eee eee 1 1 2 About This Manual 0 c cee eee eee 2 1 2 1 Comnventions 0c cece cece eens 3 1 2 2 Thistrations cojin ri ae a ees 4 1 3 CWEB Documentation 0 0 nurnerr erreen 5 1 4 Metafont and MetaPost 0 00 eee eee eee ee 6 1 57 Caveats ica a ea kg eee ae eae 7 15 1 ACCUPACY 30 8 pene sh dashing ease nee RN 7 1 5 2 No Input Routine 00 eee 8 1 6 A nals ne NN 8 1 7 Contributing to 3DLDF 0 00 eee eee 9 2 POMS cn ees Gnas aie eae OE Sian See os eas 10 2 1 Declaring and Initializing Points 10 2 2 Setting and Assigning to Points oo ooooooocooooo 11 3 Transforming Points 13 O 13 3 2 OCA AAA vd ned els Gdns 14 3 39 OCA ani eke od aie tiv eer Be 14 34 E 17 A Transforms osi 66060 esru wacis usau Ces id 19 4 1 Applying Transforms to Points 00 0000 20 4 2 Inverting Transforms 000 cee eee eee eee 21 5 Drawing and Labeling Points 24 owl Drawing Points bem cis ta ached ete ee 24 52 Labelins Points 40 aa es be rice Mies eis aed a 26 6 Paths a Ad a 28 6 1 Declaring and Initializing Paths 28 6 2 Drawing and Filling Paths 00020005 30 T Plane
170. eee 86 Color Reference sc dscns ra 0S eee a 88 16 1 Data Members vi eg soi ees a tle 88 16 2 Constructors and Setting Functions 88 16 3 Opera ii 22a A A ok ins Rea das 89 16 4 Modifying sos ogee ae ate dey beh sah Aaa e seed berets 89 16 5 Showing ica olla sae bee ne 90 16 6 Querying e a read eked 90 16 7 Defining and Initializing Colors 90 16 8 Namespace Colors 0 0000 cece cnet etn nnes 90 iv 17 Input and Output es a 92 17 1 Global Variables o oooooooooororormomooooo 92 17 2 PO PUNCHONS Sr A A AA 92 18 Shape Reference oooooooooooooo 93 18 1 Data Members srasni sueva pda med e aa a a a 93 18 2 Op ra t rS aoire ian tin aeai a E 93 183 COPYN E araa Ee cl ee ans 93 184 Modistas li NE eee 93 18 5 Affine Transformations 0000 ccc ec eee eee ees 94 18 6 Applying Transformations 0 0000 e eee ee eee 94 187 Clearing ck aye Be dette cee tei ese ko ee oh cee oie 94 18 8 QUEDE cono deeded et ie ER be be eee ae e 94 18 9 SHOWING it ee ee es 94 18 10 Out putting crre nenia eta 94 19 Transform Reference o o ooo o o o 96 19 1 Data Members ches floc etg he et ed Shee es 96 19 2 Global Variables and Constants o oooooooooooo 96 193 gt Constructors s tein het sie oe sche BE Santen be eek ares bird 96 19 4 Operators ti oll eee eee ee eae ee es 96 19 5 Matrix Inversion eae e n ccc ete n ee aes 99 1
171. eference Data Members page 165 The filling and unfilling functions only work for Paths that are cycles See Section 26 12 Path Reference Drawing and Filling page 180 If a Path is a cycle it is up to the user to make sure that it has sensible Point and connector values 3DLDF doesn t check them If they are not sensible for instance if the Path crosses itself and you try to fill it this will cause an error in MetaPost It is possible that a Path will be sensible in some projections and not in others although I have not tested this p is a pointer to the first Point that should go onto the Path The ellipsis points represent an arbitrary number of pointers to Points that should go onto the Path The final argument must be 0 which is interpreted by the C compiler as the null pointer It is admittedly a bit awkward to have to type p0 rather than pO and I have frequently forgotten to do it which causes a compiler error but all of the arguments 3 Stroustrup The C Programming Language p 88 Chapter 26 Path Reference 169 must be pointers in order to be able to use O to indicate the end of the argument list Convenience in typing function calls is not a high priority in 3DLDF because once Pve written an input routine these function calls should be generated automatically It will be more important to define a convenient syntax for the input routine Point PO Point P1 2 Point P2 2 2 Po
172. eing known 26 7 Clearing void clear void Virtual function Does the same thing the destructor Path does Calls delete on the pointers to Points on points clears points and connectors deletes draw_color and fill_ color if they point to Colors that were allocated on the free store and sets them to 0 clear is a pure virtual function in class Shape so Path must be have a clear function It is needed because it is sometimes called through a pointer to Shape so that Path cannot be accessed At least so far I haven t found a way to call a destructor through the virtual function facility 26 8 Modifying bool set_on_free_store bool b true Virtual function Sets on_free_store to b This is used in the template function create_new See Section 26 2 Path Reference Constructors and Setting Functions page 167 Chapter 26 Path Reference 174 void set_fill_draw_value const signed short s Virtual function Sets fill_draw_value to s which should be one of Shape DRAW Shape FILL Shape FILLDRAW Shape UNDRAW Shape UNFILL or Shape UNFILLDRAW void set_draw_color const Color amp c Virtual function void set_draw_color const Color c Virtual function Sets draw_color a pointer to a const Color to amp c or c depending on whether the version with a reference argument or the version with a pointer argument is used set_draw_color is used in the Solid drawing and filling functions becau
173. ement of any Modified Version 5 COMBINING DOCUMENTS You may combine the Document with other documents released under this License under the terms defined in section 4 above for modified versions provided that you include in the combination all of the Invariant Sections of all of the original documents unmodified and list them all as Invariant Sections of your combined work in its license notice and that you preserve all their Warranty Disclaimers The combined work need only contain one copy of this License and multiple identical Invariant Sections may be replaced with a single copy If there are multiple Invariant Sections with the same name but different contents make the title of each such section unique by adding at the end of it in parentheses the name of the original author or publisher of that section if known or else a unique number Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work In the combination you must combine any sections Entitled History in the vari ous original documents forming one section Entitled History likewise combine any sections Entitled Acknowledgements and any sections Entitled Dedications You must delete all sections Entitled Endorsements 6 COLLECTIONS OF DOCUMENTS You may make a collection consisting of the Document and other documents released under this License and replace the individual c
174. ence Operators page 124 performs ex actly the same function Point create_new lt Point gt const Point p Template specializations Point create_new lt Point gt const Point amp p Pseudo constructors for dynamic allocation of Points They create a Point on the free store and allocate memory for it using new Point They return a pointer to the new Point If p is a non zero pointer or a reference the new Point will be a copy of p If the new object is not meant to be a copy of an existing one 0 must be passed to create_new lt Point gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information One use for create_new lt Point gt is in the constructors for classes of objects that can contain a variable number of Points such as Path and Polygon Another use is in the drawing and filling functions where objects are copied and the copies put onto a Picture Programmers who dynamically allocate Points must ensure that they are deallocated properly using delete Chapter 22 Point Reference 124 22 5 Destructor void Point void virtual Destructor This function currently has an empty definition but its existence prevents GCC 3 3 from issuing the following warning thinspace class Point has virtual functions but non virtual destructor 22 6 Operators void operator const Point amp p Assignment operator Makes this a copy of p Transform operator const Tr
175. enes 154 24 2 Global Constants iia a ii tt it 154 24 3 ConstructOrs s cccc0hes 208cseeieuedie dia aesevera ded 154 24 A gt Operators ts terial e de Roane Sods dy hile ed Les 155 ZAS Grete Rath oes ee fade bah oases Yet eet lee baled Ton a eee 155 240 SNOWN iG x2 03 een eine Reet hele eed 155 25 Plane Reference oooooooooooo oooo 157 25 Data Members tai ia Sok Seen ag 157 25 2 Global Constants oem add adi 157 25 3 CONSTLUCUOES birds todo dida di laca 157 254 OPOrAtOTS z asea aeaa a a ia 158 25 5 Returning Information 00 ee eee eee 159 2070 Intersections ia a ie tne wa tea wig phase aa ob aes 160 DOs SU OWA TAEAE E aahl cas Ie N T eae does 163 26 Path Reference oooooooooooooo 165 26 1 Data Members 0 0 c ccc cc cece cee o 165 26 2 Constructors and Setting Functions 167 26 3 Destructor nerio riea renega A ea a a a aa a 171 26 4 OperatotS aaa ni eee a oh eek 171 26 5 Appending ocho ci as ein eee des Satan 172 20 6 COPADA radeon adnan hg es 173 26 7 Clearing vaccum cet eek he og cache ah ee ea eee 173 26 8 Modas pave iets dea ee capes ota 173 26 9 Affine Transformations 0 0000 ccc eee cece eee 174 26 10 Aligning with an Axis 0 ec cece ee eee eee 178 26 11 Applying Transformations 00000 eee 180 26 12 Drawing and Filling 0 ee eee ee 180 26 13 Labelling ruina perno edeace iaa che aa lacada 191 26 14 SHOWIN
176. epsilon returns 0 00001 If real is double it returns 0 000000001 Please note I haven t tested whether 0 000000001 is a good value yet so users should be aware of this if they set real to double The way to test this is to start with two Points P and Q at different locations Then they should be transformed using different rotations in such a way that they should end up at the same location Let e stand for the value returned by epsilon and let x y and y stand for the world_ coordinates of the Points after apply_transform has been called on them If Lp XQ YP Yq and zp zQ e is a good value Rotation causes a significant loss of precision to due to the use of the sin and cos functions Therefore neither Point epsilon nor Transform epsilon see Section 19 8 Tranform Reference Returning Information page 100 can be as small as I d like them to be If they are two small operations that test for equality of Transforms and Points will return false for objects that should be equal 2 For that matter I haven t really tested whether 0 00001 is a good value when real is float Chapter 22 Point Reference 130 22 11 Modifying bool set_on_free_store bool b true Virtual function This function is used in the template function create_new It sets on_free_store to true See Section 22 1 Point Reference Data Members page 119 and Section 22 4 Point Reference Constructors and Setting Functions page
177. er If the Polygon doesn t contain any Points a warning is issued and INVALID_POINT is returned Chapter 27 Polygon Reference 27 4 Affine Transformations Transform rotate const real x const real y 0 const real z 0 Transform rotate const Point amp p0 const Point amp p1 const real angle 180 Transform rotate const Path amp p const real angle 180 Transform scale real x real y 1 real z 1 Transform shear real xy real xz 0 real yx 0 real yz 0 real zx 0 real zy 0 Transform shift real x real y 0 real z 0 Transform shift const Point amp p void shift_times real x real y 1 real z 1 void shift_times const Point amp p 200 Virtual function Virtual function Virtual function Virtual function Virtual function Virtual function Virtual function Virtual function Virtual function The affine transformation functions for Polygon differ from the Path versions only in that center is transformed as well See Section 26 9 Path Reference Affine Transformations page 174 Please note that the classes currently derived from Polygon namely Reg_Polygon and Rectangle currently inherit these functions from Polygon The problem with this is that they have data members which are not recalculated when a Reg_Polygon or Rectangle is transformed I plan to do something about this soon It will also be necessary to add the function Reg_Polyg
178. erence Intersec tions page 217 and Section 30 2 Regular Closed Plane Curve Reference Querying page 216 real_triple get_coefficients real Slope real v_intercept const function Let x and y stand for the x and y coordinates of a point on an ellipse in the x y plane a for half of the horizontal axis axis_h 2 and b for half of the vertical axis axis_v 2 Further let y mz i be the equation of a line in the x y plane where m is the slope and i the y intercept This function returns the coefficients of the quadratic equation that results from replacing y with ma i in the equation for the ellipse x a y b 1 namely x a mz i b 1 0 b x a m a 2a ima ati a b 0 The coefficients are returned in the real_triple in the order one would expect r first is the coefficient of x r second of x and r third of the constant term 2 1 Chapter 31 Ellipse Reference 236 get_coefficients is called in Reg_Cl_Plane_Curve intersection_ points Point Point Point and resolves to this function when the latter is called on an Ellipse See Section 30 3 Regular Closed Plane Curve Reference Intersections page 217 31 11 Rectangles Rectangle out_rectangle void const function Returns the Rectangle that surrounds the Ellipse Ellipse e origin 3 4 45 30 17 e shift 1 1 2 Rectangle r e out_rectangle r filldraw black gray e unfilldraw black Figure 172 Rectang
179. ers or call its member functions directly When label or dotlabel is invoked one or more Labels is allocated dynamically and pointers to the new Labels are placed onto the vector lt Label gt labels of a Picture current_picture by default There are no explicitly defined constructors for Label nor is it intended that Labels ever be created in any way other than through label or dotlabel When a Picture is copied the Labels are copied too and when a Picture is cleared using Picture clear or destroyed the Labels are deallocated and destroyed 20 1 Data Members Point pt Private variable A pointer to the Point representing the location of the Label bool dot Private variable true if the label should be dotted otherwise false dot will be false if the label was generated by a call to label O with the dot ar gument false the default true if the label was generated by a call to dotlabel or to label with the dot argument true string text Private variable The text of the label text is always put between btex and etex in the MetaPost code so that TEX will be used to format the labels In particular this means that TEX s math mode can be used However double backslashes must be used instead of single backslashes in order that single backslashes be written to out_stream Point P 1 1 2 origin drawarrow P P label vec P Chapter 20 Label Reference 109
180. ersion includes new front matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document you may at your option designate some or all of these sections as invariant To do this add their titles to the list of Invariant Sections in the Modified Version s license notice These titles must be distinct from any other section titles Appendix A GNU Free Documentation License 286 You may add a section Entitled Endorsements provided it contains nothing but endorsements of your Modified Version by various parties for example statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard You may add a passage of up to five words as a Front Cover Text and a passage of up to 25 words as a Back Cover Text to the end of the list of Cover Texts in the Modified Version Only one passage of Front Cover Text and one of Back Cover Text may be added by or through arrangements made by any one entity If the Document already includes a cover text for the same cover previously added by you or by arrangement made by the same entity you are acting on behalf of you may not add another but you may replace the old one on explicit permission from the previous publisher that added the old one The author s and publisher s of the Document do not by this License give permission to use their names for publicity for or to assert or imply endors
181. es not point to considered to be inside However if p n point and normal are both set to INVALID_POINT and distance is set to INVALID_REAL i e this will be equal to INVALID_PLANE see Section 25 2 Planes Reference Global Constants page 157 Point P 1 1 1 Point N O 1 N rotate 35 30 20 N show N N 0 549659 0 671664 0 496732 Plane q P N cout lt lt q distance 0 618736 Figure 105 25 4 Operators const Plane amp operator const Plane amp p Assignment operator Sets point to p point normal to p normal and distance to p distance The return value is p so that invocations of this function can be chained Point pt 2 2 3 6 Point norm 1 12 36 Plane A pt norm Plane B Chapter 25 Plane Reference 159 Plane C B C A A show A 4 A normal 0 0263432 0 316118 0 948354 point 2 2 3 6 distance 5 01574 cout lt lt A B amp amp A C amp amp B C aei bool operator const Plane amp p const operator Equality operator Compares this and p and returns true if point p point normal p normal and distance p distance otherwise false bool operator const Plane amp p const operator Inequality operator Compares this and p and returns true if point p point or normal p normal or distance p distance Otherwise it returns false 25 5 Returning Information real_short get_distance const Point a
182. es o rectangs o polygons o curves o paths o planes o lines o points o pictures o shapes o transfor o colors o io o pspglb o 3dldf_OBS_REVERSED is needed because 3DLDF fails with a Segmentation fault if the executable is linked using 3d1df_OBJECTS This may cause problems if 3d1df isn t built using the GNU C compiler GCC 1 The GNU Coding Standards are available at http www gnu org prep standards_toc html 2 Automake is available for downloading from http ftp gnu org gnu automake The Automake web site is at http www gnu org software automake Chapter 39 Adding a File 274 Now add a target for widgets o between the targets for rectangs o and ellipses o and add widgets tim after rectangs tim in the list of prerequisites for ellipses o ad rectangs o loader tim pspglb tim io tim colors tim transfor tim shapes tim pictures tim points tim lines tim planes tim paths tim curves tim polygons tim rectangs cxx ellipses o loader tim pspglb tim io tim colors tim transfor tim shapes tim pictures tim points tim lines tim planes tim paths tim curves tim polygons tim rectangs tim ellipses cxx This is the result rectangs o loader tim pspglb tim io tim colors tim transfor tim shapes tim pictures tim points tim lines tim planes tim paths tim curves tim polygons tim rectangs cxx widgets o loader tim pspglb tim io tim colors tim transfor tim shapes tim
183. es of the x and y coordinates in projective_ coordinates are multiplied by factor Only relevant if coords is p i e projective_coordinates or one of its elements is to be returned The default is 1 valarray lt real gt get_all_coords char coords w const bool Function do_persp true const bool do_apply true Focus f 0 const unsigned short proj Projections PERSP real factor 1 Returns one of the sets of coordinates world_coordinates by default Returns a complete set of coordinates w for world_coordinates p for projective_ coordinates u for user_coordinates or v for view_coordinates real get_coord char c char coords w const bool do_persp Function true const bool do_apply true Focusx f 0 const unsigned short proj Projections PERSP real factor 1 Returns one coordinate x y z or w from the set of coordinates indicated or world_coordinates by default real get_x char coords w const bool do_persp true const Function bool do_apply true Focus f 0 const unsigned short proj Projections PERSP real factor 1 Returns the x coordinate from the set of coordinates indicated or world_ coordinates by default Chapter 22 Point Reference 129 real get_y char coords w const bool do_persp true const Function bool do_apply true Focus f 0 const unsigned short proj Pro
184. esenting the concatenation of this and pa this remains unchanged Neither this nor pa may be cyclical i e cycle_switch must be false for both Paths void operator const string s Function Pushes s onto connectors 26 5 Appending Path append const Path amp pa string connector bool Function assign true Appends pa to this using connector to join them and returns the resulting Path If assign true then the return value is assigned to this otherwise this remains unchanged If necessary a const version could be added for const Paths Point A 2 2 Point B 2 2 Point C 2 2 Point D 2 2 Path q false amp A amp B amp C amp D O Point E 1 2 Point F 0 4 Point G 5 3 Path r false amp E amp F amp G 0 append r true FS nu fa ees set_cycle show q q 2 2 0 2 2 0 2 2 0 2 2 0 1 2 0 0 4 0 0 5 3 0 cycle Q Q a aa Chapter 26 Path Reference 173 Figure 114 26 6 Copying Shape get_copy void const virtual function Creates a copy of the Path using create_new lt Path gt which returns a pointer to Path get_copy then casts this pointer to a pointer to Shape and returns it This function is used when copying Pictures and in Solid output where objects of types derived from Shape must be handled in the same way without their actual types b
185. espace Projections The constants are PERSP PARALLEL_X_Y PARALLEL_X_Z PARALLEL_Z_Y AXON and ISO The latter two should not be used because the axonometric and isometric projections have not yet been implemented 9 1 1 Parallel Projections When a Picture is projected onto the x y plane the x and y values from the world_ coordinates of the Points belonging to the objects on the Picture are copied to their 1 Namespaces are described in Stroustrup The C Programming Language Chapter 8 Chapter 9 Pictures 59 projective_coordinates which are used in the MetaPost code written to out_stream If a Picture p contains an object in the x y plane or in a plane parallel to the x y plane then the result of p output Projections PARALLEL_X_Y is more or less equivalent to just using MetaPost without 3DLDF Rectangle r origin 3 3 90 Circle c origin 3 90 c r shift 0 0 5 r draw c draw current_picture output Projections PARALLEL_X_Y Figure 53 If the objects do not lie in the x y plane or a plane parallel to the x y plane then the projection will be distorted current_picture output Projections PARALLEL_X_Y Figure 54 Picture output can be called with an additional real argument factor for magni fying or shrinking the Picture Rectangle r origin 4 4 90 60 Circle c origin 4 90 60 c r shift 0 0 5 r filldraw black gray c unfilldra
186. ey Mathematics p 197 outside is considered to be the side of a plane where the Points are meant to be traversed in the clockwise direction I hope that no problems arise from this discrepancy Chapter 26 Path Reference 196 Plane get_plane void const virtual function Creates and returns a Plane p corresponding to the Path if the latter is planar otherwise INVALID_PLANE If the Path is planar p point will be the Point pointed to by this gt points 0 See Chapter 25 Plane Reference page 157 Point P 1 1 1 Rectangle r P 4 4 45 20 15 Plane q r get_plane q show q 4 q normal 0 0505914 0 745607 0 664463 point 0 0178869 0 727258 1 01297 distance 0 131735 Figure 137 void set_cycle const bool c true Function Sets cycle_switch to c Path reverse bool assign Function Path reverse void const function These functions return a Path with the same Points and connectors as this but in reversed order reverse can only be applied to non cyclical Paths If this is a cycle reverse issues an error message and returns this unreversed If the first version is called with assign true this itself is reversed If this should remain unchanged the const version without an argument should be called If on the other hand the first version is called with assign false a warning message is issued but the reversed Path is returned just the same leaving this unchanged
187. f 1 must be passed for scaling in the x dimension Similarly if one wants to perform scaling in the z dimension only dummy arguments of 1 must be passed for scaling in the x and y dimensions Point pO 1 2 3 p0 scale 2 3 4 p0 show p0 4 pO 2 6 12 p0 scale 2 0 show p0 4 pO 4 6 12 p0 scale 1 3 0 show p0 4 po 4 18 12 pO scale 1 1 3 0 show p0 4 po 4 18 36 Chapter 3 Transforming Points 15 3 3 Shearing Shearing is more complicated than shifting or scaling The function shear takes six real arguments If pis a Point then p shear a b c d e f sets p to x ay b2p Yp to Yp CL dz and Zp to z ex fp In this way each coordinate of a Point is modified based on the values of the other two coordinates whereby the influence of the other coordinates on the new value is weighted according to the arguments Point p 1 1 1 p shear 1 p show p J p 2 1 1 p set 1 1 1 p shear 1 1 p show p Api 1 1 p set 1 1 1 p shear 1 1 2 2 3 3 p show p 4 p 3 5 7 Fig 1 demonstrates the effect of shearing the points of a rectangle in the x y plane Point PO Point P1 3 Point P2 3 3 Point P3 0 3 Rectangle r p0 pl p2 p3 r draw Rectangle q r q shear 1 5 q draw black evenly Pa 8 3 Chapter 3 Transforming Points Q3 4 5 3 y Q2 7 5 3 See OS A
188. f C I do use these but only in a couple of places so far real_pair INVALID_REAL_PAIR Constant first and second are both INVALID_REAL real INVALID_REAL_SHORT Constant first is INVALID_REAL and second is 0 real MAX_REAL Variable The largest real value permitted in the the elements of Transforms and the coor dinates of Points It is the second largest real value i e float or double on a given machine INVALID_REAL is the largest MAX_REAL is a variable but it should be used like a constant In other words users should never reset its value It can t be declared const because its value must be calculated using function calls which can t be done before the entry point of the program i e main Therefore the value of MAX_REAL is calculated at the beginning of main Chapter 13 Global Constants and Variables 83 real MAX_REAL_SQRT Variable The square root of MAX_REAL MAX_REAL_SQRT is a variable but it should be used like a constant In other words users should never reset its value It can t be declared const because its value is calculated using the sqrt function which can t be done before the entry point of the program i e main Therefore the value of MAX_REAL_SQRT is set after MAX_REAL is calculated at the beginning of main MAX_REAL_SQRT is used in Point magnitude see Section 22 15 Vector Operations page 136 The magnitude of a Point is found by using the formula a2 y 2 22 x
189. f its member functions are pure virtual functions and that it s only used as a base class i e no objects of type Shape may be declared All of the drawable types in 3DLDF Point Path Ellipse etc are derived from Shape Deriving all of the drawable types from Shape makes it possible to handle objects of different types in the same way This is especially important in the Picture functions where objects of various types but all derived from Shape are accessed through pointers to Shape See Chapter 21 Picture Reference page 111 18 1 Data Members signed short DRAWDOT Protected static constants signed short DRAW signed short FILL signed short FILLDRAW signed short UNDRAWDOT signed short UNDRAW signed short UNFILL signed short UNFILLDRAW Values used in the output functions of the classes derived from Shape For example in Path if the data member fi11_draw_value DRAW then the MetaPost command draw is written to out_stream when that Path is output 18 2 Operators Transform operator const Transform amp t Pure virtual function 18 3 Copying Shape get_copy void const pure virtual function Copies an object allocating memory on the free store for the copy and returns a pointer to Shape for accessing the copy Used in the drawing and filling functions for copying the Shape and putting a pointer to the copy onto the vector lt Shape gt shapes of the Picture 18 4 Modifying bool set_on_free_s
190. f the CPU of the system on which 3DLDF is being run has a register width of 64 bits otherwise false Chapter 15 System Information 87 15 3 Get Second Largest Real template lt class Real gt Real get_second_largest Real Template function MAX_VAL bool verbose false float get_second_largest float bool Template specialization double get_second_largest double bool Template specialization get_second_largest returns the second largest floating point number of the type specified the template paramater Real If verbose is true messages are printed to standard output This function is used for setting the value of MAX_REAL See Chapter 13 Global Constants and Variables page 82 get_second_largest depends on there being an unsigned integer type with the same length as Real This should always be the case for float and double but may not be long double MAX_VAL should be the largest number of type Real on a given architecture The GNU C compiler GCC 3 3 does not currently supply the numeric_limits template so it is necessary to pass one of the macros FLT_MAX or DBL_MAX explicitly depending on which specialization you use When and if GCC supplies the numeric_limits template I will eliminate the MAX_REAL argument l If your system supplies an unsigned integer type with the same length as long double then you can instantiate get_second_largest lt long double gt and call get_second_largest lt long double gt
191. false is equivalent to calling the const version with no assignment If unit_vector is called with assign and silent both false it issues a warning message is issued and the const version is called If silent is true the message is suppressed Point P 21 45 677 91 Point Q P unit_vector Q show Q 4 Q 0 201994 0 439357 0 875308 P rotate 30 25 10 P show P P 19 3213 82 9627 59 6009 cout lt lt P magnitude 4 103 963 P unit_vector true Chapter 22 Point Reference 140 P show P P 0 185847 0 797999 0 573287 cout lt lt P magnitude ly 2 22 16 Points and Lines Line get_line const Point amp p const function Returns the Line corresponding to the line from this to p lposition will be this and I direction will be p this See Chapter 24 Line Reference page 154 real slope Point p char m x char n y const function Returns a real number representing the slope of the trace of the line defined by this and p on the plane indicated by the arguments m and n Point p0 3 4 5 Point p1 2 7 12 real r p0 slope p1 x y ae a 3 r pO slope pl x z gt r 7 r p0 slope p1 z y gt r 0 428571 bool_real is_on_segment Point p0 Point p1 Function bool_real is_on_segment const Point amp p0 const Point amp p1 const function These functions return a bool_real wher
192. flush return 0 else if u Char sizeof long 1 1 if verbose cout lt lt Processor is big endian lt lt endl lt lt endl lt lt flush return 1 else cerr lt lt ERROR In System get_endianness n lt lt Can t determine endianness Returning 1 lt lt endl lt lt endl lt lt flush return 1 bool is_big_endian const bool verbose false Function Returns true if the processor is big endian otherwise false If verbose is true messages are printed to standard output bool is_little_endian const bool verbose false Function Returns true if the processor is little endian otherwise false If verbose is true messages are printed to standard output 15 2 Register Width unsigned short get_register_width void Function Returns the register width of the CPU of the system on which 3DLDF is being run This will normally be either 32 or 64 bits This is the C code return sizeof void CHAR_BIT This assumes that an address will be the same size as the processor s registers and that CHAR_BIT will be the number of bits in a byte These are reasonable assumptions that apply to all architectures I know about This function is called by is_32_bit and is_64_bit bool is_32_bit void Function Returns true if the CPU of the system on which 3DLDF is being run has a register width of 32 bits otherwise false bool is_64_bit void Function Returns true i
193. fortunate that the terms array matrix and vector have different meanings in C and in normal mathematical usage However in practice these discrepancies turn out not to cause many problems Stroustrup The C Programming Language 22 4 p 662 In fact none of the operations for transformations require all of the elements of a 4 x 4 matrix In many 3D graphics programs the matrix operations are modified to use smaller transformation matrices which reduces the storage requirements of the program This is a bit tricky because the affine trans formations and the perspective transformation use different elements of the matrix I consider that the risk of something going wrong possibly producing hard to find bugs outweighs any benefits from saving memory which is usually no longer at a premium anyway In addition there may be some interesting non affine transformations that would be worth implementing Therefore I ve decided to use full 4 x 4 matrices in 3DLDF Chapter 4 Transforms 20 5 p show p 4 p 1 1 0 When a Transform is declared line 1 it is initialized to an identity matrix All identity matrices are square all of the elements of the main diagonal upper left to lower right are 1 and all of the other elements are 0 So a 4 x 4 identity matrix as used in 3DLDF looks like this 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 If a matrix A is multiplied with an identity matrix J the result is ident
194. gon Currently Reg_Polygon and Rectangle are the only classes derived from Polygon 3 Two Polygons 4 A line and a Regular Closed Plane Curve Reg_C1_Plane_Curve see Section 30 3 Regular Closed Plane Curve Reference Intersections page 217 Currently Ellipse and Circle are the only classes derived from Reg_C1_Plane_Curve 5 Two Ellipses Since a Circle is also an Ellipse one or both of the Ellipses may be a Circle See Section 31 9 Ellipse Reference Intersections page 230 Adding more functions for finding the intersections of various geometric figures is one of my main priorities with respect to extending 3DLDF There are currently no special functions for finding the intersection points of a line and a Circle or two Circles Since the class Circle is derived from class Ellipse Circle intersection_points resolves to Ellipse intersection_points which in turn calls Reg_Cl_Plane_Curve intersection_points This does the trick but it s much easier to find the intersections for Circles that it is for Ellipses In particular the intersections of two coplanar Circles can be found algebraically whereas I ve had to implement a numerical solution for the case of two coplanar Ellipses with different centers and or axis orientation It may also be worthwhile to write a specialization for finding the intersection points of a Circle and an Ellipse The theory of intersections is a fascinating and non trivial branch of mat
195. gument If convert eps is called interactively with a prefix argument or non interactively with a non nil do not delete files argument these files will not be deleted convert eps loop arg start end Emacs Lisp function Converts a set of EPS image files to the PS and PNG formats The files must all have the same filename and the extensions must form a range of positive integers For ex ample convert eps loop can be used to convert the files 3DLDFmp 1 3DLDFmp 2 and 3DLDFmp 3 to 3DLDFmp 1 ps 3DLDFmp 2 ps and 3DLDFmp 3 ps on the one hand and 3DLDFmp 1 png 3DLDFmp 2 png 3DLDFmp 3 png on the other If convert eps loopis called interactively it prompts for filename with no extension and the starting and ending numbers of the range For all 2 Z and start lt i lt end convert eps loop checks whether a file named filename i exists If it does it calls convert eps passing filename i as the latter s filename argument do not delete files is also passed to convert eps If it s nil the tex dvi and log files will be deleted This is the case when convert eps loop is called inter actively with no prefix argument If convert eps loop is called interactively with a prefix argument or non interactively with a non nil do not delete files argument these files will not be deleted 11 2 2 Command Line Arguments 3dldf can be called with the following c
196. gument in Picture output described in Section 21 8 2 Picture Reference Outputting Functions page 115 below 2 Actually it s printed to standard output even if it is the empty string you just don t see it Chapter 21 Picture Reference 115 21 8 1 2 Namespace Sorting The namespace Sorting is defined in pictures web const unsigned short NO_SORT Constant const unsigned short MAX _Z Constant const unsigned short MIN_Z Constant const unsigned short MEAN_Z Constant These constants can be used for the sort_value argument in Picture output described in Section 21 8 2 Picture Reference Outputting Functions page 115 below 21 8 2 Output Functions void output const Focus amp f const unsigned short projection Function Projections PERSP real factor 1 const unsigned short sort_value Sorting MAX_Z const bool do_warnings true const real min_x_proj 40 const real max_x_proj 40 const real min_y_proj 40 const real max_y_proj 40 const real min_z_proj 40 const real max_z_proj aoj void output const unsigned short projection Function Projections PERSP real factor 1 const unsigned short sort_value Sorting MAX_Z const bool do_warnings true const real min_x_proj 40 const real max_x_proj 40 const real min_y_proj 40 const real max_y_proj 40 const real min_z_proj 40 const real max_z_proj 40 JJlll These funct
197. he first connector Then pointer to Point arguments alternate with string arguments for the connectors Again the list of arguments ends in 0 There is no need for a bool to indicate whether the Path is cyclical or not if it is the last non zero argument will be a connector otherwise it will be a pointer to Point Point p 8 2 It s easy to forget to use Point arguments rather than plain Point arguments and to forget to end the list of arguments with 0 If plain Point arguments are used compilation fails with GCC With the DEC compiler compilation succeeds but a memory fault error occurs at run time If the argument list doesn t end in 0 neither compiler signals an error but a memory fault error always occurs at run time Chapter 6 Paths 30 pl0 set 2 pli set 2 p 21 set 0 0 2 p 3 set 0 0 2 p 4 p 0 mediate p 21 p 5 p 21 mediate p 1 p 6 p 1 mediate p 3 p 7 p 3 mediate p 0 p 4 p 5 p 6 p 7 shift 0 1 Path pa amp p 0 amp p 4 amp p 2 1 amp p 5 amp pli amp p 6 Woe Me Bp 3d PL AO pa draw Figure 11 As mentioned above see Section 1 5 1 Accuracy page 7 specifying connectors is prob lematic for three dimensional Paths because MetaPost ultimately calculates the most pleasing curve based on the two dimensional points in the MetaPost code written by 3DLDF For this reason it s advisable t
198. he horizontal axis lies along the x axis and the vertical axis lies along the z axis The three subsequent arguments specify the amounts of rotation about the x y and z axes respectively and default to 0 Finally Ellipse is shifted such that its center comes to lie at the Point specified in the first argument Point pt 1 1 1 Ellipse e pt 3 6 90 e draw Chapter 7 Plane Figures As you may expect this constructor has a corresponding setting function Ellipse e real h_save 1 5 real v_save 2 real h h_save real v v_save Point p 1 for int i 0 i lt 5 i e set p h v 90 e draw h_save 25 v_save 25 h sqrt h_save v sqrt v_save p shift 0 0 2 Figure 33 44 Chapter 7 Plane Figures 45 Figure 34 7 4 Circles Circles are constructed just like Ellipses except that the vertical and horizontal axes are per definition the same so there s only one argument for the diameter instead of two for the horizontal and vertical axes Point P 0 2 1 Circle c P 3 5 90 90 c draw Figure 35 Chapter 7 Plane Figures 46 This constructor too has a corresponding setting function Circle c Point p 1 0 5 for int i 0 i lt 16 i c set p 5 i 22 5 0 O 64 c draw Figure 36 In the preceding example the last argument to set namely 64 is for the number of Points used for constructing the perimete
199. he new Ellipse If e is a non zero pointer or a reference the new Ellipse will be a copy of e If the new object is not meant to be a copy of an existing one 0 must be passed to create_new lt Ellipse gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information 31 3 Performing Transformations Transform do_transform const Transform t bool check Virtual function false Performs a transformation on an Ellipse The Points on the Ellipse are multiplied by t Then if check is true is_elliptical is called on the Ellipse If the transformation has caused it to become non elliptical axis_h and axis_v are set to INVALID_REAL and a warning is issued to stderr center focus0 and focus1 are not set to INVALID_POINT They may may no longer really be the center and foci of the non elliptical Ellipse but they may have some use for the programmer and or user If check is true and the transformation does not cause this to become non elliptical axis_h axis_v linear_eccentricity numerical_eccentricity focus0 and focus1 are recalculated 31 4 Operators Ellipse amp operator const Ellipse amp e Assignment operator Makes the Ellipse a copy of e Transform operator const Transformg t Virtual function Calls do_transform t true and returns the latter s return value See Section 31 3 Ellipse Reference Performing Transformations page 224 31 5 Labeling void label
200. he red_part green_part or blue_part of the Color re spectively If decimal is false the default the actual real value of the part is returned Otherwise the corresponding whole number n such that 0 lt n lt 255 is returned bool get_use_name void const function Returns use_name string get_name void Inline const function Returns name 16 7 Defining and Initializing Colors void define_color_mp const function Writes MetaPost code to out_stream in order to define objects of type color within MetaPost and set their redparts greenparts and blueparts void initialize_colors void Static function Calls define_color_mp described above for the Colors that are defined in namespace Colors see Section 16 8 Namespace Colors page 91 Chapter 16 Color Reference 16 8 Namespace Colors const Color red const Color green const Color blue const Color cyan const Color yellow const Color magenta const Color orange red const Color violet_red const Color pink const Color green_yellow const Color orange const Color violet const Color purple const Color blue_violet const Color yellow_green const Color black const Color white const Color gray const Color light_gray These constant Colors can be used in drawing and filling commands const Color default_background The default background color Equal to white per default const Color background_color Points to default_background by defa
201. hedra have a single dihedral angle so dihedral_angle is not a member of Polyhedron This means that it must be a member of all of the classes representing Platonic polyhedra real triangle_radius Protected variable The radius of the circle enclosing a triangular face of the Tetrahedron Chapter 37 Polyhedron Reference 261 37 2 1 2 Constructors and Setting Functions void Tetrahedron void Default constructor Creates an empty Tetrahedron void Tetrahedron const Point amp p const real Constructor diameter_of_triangle real angle_x 0 real angle_y 0 real angle_z 0 Creates a Tetrahedron with its center at the origin The faces have enclosing circles of diameter diameter_of_triangle If any of angle_x angle_y or angle_z is non zero the Tetrahedron is rotated by the amounts specified around the corresponding axes Finally if p is not the origin the Tetrahedron is shifted such that center comes to lie at p The center of a Tetrahedron is the intersection of the line segments connecting the vertices with the centers of the opposite faces Tetrahedron t origin 3 t draw Figure 187 Point P 1 0 1 Tetrahedron t P 2 75 30 32 5 20 t draw Chapter 37 Polyhedron Reference 262 Figure 188 void set const Point amp p const real diameter_of_triangle Setting function real angle_x 0 real angle_y 0 real angle_z 0 Corresponds to the constructor above 37 2 1
202. hematics As I learn more about it I plan to define more classes to represent various curves two dimensional ones to start with and functions for finding their intersection points 1 The books on computer graphics and the fairly elementary mathematics books that I own or have referred to don t go into intersections very deeply One that does is Fischer Gerd Ebene Algebraische Kurven which is a bit over my head Chapter 11 Installing and Running 3DLDF 74 11 Installing and Running 3DLDF 11 1 Installing 3DLDF 3DLDF is available for downloading from http ftp gnu org gnu 3dldf The official 3DLDF website is http www gnu org software 3dldf The tarball i e the compressed archive file 3DLDF 1 1 5 1 tar gz unpacks into a directory called 3DLDF 1 1 5 1 On a typical Unix like system entering the following commands at the command line in a shell will unpack the 3DLDF distribution Please note that the form of the commands may differ on your system gunzip 3DLDF 1 1 5 1 tar gz tar xpvf 3DLDF 1 1 5 1 tar The p option to tar ensures that the files will have the same permissions as when they were packed The directory 3DLDF 1 1 5 1 contains a configure script which should be called from the command line in the shell using the absolute path of 3DLDF 1 1 5 1 as the pre fix argument For example if the path is usr local mydir 3DLDF 1 1 5 1 configure should be invoked as follows
203. her of the Modified Version as given on the Title Page If there is no section Entitled History in the Docu ment create one stating the title year authors and publisher of the Document as given on its Title Page then add an item describing the Modified Version as stated in the previous sentence Preserve the network location if any given in the Document for public access to a Transparent copy of the Document and likewise the network locations given in the Document for previous versions it was based on These may be placed in the History section You may omit a network location for a work that was published at least four years before the Document itself or if the original publisher of the version it refers to gives permission For any section Entitled Acknowledgements or Dedications Preserve the Title of the section and preserve in the section all the substance and tone of each of the contributor acknowledgements and or dedications given therein Preserve all the Invariant Sections of the Document unaltered in their text and in their titles Section numbers or the equivalent are not considered part of the section titles Delete any section Entitled Endorsements Such a section may not be included in the Modified Version Do not retitle any existing section to be Entitled Endorsements or to conflict in title with any Invariant Section Preserve any Warranty Disclaimers If the Modified V
204. his a copy of p destroying the old contents of this void operator const Picture amp p Operator Adds the contents of p to this p remains unchanged void operator Shape s Operator Puts s onto shapes Note that the pointer s itself is put onto shapes so any allocation and copying must be performed first This is a low level function that users normally won t need to use directly void operator Label label Operator Puts label onto labels Note that the pointer label itself is put onto labels so any allocation and copying must be performed first This is a low level function that users normally won t need to invoke directly Transform operator const Transformk t Operator Multiplies transform by t This has the effect of transforming all of the Shapes on shapes and all of the Points of the Labels on labels by t upon output Transform t t rotate 0 0 180 t shift 3 Reg_Polygon pl origin 5 3 90 pl draw pl label Chapter 21 Picture Reference 113 current_picture output Projections PARALLEL_X_Y current_picture t current_picture output Projections PARALLEL_X_Y Figure 78 21 5 Affine Transformations The functions in this section all operate on the transform data member of the Picture and return a Transform representing the transformation not transform Transform scale real x real y 1 real z 1 Function Performs transform scale x y z and returns the
205. hort double_rows Default 10 The number of double rows drawn Chapter 33 Pattern Reference 243 unsigned short row_shift Default 2 For row_shift 0 the number of sets of hexagons in each single row is increased by 2 every row_shift rows If row_shift 0 the number sets of hexagons remains constant The rows remain centered around the z axis Color draw_color_outer Default Colors default_color The Color used for drawing the outer hexagons Color fill_color_outer Default Colors background_color The Color used for filling the outer hexagons Color draw_color_middle Default Colors default_color The Color used for drawing the middle hexagon Color fill_color_middle Default Colors background_color The Color used for filling the middle hexagons Color draw_color_inner Default Colors default_color The Color used for drawing the inner hexagons Color fill_color_inner Default Colors background_color The Color used for filling the inner hexagons string pen_outer Default pencircle scaled 5mm The pen used for drawing the outer hexagons string pen_middle Default pencircle scaled 3mm The pen used for drawing the mid dle hexagons string pen_inner Default pencircle scaled 3mm The pen used for drawing the inner hexagons Picture amp picture Default current_picture The Picture onto which the pattern is put unsigned int max_hexagons Default 1000 The maximum number of hexagons
206. ical to A i e Ax I A This is the salient property of an identity matrix The same affine transformations are applied in the same way to Transforms as they are to Points i e the functions scale shift shear and rotate correspond to the Point versions of these functions and they take the same arguments Point p Transform t p shift 3 4 5 t shift 3 4 5 gt p transform t p show_transform p 4 p Transform 0 0 707 0 707 0 0 866 0 354 0 354 0 0 5 0 612 0 612 0 0 0 0 1 t show t di EN 0 0 707 0 707 0 0 866 0 354 0 354 0 0 5 0 612 0 612 0 0 0 0 1 4 1 Applying Transforms to Points A Transform t is applied to a Point P using the binary operation Point operator const Transform amp which performs matrix multiplication of P transform by t See Section 22 6 Point Reference Operators page 124 Point P 0 1 Transform t t rotate 90 t show t a2 Chapter 4 Transforms 21 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 P t P show_transform P 4 P Transform 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 P show P 4 P 0 O 1 In the example above there is no real need to use a Transform since P rotate 90 could have been called directly As constructions become more complex the power of Transforms becomes clear Point p0 0 0 0 Point p1 10 5 10 Point p2 16 14 32 Point p3 25 50 99 Point p4 12 6 88 Transform a jae Shift 2 3 4 a
207. icture current_picture rotate 0 60 current_picture current_picture 118 suppress_labels output Projections PARALLEL_X_Z output Projections PARALLEL_X_Z Figure 79 void unsuppress _labels void Inline function Sets do_labels to true If a Picture contains Labels unsuppress_labels en sures that they will be output when Picture output is called so long as there is no intervening call to suppress_labels or kill_labels Chapter 22 Point Reference 119 22 Point Reference Class Point is defined in points web It is derived from Shape using protected derivation The function Transform Transform align_with_axis Point Point char isa friend of Point 22 1 Data Members valarray lt real gt world_coordinates Private variable The set of four homogeneous coordinates x y z and w that represent the position of the Point within 3DLDF s global coordinate system valarray lt real gt projective_coordinates Private variable The set of four homogeneous coordinates x y z and w that represent the position of the projection of the Point onto a two dimensional plane for output The x and y values are used in the MetaPost code written to out_stream The z value is used in the hidden surface algorithm which is currently rather primitive and doesn t work very well see Section 9 3 Surface Hiding page 67 The w value can be 1 depending on the projection used the perspe
208. icture shapes The data members of the Shapes belonging to the copy are set appropriately so that they can be unfilled when Picture output is called unfilldraw const string ddashed const const virtual function string ppen Picture amp picture current_picturel undraw const string ddashed const const virtual function string ppen Picture amp picture current_picturel Unfilldraws the Solid This function allocates a new Solid makes it a copy of this and puts a pointer to it onto picture shapes The data members of the Shapes belonging to the copy are set appropriately so that they can be unfilldrawn when Picture output is called A Solid can currently only be unfilldrawn using a single dash pattern ddashed and pen ppen 34 14 Clearing void clear void Virtual function Calls clear on all the Shapes belonging to the Solid Used in Picture clear for deallocating and destroying Solids Currently lt Shape gt clear always resolves to Path clear since none of the other types of Shape that a Solid can contain e g Ellipse Circle etc overloads Path clear Chapter 35 Faced Solid Reference 257 35 Faced Solid Reference Class Solid_Faced is defined in solfaced web It is derived from Solid using public derivation Solid_Faced currently has no member functions It is intended for use as a base class The classes Cuboid and Polyhedron are de
209. igures 49 en Figure 39 8 2 2 Dodecahedron A dodecahedron has 12 similar regular pentagonal faces The following examples show the same Dodecahedron using different projections default_focus set 2 5 10 2 5 10 10 Dodecahedron d origin 3 d draw Parallel projection x y plane Figure 40 Chapter 8 Solid Figures Parallel projection x z plane Figure 41 Please note that the Dodecahedron in Fig 42 is drawn and not filldrawn Parallel projection z y plane Figure 42 50 Chapter 8 Solid Figures 51 Perspective projection Figure 43 In Fig 44 d is filldrawn In this case the surface hiding algorithm has worked properly See Section 9 3 Surface Hiding page 67 Perspective projection Figure 44 8 2 3 Icosahedron An icosahedron has 20 similar regular triangular faces The following examples show the same Icosahedron using different projections default_focus set 3 0 10 2 0 10 10 Icosahedron i origin 3 i draw Chapter 8 Solid Figures 52 Parallel projection x y plane Figure 45 Parallel projection x z plane Figure 46 Parallel projection z y plane Figure 47 Chapter 8 Solid Figures 53 Perspective projection drawn Figure 48 In Fig 49 i is filldrawn In this case the surface hiding algorithm has worked properly See Section 9 3 Surface Hiding page 67 Perspective pro
210. ince Circle is just a special kind of Ellipse there is often no need to define special functions for Circles Currently Circle inherits the transformation functions and operator const Transform amp from Ellipse Consequently the data member radius described below is not recalculated when transformations are performed on a Circle I plan to change this soon 32 1 Data Members real radius Private variable The radius of the Circle 32 2 Constructors and Setting Functions void Circle void Default constructor Creates an empty Circle void Circle const Point amp ccenter const real ddiameter const Constructor real angle_x 0 const real angle_y 0 const real angle_z 0 const unsigned short nnumber_of_points DEFAULT_NUMBER_OF_POINTS Creates a Circle with radius ddiameter 2 in the x z plane and centered at the origin with nnumber_of points Points If any of the arguments angle_x angle_y or angle_z is 4 0 the Circle is rotated around the major axes by the angles indicated by the arguments Finally the Circle is shifted such that center comes to lie at ccenter void set const Point amp ccenter const real ddiameter const Setting function real angle_x 0 const real angle_y 0 const real angle_z 0 Corresponds to the constructor above Circle create_new lt Circle gt const Circlex c Template specializations Circle x create_new lt Circle gt const Circle amp c Pseudo constru
211. ing the connector The curved segment is joined to the line using amp on each side Circle c origin 4 30 30 30 Path p c segment 3 130 p show p 1 Pp points size connectors size 8 0 00662541 0 888379 1 79185 0 741088 0 673392 1 73128 1 37598 0 355887 1 40714 1 80139 0 0157987 0 868767 1 95255 0 385079 0 198137 1 80646 0 695735 0 502658 amp 1 80646 0 695735 0 502658 0 00662541 0 888379 1 79185 amp cycle Chapter 30 Regular Closed Plane Curve Reference 220 Figure 156 Path half real angle 0 bool closed true const inline function Returns a Path using half of the Points on the Reg_C1_Plane_Curve The effect of the arguments angle and closed is similar to that in segment above Ellipse e origin 3 5 20 15 12 5 Path p e half 0 false Figure 157 Path quarter real angle 0 bool closed true const inline function Returns a Path using a quarter of the Points on the Reg_Cl_Plane_Curve The effect of the arguments angle and closed is similar to that in segment above Ellipse e origin 3 5 60 5 2 5 Path p e quarter 180 false Chapter 30 Regular Closed Plane Curve Reference 221 Figure 158 Chapter 31 Ellipse Reference 222 31 Ellipse Reference Class Ellipse is defined in ellipses web It is derived from Reg_C1_Plane_Curve using public derivation 31 1 Data
212. ings The next step is to combine them into Paths which are similar to Metafont s paths except that they are three dimensional A Path consists of a number of Points and strings representing the connectors The latter are not processed by 3DLDF but are passed unchanged to the output file They must be valid connectors for MetaPost e g amp curl 2 dir 60 zi z2 tension 1 and 1 5 controls z1 and z2 Usually it will only make sense to use or and not tension curl controls or any of the other possibilities in Paths unless you are sure that they will only be viewed with no foreshortening due to the perspective projection This can be the case when a Path lies in a plane parallel to one of the major planes and is projected using parallel projection onto that plane Otherwise the result of using these connectors is likely to be unsatisfactory because MetaPost performs its calculations based purely on the two dimensional values of the points in the perspective projection While the Points on the Path will be projected correctly the course of the Path between these Points is likely to differ depending on the values of the Focus used see Section 9 2 Focuses page 63 so that different views of the same Path may well be mutually inconsistent This problem doesn t arise with since the perspective projection does not unstraighten straight lines but it does with even without ten
213. int P 3 2 12 Cuboid c P 3 5 2 93 35 10 60 Chapter 36 Cuboid Reference 259 Figure 186 Cuboid create_new lt Cuboid gt const Cuboid c Template specializations Cuboid create_new lt Cuboid gt const Cuboid amp c Pseudo constructors for dynamic allocation of Cuboids They create a Cuboid on the free store and allocate memory for it using new Cuboid They return a pointer to the new Cuboid If c is a non zero pointer or a reference the new Cuboid will be a copy of c If the new object is not meant to be a copy of an existing one 0 must be passed to create_ new lt Cuboid gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information void Cuboid void Destructor Deallocates the Rectangles pointed to by the pointers on rectangles a Solid data member and calls rectangles clear Cuboids consist entirely of Rectangles so nothing must be done to the other vectors 36 3 Operators void operator const Cuboid amp c Assignment operator Makes the Cuboid a copy of c The old contents of this are deallocated where necessary and discarded Chapter 37 Polyhedron Reference 260 37 Polyhedron Reference Class Polyhedron is defined in polyhed web It is derived from Solid_Faced using public derivation It is intended for use as a base class for specific types of polyhedra Currently the classes Tetrahedron Dodecahedron Icosahedron and Trunc_Octahedron tr
214. int P3 0 2 Path p true amp PO amp P1 amp P2 amp P3 0 p draw Figure 111 void set string connector bool cycle Point p 0 Setting function Corresponds to the constructor above Point P 4 P O set 2 1 3 P 3 P 2 P 1 P O P 3 P 2 x P 1 rotate 3 12 18 P 3 P 2 shift 2 1 3 P 3 shear 1 5 5 3 5 Path q false amp P 0 amp P 1 amp P 2 amp P 3 0 q show q 4 q 2 1 3 0 92139 1 51449 3 29505 1 07861 0 514487 6 29505 2 84065 3 26065 6 29505 Chapter 26 Path Reference 170 Figure 112 void Path Point first_point_ptr char s Point p 0 Constructor Constructor for Paths with an arbitrary number of Points and connectors The first required argument is a pointer to a Point followed by pointers to char alternating with pointers to Points The last argument must be 0 i e the null pointer There is no need to indicate by means of an argument whether the Path is a cycle or not If it is the last argument before the 0 will be a char pointer to char if not it will be a Point The data member cycle_switch of type bool will be set to true or false accordingly Point A Point B 2 0 Point C 3 2 Point D 1 3 Path p amp A amp B amp C 8D 0 D C Figure 113 void set Point first_point_ptr string s Point p Setting function 0
215. ion shape_type const unsigned short s Copies one of the objects belonging to the Solid and returns a pointer to Shape that points to the copy The object is found by dereferencing one of the pointers on one of the vectors of pointers belonging to the Solid Currently these vectors are circles ellipses paths rectangles and reg_polygons The argument shape_type spec ifies the vector and the argument s specifies which element of the vector should be accessed The following public static const data members of Solid can and probably should be passed as the shape_type argument CIRCLE ELLIPSE PATH RECTANGLE and REG_POLYGON This function was originally intended to be called within the more specialized func tions in this section namely get_circle_ptr get_ellipse_ptr get_path_ ptr get_rectangle_ptr and get_reg_polygon_ptr However these functions no longer use get_shape_ptr so this function is probably no longer needed Icosahedron I origin 3 I filldraw Reg_Polygon t static_cast lt Reg_Polygon gt I get_shape_ptr Solid REG_POLYGON 9 t gt fill gray Figure 184 Chapter 34 Solid Reference 253 const Reg_Polygon get_circle_ptr const unsigned const virtual functions short s const Reg_Polygon get_ellipse_ptr const unsigned short s const Reg_Polygon get_path_ptr const unsigned short s const Reg_Polygon get_rectangle_ptr const unsigned short s const Reg_Polygon get_reg_polyg
216. ions create a two dimensional projection of the objects on the Picture and write MetaPost code to out_stream for drawing it The arguments const Focus amp f The Focus used for projection also known as the center of projection or the camera This argument is used in the first version only The second version without a const Focus amp f argument merely calls the first version and passes it the global variable default_focus as its first argument so default_focus is effectively the default for f Defining two versions in this way makes it possible to call output with projection as its first and possibly only argument If instead f were an optional argument with default_focus as its default this wouldn t have been possible It also wouldn t be possible to have f have a default in the first version and to retain the second version because the compiler wouldn t be able to resolve a call to output with no arguments const unsigned short projection Default Projections PERSP The type of projection Valid values are const unsigned shorts defined in namespace Projections see Sec tion 21 8 1 1 Namespace Projections page 114 PERSP for the perspective projection Chapter 21 Picture Reference 116 PARALLEL_X_Y for parallel projection onto the x y plane PARALLEL_X_Z for parallel projection onto the x z plane and PARALLEL_Z_Y for parallel projection onto the z y plane TO DO I plan to add isometric and axionometri
217. is equivalent to transforming the Focus so that it lies on a major axis Focus f 5 5 10 2 4 10 10 180 gt 0 989 0 00733 0 148 0 0 999 0 0494 0 148 0 0488 0 988 3 46 4 47 0 865 f transform Transform persp Rr Oooo Private variable The Transform representing the perspective transformation for a particular Focus Let d stand for distance then 100 0 MO TO 4 SE i Ox 0 0 1 d iO oO 1 Chapter 23 Focus Reference 152 23 2 Global Variables Focus default _focus Variable Effectively the default Focus in Picture output See Section 21 8 2 Picture Reference Outputting Functions page 115 It s not really the default but the version of output that doesn t take a Focus argument calls another version that does take one passing default_focus to the latter as its Focus argument It s necessary to do this in such a roundabout way because Picture output must be declared before class Focus is completely defined and default_focus is declared The declaration Focus amp f default_focus makes f a reference to default_ focus i e it makes f another name for default_focus This may be convenient if you don t feel like typing default_focus 23 3 Constructors and Setting Functions void Focus void Default constructor Creates an empty Focus void Focus const real pos_x const real pos_y const real Constructor pos_z const real dir_x const real dir_y con
218. is the case this function returns INVALID_REAL If the Ellipse is still elliptical axis_v is recalculated and returned In the non const version axis_v is also reset to the new value real get_axis_h void Function real get_axis_h void const function Calculates and returns the value of axis_h get_axis_h first checks if the Ellipse is still elliptical using is_elliptical O see Section 31 7 Ellipse Reference Querying page 227 Operations such as scale and shear can cause an Ellipse to become non elliptical If this is the case this function returns INVALID_REAL If the Ellipse is still elliptical axis_h is recalculated and returned In the non const version axis_h is also reset to the new value signed short location Point p const virtual function Returns a value indicating the location of the Point argument p with respect to the Ellipse Let e stand for the Ellipse The return values are as follows 0 p lies on the perimeter of e 1 p lies in the plane of e within its perimeter 1 p lies in the plane of e outside its perimeter 2 p and e do not lie in the same plane 3 e is not elliptical possibly due to having been transformed Ellipse e origin 3 5 45 15 3 e shift 2 1 1 Point A e get_point 7 cout lt lt e location A 4 0 Point B center mediate e get_point 2 cout lt lt e location B 4 1 Point C center mediate e get_point 2 1 5 cout lt lt e location C
219. jection filldrawn Figure 49 Chapter 9 Pictures 54 9 Pictures Applying drawing and filling operations to the drawable objects described in the previous chapters isn t enough to produce output These operations merely modify the Picture object that was passed to them as an argument current_picture by default Pictures in 3DLDF are quite different from pictures in MetaPost When a drawing or filling operation is applied to an object O a copy of O C is allocated on the free store a pointer to Shape S is pointed at C and S is pushed onto the vector lt Shape gt shapes on the Picture P which was passed as an argument to the drawing or filling command The arguments for the pen dash pattern Color and any others are used to set the corresponding data members of C not O In order to actually cause MetaPost code to be written to the output file it is necessary to invoke P output Now the appropriate version of output is applied to each of the objects pointed to by a pointer on P shapes output is a pure virtual function in Shape so all classes derived from Shape must have an output O function So if shapes 0 points to a Path Path output is called if shapes 1 points to a Point Point output is called and if shapes 2 points to an object of a type derived from Solid Solid output is called Point Path and Solid are namely the only classes derived from Shape for which a version of output is
220. jections PERSP real factor 1 Returns the y coordinate from the set of coordinates indicated or world_ coordinates by default real get_z char coords w const bool do_persp true const Function bool do_apply true Focus f 0 const unsigned short proj Projections PERSP real factor 1 Returns the z coordinate from the set of coordinates indicated or world_ coordinates by default real get_w char coords w const bool do_persp true const Function bool do_apply true Focus f 0 const unsigned short proj Projections PERSP real factor 1 Returns the w coordinate from the set of coordinates indicated or world_ coordinates by default 22 10 Returning Information real epsilon void Static function Returns the positive real value of smallest magnitude e that should be used as a coordinate value in a Point A coordinate of a Point may also contain e The value e is used for testing the equality of Points in Point operator see Section 22 6 Point Reference Operators page 124 Let e be the value returned by epsilon P and Q be Points and Pz Qz Py Qy P and Q the updated x y and z coordinates of P and Q respectively If and only if Pel Qal lt LPy Qyll lt e and P Q lt e then P Q epsilon returns different values depending on whether real is float or double If real is float the default
221. le in_rectangle void const function Returns the Rectangle enclosed within the Ellipse Rectangle r e in_rectangle e filldraw black gray r unfilldraw black Figure 173 Chapter 31 Ellipse Reference 237 Rectangle draw_out_rectangle const Color amp ddraw_color const function Colors default_color string ddashed string ppen Picture amp picture current_picture l Draws the Rectangle that surrounds the Ellipse The arguments are like those of Path draw The return value is the surrounding Rectangle See Section 26 12 Path Reference Drawing and Filling page 180 Ellipse e origin 2 5 5 10 12 15 5 e shift 1 1 1 e draw_out_rectangle black evenly pencircle scaled 3mm Figure 174 Rectangle draw_in_rectangle const Color amp ddraw_color const function Colors default_color string ddashed string ppen Picture amp picture current_picture l Draws the Rectangle enclosed within the Ellipse The arguments are like those of Path draw The return value is the enclosed Rectangle See Section 26 12 Path Reference Drawing and Filling page 180 Ellipse e origin 3 5 6 10 12 15 5 e shift 1 1 1 e draw_in_rectangle black evenly pencircle scaled 3mm Figure 175 Chapter 32 Circle Reference 238 32 Circle Reference Class Circle is defined in circles web It is derived from Ellipse using public deriva tion S
222. led 1cm P undrawdot pencircle scaled 5cm P Figure 97 void draw const Point amp p const Color amp ddraw_color Function Colors default_color string ddashed string ppen Picture amp picture current_picture bool aarrow false void draw Picture amp picture current_picture const Point amp p Function const Color amp ddraw_color Colors default_color string ddashed string ppen bool aarrow falsel Draws a line from this to p Returns the Path this p1 See Section 26 12 Path Reference Drawing and Filling page 180 for more information Point P 1 1 1 Point Q 2 3 5 P draw Q Colors gray pensquare scaled 5cm Chapter 22 Point Reference 146 Figure 98 void undraw const Point amp p string ddashed string ppen Function Pictureg picture current_picturel void undraw Picture amp picture const Point amp p string ddashed n string ppen Undraws a line from this to p Returns the Path this p1 See Section 26 12 Path Reference Drawing and Filling page 180 for more information Function Point P 1 1 1 Point Q 2 3 5 P draw Q Colors gray pensquare scaled 5cm P undraw Q evenly scaled 6 pencircle scaled 3cm Figure 99 Chapter 22 Point Reference 147 Path draw_help const Point amp p const Color amp ddraw_color Function Color
223. lling on a straight line is a trochoid If the point is inside the circle the trochoid has inflexions if it is outside the circle but rigidly attached to it the trochoid has loops In the particular case when the point is on the circumference of the rolling circle the roulette is a cycloid When the circle rolls on the outside of Chapter 33 Pattern Reference 245 another circle the corresponding curves are the epitrochoids and epicycloids if it rolls on the inside they are the hypotrochoids and hypocycloids H Martyn Cundy and A P Rollett Mathematical Models p 46 33 2 1 Epicycloids unsigned int epicycloid_pattern_1 real diameter_inner real Function diameter_outer_start real diameter_outer_end real step int arc_divisions unsigned int offsets vector lt const Color gt colors Colors default_color_vector Draws a pattern consisting of epicycloids The outer circle rolls around the circum ference of the inner circle and a Point on the outer circle traces an epicycloid If offsets is greater than 1 the outer circle is rotated offset times around the center of the inner circle by 360 offsets starting from the outer circle s original position From each of these new positions an epicycloid is drawn While diameter_outer_start is greater than or equal to diameter_outer_end the diam eter of the outer circle is reduced by step and another set of epicycloids is traced as described above Each time the dia
224. lor gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information This function is used in the drawing and filling functions for Path and Solid Point drawdot should be changed to use it too but I haven t gotten around to doing this yet 16 3 Operators void operator const Color amp c Assignment operator Sets name to the empty string use_name to false and red_part green_part and blue_part to c red_part c green_part and c blue_part respectively bool operator const Color amp c const operator Equality operator Returns true if the red_parts green_parts and blue_parts of this and c are equal otherwise false The names and use_names are not compared bool operator const Color amp c const operator Inequality operator Returns false if the red_parts green_parts and blue_ parts of this and c are equal otherwise true The names and use_names are not compared ostream amp operator lt lt ostream amp o const Color amp c Non member function Output operator Writes the MetaPost code for the Color to out_stream when a Picture is output This occurs when the Color has been used as an argument to drawing or filling functions If use_name is true name is written to out_stream Otherwise red_part green_ part blue_part is written to out_strean 16 4 Modifying void set_name const string s Function Sets name to s use_name is not reset void set_us
225. m t t align_with_axis c get_center n y t show t ts 0 686 0 379 0 621 0 0 543 0 3 0 784 0 0 483 0 875 0 0 3 1 66 1 11 1 n c t c draw c show c dc fill_draw_value 0 1 31 0 0 728 1 49 O 0 171 1 44 0 0 413 1 17 0 0 933 0 728 0 1 31 0 171 O 1 49 0 413 0 1 44 0 933 0 1 17 1 31 0 0 728 1 49 0 0 171 1 44 0 0 413 1 17 0 0 933 0 728 0 1 31 0 171 0 1 49 0 413 0 1 44 0 933 0 1 17 cycle n show n 4n 0 1 0 Chapter 19 Transform Reference 107 Figure 75 19 12 Resetting void reset void Function Resets matrix to the identity matrix 19 13 Cleaning void clean void Function Sets elements in matrix whose absolute values are lt epsilon to 0 Chapter 20 Label Reference 108 20 Label Reference Class Label is defined in pictures web Point and Picture are friends of Label Labels can be included in drawings by using the label and dotlabel O functions which are currently defined for the classes Point and Path and the classes derived from them See Section 22 19 Point Reference Labelling page 147 and See Section 26 13 Path Reference Labelling page 191 They are currently not defined for Solid and its derived classes I plan to add them for Solid soon Users will normally never need to declare objects of type Label access its data memb
226. me for both Transforms Let e stand for the value returned by epsilon If for all sets of corresponding elements Ej and FE of t and ta E E2 lt e then e is a good value It will be easier to test this when I ve added Transform operator Rotation causes a significant loss of precision to due to the use of the sin and cos functions Therefore neither Transform epsilon nor Point epsilon see Section 22 10 Point Reference Returning Information page 129 can be as small as I d like them to be If they are two small operations that test for equality of Transforms and Points will return false for objects that should be equal 19 9 Showing void show string text const function If the optional argument text is used and is not the empty string text is printed on a line of its own to the standard output first Otherwise Transform is printed on a line of its own to the standard output Then the elements of matrix are printed to standard output 1 For that matter I haven t really tested whether 0 00001 is a good value when real is float Chapter 19 Transform Reference 101 Transform t t show t Tb 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 t scale 1 2 3 t shift 1 1 1 t rotate 90 90 90 t show t bs 0 0 1 0 0 2 0 0 3 0 0 0 1 1 1 1 19 10 Affine Transformations The affine transformation functions use their arguments to create a new Transform t local to
227. me wks EY Ba eat Pe EE Pale eels ie ARE 157 POTN GC tae A REA 10 119 Point measurement_units 10 Point projective_coordinates 10 Point user_coordinates 10 Point view_coordinates 10 Point world_coordinates 10 point pairs thio Sie eal oe eee 121 POAN ES at a de wee etch ti ae ad oS 167 POLY GON posre Tea oe a 36 199 Polyhedron ssai padi bi oo Ste ah 48 260 POSTED OM sie ta 109 151 154 projective_coordinates 119 projective_coordinates Point 10 projective_extremes 120 166 248 PE lia 108 A AAA A els cbihet S 91 R Tdi da ea 205 238 COVA E e Saeed Nob are he 81 teal PART cia seca uee lei ee Paces ote wacko Sans Gis 81 Teal SHOT iis ess Wi AB ee gee cap es Bec 81 Teal CLEP Sys sae e ca ig dde hosts 81 Rectangle Vico dl alitas 36 211 RECTANGLES rta a r e A a EAE 248 rectangles eadar a e e A avg de 248 Ted eot a N a ita 2 91 red PAU a A 88 Reg_Cl_Plane_Curve o o oocooooooo 36 216 Reg Polygon enseia e 36 205 REG POLYGON eaa otis E dde cea tend 248 Leg polyPons oeiee ondene da eS 248 S Shapes ia dia ihe tad ri Wanda 93 SHAPES ao wh kts apuchi a apli oe iae WAE Ta 111 S ako E EA EE E TES 205 Solid oie oaa ee TON 248 ER Faced AAA A aN 257 Data Type and Variable Index T Tetrahedron iii at 48 260 tex o ond c6cbs ade eh el de cee eh 92 COD i adhe ana A ee 108 transform
228. meter of the outer circle is reduced a new Color is taken from colors for the drawing commands If there are more iterations than Colors the last Color on colors is used for the remaining iterations The arguments real diameter_inner The diameter of the inner circle real diameter_outer_start The diameter of the outer circle for the first iteration It must be greater than or equal to diameter_outer_end real diameter_outer_end The diameter of the outer circle for the last iteration It must be less than or equal to diameter_outer_start real step The amount by which the diameter of the outer circle is reduced upon each iteration int arc_divisions The number of divisions of the circle used for calculating Points on the epicycloid For instance if arc_divisions is 90 then the Path for each epicycloid will only have 4 Points since 360 90 4 unsigned int offsets The number of epicycloids drawn upon each iteration Each one is rotated by 360 offsets around the center of the inner circle offsets must be greater than or equal to 1 vector lt const Color gt colors Default Colors default_color_vector The Colors pointed to by the pointers on this vector are used for drawing the epicycloids One Color is used for each iteration Chapter 33 Pattern Reference 246 Example epicycloid_pattern_1 5 3 3 1 72 current_picture output Projections PARALLEL_X_Z Figure 180 Example default_focus set 2 5 1
229. mp p const function real_short get_distance void const function The version of this function taking a Point argument returns a real_short r whose real part r first represents the distance of p from the Plane This value is always positive r second can take on three values 0 Tf the Point lies in the Plane 1 If it lies on the side of the Plane pointed at by the normal to the Plane considered to be the outside 1 If it lies on the side of the Plane not pointed at by the normal to the Plane considered to be the inside The version taking no argument returns the absolute of the data member distance and its sign i e the distance of origin to the Plane and which side of the Plane it lies on It would have been possible to use origin as the default for an optional Point argu ment but I ve chosen to overload this function because of problems that may arise when I implement user_coordinates and view_coordinates see Section 22 1 Point Reference Data Members page 119 Point N O 1 N rotate 10 20 20 Point P 1 1 1 Plane q P N Point A 4 2 4 Point B 1 3 2 Point C q intersection_point A B pt real_short bp Chapter 25 Plane Reference 160 bp q get_distance l cout lt lt bp first 0 675646 cout lt lt bp second qt bp q get_distance A cout lt lt bp first 3 40368 cout lt lt bp second 4 1 bp q get_distance B cout lt lt bp first
230. n Trunc_Octahedron does not yet have a functioning constructor so it cannot be used as yet 37 3 1 1 Data Members real angle_hex_square Protected static const variable The angle between the hexagonal and the square faces of the truncated octahedron namely 125 16 real angle_hex_hex Protected static const variable The angle between the hexagonal faces of the truncated octahedron namely 109 28 real hexagon_radius Protected variable The radius of the circle enclosing a hexagonal or square face of the Trunc_Octahedron 37 3 1 2 Constructors and Setting Functions void Trunc_Octahedron void Default constructor Creates an empty Trunc_Octahedron void Trunc_Octahedron const Point amp p const real Constructor diameter_of_hexagon real angle_x 0 real angle_y 0 real angle_z 0 This function does not yet exist When it does it will create a Trunc_Octahedron with its center at the origin where the hexagonal and square faces have enclosing Chapter 37 Polyhedron Reference 270 circles of diameter diameter_of_hexagon If any of angle_x angle_y or angle_z is non zero the Trunc_Octahedron will be rotated by the amounts specified around the corresponding axes Finally if p is not the origin the Trunc_Octahedron will be shifted such that center comes to lie at p 37 3 1 3 Net vector lt Reg_Polygon gt get_net const real Static function hexagon_diameter bool do_half false This function
231. n Called in Picture output Sets do_output to false if the Path cannot be output using the arguments passed to Picture output O void unsuppress_output void Virtual function Called in Picture output Resets do_output to true after output is called on the Shapes on shapes in a Picture so that the Path can be output if Picture output is called again with arguments that allow the Path to be output void output void Virtual function Called in Picture output Writes the MetaPost code to out_stream for drawing filling filldrawing undrawing unfilling or unfilldrawing the Path if the latter was projectable using the arguments passed to Picture output Chapter 26 Path Reference 198 26 17 Intersections bool_point intersection_point const Path amp p const bool trace Function Finds the intersection point if any of two linear Paths Let bp be the bool_point returned by this function bp pt will contains the intersection point if it exists If not it will contain INVALID_POINT If the intersection point exists and lies on both of the line segments represented by the Path and p bp b will be true otherwise false This function calls Point intersection_points passing the first and last Points on this and p as its arguments If the trace argument is false the version of Point intersection_points that finds the intersection point by means of a vector calculation is used If it s true the
232. n constant objects should be declared locally within the figure They may be locally declared copies of global objects Alternatively beginfig could be changed so that objects could be passed to it as arguments perhaps as a vector lt void gt and or a vector lt Shape gt Chapter 41 Changes 278 41 Changes Updated 16 January 2004 41 1 3DLDF 1 1 5 1 e Added missing Texinfo files to the 3d1df_TEXINFOS variable in 3DLDF 1 1 5 1 DOC TEXINFO Makefil and reordered the filenames e Changed the names of the PNG Portable Network Graphics files included in the HTML version of this manual Changed the names in the commands for including these files in the Texinfo files I wasn t able to write some of the files with the old names to a CD R Compact Disk Recordable 41 2 3DLDF 1 1 5 In release 1 1 5 P ve tied up some loose ends I wanted to do this before starting on the input routine e Added const real step argument to the version of Ellipse intersection_points that takes an Ellipse argument See Section 31 9 Ellipse Reference Intersections page 230 e It is now possible to typedef real to either float or double This means that real can now be made a synonym for either float or double by using a typedef declaration real is typedeffed to float by default e Added const bool 1df_real_float and extern const bool ldf_real_double for use in non conditionally compiled code They are set according to the values of LDF
233. n the Title Page and on the covers if any a title distinct from that of the Document and from those of previous versions which should if there were any be listed in the History section of the Document You may use the same title as a previous version if the original publisher of that version gives permission Appendix A GNU Free Documentation License 285 N O List on the Title Page as authors one or more persons or entities responsible for authorship of the modifications in the Modified Version together with at least five of the principal authors of the Document all of its principal authors if it has fewer than five unless they release you from this requirement State on the Title page the name of the publisher of the Modified Version as the publisher Preserve all the copyright notices of the Document Add an appropriate copyright notice for your modifications adjacent to the other copyright notices Include immediately after the copyright notices a license notice giving the public permission to use the Modified Version under the terms of this License in the form shown in the Addendum below Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document s license notice Include an unaltered copy of this License Preserve the section Entitled History Preserve its Title and add to it an item stating at least the title year new authors and publis
234. nce Drawing and Filling page 180 The return value is the enclosed Ellipse Chapter 30 Regular Closed Plane Curve Reference 216 30 Regular Closed Plane Curve Reference Class Reg_C1_Plane_Curveis defined in curves web It is derived from Path using public derivation Reg_C1_Plane_Curveis not called Regular_Closed_Plane_Curve because the longer name causes too many Overfull boxes in the CWEAVE output of the program code See Section 1 3 CWEB Documentation page 5 Reg_C1_Plane_Curve is meant to be used as a base class no objects should be declared of type Reg_C1_Plane_Curve Currently class Ellipses is derived from Reg_C1_Plane_ Curve and class Circle is derived from Ellipse At present I have no fixed definition of what constitutes regularity as far as Reg_ Cl_Plane_Curves are concerned Ellipses and circles are regular in the sense that they have axes of symmetry There must be an equation for a Reg_C1_Plane_Curve such as x y r for a circle A derived class should have a solve function that uses this equation Reg_C1_Plane_Curve intersection_points in turn uses solve to find the intersection points of a line with the Reg_C1_Plane_Curve This way the derived classes don t need their own functions for finding their intersections with a line However such functions can be added if desired It is assumed that classes derived from Reg_C1_Plane_Curve are fillable which implies that the
235. nction Circle amp c const bool verbose false Returns the intersection points of two Circles If the Circles are coplanar they can intersect at at most two points There is an easy algebraic solution for this so in this case this function is faster than Ellipse intersection_points Ellipse bool which uses an iterative procedure to find the points If the Circles are non coplanar the intersection points of each Circle with the plane of the other Circle are returned so a maximum of four Points can be found Circle t origin 5 90 Circle c origin 3 90 c shift 3 c rotate 0 0 45 bool_point_quadruple bpq t intersection_points c bpq first pt dotlabel f Chapter 32 Circle Reference 241 bpq second pt dotlabel s Figure 177 Chapter 33 Pattern Reference 242 33 Pattern Reference There is no currently no class Pattern If it turns out to be useful for this purpose I will define a Pattern class and perhaps additional derived classes 33 1 Plane Tesselations 3DLDF can be used to make perspective projections of plane tesselations and other two dimensional patterns These can be used for drawing tiled floors and other architectural items among other things While patterns can be generated by using the basic facilities of C and 3DLDF without any specially defined functions it can be useful to define such functions 3DLDF currently contains only one function for drawing pattern
236. nds for position and D for direction so a Focus contains a third Point up to indicate which direction will be up on the projection when a Picture is projected The projection plane q will always be perpendicular to PD or to put it another way PD is normal to q Unlike the traditional perspective construction where the distance from the focus to the center of vision fixes both the location of the focus in space and its distance to the picture plane these two parameters can be set independently when the perspective transformation is used The distance from a Focus to the picture plane is stored in the data member distance of type real A Focus can be declared using two Point arguments for position and direction and a real argument for distance in that order Point pos 0 5 10 Point dir 0 5 10 Focus f pos dir 10 Point center 2 0 3 Rectangle r center 3 3 4 I believe this to be true but I m not 100 certain Chapter 9 Pictures 64 r draw current_picture output f Figure 60 The up direction is calculated by the Focus constructor automatically An optional argument can be used to specify the angle by which to rotate the Focus about PD Point pos 0 5 10 Point dir 0 5 10 Focus f pos dir 10 30 Point center 2 0 3 Rectangle r center 3 3 r draw current_picture output f Figure 61 Alternatively a Focus can be declared using three real a
237. ngle_radius Protected variable The radius of the circle enclosing a triangular face of the Icosahedron Chapter 37 Polyhedron Reference 267 37 2 3 2 Constructors and Setting Functions void Icosahedron void Default constructor Creates an empty Icosahedron void Icosahedron const Point amp p const real Constructor diameter_of_triangle real angle_x 0 real angle_y 0 real angle_z 0 Creates an Icosahedron with its center at the origin where the triangular faces have enclosing circles of diameter diameter_of_triangle If any of angle_x angle_y or angle_z is non zero the Icosahedron is rotated by the amounts specified around the corresponding axes Finally if p is not the origin the Icosahedron is shifted such that center comes to lie at p Icosahedron i origin 3 0 10 i draw Figure 195 i filldrawQ Figure 196 Chapter 37 Polyhedron Reference 268 37 2 3 3 Net vector lt Reg_Polygon gt get_net const real Static function triangle_diameter bool do_half false Returns the net i e the two dimensional pattern of triangles that can be folded into a model of an icosahedron The net lies in the x z plane The triangles have enclosing circles of diameter triangle_diameter If the argument do_half true only the first half of the net is created This is used in the non default constructor See Section 37 2 3 2 Polyhedron Reference Regular Platonic Polyhedra Icosahedron Constru
238. ns 266 37 2 3 1 Data Members 00065 266 37 2 3 2 Constructors and Setting Functions 266 A A a i AREA aang ee 267 37 3 Semi Regular Archimedean Polyhedra 269 37 3 1 Truncated Octahedron oooooo o o 269 37 3 1 1 Data Members oooooo oooo 269 37 3 1 2 Constructors and Setting Functions 269 A N t eee ai ave caine h a a a aa 270 38 Utility Functions oes de cnc 271 38 1 Perspective Functions 00 cee eee eee eee eee 271 39 Adding a Pile ser daria Sees ati at 273 40 F ture P lanes AAA RAN 275 ADT Geometria dd 275 40 2 Curves and Surfaces 0 00 cece etc eeeeeeee ee ees 275 40 3 Shadows Reflections and Rendering 276 40 4 Multi Threading 00 c cece eee eee eee 277 41 Chan Ges tia a a 278 PeT IDEDE Tl Orde its a AA Ad nd 278 AL SPW Td tt cat a stat 278 7 1 Pts Yaumees 9 DB cae LEE err TO a re ee Ee 279 41 4 3D LDF Til aa ee eae Rea eee 279 Alb IDEDE Wel Ayes i335 a E ea LS 279 ODLO A aoe ata ow eee nena ea ache A 279 Bibliography oss 2 40t60045 ons eho bes Seu biiw as 280 Appendix A GNU Free Documentation License DAME DDD ee Te EA ee ee eee 282 A 0 1 ADDENDUM How to use this License for your GOCUMENS quitar ad Da Redes ea 288 Data Type and Variable Index 289 Function Index 00d yA 292 Concept Index apa 295 Chapter 1 Introduction 1 1 Introduction 3DLDF is a free soft
239. nside this Fourth point lies on the perimeter of e Figure 170 In Fig 171 the two Ellipses lie in skew planes The plane of f intersects with e at the Points labelled 1 and 2 The plane of e does not intersect with f so bpq third pt and bpq fourth pt are INVALID_POINT Ellipse e origin 5 3 Ellipse f origin 2 5 45 f shift 0 2 5 3 bool_point_quadruple bpq e intersection_points f true bpq first pt dotlabel 1 bpq second pt dotlabel 2 First point lies on the perimeter of this First point lies outside e Second point lies on the perimeter of this Second point lies outside e Third intersection point is INVALID_POINT Fourth intersection point is INVALID_POINT Chapter 31 Ellipse Reference 235 2 1 Figure 171 31 10 Solving real_pair solve char axis_unknown real known const function Returns two possible values for either the horizontal or vertical coordinate This function assumes that the Ellipse lies in a major plane with center at the origin Code that calls it must ensure that these conditions are fulfilled solve is called in Reg_C1_Plane_Curve intersection_points Point Point Point and Reg_C1_Plane_Curve location and resolves to this function when these functions are called on an Ellipse However Ellipse location over loads Reg_C1_Plane_Curve location so the latter won t normally be called on an Ellipse See Section 30 3 Regular Closed Plane Curve Ref
240. nstructor above A Reg_Polygon can theoretically have any number of sides however I haven t tested it for unreasonably large values The following example demonstrates that set can be used to change a Reg_Polygon Reg_Polygon r real j 5 for int i 3 i lt 16 i r set origin i j r draw j t 5 Chapter 28 Regular Polygon Reference 207 Figure 146 Reg_Polygon create_new lt Reg_Polygon gt const Template specializations Reg_Polygon r Reg_Polygon create_new lt Reg_Polygon gt const Reg_Polygong r Pseudo constructors for dynamic allocation of Reg_Polygons They create a Reg_ Polygon on the free store and allocate memory for it using new Reg_Polygon They return a pointer to the new Reg_Polygon If r is a non zero pointer or a reference the new Reg_Polygon will be a copy of r If the new object is not meant to be a copy of an existing one 0 must be passed to create_new lt Reg_Polygon gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information 28 3 Operators const Reg_Polygong operator const Reg_Polygong p Operator Makes the Reg_Polygon a copy of p 28 4 Querying real get_radius void const inline function Returns radius 28 5 Circles Circle in_circle void const function Returns the enclosed Circle of the Reg_Polygon Point P 0 1 1 Reg_Polygon h P 6 4 15 12 11 5 h filldraw black gray Chapter 2
241. nt and sometimes to MetaPost The reason is that Metafont inherited much of its functionality from Metafont Certain operations in Metafont have no meaning in MetaPost and so have been removed while MetaPost s function of interfacing with PostScript has caused other operations to be added For example in MetaPost color is a data type but not in Metafont Unless otherwise stated when I refer to Metafont it can be assumed that what I say applies to MetaPost as well However when I refer to MetaPost it will generally be in connection with features specific to MetaPost 1 5 Caveats 1 5 1 Accuracy When 3DLDF is run it uses the three dimensional data contained in the user code to create a two dimensional projection Currently this can be a perspective projection or a parallel projection onto one of the major planes MetaPost code representing this projection is then written to the output file 3DLDF does no scan conversion so all of the curves in the 5 METAFONT deals only with numbers in a limited range A numeric token must be less than 4096 and its value is always rounded to the nearest multiple of 05530 Knuth The METAFONTbook p 50 Scan conversion is the process of digitizing geometric data The ultimate result is a 2 x 2 map of pixels which can be used for printing or representing the projection on a computer screen The number of pixels per a given unit of measurement is the resolution of a given output device e g 3
242. nted covers that bracket the whole aggregate TRANSLATION Translation is considered a kind of modification so you may distribute translations of the Document under the terms of section 4 Replacing Invariant Sections with translations requires special permission from their copyright holders but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections You may include a translation of this License and all the license notices in the Document and any Warranty Disclaimers provided that you also include the original English version of this License and the original versions of those notices and disclaimers In case of a disagreement between the translation and the original version of this License or a notice or disclaimer the original version will prevail If a section in the Document is Entitled Acknowledgements Dedications or His tory the requirement section 4 to Preserve its Title section 1 will typically require changing the actual title TERMINATION You may not copy modify sublicense or distribute the Document except as expressly provided for under this License Any other attempt to copy modify sublicense or distribute the Document is void and will automatically terminate your rights under this License However parties who have received copies or rights from you under this License will not have their licenses terminated so long as such p
243. ntioned above 3DLDF has been programmed using CWEB which is a literate programming tool developed by Donald E Knuth and Silvio Levy See Section 1 1 Sources of Information page 1 for a reference to the CWEB manual Knuth s TgEX The Program and Metafont The Program both include a section How to read a WEB pp x xv in both volumes 1 ctangle creates lt filename gt c from lt filename gt web so the compiler must compile the C files using the x c option Otherwise it would handle them as if they contained C code If you want to try generating the illustrations yourself you can save a little run time by calling tex 3DLDF texi the first time rather than texi2dvi The latter program runs TX twice because it needs two passes in order to generate the contents indexing and cross reference information and maybe some other things too Chapter 1 Introduction 6 CWEB files combine source code and documentation Running ctangle on a CWEB file for example main web produces the file main c containing C or C code Running cweave main web creates a TFX file with pretty printed source code and nicely formatted documentation I find that using CWEB makes it more natural to document my code as I write it and makes the source files easier to read when editing them It does have certain consequences with regard to compilation but these are taken care of by make See Chapter 39 Adding a File
244. nue the rest onto adjacent pages If you publish or distribute Opaque copies of the Document numbering more than 100 you must either include a machine readable Transparent copy along with each Opaque copy or state in or with each Opaque copy a computer network location from which the general network using public has access to download using public standard network protocols a complete Transparent copy of the Document free of added material If you use the latter option you must take reasonably prudent steps when you begin distribution of Opaque copies in quantity to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy directly or through your agents or retailers of that edition to the public It is requested but not required that you contact the authors of the Document well before redistributing any large number of copies to give them a chance to provide you with an updated version of the Document 4 MODIFICATIONS You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above provided that you release the Modified Version under precisely this License with the Modified Version filling the role of the Document thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it In addition you must do these things in the Modified Version A Use i
245. nvoked in main Look for the line Your code here in main web This is an example of what you could write in main Feel free to make it more complicated if you wish beginfig 1 default_focus set 2 3 10 2 3 10 20 Rectangle R origin 5 3 1 Stallman Richard M Using and Porting the GNU Compiler Collection p 285 Chapter 11 Installing and Running 3DLDF 76 Circle C origin 3 90 C half 180 filldraw black light_gray R filldraw C half filldraw black light_gray Point p C get_point 4 p shift 0 5 p get_y p label C Point q R get_mid_point 0 q shift 0 0 5 q get_z Q q label R current_picture output default_focus PERSP 1 NO_SORT endfig 1 Figure 72 1 Save main web and any other CWEB files you ve changed Since these files have changed they must be ctangled and the resulting C files must be recompiled If you ve changed any files other than main web ctangle will also generate a header file for each of these files If a header file differs from the version that existed before ctangle was run all of the C files that depend on it must be recompiled Then 3dldf must be relinked To do this call make 3dldf from the command line If you ve made any errors in typing your code the compiler should have issued error messages so go back into the appropriate CWEB file and correct your errors Then call make
246. o avoid specifying curl dir tension or control points in connectors The more Points a 3DLDF Path or other object contains the less freedom MetaPost has to determine the MetaPost path through them So a three dimensional Path or other object in 3DLDF should have enough Points to ensure satisfactory results The Path in Fig 11 does not really have enough Points It may re quire some trial and error to determine what a sufficient number of Points is in a given case Paths are very flexible but not always convenient 3DLDF provides a number of classes representing common geometric Shapes which will be described in subsequent sections and I intend to add more in the course of time 3 Knuth The METAFONT book Chapter 14 p 127 Chapter 6 Paths 31 6 2 Drawing and Filling Paths The easiest way to draw a Path is with no arguments Point pt 5 pt 0 set 1 2 pt 1 set 0 3 pt 2 set 1 0 pt 3 set 2 1 pt 4 set 1 2 Path pa true amp pt 0 amp pt 1 amp pt 2 amp pt 3 pt 4 0 pa draw Figure 12 Since pa is closed it can be filled as well as drawn The following example uses fi11 O with a Color argument in order to avoid having a large splotch of black on the page Common Colors are declared in the namespace Colors See Chapter 16 Color Reference page 88 pa fill Colors gray Chapter 6 Paths 32 Figure 13 Closed Paths can be fille
247. o be changed or rewritten again it s possible that the Polyhedron constructors will have to be too It has also occurred in the past that the Polyhedra were constructed correctly on one platform using a particular compiler but not on another platform using a different compiler void draw_net const real triangle_diameter bool Static function make_tabs true Draws the net for a Tetrahedron in the x y plane The triangles have enclosing circles of diameter triangle_diameter The origin is used as the center of the middle triangle The centers of the triangles are numbered If the argument make_tabs is used tabs for gluing and or sewing a cardboard model of the Tetrahedron together will be drawn too The dots on the tabs mark where to stick the needle through when sewing the model together I ve had good results with sewing Tetrahedron draw_net 3 true Chapter 37 Polyhedron Reference 264 Figure 190 The net is drawn in the x y plane because it currently doesn t work to draw it in the x z plane I haven t gotten around to fixing this problem yet 37 2 2 Dodecahedron Class Dodecahedron is defined in polyhed web It is derived from Polyhedron using public derivation Dodecahedra have 12 regular pentagonal faces 37 2 2 1 Data Members real dihedral_angle Protected static const variable The angle between the faces of the Dodecahedron namely 116 34 m arctan 2 real pentagon radius
248. of the pointers on points Following this it calls points clear and connectors clear draw_color and fill_color may or may not have been allo cated on the free store so Path checks this first and deletes them if they were Then it sets them to 0 26 4 Operators Transform operator const Transformk t Virtual function Calls Point operator t on each of the Points on the Path See Section 22 6 Point Reference Operators page 124 This has the effect of transforming the entire Path by t Please note that Path does not have a transform data member of its own void operator const Point amp pt Function Copies pt and pushes a pointer to the copy onto points The last connector in the Path will be used to connect the new Point and the previous one Point A 1 2 3 Point B 3 4 5 Path q q A q B q show q 3 q 1 2 3 3 4 5 Chapter 26 Path Reference 172 Path operator const Point amp pt const function Copies the Path and pt and pushes a pointer to the copy of pt onto points in the new Path The last connector in the new Path will be used to connect the new Point and the previous one The Path remains unchanged void operator z const Path amp pa Function Concatenates two Paths The result is assigned to this Neither this nor pa may be cyclical i e cycle_switch must be false for both Paths Path operator amp const Path amp pa const function Returns a Path repr
249. often more convenient to use the second version The following example puts Path p onto temp_picture It also demonstrates how the labels are put onto temp_picture and how a Hobby A User s Manual for MetaPost p 32 6 Knuth The METAFONTbook Chapter 4 p 21ff Hobby A User s Manual for MetaPost p 32 Chapter 26 Path Reference 183 temp_picture is output In the previous examples the commands for making the labels and outputting current_picture were left out in order to reduce clutter See Section 22 19 Point Reference Labelling page 147 and Section 21 8 2 Picture Reference Outputting Output Functions page 115 Picture temp_picture draw temp_picture dotlabel A bot temp_picture dotlabel B bot temp_picture dotlabel C top temp_picture dotlabel D top temp_picture dotlabel E lft temp_picture temp_picture output Projections PARALLEL_X_Y mH o aW es Figure 124 void draw_help const Color amp ddraw_color help_color const function string ddashed help_dash_pattern string ppen Picture amp picture current_picture void draw_help Picture amp picture const Color amp ddraw_color const function help_color string ddashed help_dash_pattern string ppen This functions are for drawing help lines They are like draw except that draw_ help returns immediately if do_help_lines a static data member in Path is
250. oint 0 eee eee eee 122 bool_real_point operator 122 C A AN 238 A O Bede 107 130 Cl la io 94 113 130 173 256 COMU a o 88 CONVE EP at ii 79 convert eps Loop eiii a e 79 COLMO aos ate Beebe aes 213 A A BE Ee A elle 84 Create news lt Circled ita Mei aoe Ps 238 create_new lt Color gt cece ee ees 89 create_new lt Cuboid gt 0c cee ee eee 259 create_new lt Ellipse gt 00 224 create_new lt Path gt 171 create_new lt Point gt o o o o ooo 123 create_new lt Rectangle gt 212 create_new lt Reg_Polygon gt 207 create_new lt Solid gt ooo 249 CTOSS PEO dC diri a a 137 G boid s a da A 258 D define_color_mp 0 ce cece eee eee ee 90 do transform a bts ains 224 Dod cahedr O viii a 264 dot product suis ce ges he See e Mieke 136 Gotlabe ds shin ae ace arhe kha eee 149 192 225 dram sees oe ee Se fed 145 180 255 292 draw axes Se ar e a a e TE E Ana EE N oE 184 draw help misrai miris hi fae O ia 146 147 183 dr p in circle mi a a 208 draw in ellipses eiir is dad 215 draw_in_rectangle o o o ooooocoocooo 237 A hoe hos eee 263 266 268 draw ut circle heere r eee dee 209 210 draw out ellipse nter erp i ui aaa pa ia 214 draw_out_rectangle oo oooooocooooo 237 AY AWATIOW e eni ae Aa bate oe eee Bred 147 183 Gra WAO E ena Sa e
251. oint_quadruple bool_point a bool_point b Constructor bool_point c bool_point d Creates a bool_point_quadruple and sets first to a second to b third to c and fourth to d void bool_point_quadruple operator const Assignment operator bool_point_quadruple amp arg Makes this a copy of arg bool_real_point b r pt struct b is a bool r is a real and pt is a Point bool_real_point also contains three constructors and an assignment operator described below void bool_real_point void Default constructor Creates a bool_real_point and sets b to false r to INVALID_REAL and pt to INVALID_POINT void bool_real_point const bool_real_point amp brp Copy constructor Creates a bool_real_point and sets b to brp b r to brp r and pt to brp pt void bool_real_point const bool amp bb const real amp rr const Constructor Point amp ppt Creates a bool_real_point and sets b to bb r to rr and pt to ppt void bool_real_point operator const Assignment operator bool_real_point amp brp Makes this a copy of brp 22 3 Global Constants and Variables Point INVALID_POINT Constant The x y and z values in world_coordinates are all INVALID_REAL Point origin Constant The x y and z values in world_coordinates are all 0 bool_point INVALID_BOOL_POINT Constant b is false and pt is INVALID_POINT bool_point_pair INVALID_BOOL_POINT_PAIR Constant first and second are both INVALID_BOOL_POINT bool_real_point I
252. oj Projections PERSP Function real factor 1 These functions calculate projective_coordinates proj indicates which projection is to be performed If it is Projections PERSP then f indicates which Focus is to be used in the first version or the global variable default_focus is used in the second If Projections PARALLEL_X_Y Projections PARALLEL_X_Z or Projections PARALLEL_Z_Y is used f is ignored since these projections don t use a Focus Currently no other projections are defined The x and y coordinates in projective_coordinates are multiplied by factor with the default being 1 Chapter 22 Point Reference 136 22 15 Vector Operations Mathematically speaking vectors and points are not the same However they can both be represented as triples of real numbers in a three dimensional Cartesian space It is sometimes convenient to treat points as though they were vectors and vice versa In particular it is convenient to use the same data type namely class Point to represent both points and vectors in 3DLDF real dot_product Point p const function Returns the dot or scalar product of this and p If P and Q are Points Pe Q p1Q ypyg 2P2q P Q cos 0 where P and Q are the magnitudes of P and Q respectively and 0 is the angle between P and Q Since 0 arccos a 7 IPIIQI J the dot product can be used for finding the angle between two vectors Point P 1 1 1 Point Q 3
253. ometric figures Polygon Reg_C1_Plane_Curve Regular Closed Plane Curve Reg_Polygon Regular Polygon Rectangle Ellipse and Circle Polygon and Reg_C1_Plane_Curve are derived from Path Reg_Polygon and Rectangle are derived from Polygon and Ellipse and Circle are derived from Reg_C1_Plane_Curve Polygon and Reg_C1_Plane_Curve are meant to be used as base classes only so objects of these types should normally never be declared Since Reg_Polygon Rectangle Ellipse and Circle all ultimately derive from Path they are really just special kinds of Path In particular they inherit their drawing and filling functions from Path and their transformation functions take the same arguments as the Path versions They also have constructors and setting functions that work in a similar way with a few minor differences to account for their different natures See Chapter 27 Polygon Reference page 199 Chapter 29 Rectangle Reference page 211 Chapter 31 Ellipse Reference page 222 and Chapter 32 Circle Reference page 238 for complete information on these classes 7 1 Regular Polygons The following example creates a pentagon in the x z plane centered about the origin whose enclosing circle has a radius equal to 3cm default_focus set 2 3 10 2 3 10 10 Reg_Polygon p origin 5 3 p draw Figure 20 Three additional arguments cause the pentagon to be rotated about the x y and z axes by the amount indicate
254. ommand line arguments help Prints information about the valid command line options to standard output and exits with return value 0 silent Suppresses some output to standard output and standard error when 3dldf is run verbose Causes status information to be printed to standard output when 3dldf is run version Prints the version number of 3DLDF to standard output and exits with return value 0 Chapter 11 Installing and Running 3DLDF 80 Currently 3dldf can only handle long options cannot be substituted for How ever the names of the options themselves can be abbreviated as long as the abbreviation is unambigous For example 3dldf h and 3dldf verb are valid but 3dldf ver is not Chapter 12 Typedefs and Utility Structures 81 12 Typedefs and Utility Structures 3DLDF defines a number of data types for various reasons e g for the sake of convenience for use in conditional compilation or as return values of functions Some of these data types can be defined using typedef while others are defined as structs The typedefs and utility structures described in this chapter are found in pspglb web Others that contain objects of types defined in 3DLDF are described in subsequent chap ters real typedef Synonymous either with float or double depending on the values of the prepro cessor variables LDF_REAL_FLOAT and LDF_REAL_DOUBLE The meaning of real is determined b
255. on is_reg_polygonal in order to test whether operations on a Reg_Polygon have caused it to become irregular and or non polygonal Similarly the function Rectangle is_rectangular must be added to test whether operations on a Rectangle has caused it to become non rectangular See Section 28 1 Regular Polygon Reference Data Members page 205 and Section 29 1 Rectangle Reference Data Members page 211 27 5 Intersections bool_point_pair intersection_points const Point amp po const Point amp p1 bool_point_pair intersection_points const Path amp p const function const function These functions find the intersections of the Polygon and a line In the first version the Point arguments are the end points of the line The argument to the second version must be a linear Path A line and a regular polygon or rectangle can intersect at two points at most Let b be a bool_point_pair returned by intersection_points If no intersection points are found b first pt and b second pt will be INVALID_POINT and b first b and b second b will be false Ifa single intersection point is found the correspond ing Point will be stored in b first pt If the Point is on the line segment Popi b first b will be true otherwise false If a second intersection point is found it will be stored in b second pt and b second b is set analogously to b first b 1 Reg_Polygon and Rectangle are currently the only classes derived from Polygon
256. on_ptr const unsigned short s Each of these functions returns a pointer from one of the vectors of Shape pointers belonging to the Solid The argument s specifies which element of the appropriate vector should be returned For example get_reg_polygon_ptr 2 returns the Reg_ Polygon in reg_polygons 2 Since these functions return const pointers they must be invoked in such a way that the const qualifier is not discarded as noted at the beginning of this section The following example demonstrates two ways of invoking get_reg_polygon_ptr Dodecahedron d origin 3 d draw const Reg_Polygon ptr d get_reg_polygon_ptr 0 ptr gt draw black evenly scaled 4 pencircle scaled 1mm Reg_Polygon A d get_reg_polygon_ptr 5 A fill gray Figure 185 34 9 Showing void show string text char coords w const virtual function const bool do_persp true const bool do_apply true Focus f 0 const unsigned short proj Projections PERSP const real factor 00D Prints text and the value of on_free_store to the standard output stdout and then calls show on the objects pointed to by the pointers on paths circles ellipses reg_polygons and rectangles unless the vectors are empty The argu ments are passed to Path show Ellipse show etc If a vector is empty a message to this effect is printed to the standard output Chapter 34 Solid Reference 254 34 10 Affine Tran
257. onst function Returns true if the Path is cyclical i e cycle_switch true otherwise false Only cyclical Paths are fillable int size void Inline function Returns the number of Points on points i e points size bool get_line_switch void Inline const function Returns the value of line_switch line_switch is only true if the Path was created directly or indirectly using the constructor taking two Point arguments only See Section 26 2 Path Reference Constructors and Setting Functions page 167 real slope char a x char b y Function Returns the slope of the Path in the plane indicated by the arguments if is_linear returns true Otherwise slope issues an error message and returns INVALID_REAL Path subpath size_t start size_t end const bool cycle const function false const string connector Returns a new Path using points start through points end 1 If cycle is true then the new Path will be a cycle whether this is or not One optional connector argument can be used If it is it will be the only connector Otherwise the appropriate connectors from this are used start must be lt end It is not possible to have start gt end even if this is a cycle const Point amp get_point const unsigned short a const function Returns the Point points a if a lt points size and the Path is non empty otherwise INVALID_POINT Chapter 26 Path Reference 195 cons
258. opies of this License in the various documents with a single copy that is included in the collection provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects You may extract a single document from such a collection and distribute it individu ally under this License provided you insert a copy of this License into the extracted document and follow this License in all other respects regarding verbatim copying of that document 7 AGGREGATION WITH INDEPENDENT WORKS A compilation of the Document or its derivatives with other separate and independent documents or works in or on a volume of a storage or distribution medium is called Appendix A GNU Free Documentation License 287 10 an aggregate if the copyright resulting from the compilation is not used to limit the legal rights of the compilation s users beyond what the individual works permit When the Document is included in an aggregate this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document If the Cover Text requirement of section 3 is applicable to these copies of the Document then if the Document is less than one half of the entire aggregate the Document s Cover Texts may be placed on covers that bracket the Document within the aggregate or the electronic equivalent of covers if the Document is in electronic form Otherwise they must appear on pri
259. otate 10 12 5 3 bool_point_quadruple bpq e intersection_points f true bpq first pt dotlabel 1 urt O O Fh Fh fh Chapter 31 Ellipse Reference 233 bpq second pt dotlabel 2 ulft Figure 169 If the planes of the Ellipses are parallel there are of course no intersection points If the Ellipses are non coplanar and their planes are not parallel to each other intersection_points first finds the line of intersection of the planes of the Ellipses It then returns the Points of intersection of this line with the Ellipses if they exist If the verbose argument is true information about the Points is printed to standard output In Fig 170 the two Ellipses lie in skew planes The plane of f intersects with e at the Points labelled 1 and 2 while the plane of e intersects with f at the Points labelled 3 and 4 Ellipse e origin 5 3 Ellipse f origin 2 5 f rotate 0 0 30 f rotate 0 10 f rotate 45 f shift 1 5 1 bool_point_quadruple bpq e intersection_points f true bpq first pt dotlabel 1 bpq second pt dotlabel 2 bpq third pt dotlabel 3 rt bpq fourth pt dotlabel 4 urt First point lies on the perimeter of this First point lies inside e Second point lies on the perimeter of this Second point lies outside e Chapter 31 Ellipse Reference 234 Third point lies outside this Third point lies on the perimeter of e Fourth point lies i
260. over Texts A copy of the license is included in the section entitled GNU Free Documentation License If you have Invariant Sections Front Cover Texts and Back Cover Texts replace the with Texts line with this with the Invariant Sections being list their titles with the Front Cover Texts being list and with the Back Cover Texts being list If you have Invariant Sections without Cover Texts or some other combination of the three merge those two alternatives to suit the situation If your document contains nontrivial examples of program code we recommend releasing these examples in parallel under your choice of free software license such as the GNU General Public License to permit their use in free software Data Type and Variable Index Data Type and Variable Index A Meli it a abn are fea a aS ada 151 angle_hex_hex 0 cece cece eens 269 angle_hex_square 000 E 269 ALT OW oe eae aa De RS aslo se 166 ARTS 5 ois A A ee ease Se alee ecg 151 ATS LT Fees Seg ia E a ide due eval Ss 211 222 AI lees E 211 222 RGN yi eea ke hE a ed ek aA etek Bre ne 114 B background Color sates adi 2 cece cece eee 91 background_color_vector 0 4 91 BLACK stati ro lat tt DR eh as 91 DIC Li A ale ike acia et 91 prue Part ii eat kts eh E ewe swe ae 88 ble violet poseia ia rta 91 Boo Patrias dd 81 bool point Puri Macaca ee Ro 121 boos point pair sw here ae wa tee 121 bool_point_quadrupl
261. pecify a pen argument currentpen with its final value is used for both of the MetaPost draw commands For any given invocation of Picture output there can only be one value of currentpen All other pens must be passed as arguments to the drawing commands 9 1 Projections In order for a 3D graphic program to be useful it must be able to make two dimensional projections of its three dimensional constructions so that they can be displayed on computer screens and printed out These are some of the possible projections e Parallel projection onto one of the major planes These projections are trivial and can be performed by 3DLDF They are dis cussed in the following section e Parallel projection onto another plane I haven t programmed these projections yet but they might be useful so I probably will when I get around to it e The perspective projection This is the projection most people think of when they think of 3D graphics It is discussed in detail in Section 9 1 2 The Perspective Projection page 60 e The isometric and axonometric projections These projections are important for engineering and drafting I have not yet implemented them in 3DLDF but they are on my list of Things To Do The function Picture output takes a const unsigned short argument specifying the projection to be used The user should probably avoid using explicit unsigned shorts but should use the constants defined for this purpose in the nam
262. projected using the values of f proj and factor see Section 26 16 Path Reference Outputting page 197 Otherwise the values currently stored in projective_coordinates are shown The Points and connectors are printed out al ternately to standard output followed by the word cycle if cycle_switch true default_focus set 0 3 10 O 3 10 10 Reg_Polygon r origin 5 3 45 r fill gray Point p 10 for int i 0 i lt 5 i pli r get_point i p 5 Point intersection_point p 4 p 0 p 21 p 11 pt pl6 Point intersection_point p 0 pl1 p 21 p 31 pt p 7 Point intersection_point p 1 p 21 p 4 p 31 pt p 8 Point intersection_point p 2 p 31 p 0 p 4 pt p 9 Point intersection_point p 3 p 4 p 0 pl1 pt Path q true amp p 0 amp p 5 amp p 1 amp p 6 amp pl2 amp p 7 amp p 3 amp pl8 amp pl4 amp p 9 0 q draw q show q 4 q fi11_draw_value 8 The following example shows only one Point per line In actual use two Points are shown but this causes overfull boxes in Texinfo Chapter 26 Path Reference 193 0 1 06066 1 06066 2 30826 2 24651 2 24651 1 42658 0 327762 0 327762 3 73485 0 858092 0 858092 0 881678 0 858092 0 858092 4 92996e 07 2 77684 2 77684 0 881678 0 858092 0 858092 3 73485 0 858092 0 858092 1 42658 0 327762 0 327762 2 30826 2 24651 2 24651 c
263. r default_focus set 0 4 6 0 4 6 6 Rectangle r Point center 0 2 r set center 2 5 0 0 0 5 r draw r set center 2 5 0 0 2 5 3 I believe the following to be correct but I m not entirely sure Let Y be the line of sight By definition the plane of projection will be a plane p such that Y is normal to p Let qo and q be planes such that qo q1 or qo q1 and qo L p It follows that q 1 p Let lo and l be lines such that lo 4 l1 lo la lo qo l1 91 lo L 5 and l 1 7 Under these circumstances the projections of l and l in p will also be parallel Chapter 9 Pictures 63 r draw r set center 2 5 0 0 5 r draw current_picture output Figure 59 9 2 Focuses The perspective transformation requires a focus as a consequence outputting a Picture requires an object of class Focus Picture output takes an optional pointer to Focus argument which is 0 by default If the default is used or 0 is passed explicitly the global variable default_focus is used See Section 23 2 Focus Reference Global Variables page 152 A Focus can be thought of as the observer of a scene or a camera It contains a Point position for its location with respect to 3DLDF s coordinate system and a Point direction specifying the direction where the observer is looking or where the camera is pointed The Focus can be rotated freely about the line PD where P sta
264. r GCC 2 95 While I would like 3DLDF to run on as many platforms as possible I would 7 Knuth The METAFONTbook Chapter 14 p 127 8 Flex isa program for generating text scanners and Bison is a parser generator They are available from http www gnu org Chapter 1 Introduction 9 rather spend my time developing it than porting it This is something where I would be grateful for help from other programmers Although I am no longer supporting ports to other systems I have left some conditionally compiled code for managing platform dependencies in the CWEB sources of 3DLDF This may make it easier for other people who want to port 3DLDF to other platforms Currently the files io web loader web main web points web and pspglb web contain conditionally compiled code depending on which compiler or in the case of GCC which version of the compiler is used The DEC C compiler defines the preprocessor macro __DECCXX and GCC defines __GNUC__ In order to distinguish between GCC 2 95 3 and GCC 3 3 Pve added the macros LDF_GCC_2_95 and LDF_GCC_3_3 in loader web which should be defined or undefined depending on which compiler you re using In the distribution LDF_GCC_3_3 is defined and LDF_GCC_2_95 is undefined so if you want to try using GCC 2 95 you ll have to change this it s not guaranteed to work 3DLDF 1 1 5 1 now uses Autoconf and Automake and the
265. r 22 Point Reference 148 an argument current_picture by default See Chapter 20 Label Reference page 108 for more information void label const string text_str const string position_str const function top const bool dot false Picture amp picture current_picturel void label const short text_short const string const function position_str top const bool dot false Picture amp picture current_picturel These functions cause a Point to be labelled in the drawing The first argument is the text of the label It can either be a string in the first version or a short in the second It will often be the name of the Point in the C code for example po It is not possible to automate this kind of labelling because it is not possible to access the names of variables through the variables themselves in C text_str is always placed between btex and etex in the MetaPost label com mand written to out_stream This makes it possible to include math mode material in the text of labels as in the following example Point p0 2 3 p0 label p_0 Figure 101 If backslashes are needed in the text of the label then text_str must contain double backslashes so that single backslashes will be written to out_stream Point P Point Q 2 2 Point R P mediate Q R label overrightarrow PQ ulft Figure 102 The position argument indicates where the text of the
266. r of the Circle The default value is 16 however if it is used foreshortening distorts the most nearly horizontal Circle Increasing the number of points used improves its appearance However there may be a limit to how much improvement is possible See Section 1 5 1 Accuracy page 7 Chapter 8 Solid Figures 47 8 Solid Figures 8 1 Cuboids A cuboid is a solid figure consisting of six rectangular faces that meet at right angles A cube is a special form of cuboid whose faces are all squares The constructor for the class Cuboid follows the pattern familiar from the constructors for the plane figures The first argument is the center of the Cuboid followed by three real arguments for the height width and depth and then three more real arguments for the angles of rotation about the x y and z axes The Cuboid is first constructed with its center at the origin Its width height and depth are measured along the x y and z axes respectively If rotations are specified it is rotated about the x y z axes in that order Finally it is shifted such that its center comes to lie on its Point argument if the latter is not the origin If the width height and depth arguments are equal the Cuboid is a cube Cuboid cO origin 3 3 3 0 30 cO draw Figure 37 In the following example the Cuboid is filldrawn so that the lines dilineating the hidden surfaces of the Cuboid are covered Cuboid ci origin 3 4 5 O
267. r r solve_quadratic 1 6 8 gt r first 2 gt r second 4 real_pair r solve_quadratic 1 2 4 gt r first INVALID_REAL gt r second INVALID_REAL 38 1 Perspective Functions void persp_O const real front_corner_x const real Function front_corner_z const real side_1ft const real side_rt const real angle_rt const real f_2_cv const real gl_2_cv const real horizon_1ft 6 real horizon_rt 0 real gl_1ft 0 real gl_rt 01111 Defined in utility web This function is used for the figure in Section 9 1 2 The Perspective Projection page 60 illustrating a perspective projection as it could be done by hand It draws a rectangle in the ground plane and the construction lines used for putting it into perspective It also labels the vanishing and measuring points The arguments const real front_corner_x The x coordinate of the front corner of the rectangle const real front_corner_z The z coordinate of the front corner of the rectangle const real side_lft The length of the left side of the rectangle const real side_rt The length of the right side of the rectangle Chapter 38 Utility Functions 272 const real angle_rt The angle at which the right side of the rectangle recedes to the horizon const real f 2 cv The distance from the focus to the center of vision const real gl_2_cv The distance of the ground line to the center of vision const real horizon_lft Default 6
268. r translated into another language A Secondary Section is a named appendix or a front matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document s overall subject or to related matters and contains nothing that could fall directly within that overall subject Thus if the Document is in part a textbook of mathematics a Secondary Section may not explain any mathematics The relationship could be a matter of historical connection with the subject or with related matters or of legal commercial philosophical ethical or political position regarding them The Invariant Sections are certain Secondary Sections whose titles are designated as being those of Invariant Sections in the notice that says that the Document is released Appendix A GNU Free Documentation License 283 under this License If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant The Document may contain zero Invariant Sections If the Document does not identify any Invariant Sections then there are none The Cover Texts are certain short passages of text that are listed as Front Cover Texts or Back Cover Texts in the notice that says that the Document is released under this License A Front Cover Text may be at most 5 words and a Back Cover Text may be at most 25 words A Transparent copy of the Document means
269. re so that operations can be applied to them as a group default_focus set 7 5 10 7 5 10 10 Cuboid cO origin 5 5 5 cO shift 0 0 3 cO draw Circle z0 c0 get_rectangle_center 0 2 5 90 O O 64 Chapter 9 Pictures 56 zO draw Circle z1 z0 z1 shift 0 0 1 zi draw int i int j z0 get_size for i 0 i lt 8 i z0 get_point i j 8 draw z1 get_point i j 8 Cuboid c1 c0 get_rectangle_center 4 5 3 3 ci shift 0 2 5 ci draw Rectangle r0 cl get_rectangle_ptr 3 Point p 10 for i 0 i lt 4 i pli r0 get_point i p 4 r0 get_mid_point 0 p 5 r0 get_mid_point 2 p 6 p 4 mediate p 5 2 3 0 Circle z2 p 6 2 90 90 O 16 z2 draw Circle z3 z2 z3 shift 3 z3 draw j z2 get_size for i 0 i lt 8 i z2 get_point i j 8 draw z3 get_point i j 8 p 7 c0 get_rectangle_center 2 p 7 shift 4 p 8 c0 get_rectangle_center 3 p 8 shift 4 current_picture output current_picture rotate 45 45 current_picture shift 10 0 3 current_picture output Chapter 9 Pictures 57 Figure 52 Let s say the complex object in Fig 52 represents a furnace From the point of view of 3DLDF however it s not an object at all and the drawing consists of a collection of unrelated Cuboids Circles Rectangles and Paths If we hadn t put i
270. reg_polygon_center I don t expect it to be needed in user code very often Dodecahedron d origin 3 d filldraw Point C d get_shape_center Solid REG_POLYGON 1 C dotlabel C Chapter 34 Solid Reference 251 Figure 182 Note that this function will have to be changed if new vectors of Shape pointers are added to class Solid const Point amp get_circle_center const unsigned const virtual functions short s const Point amp get_ellipse_center const unsigned short s const Point amp get_rectangle_center const unsigned short s const Point amp get_reg_polygon center const unsigned short s These functions all return the center of the Shape pointed to by a pointer on one of the vectors of Shapes belonging to the Solid The argument s indicates which element on the vector is to be accessed For example get_rectangle_center 2 returns the center of the Rectangle pointed to by rectangles 2 Cuboid c origin 3 4 5 0 30 c draw for int i 0 i lt 6 i c get_rectangle_center i label i Figure 183 Chapter 34 Solid Reference 252 Getting Shapes The functions in this section all return const pointers to Shape or one of its derived classes Therefore they must be invoked in such a way that the const qualifier is not discarded See the description of get_reg_polygon_ptr below for an example Shape get_shape_ptr const unsigned short const virtual funct
271. result This has the effect of scaling all of the elements of shapes and labels Transform shift real x real y 0 real z 0 Function Performs transform shift x y z and returns the result This has the effect of shifting all of the Shapes and Labels on the Picture Transform shift const Point amp p Function Performs transform shift p and returns the result This has the effect of shifting all of the Shapes and Labels on the Picture by the x y and z coordinates of p Transform rotate const real x const real y 0 const real z Function 0 Performs transform rotate x y z and returns the result This has the effect of rotating all of the elements of shapes and labels Transform rotate const Point amp p0 const Point amp p1 const real Function angle 180 Performs transform rotate p0 p1 angle and returns the result This has the effect of rotating all of the elements of shapes and labels about the line Pop 21 6 Modifying void clear void Function Destroys the Shapes and Labels on the Picture and removes all the Shape pointers from shapes and the Label pointers from labels All dynamically allocated objects Chapter 21 Picture Reference 114 are deallocated namely the Shapes the Labels and the Points belonging to the Labels transform is reset to the identity Transform void reset_transform void Function Resets transform to the identity Transform Transform set_transform const Tr
272. rguments each for the x y and z coordinates of position and direction respectively followed by the real arguments for distance and the angle of rotation Focus f 3 5 5 0 3 0 10 10 Point center 2 0 3 Chapter 9 Pictures 65 Rectangle r center 3 3 r draw current_picture output f Figure 62 Focuses contain two Transforms transform and persp Focus can be located any where in 3DLDF s coordinate system However performing the perspective projection is more convenient if position and direction both lie on one of the major axes and the plane of projection corresponds to one of the major planes transform is the transforma tion which would have this affect on the Focus and is calculated by the Focus constructor When a Picture is output using that Focus transform is applied to all of the Shapes on the Picture maintaining the relationship between the Focus and the Shapes while making it easier to calculate the projection The Focus need never be transformed by transform The actual perspective transformation is stored in persp Focuses can be moved by using one of the setting functions which take the same ar guments as the constructors Currently there are no affine transformation functions for moving Focuses but I plan to add them soon If 3DLDF is used for making animation resetting the Focus can be used to simulate camera movements beginfig 1 Point pos 2 10 3 Point dir 2 10 3 Focus f
273. rived from Solid_Faced See Chapter 36 Cuboid Reference page 258 and Chapter 37 Polyhedron Reference page 260 35 1 Data Members unsigned short faces Protected variable The number of faces of the Solid_Faced unsigned short vertices Protected variable The number of vertices of the Solid_Faced unsigned short edges Protected variable The number of edges of the Solid_Faced Chapter 36 Cuboid Reference 258 36 Cuboid Reference Class Cuboid is defined in cuboid web It is derived from Solid_Faced using public derivation 36 1 Data Members real height Protected variables real width real depth The height width and depth of the Cuboid respectively Please note that height width and depth are conventional terms There are no restrictions on the orientation of a Cuboid 36 2 Constructors and Setting Functions void Cuboid void Default constructor Creates an empty Cuboid void Cuboid const Cuboid amp c Copy constructor Creates a new Cuboid and makes it a copy of c void Cuboid const Point amp c const real h const real w const Constructor real d const real x 0 const real y 0 const real z 0 Creates a Cuboid with center at the origin with height h width w and depth d If x y or z is non zero the Cuboid is rotated by the amounts indicated around the corresponding main axes Finally the Cuboid is shifted such that center comes to lie at c Po
274. rote it to pspglb h it would be included by all of the CWEB files except for loader web causing unnecessarily bloated object code The other reason is because of the way way 3DLDF is built using Automake and make I originally tried to define get_second_largest in pspglb web and wrote the definition to gsltmplt cc which is no problem with CWEB However I was unable to express the dependencies among the CWEB C and object files in such a way that 3DLDF was built properly Therefore all template functions will be put into files either by themselves or in small groups 15 1 Endianness signed short get_endianness const bool verbose false Function Returns the following values 0 if the processor is little endian 1 if the processor is big endian 1 if the endianness cannot be determined It is called by is_little_endian and is_big_endian If verbose is true messages are printed to standard output This function has been adapted from Harbison Samuel P and Guy L Steele Jr C A Reference Manual pp 163 164 This book has the clearest explanation of endianness that I ve found so far This is the C code Signed short System get_endianness const bool verbose union long Long char Char sizeof long u u Long 1 if u Char 0 1 if verbose Chapter 15 System Information 86 cout lt lt Processor is little endian lt lt endl lt lt endl lt lt
275. round_color by default This makes it possible to unfill the Path while drawing the outline with a visible Color On the other hand it also makes it necessary to specify Colors background_color or Colors white if the user wants to use the dash pattern and or pen arguments without drawing the Path pa fill gray q unfilldraw white pensquare xscaled 3mm yscaled imm Figure 18 Chapter 6 Paths 35 The following example demonstrates the use of unfilldraw with black as its Color argument Unfortunately it also demonstrates one of the limitations of the surface hiding algorith The line from pO to p1 is hidden by the filled Path pa Since the portion of pa covered by Path q has been unfilled pop should be visible as it passes through q However from the point of view of 3DLDF there is no relationship between pa and q nor does it know whether a Path has been filled or unfilled If it s on a Picture it will hide objects lying behind it unless the surface hiding algorithm fails for another reason See Section 9 3 Surface Hiding page 67 for more information p0 draw p1 pa fill gray q unfilldraw black pensquare xscaled 3mm yscaled 1mm Figure 19 See Section 26 12 Paths Drawing and Filling page 180 for more information and complete descriptions of the functions Chapter 7 Plane Figures 36 7 Plane Figures 3DLDF currently includes the following classes representing plane ge
276. rror message which said that landscape would be ignored When I called dvips with the t landscape option alone it worked and Ghostview showed the entire drawing Another problem was Adobe Acrobat It would display the entire DIN A3 page but not always in landscape format I was unable to find a way of rotating the pages in Acrobat I finally found out that if I included even a single letter of text in a label Acrobat would display the document correctly 11 2 1 Converting EPS Files ImageMagick http www imagemagick org is a collection of tools and libraries for image manipulation It provides a convert utility which can convert images from one for mat to another It can convert structured PostScript PS to to Portable Network Graph ics PNG http www libpng org pub png index htm1 but not EPS Encapsulated PostScript to PNG Nor can it convert EPS to structured PostScript It is possible to have MetaPost generate structured PostScript directly by including the command prologues 1 at the beginning of the MetaPost input However this generally doesn t work when you use T X fonts This is a significant problem if your labels contain math mode material and you haven t already taken steps to ensure that appropriate fonts will be used in the PS output In the following I describe the only way I ve found to convert an EPS image to PNG format while still using TFX fonts There may be other and be
277. rue the default then project is called thereby generating Chapter 22 Point Reference 128 values for projective_coordinates If do_persp is false then projective_ coordinates or one of its elements is returned unchanged which may some times be useful const bool do_apply If true the default apply_transform is called thereby updating the world_coordinates Otherwise it s not so that the values stored in world_coordinates remain unchanged Note that if coords is p and do_persp is true apply_transform will be called in project whether do_apply is true or false If for some reason one wanted get projective_coordinates or one of its values based on the projection of world_coordinates without first updating them one would have to call reset_transform before calling one of these functions It would probably be a good idea to save transform before doing so Focus f Indicates what Focus is to be used for projection Only relevant if coords is p i e projective_coordinates or one of its elements is to be returned The default is 0 in which case f points to the global variable default_focus const unsigned short proj Indicates what form of projection is to be used Only relevant if coords is p i e projective_coordinates or one of its elements is to be returned The default is Projections PERSP which causes the perspective projection to be applied real factor Passed to project The valu
278. ruel Creates a Color and makes it a copy of c If n is not the empty string and u is true use_name is set to true Otherwise its set to false void Color const string n const unsigned short r const Constructor unsigned short g const unsigned short b const bool u true Creates a Color with name n Its red_part green_part and blue_part are set to r 255 0 g 255 0 and b 255 0 respectively use_name is set to u void set const string n const unsigned short r const Setting function unsigned short g const unsigned short b const bool u false Corresponds to the constructor above except that u is false by default void Color const real r const real g const real b Constructor Creates an unnamed Color using the real values r g and b for its red_part green_ part and blue_part respectively Chapter 16 Color Reference 89 void set const real r const real g const real b Setting function Corresponds to the constructor above Color create_new lt Color gt const Color c Template specializations Color create_new lt Color gt const Color amp c Pseudo constructors for dynamic allocation of Colors They create a Color on the free store and allocate memory for it using new Color They return a pointer to the new Color If c is a non zero pointer or a reference the new Color will be a copy of c If the new object is not meant to be a copy of an existing one 0 must be passed to create_ new lt Co
279. ry to store the information that a Path is a line Point A 2 2 5 1 Point B 3 2 2 5 Path p A B p show p 4 p 2 2 5 1 3 2 2 5 1 Stroustrup The C Programming Language p 96 2 It isn t sufficient to check whether a Path consists of only two Points to determine whether it is a line or not since a connector with curl could cause it to be non linear On the other hand Paths containing only colinear Points and the connector are perfectly legitimate lines I m in the process of changing all of the code that tests for linearity by checking the value of line_switch so that it uses is_linear instead When I ve done this it may be possible to eliminate line_switch See Section 26 1 Path Reference Data Members page 165 and Section 26 15 Path Reference Querying page 194 Chapter 26 Path Reference 168 Figure 110 void set const Point amp p0 const Point amp p1 Setting function Corresponds to the constructor above Point PO t 2 3 Point P1 3 5 12 75 Path q q set PO P1 q show q 4d q 1 2 3 3 5 12 75 void Path string connector bool cycle Point p 0 Constructor For Paths with an arbitrary number of Points and one type of connector connector is passed unchanged to out_file so it must be a valid connector in Meta Post cycle indicates whether the Path is a cycle or not cycle_switch is set to cycle See Section 26 1 Path R
280. s help_color string ddashed string ppen Picture amp picture current_picture l Path draw_help Picture amp picture const Point amp p const Color amp Function ddraw_color Colors help_color string ddashed string ppen 1 Draws a help line from this to p but only if the static Path data member do_help_lines is true See Section 26 1 Path Reference Data Members page 165 Help lines are lines that are used when constructing a drawing but that should not be printed in the final version Path drawarrow const Point amp p const Color amp ddraw_color Function Colors default_color string ddashed string ppen Picture amp picture current_picture Path drawarrow Picture amp picture const Point amp p const Color amp Function ddraw_color Colors default_color string ddashed string ppen Draws an arrow from this to p and returns the Path this p The second version is convenient for passing a Picture argument without having to specify all of the other arguments Point P 3 2 1 Point Q 3 3 5 P drawarrow Q Figure 100 22 19 Labelling Labels make it possible to include T X text within a drawing Labels are implemented by means of class Label The functions label and dotlabel described in this section create objects of type Label and add them to the Picture which was passed to them as Chapte
281. s and Rendering Shadows and reflections are closely related to transformations and projections A shadow is the projection of the outline of an object onto a surface or surfaces and reflection in a plane is an affine transformation 3D rendering software generally implements shadows or more generally shading reflec tions and certain other effects using methods involving the calculation of individual pixel values Surface hiding is also often implemented at the pixel level 3DLDF does no scan converting see Section 1 5 1 Accuracy page 7 and hence no calculation of pixel values at all so these methods cannot be used in 3DLDF at present However it is possible to define functions for generating shadows and reflections within 3DLDF by other means I have defined the function Point reflect for reflecting a Point in a Plane and have begun definining versions for other classes However in order for reflections to work I must define functions for breaking up objects into smaller units This is also necessary for surface hiding to work properly For MetaPost output I will have to implement shadows reflections and surface hiding in this way However 3DLDF could be made to produce output in other formats There are two possibilities implementing rendering functionality within 3DLDF or interfacing to 3 Huw Jones Computer Graphics through Key Mathematics and David Salomon Computer Graphics and Geometric Modeling are my main
282. s a copy of the Path on the free store puts a pointer to the copy onto picture shapes sets its fill_draw_value to FILLDRAW its draw_color and fi11_ color to ddraw_color and ffill_color respectively its dashed to ddashed and its pen to ppen The second version is convenient for passing a Picture argument without having to specify all of the other arguments The arguments are similar to those of draw and fill except that both ddraw_color and ffill_color are used 3DLDF s filldraw differs from Metafont s and MetaPost s filldraw commands In Metafont and MetaPost filldrawing is equivalent to filling a path and then drawing its border using the pen Metafont does not have colors While MetaPost does its filldraw command does not foresee the use of different colors for drawing and filling p filldraw black gray pencircle scaled 2mm Chapter 26 Path Reference 188 Figure 130 It can often be useful to draw the outline of a Path but to have it hide objects that lie behind it This is why the default for ffill_color is Colors background_color default_focus set 3 0 10 3 10 10 10 Point pl 8 plo p 1 p 2 p 3 p 4 p 5 p 6 p 7 set 1 1 5 p 11 p 2 p 3 p 4 p 5 x p 6 p 7 rotate 0 0 45 p 21 p 31 p 4 x p 5 p 6 p 7 rotate 0 0 45 p 3 p 4 p 5 pl6 p 7 rotate 0 0 45 p 4 p 5 p 6 p 7 rotate 0
283. s based on a plane tessellation I plan to add more soon unsigned int hex_pattern_1 real diameter_outer 5 real Function diameter_middle 0 real diameter_inner 0 unsigned short first_row 5 unsigned short double_rows 10 unsigned short row_shift 2 Color draw_color_outer Colors default_color Color fill_color_outer Colors background_color Color draw_color_middle Colors default_color Color fill_color_middle Colors background_color Color draw_color_inner Colors default_color Color fill_color_inner Colors background_color string pen_outer pencircle scaled 5mm string pen_middle pencircle scaled 3mm string pen_inner pencircle scaled 3mm Picture amp picture current_picture unsigned int max_hexagons 1000 l JIIJJIII Draws a pattern consisting of hexagons forming a tesselation of the x z plane with additional hexagons within them The arguments real diameter_outer Default 5 The diameter of the outer hexagon in each set of three hexagons The outer hexagons form a tessellation of the plane real diameter_middle Default 0 The diameter of the middle hexagon in a set of three hexagons real diameter_inner Default 0 The diameter of the inner hexagon in a set of three hexagons unsigned short first_row Default 5 The number of sets of hexagons in the first single row The second single row will have first_row 1 sets of hexagons unsigned s
284. s described in Sec tion 22 9 Returning Coordinates page 127 Point P 1 3 5 P rotate 15 67 98 P show P 4 P 3 68621 3 89112 2 50421 void show_transform string text Function Prints text to standard output stdout or transform if text is the empty string the default and then calls transform show Point A 1 1 1 Point B 13 12 6 Point Q 31 17 31 6 Q rotate A B 32 Q show_transform Q transform 4 Q transform Transform 0 935 0 212 0 284 0 0749 0 902 0 426 0 346 0 377 0 859 0 336 0 687 0 569 POOO Chapter 22 Point Reference 150 22 21 Outputting ostream amp operator lt lt ostream amp o Point amp p Non member function Used in Path output for writing the x and y values of the projective_ coordinates of Points to out_stream See Section 26 16 Path Reference Outputting page 197 This is a low level function that ordinary users should never have to invoke directly void output void Function Writes the MetaPost code for drawing or undrawing a Point to out_stream Called by Picture output when a Shape on the Picture is a Point See Section 21 8 Picture Reference Outputting page 114 void suppress_output void Virtual function Sets do_output to false which causes a Point not to be output This function is called in Picture output when a Point cannot be projected See Section 21 8 Picture Reference Outputting page 114 virtu
285. s such following pages as are needed to hold legibly the material this License requires to appear in the title page For works in formats which do not have any title page as such Title Page means the text near the most prominent appearance of the work s title preceding the beginning of the body of the text A section Entitled XYZ means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language Here XYZ stands for a specific section name mentioned below such as Acknowledgements Dedications Endorsements or History To Preserve the Title of such a section when you modify the Document means that it remains a section Entitled XYZ according to this definition The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document These Warranty Disclaimers are considered to be included by reference in this License but only as regards disclaiming warranties any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License 2 VERBATIM COPYING You may copy and distribute the Document in any medium either commercially or noncommercially provided that this License the copyright notices and the license notice saying this License applies to the Document are reproduced in all copies and Appendix A
286. s to these functions are of type real As you may know there is no such data type in C I have defined real using typedef to be either float or double depending on the value of a preprocessor switch for conditional compilation 3DLDF uses many real values and I wanted to be able to change the precision used by making one change in the file pspglb web rather than having to examine all the places in the program where float or double are used Unfortunately setting real to double currently doesn t work 3 1 Shifting The function shift adds its arguments to the corresponding world_coordinates of a Point In the following example the function show is used to print the world_ coordinates of pO to standard output Point p0 0 O O pO shift 1 2 3 p0 show p0 4 p0 1 2 3 pO shift 10 0 show p0 p0 11 2 3 p0 shift 0 20 0 show p0 po 11 22 3 p0 shift 0 0 30 0 show p0 gt 4 pO 11 22 33 1 Affine transformations are operations that have the property that parallelity of lines is maintained That is if two lines each determined by two points are parallel before the transformation they will also be parallel after the transformation Affine transformations are discussed in many books about computer graphics and geometry For 3DLDF I ve mostly used Jones Computer Graphics through Key Mathematics and Salomon Computer Graphics and Geometric Modeling N I try to
287. s were generated For some reason GCC 3 3 has difficulty with them It works to generate them in batches of about 50 with GCC 3 3 MetaPost outputs Encapsulated PostScript files These can be included in T X files as explained below However in order to display the illustrations in the HTML ver sion of this manual I had to convert them to PNG Portable Network Graphics for mat http www libpng org pub png index html See Section 11 2 1 Converting EPS Files page 77 for instructions on how to do this Please note that the illustrations cannot be shown in the Info output format If you have problems including the illustrations in the printed version for example if your installation doesn t have dvips look for the following lines in 3DLDF texi doepsftrue hh One of these two lines should be commented out 4 doepsffalse Now remove the W from in front of doepsffalse and put one in front of doepsftrue This will prevent the illustrations from being included This should only be done as a last resort however because it will make it difficult if not impossible to understand this manual The C code in an example is not always the complete code used to create the illustra tion that follows it since the latter may be cluttered with commands that would detract from the clarity of the example The actual code used always follows the example in the Texinfo source file so the latter may be referred
288. se Path draw_color is protected and the Solid cannot access it directly See Section 34 13 Solid Reference Drawing and Filling page 255 void set_fill_color const Color amp c Virtual function void set_fill_color const Color c Virtual function Sets ill_color a pointer to a const Color to amp c or c depending on whether the version with a reference argument or the version with a pointer argument is used set_fill_color is used in the Solid drawing and filling functions because Path fill_color is protected and the Solid cannot access it directly See Section 34 13 Solid Reference Drawing and Filling page 255 void set_dash_pattern const string s Virtual function Sets dashed to s void set_pen const string s Virtual function Sets pen to s void set_connectors const string s Virtual function Clears connectors and then pushes s onto it making s the only connector Ad ditional connectors can be added by using Path operator const string See Section 26 4 Path Reference Operators page 171 I plan to add a version of this function taking a vector of strings as its argument to make it possible to set several connectors at one time 26 9 Affine Transformations Transform rotate const real x const real y 0 const Virtual function real z 0 Creates a Transform t locally and calls t rotate x y z t is then applied to all of the Points on points The return val
289. sformations Transform scale real x real y 0 real z 0 Virtual functions Solid Transform shear real xy real xz 0 real yx 0 real yz 0 real zx 0 real zy 0 Transform shift real x real y 0 real z O Transform shift const Point amp pt Transform rotate const real x const real y 0 const real z 0 Transform rotate const Point amp p0 const Point amp p1 const real angle 180 These functions perform the corresponding transformations on all of the Shapes be longing to the Solid See Section 19 10 Transform Reference Affine Transforma tions page 101 34 11 Applying Transformations void apply_transform void Virtual function Calls apply_transform on all of the Shapes belonging to the Solid 34 12 Outputting The functions in this section are are called directly or indirectly by Picture output See Section 21 8 Picture Reference Outputting page 114 void output void Virtual function Writes the MetaPost code for drawing filling filldrawing undrawing unfilling or unfilldrawing the Solid to out_stream void suppress_output void Virtual function Used in Picture output Sets do_output to false if the Solid cannot be projected using a particular set of arguments to Picture output void unsuppress_output void Virtual function Used in Picture output Resets do_output to true so that the Solid will be tested for projectability again
290. sion this is copied clean is called on the copy and the elements of the copy s matrix are compared with 0 and 1 real get_element const unsigned short row const unsigned const function short col Returns the value stored in the element of matrix indicated by the arguments Transform t t shift 1 2 3 Chapter 19 Transform Reference 100 t scale 2 5 1 2 4 t rotate 30 15 60 t show t 4 t 1 21 2 09 0 647 0 0 822 0 654 0 58 0 2 18 0 224 3 35 0 3 69 1 45 11 8 1 cout lt lt t get_element 2 1 0 224 19 8 Returning Information real epsilon void Static function Returns the positive real value of smallest magnitude e which an element of a Transform should contain An element of a Transform may also contain e The value e is used for in the function clean see Section 19 13 Transform Refer ence Cleaning page 107 It will also be used for comparing Transforms when I ve added the equality operator Transform operator epsilon returns different values depending on whether real is float or double If real is float the default epsilon returns 0 00001 If real is double it returns 0 000000001 Please note I haven t tested whether 0 000000001 is a good value yet so users should be aware of this if they set real to double The way to test this is to transform two different Transforms t and t using different rotations in such a way that the end result should be the sa
291. sion curl or controls The solution is to use enough Points since a greater number of Points on a Path tends to reduce the number of possible courses through the Points 6 1 Declaring and Initializing Paths There are various ways of declaring and initializing Paths The simplest is to use the constructor taking two Point arguments Point A Point B 2 2 Path p A B p draw 1 I believe that counter examples could probably constructed but for the most common cases the principle applies Chapter 6 Paths 29 Figure 9 Paths created in this way are important because they are guaranteed to be linear as long as no operations are performed on them that cause them to become non linear Linear Paths can be used to find intersections See Section 26 17 Path Intersections page 198 Paths can be declared and initialized using a single connector and an arbitrary number of Points The first argument is a string specifying the connector It is followed by a bool indicating whether the Path is cyclical or not Then an arbitrary number of pointers to Point follow The last argument must be 0 Point p 3 p 0 shift 1 pli set 1 2 2 p 21 set 1 0 2 Path pa true amp p 0 amp p 1 amp p 2 0 pa draw Figure 10 Another constructor must be used for Paths with more than one connector and an arbitrary number of Points The argument list starts with a pointer to Point followed by string for t
292. sn t remember what the default is for that label draw_axes 0 bot rt current_picture output Projections PARALLEL_X_Y Figure 126 In addition the arguments shift_x shift_y and shift_z can be used to adjust the positions of the labels further see below ddraw_color ddashed ppen Arguments for the drawarrow command described above in this sec tion shift_x shift_y shift_z Offsets for the labels These arguments make it possible to adjust the positions of the labels The defaults are origin so no shifting takes place if they are used In Fig 127 draw_axes is called without any arguments so the defaults are used draw_axes 7 The usual interpretation of as a position argument to a labelling command would be to put it directly onto Label pt which in this case would put it onto the arrowhead Since this will probably never be desirable I ve decided to use to suppress drawing axes Formerly draw_axes used three additional arguments for this purpose Chapter 26 Path Reference 186 Ya Y gt Figure 127 In Fig 128 the Point P is used to shift the labels Please note that placeholders must be used for the first arguments Point P 5 5 5 draw_axes 0 ta ait gr black HN waen P P P Figure 128 Please note that the Points used for placing the labels are three dimensional Points whether the shift_x shift_y and or shift_z
293. st real dir_z const real dist const real ang 0 char ax z Constructs a Focus using the first three real arguments as the x y and z coordinates of position and the fourth through the sixth argument as the x y and z coordinates of direction dist specifies the distance of the Focus from the plane of projection ang the angle of rotation which affects which direction is considered to be up and ax the major axis to which the Focus is aligned void set const real pos_x const real pos_y const real Setting function pos_z const real dir_x const real dir_y const real dir_z const real dist const real ang 0 char ax z Resets an existing Focus Corresponds to the constructor above void Focus const Point amp pos const Point amp dir const real Constructor dist const real ang 0 char ax z Constructs a Focus using Point arguments for position and direction Otherwise the arguments of this constructor correspond to those of the one above void set const Point amp pos const Point amp dir const real Setting function dist const real ang 0 char ax z Resets an existing Focus Corresponds to the constructor above 23 4 Operators const Focus amp operator const Focus amp f Assignment operator Sets the Focus to f Chapter 23 Focus Reference 153 23 5 Modifying void reset_angle const real ang Function Resets the value of angle and recalculates the
294. t Point amp get_last_point void const function Returns the Point pointed to by the last pointer on points Equivalent to get_ point get_size 1 but more convenient to type Returns INVALID_POINT if the Path is empty size_t get_size void const inline virtual function Returns points size Line get_line void const function Returns a Line corresponding to the Path if the latter is linear Otherwise INVALID_ LINE is returned See Chapter 24 Line Reference page 154 Point get_normal void const virtual function Returns a Point representing a unit vector in the direction of the normal to the plane of the Path or INVALID_POINT if the Path is non planar Point P 1 1 1 Rectangle r P 4 4 30 30 30 Point N r get_normal Figure 136 In 3DLDF plane figures generally have constructors taking a Point argument for the center a variable number of real arguments for the dimensions and three real arguments for the rotation about the major axes The object is first created in the x z plane and the Points are generated to be traversed in the counter clockwise direction when seen from a Point with a positive y coordinate If no rotation is specified the normal will point in the direction of the positive y axis If non zero arguments are used for rotation the normal will be rotated accordingly This direction considered to be outside However according to Huw Jones Computer Graphics Through K
295. t into a Picture we could still have rotated and shifted it but only by applying the operations to each of the sub objects individually One consequence of the way Pictures are output in 3DLDF is that the following code will not work beginfig 1 Point p 1 2 Point q 1 3 out_stream lt lt pickup pencircle scaled 5mm lt lt endl origin draw p out_stream lt lt pickup pensquare xscaled 3mm rotated 30 lt lt endl origin draw q current_picture output endfig This is the MetaPost code that results beginfig 1 pickup pencircle scaled 5mm pickup pensquare xscaled 3mm rotated 30 Chapter 9 Pictures 58 draw 0 000000cm 3 000000cm 1 000000cm 1 000000cm draw 0 000000cm 3 000000cm 1 000000cm 0 000000cm endfig It s perfectly legitimate to write raw MetaPost code to out_stream as in lines 4 and 6 of this example However the draw commands do not cause any output to out_ stream The MetaPost drawing commands are written to out_stream when current_ picture output is called Therefore the pickup commands are bunched up before the drawing commands In this example setting currentpen to pencircle scaled 5mm has no effect because it is immediately reset to pensquare xscaled 3mm rotated 30 in the MetaPost code before the draw commands It is not possible to change currentpen in this way within a Picture Since the draw commands in the 3DLDF code didn t s
296. t is not meant to be a copy of an existing one 0 must be passed to create_ new as its argument create_new is called like this Point p create_new lt Point gt 0 p gt show p p 0 0 0 Color c 3 5 25 Color d create_new lt Color gt c d gt show d 4 d name use_name 0 red_part 0 3 green_part 0 5 blue_part 0 25 Point a0 3 2 5 6 Point a1 10 11 14 Path q a0 al Path r create_new lt Path gt amp q r gt show r 4 r points size connectors size 3 2 5 6 10 11 14 Specializations of this template function are currently declared for Color Point Path Reg_Polygon Rectangle Ellipse Circle Solid and Cuboid Chapter 15 System Information 85 15 System Information The functions described in this chapter are all declared in the namespace System They are for finding out information about the system on which 3DLDF is being run They are declared and defined in pspglb web except for the template function get_second_ largest which is declared and defined in gsltmplt web There are two reasons for this The first is that template definitions must be available in the compilation units where specializations are instantiated I therefore write the template definition of get_second_largest to gsltmplt h so it can be included by the CWEB files that need it currently main web only If I w
297. t2 const Point amp pt3 Corresponds to the constructor above Rectangle create_new lt Rectangle gt const Template specializations Rectangle r Rectangle create_new lt Rectangle gt const Rectangle amp r Pseudo constructors for dynamic allocation of Rectangles They create a Rectangle on the free store and allocate memory for it using new Rectangle They return a pointer to the new Rectangle If r is a non zero pointer or a reference the new Rectangle will be a copy of r If the new object is not meant to be a copy of an existing one 0 must be passed to create_new lt Rectangle gt as its argument See Chapter 14 Dynamic Allocation of Shapes page 84 for more information 29 3 Operators const Rectangleg operator const Rectangle amp r Assignment Operator Makes the Rectangle a copy of r Chapter 29 Rectangle Reference 213 29 4 Returning Points Point corner unsigned short c Function Returns the corner Point indicated by the argument c which must be between 0 and 3 Point mid_point unsigned short m const function Returns the mid point of one of the sides The argument c must be between 0 and 3 29 5 Querying real get_axis_h void const functions real get_axis_v void These functions return axis_h and axis_v respectively Please note that axis_h and axis_v are currently not recalculated when a Rectangle is transformed I plan to do something about this soon bool is_rectangular voi
298. te eara 165 linear_eccentricity 00 222 M MAGN GAs is tee foe ht a Ae ath ele ts 91 mati sa ota ee Al 96 MACIAS 81 MAX REAL 3 in aid o E genie settee 82 MAX REAL SQRT Si e eens ae 83 MAK ra AS ES AnS aa 115 MEANE Zoco rado e N A ra oad deba A toes 115 measurement_UNitS cece cece ee 120 measurement_units Point 10 MIN o ane akan es ad 115 N HAMS er bb tes ou oros ida 88 NO SORT 22st ates e cea e te es esate 115 DOTA Ss sess a eas eS ee to A eae Aha 157 null_coordinates ooooooooooooo 82 number of points carie erres Enri ena 216 number_of_polygon_types 260 numerical_eccentricity 222 O on_free_store 88 119 166 205 211 248 OVEN GE s vices ee pease ts ha ea heals a ee tore T 91 orango TEAN ie tics cisiesns tetrad ats pl een 91 on aB RING 2 6 tect eae winks bea mene reid beet coe ies 122 DUETO AM o ek os Pe ah holed 54 92 290 P PARALLEL X Y recs da ck dida dd ds cdas 114 PARALLEL X Z pag ais td ur las daa laa atts Tutte ase 114 PARALLEL IZ Y necia a dis 114 Pathe ss 2c ted A ba le 28 165 PATH Saa a ada 248 A de eee ek ee ae a Bh 248 POU eee cle he Soha oe ig o 120 166 pentagon_radius cee eee ee eae 264 POTS Pen siete Ris a aee A EE Be Daeg deen 151 PERS titi EE E EE nue ve EAER ENEE 114 E niyun Sao 82 PL CEUL E yest seek oE tias 54 111 Peres a ada ad opty agp 91 PUAN C32 a da 157 Point aeee ete
299. ted by Donald E Knuth for generating fonts in particular for use with TFX his well known typsetting system Expressed in a somewhat simplified way Metafont is a system for programming curves which are then digitized and output in the form of run time encoded bitmaps See Knuth s The Metafontbook for more information John D Hobby modified Metafont s source code to create MetaPost which functions in much the same way but outputs encapsulated PostScript EPS files instead of bitmaps MetaPost is very useful for creating graphics and is a convenient interface to PostScript It is also easy both to imbed T X code in MetaPost programs for instance for typesetting labels and to include MetaPost graphics in ordinary TFX files e g by using dvips Apart from simply printing the PostScript file output by dvips there are many programs that 3 Knuth Donald E The T Xbook Computers and Typesetting A Addison Wesley Publishing Company Reading Massachusetts 1986 S Rokicki Tomas Dvips A DVI to PostScript Translator February 1997 Available from CTAN See Section 1 1 Sources of Information page 1 Chapter 1 Introduction 7 can process ordinary or encapsulated PostScript files and convert them to other formats Just two of the many possibilities are ImageMagick and GIMP both of which can be used to create animations from MetaPost graphics However MetaPost inherited a significant limitation from Metafont it s not possible to
300. ten in C in main web or some other file and compiled Then 3DLDF must be relinked together with the new file of object code resulting from the compilation For now the important point is that the text of the examples in this manual represent C code See Chapter 11 Installing and Running 3DLDF page 74 for more information Chapter 2 Points 10 2 Points 2 1 Declaring and Initializing Points The most basic drawable object in 3DLDF is class Point It is analogous to pair in 6679 Metafont For example in Metafont one can define a pair using the z syntax as follows zO 1cm 1cm There are other ways of defining pairs in Metafont and MetaPost but this is the usual way In 3DLDF a Point is declared and initialized as follows Point ptO 1 2 3 This simple example demonstrates several differences between Metafont and 3DLDF First of all there is no analog in 3DLDF to Metafont s z syntax If I want to have Points called pto pt1 pt2 etc then I must declare each of them to be a Point Point pto 10 15 2 Point pti 13 41 5 5 Point pt2 62 9 7 02 8 Alternatively I could declare an array of Points Point pt 3 Now I can refer to pt 0 pt 1 and pt 2 In the Metafont example the x and y coordinates of the pair z0 are specified using the unit of measurement in this case centimeters This is currently not possible in 3DLDF The current unit of measurement is
301. the intersection points of a line with an Ellipse In the first version the line is specified by the two Point arguments In the second version p is_linear must return true otherwise intersection_points issues an error message and returns INVALID_BOOL_POINT_PAIR If the line and the Ellipse are coplanar there can be at most two intersection points Otherwise there can be at most one Ellipse e origin 5 7 30 30 30 Chapter 31 Ellipse Reference 231 e shift 3 0 3 Point pO e get_center mediate e get_point 3 Point normal e get_normal Point A normal A 2 5 A shift p0 Point B normal B x 2 5 B shift p0 bool_point_pair bpp e intersection_points A B bpp first pt dotlabel i_0 rt Point C e get_point 15 mediate e get_point 11 1 25 Point D e get_point 11 mediate e get_point 15 1 5 Path q C draw D bpp e intersection_points q bpp first pt dotlabel i_1 1llft bpp second pt dotlabel i_2 ulft Figure 167 bool_point_quadruple intersection_points Ellipse const virtual function e const real step 3 bool verbose false Returns the intersection points of two Ellipses Two Ellipses can intersect at at most four points Let bpq be the boo1_point_quadruple returned by intersection_points If one or more intersection points are found the corresponding Points are stored in the pt elements of the four bool_points belonging to
302. tical axis Ellipse e origin 5 2 90 e draw Point P e angle_point 35 cout lt lt P get_x P get_x e get_axis_h 2 e get_axis_h 2 P get_yO P get yO e get_axis_v 2 e get_axis_v 2 P 24007 0 868307 Figure 163 bool is_cubic void const virtual functions bool is_quartic void These functions both return false because the equation of an ellipse is neither a cubic nor a quartic function 31 8 Returning Elements and Information Point amp get_center void Virtual function Point get_center void const virtual function These functions return center const Point amp get_focus const unsigned short s Function Point get_focus const unsigned short s const function These functions return focusO or focus1 depending on the value of s which must be 0 or 1 If s is not 0 or 1 get_focus returns INVALID_POINT Chapter 31 Ellipse Reference 228 real get_linear_eccentricity void const function Returns linear_eccentricity real get_numerical_eccentricity void const function Returns numerical_eccentricity real get_axis_v void Function real get_axis_v void const function Calculates and returns the value of axis_h get_axis_v first checks if the Ellipse is still elliptical using is_elliptical O see Section 31 7 Ellipse Reference Querying page 227 Operations such as scale and shear can cause an Ellipse to become non elliptical If this
303. tion Colors default_color const string ppen Picture amp picture current_picturel void drawdot Picture amp picture current_picture const const function Color amp ddrawdot_color Colors default_color const string ppen wu i 11 Draws a dot on picture If ppen is specified a pen expression is included in the drawdot command written to out_stream Otherwise MetaPost s currentpen is used If ddrawdot_color is specified the dot will be drawn using that Color Oth erwise the Color currently pointed to by the pointer Colors default_color will Chapter 22 Point Reference 145 be used This will normally be Colors black See Chapter 16 Color Reference page 88 for more information about Colors and the namespace Colors Please note that the dot will always be parallel to the plane of projection Even where it appears to be a surface as in Fig 96 it is never put into perspective but will always have the same size and shape Point P 1 1 P drawdot gray pensquare scaled 1cm P Figure 96 void undrawdot string pen Picture amp picture Function current_picture void undrawdot Picture amp picture current_picture string pen Function Undraws a dot on picture If ppen is specified a pen expression is included in the undrawdot command written to out_stream Otherwise MetaPost s currentpen is used Point P 1 1 P drawdot gray pensquare sca
304. tiple Inheritance pp 390 92 A Cundy and Rollet Mathematical Models Chapter 3 Polyhedra pp 76 160 Chapter 40 Future Plans 276 40 2 Curves and Surfaces 3D modelling software usually supports the creation and manipulation of various kinds of spline curves B zier curves B splines and non uniform rational B splines or NURBS These curves can be used for generating surfaces paths in Metafont and MetaPost are B zier curves It would be possible to implement three dimensional B zier curves in 3DLDF but unfortunately they are not projectively invariant Let cy represent a B zier curve in three dimensions P the control points of cy and ta projection transformation Further let Q represent the points generated from applying t to P and c the curve generated from Q Finally let R represent the points generated from applying t to all of the points on cg and cy the curve through R c co NURBS on the other hand are projectively invariant so I will probably concentrate on implementing them On the other hand it would be nice to be able to implement Metafont s way of specifying paths using curl tension and dir in 3DLDF This may prove to be difficult or impossible I do not yet know whether Metafont s path creation algorithm can be generalized to three dimensions Curves and surfaces are advanced topics so it may be a while before I implement them in 3DLDF 40 3 Shadows Reflection
305. to pt0 set 34 99 107 5 pt0 show pt0 pt0 34 99 107 5 pt1 show pt1 4 pti 2 3 3 7 In this example pto is initialized with the coordinates 2 3 3 7 and pt1 with the coordinates 0 0 0 pt1 pt0 causes pt1 to have the same coordinates as pt0 then the coordinates of ptO are changed to 34 99 107 5 This doesn t affect pt1 whose coordinates remain 2 3 3 7 Another way of declaring and initializing Points is by using the copy constructor Point ptO0 1 3 5 19 Point pt1 pt0 Point pt2 pt0 Point pt3 pt3 pto Chapter 2 Points 12 In this example pt1 and pt2 are both declared and initialized using the copy constructor Point pt2 pt0 does not invoke the assignment operator pt3 on the other hand is declared using the default constructor and not initialized In the following line pt3 pto does invoke the assignment operator thus resetting the coordinate values of pt3 to those of pto Chapter 3 Transforming Points 13 3 Transforming Points Points don t always have to remain in the same place There are various ways of moving or transforming them e Shifting This is often called translating but the operation in Metafont that performs translation is called shift so I call it shifting e Scaling e Shearing e Rotating about an axis class Point has several member functions for applying these affine transformations to a Point Most of the argument
306. to if the reader wishes to see exactly what code was used to generate the illustration You may want to skip the following paragraphs in this section if you re reading this manual for the first time Don t worry if you don t understand it it s meaning should become clear after reading the manual and some experience with using 3DLDF The file 3DLDF texi in the directory 3DLDF 1 1 5 1 DOC TEXINFO the driver file for this manual contains the following TFX code Chapter 1 Introduction 5 newif ifmakeexamples makeexamplestrue hh One of these two lines should be commented out Nmakeexamplesfalse When texi2dvi is run on 3DLDF texi makeexamplestrue is not commented out and makeexamplesfalse is the C code for the illustrations is written to the file examples web If the EPS files don t already exist in the directory 3DLDF 1 1 5 1 DOC TEXINFO EPS the T X macro PEX which includes them in the Texinfo files will signal an error each time it can t find one Just type s at the command line to tell TEX to keep going If you want to be sure that these are indeed the only errors you can type lt RETURN gt after each one instead texi2dvi 3DLDF texi also generates the file extext tex which contains TX code for including the illustrations by themselves examples web must now be moved to 3DLDF 1 1 5 1 CWEB and ctangled examples c must compiled and 3DLDF m
307. tore bool b true Pure virtual function Sets the data member on_free_store to b All classes derived from Shape must therefore also have a data member on_free_store Chapter 18 Shape Reference 94 This function is used in the template function create_new lt type gt See Chapter 14 Dynamic Allocation of Shapes page 84 for more information 18 5 Affine Transformations Transform rotate const real x const real y const Pure virtual functions real z Transform scale real x real y real z Transform shear real Xy real xz real yx real yz real zx real zy Transform shift real x real y real z Transform rotate const Point amp p0 const Point amp p1 const real r See Section 22 12 Point Reference Affine Transformations page 130 18 6 Applying Transformations void apply_transform void Pure virtual function Applies the Transform stored in the transform data member of the Points belonging to the Shape to their world_coordinates The transforms are subsequently reset to the identity Transform 18 7 Clearing void clear void Pure virtual function The precise definition of this function will depend on the nature of the derived class In general it will call the destructor on dynamically allocated objects belonging to the Shape and deallocate the memory they occupied 18 8 Querying bool is_on_free_store void const pure virtual function Returns true if the object was allocated on the free store other
308. tter ways of doing this but I haven t found them 2 Hobby A User s Manual for MetaPost pp 21 22 Chapter 11 Installing and Running 3DLDF 78 1 Assume the EPS image is in the file 3DLDFmp 1 Include the EPS image in a T X file which looks like this advance voffset by 1in advance hoffset by 1in nopagenumbers input epsf epsfverbosetrue def epsfsize 1 2 1 setbox0 vbox epsffile 3DLDFmp 1 vsize ht0 hsize wd0 special papersize the wd0 the ht0 box0 bye Do not name this file 3DLDFmp 1 tex While this worked fine for me on a DECalpha Personal Workstation running under Tru64 Unix 5 1 with TEX Version 3 1415 C version 6 1 and dvipsk 5 58f it failed on a PC Pentium 11 XEON under Linux 2 4 with TeX Version 3 14159 Web2C 7 4 5 and dvips k 5 92b kpathsea version 3 4 5 with the following error message No BoundingBox comment found in file examples 1 using defaults The resulting PS image had the wrong size and the the graphic was positioned improp erly Apparently it confuses the EPSF macros when the name of an included image is the same as jobname So for this example let s call it 3DLDFmp 1_ tex You don t really need to call the macro epsfverbosetrue If you do it will print the measurements of the bounding box and other information to standard output 2 Run tex 3DLDFmp 1_ tex 3 Run dvips o 3DLDF 1 ps 3DLDFmp 1_ dvi 4
309. two planes intersect with p However it does intersect with p at the labelled Points Point A 1 1 1 Rectangle r A 4 4 Reg_Polygon p A 5 5 Chapter 27 Polygon Reference 204 p rotate 90 30 p shift 4 3 3 vector lt Point gt v r intersection_points p int i 0 for vector lt Point gt iterator iter v begin iter v end iter iter gt dotlabel i bot Figure 144 Chapter 28 Regular Polygon Reference 205 28 Regular Polygon Reference Class Reg_Polygon is defined in polygons web and is derived from Polygon using public derivation As noted above in Section 27 4 Polygon Reference Affine Transformations page 200 class Reg_Polygon like class Rectangle currently inherits its transformation functions and operator const Transform amp from Polygon Consequently the data members of a Reg_Polygon except for center are not recalculated when it s transformed I plan to change this soon It will also be necessary to add the function Reg_Polygon is_reg_ polygonal in order to test whether a Reg_Polygon is still regular and polygonal 28 1 Data Members real internal_angle Private variable The angle at the center of the Reg_Polygon of the triangle formed by the center and two adjacent corners If n is the number of sides of a Reg_Polygon internal_angle will be 360 0 n so internal_angle will be 120 for a regular triangle 90 for a square 72 for a pentagon etc
310. ue is t Transform scale real x real y 1 real z 1 Function Creates a Transform t locally and calls t scale x y z t is then applied to all of the Points on points The return value is t The Points on the Path are scaled according to the arguments Point pt 8 ptlo 1 1 for int i 1 i lt 8 i Chapter 26 Path Reference 175 1 pt il pt 0 pt il rotate 0 0 i 45 Path p true amp pt 0 amp ptli amp pt 2 amp pt 3 amp pt 4 amp pt 5 eptL6l amp pt 7 0 p draw p scale 2 2 p draw Figure 115 Transform shear real xy real xz 0 real yx 0 real yz 0 Function real zx 0 real zy 0 Creates a Transform t locally and calls t shear xy xz yx yZ ZX zy tis then applied to all of the Points on points The return value is t Point po Point p1 1 Point p2 1 1 Point p3 0 1 Path q true p0 p1 amp p2 amp p3 0 rotate 0 45 shift 1 filldraw black light_gray Shear 1 5 2 2 5 3 3 5 5 filldraw black light_gray Q Q Q Q Q Chapter 26 Path Reference 176 3 12132 6 38909 6 68198 4 62132 7 38909 11 682 2 5 3 5 8 5 1 1 0 1 70711 1 0 707107 ee 1 0 0 x Figure 116 Transform shift real x real y 0 real z 0 Function Creates a Transform t locally and calls t shift x y z t is then applied to all of the Points on points The return v
311. ult const Color default_color Points to black by default const Color help_color Points to green by default 91 Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Constant Pointer Pointer Pointer The following vectors of pointers to Color can be used in the drawing and filling functions for Solid see Section 34 13 Solid Reference Drawing and Filling page 255 const vector lt const Color gt default_color_vector Contains one pointer namely default_color const vector lt const Color gt help_color_vector Contains one pointer namely help_color const vector lt const Color gt background _color_vector Contains one pointer namely background_color Vector Vector Vector Chapter 17 Input and Output 92 17 Input and Output 17 1 Global Variables ifstream in_stream Variable Intended for inputting files of input code However 3DLDF does not currently have a routine for reading input code in_stream is currently attached to the file ldfinput ldf by initialize_io see Section 17 2 I O Functions page 92 in_stream is read in character by character in main however this serves no useful purpose as yet ofstream out_stream Variable Used for writing the file of MetaPost code which is 3DLDF s output Currently attached to the file
312. uncated octahedron are derived from Polyhedron There is a great deal of work left to do on the polyhedra 37 1 Data Members unsigned short number_of_polygon_types Protected variable The number of different types of polygon making up the faces of a Polyhedron The Platonic polyhedra have only one type of face while the Archimedean can have more real face_radius Protected variable The radius of the sphere that touches the centers of the polygonal faces of the poly hedron Inkugel in German real edge radius Protected variable The radius of the sphere that touches the centers of the edges of the polyhedron real vertex_radius Protected variable The radius of the sphere touching the vertices of the polyhedron Umkugel in Ger man 37 2 Regular Platonic Polyhedra 3DLDF currently has classes for three of the five regular Platonic polyhedra Tetrahedron Dodecahedron and Icosahedron There is no need for a special Cube class because cubes can be created using Cuboid with equal width height and depth arguments see Chapter 36 Cuboid Reference page 258 Octahedron is missing at the moment but I plan to add it soon 37 2 1 Tetrahedron Class Tetrahedron is defined in polyhed web It is derived from Polyhedron using public derivation 37 2 1 1 Data Members real dihedral_angle Protected static const variable The angle in radians between the faces of the Tetrahedron namely 70 32 Only the Platonic poly
313. ust be relinked ctangle examples also generates the header file example h which is included in main web Therefore if the contents of examples h have changed since the last time main web was ctangled main web will have to be ctangled and main c recompiled before 3d1df is relinked Running 3dldf and MetaPost now generates the EPS Encapsulated PostScript files 3DLDFmp 1 through currently 3DLDFmp 199 for the illustrations They must be moved to 3DLDF 1 1 5 1 DOC TEXINFO EPS Now when texi2dvi 3DLDF texi is run again the dvips command epsffile includes the EPS files for the illustrations in the manual 3DLDF texi includes the line input epsf so that epsffile works Of course dvips or some other program that does the job must be used to convert 3DLDF dvi to a PostScript file To see exactly how this is done take a look at the texi source files of this manual In the 3DLDF texi belonging to the 3DLDF distribution makeexamplestrue will be commented out and makeexamplesfalse won t be because the EPS files for the illustra tions are included in the distribution The version of examples web in 3DLDF 1 1 5 1 CWEB merely includes the files subex1 web and subex2 web If you rename 3DLDF 1 1 5 1 CWEB exampman web to examples web you can generate the illustrations 1 3 CWEB Documentation As me
314. utting this in one of the major planes Point angle_point real angle Virtual function Returns INVALID_POINT Intended to be overloaded by member functions of derived classes 30 3 Intersections bool_point_pair intersection_points Point ref_pt Point const function pO Point p1 bool_point_pair intersection_points const Point amp ref_pt const function const Path amp p The version of this function taking Point arguments finds the intersection points if any of the Reg_C1_Plane_Curve and the line p that passes through the Points Po and p In the other version the Path argument must be a linear Path and its Chapter 30 Regular Closed Plane Curve Reference 218 first and last Points are passed to the first version of this function as p0 and pl respectively Let C be the Reg_C1_Plane_Curve C and p can intersect at at most two intersection points 7 and 22 Let bpp be the return value of this function The intersection points need not be on the line segment between pt0 and pti bpp first pt will be set to the first intersection point if it exists or INVALID_POINT if it doesn t If the first intersection point exists and is on the line segment between pt0 and pt1 In Fig 154 the line AB is normal to the Ellipse e or to put it another way AB is perpendicular to the plane of e The intersection point y lies within the perimeter of e The line DE is skew to the plane of e and intersects e at on the perimeter of e
315. w black current_picture output Projections PARALLEL_X_Y 5 current_picture shift 2 5 current_picture output Projections PARALLEL_X_Y Chapter 9 Pictures 60 current_picture shift 1 current_picture output Projections PARALLEL_X_Y 2 Normal size Figure 55 Parallel projection onto the x z and z y planes are completely analogous to parallel projection onto the x y plane 9 1 2 The Perspective Projection The perspective projection obeys the laws of linear perspective In 3DLDF it is performed by means of a transformation whose effect is to the best of my knowledge exactly equiv alent to the result of a perspective projection done by hand using vanishing points and rulers It is very helpful to the artist to understand the laws of linear perspective and to know how to make a perspective drawing by hand However it is a very tedious and error prone procedure I know I ve done it One of my main motivations for writing 3DLDF was so I wouldn t have to do it anymore Fig 56 shows a perspective construction the way it could be done by hand The point of view or focus is located 6cm from the picture plane and 4cm above the ground or x z plane at the point 0 4 6 The rectangle R lies in the ground plane with the point ro at 2 0 1 5 The right side of R with length 2cm lies at an angle of 40 to the ground line which corresponds to the intersection line of
316. ware package for three dimensional drawing written by Laurence D Finston who is also the author of this manual It is written in C using CWEB and it outputs MetaPost code 3DLDF is a GNU package It is part of the GNU Project of the Free Soft ware Foundation and is published under the GNU General Public License See the website http www gnu org for more information 3DLDF is available for downloading from http ftp gnu org gnu 3dldf The official 3DLDF website is http www gnu org software 3dldf More information about 3DLDF can be found at the author s website http wwwuser gwdg de lfinsto1 Please send bug reports to bug 3DLDF gnu org and Two other mailing lists may be of interest to users of 3DLDF help 3DLDF gnu org is for people to ask other users for help and info 3DLDF gnu org is for sending announcements to users To subscribe send an email to the appropriate mailing list or lists with the word subscribe as the subject The author s website is http wwwuser gwdg de 1finstol My primary purpose in writing 3DLDF was to make it possible to use MetaPost for three dimensional drawing I ve always enjoyed using MetaPost and thought it was a shame that I could only use it for making two dimensional drawings 3DLDF is a front end that operates on three dimensional data performs the necessary calculations for the projection onto two dimensions and writes its output in the form of MetaPost code While 3DLDF s d
317. wise false 18 9 Showing void show string text char coords w const pure virtual function const bool do_persp true const bool do_apply true Focus f 0 const unsigned short proj 0 const real factor 1 Prints information about an object to standard output See the descriptions of show for the classes derived from Shape for more information Chapter 18 Shape Reference 95 18 10 Outputting void output void Pure virtual function Called by Picture output for writing MetaPost code to out_stream for a Shape pointed to by a pointer on the vector lt Shape gt shapes belonging to the Picture Such a Shape will have been created by a drawing or filling function vector lt Shape gt extract const Focus amp f const Pure virtual function unsigned short proj real factor Called in Picture output It determines whether a Shape can be output If it can and an output function for the type of the Shape exists a vector lt Shape gt containing a pointer to the Shape is returned On the other hand it is possible to define a type derived from Shape without an output function of its own and not derived from a type that has one It may then consist of one or more objects of types that do have output functions In this case the vector lt Shape gt returned by extract will contain pointers to all of these subsidiary Shapes and Picture output will treat them as independent o
318. xes e I have started defining class Triangle which can be used for calculating triangle solutions e Add a class Conic_Section and derive Ellipse from it This will be the first case of multiple inheritance in 3DLDF since Ellipse is already derived from Path See Chapter 31 Ellipse Reference page 222 Add the classes Parabola and Hyperbola e Add more functions for finding the intersections of objects of various types starting with the plane figures In particular I believe I ve found an algebraic solution for the intersection of an Ellipse and a Circle in a plane but I haven t had a chance to try implementing it yet If this works I think it will make it possible to find the intersection of two coplanar ellipses algebraically because it will be possible to transform them both such that one of them becomes circular e Class Octahedron will complete the set of regular Platonic polyhedra e Add classes for the Kepler Poinsot polyhedra the semi regular Archimedean polyhedra the dual solids the stellated Archimedean polyhedra and the regular compounds e Add class Ellipsoid and a derived class Sphere e Improve the specification of Solid and Solid_Faced In particular it would help to store the vertices of Polyhedra as individual Points rather than using Reg_Polygons Pd also like to find a better way of generating Solids without using rotations if possible 1 Stroustrup The C Programming Language 815 2 Mul
319. y and z are all tested against MAX_REAL_SQRT to ensure that x y and 2 will all be less than or equal to MAX_REAL before trying to calculate them Metafont implements an operation called Pythagorean addition notated as which can be used to calculate distances without first squaring and then taking square roots a b a2 b and a b c 4 a 6 c This makes it possible to calculate distances for greater values of a b and c that would otherwise cause floating point errors Metafont also implements the inverse operation Pythagorean subtraction notated as a b 1 a b Unfortunately 3DLDF implements neither Pythagorean addition nor subtraction as yet but it s on my list of things to do 1 Knuth Donald E The Metafontbook p 66 Chapter 14 Dynamic Allocation of Shapes 84 14 Dynamic Allocation of Shapes template lt class C gt C create_new const C arg Template function template lt class C gt C create_new const C amp arg Template function These functions dynamically allocate an object derived from Shape on the free store returning a pointer to the type of the Shape and setting on_free_store to true If a non zero pointer or a reference is passed to create_new the new object will be a copy of arg It is not possible to instantiate more than one specialization of create_new that takes no argument because calls to these functions would be ambiguous If the new objec
320. y means of conditional compilation If real is float 3DLDF will re quire less memory than if real is double but its calculations will be less precise real is typedeffed to float by default real_pair first second typedef Synonymous with pair lt real real gt real_triple first second third struct All three data elements of real_triple are reals It also has two constructors described below There are no other member functions void real_triple void Constructor void real_triple real a real b real c Constructor The constructor taking no arguments sets first second and third to 0 The constructor taking three real arguments sets first to a second to b and third to c Matrix typedef A Matrix is a 4 x 4 array of real e g Matrix M real M 4 4 It is used in class Transform for storing transformation matrices See Chapter 4 Transforms page 19 and See Chapter 19 Transform Reference page 96 for more information real_short first second typedef Synonymous with pair lt real signed short gt It is the return type of Plane get_ distance bool_pair first second typedef Synonymous with pair lt bool bool gt bool_real first second typedef Synonymous with pair lt bool real gt Chapter 13 Global Constants and Variables 82 13 Global Constants and Variables The global constants and variables described in this chapter are found in pspglb web Others of types defined in 3DLDF
321. y must be closed Paths Reg_C1_Plane_Curves inherit their drawing and filling functions from Path The constructors and setting functions of classes derived from Reg_C1_Plane_Curve must ensure that the resulting geometric figures are planar convex and that the number of Points they contain is a multiple of 4 The latter assumption is of importance in intersection_points segment half and quarter See Section 30 3 Regular Closed Plane Curve Reference Intersections page 217 and Section 30 4 Regular Closed Plane Curve Reference Segments page 219 30 1 Data Members Point center Protected variable The center of the Reg_C1_Plane_Curve if it has one unsigned short number_of_points Protected variable The number of Points on points in a Reg_C1_Plane_Curve 30 2 Querying bool is_quadratic void const inline virtual functions bool is_cubic void bool is_quartic void These functions all return false They are intended to be overloaded by member functions of derived classes lif you don t know what overfull boxes are don t worry about it It has to do with T X s line and page breaking algorithms If you want to know more see Knuth Donald E The TRXbook Chapter 30 Regular Closed Plane Curve Reference 217 real_triple get_coefficients real Slope real const inline virtual function v_intercept Returns a real_triple with all three values INVALID_REAL Intended to be over loaded by member fun
322. y others This License is a kind of copyleft which means that derivative works of the document must themselves be free in the same sense It complements the GNU General Public License which is a copyleft license designed for free software We have designed this License in order to use it for manuals for free software because free software needs free documentation a free program should come with manuals providing the same freedoms that the software does But this License is not limited to software manuals it can be used for any textual work regardless of subject matter or whether it is published as a printed book We recommend this License principally for works whose purpose is instruction or reference APPLICABILITY AND DEFINITIONS This License applies to any manual or other work in any medium that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License Such a notice grants a world wide royalty free license unlimited in duration to use that work under the conditions stated herein The Document below refers to any such manual or work Any member of the public is a licensee and is addressed as you You accept the license if you copy modify or distribute the work in a way requiring permission under copyright law A Modified Version of the Document means any work containing the Document or a portion of it either copied verbatim or with modifications and o
323. ycle q show q p 4 q fill_draw_value Projective coordinates 0 1 75337 0 0958948 1 88483 0 615265 0 183441 1 38131 2 58743 0 031736 4 08541 4 22023 0 0938636 0 964435 4 22023 0 0938636 0 7 99767 0 384436 0 964436 4 22023 0 0938636 4 08541 4 22023 0 0938636 1 38131 2 58743 0 031736 1 88483 0 615266 0 183441 cycle Figure 135 Chapter 26 Path Reference 194 void show_colors boo1 false Function Shows the values of draw_color and fill_color These will normally be 0 unless the Path is on a Picture 26 15 Querying bool is_on_free_store void const function Returns true if the Path was dynamically allocated on the free store otherwise false bool is_planar const bool verbose false string const virtual function text Uses get_normal to determine whether the Path is planar or not Returns true if it is otherwise false If verbose is true text is written to standard output or Path if text is the empty string followed by a message saying whether the Path is planar or not bool is_linear const bool verbose false string text const function Returns true if line_switch is true Otherwise is_linear uses get_normal to determine whether the Path is linear If it is is_linear returns true otherwise false bool is_cycle void Inline c

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