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1. 46 Graphics Drawing Graphs with MetaPost John D Hobby Abstract This paper describes a graph drawing package that has been implemented as an extension to the Meta Post graphics language MetaPost has a powerful macro facility for implementing such extensions There are also some new language features that support the graph macros Existing features for generating and manipulating pictures allow the user to do things that would be difficult to achieve in a stand alone graph package 1 Introduction MetaPost is a batch oriented graphics language based on Knuth s METAFONT but with PostScript output and numerous features for integrating text and graphics The author has tried to make this paper as independent as possible of the user s man ual 6 but fully appreciating all the material re quires some knowledge of the MetaPost language We concentrate on the mechanics of producing particular kinds of graphs because the question of what type of graph is best in a given situation is covered elsewhere e g Cleveland 2 4 3 and Tufte 11 The goal is to provide at least the power of UNIX grap 1 but within the MetaPost language Hence the package is implemented using MetaPost s powerful macro facility The graph macros provide the following func tionality 1 Automatic scaling 2 Automatic generation and labeling of tick marks or grid lines Multiple coordinate systems Linear and logarithmic scales Separate data f2. ordinary decimal notation but reverts to scientific notation if the number is at least 10000 The g and G formats also revert to scientific notation for non zero numbers of magnitude less than 0 001 The format macro needs a set of templates to determine what font to use how to position the exponent etc The templates are normally initialized automatically but it is possible to set them explicitly by passing five picture expressions to init_numbers For instance the default definition for TEX users is init_numbers btex etex btex 1 etex btex times 10 etex btex etex btex 2 etex The first argument tells how to typeset a leading minus sign the second argument is an example of a 1 digit mantissa third comes whatever to put after the mantissa in scientific notation next come a leading minus sign for the exponent and a sample 1 digit exponent Picture variable Fe_plus gives a leading plus sign for positive numbers and Fe_base gives what ever should precede the exponent when typeset ting a power of ten Calling init_numbers initial izes Fe_plus to an empty picture and constructs Fe_base from its second and third arguments 5 Conclusion The graph package makes it convenient to generate graphs from within the MetaPost language The primary benefits are the power of the MetaPost language and its ability to interact with TEX or troff for typesetting labels Typeset labels can be stored in picture variables and mani
3. pages 21 36 September 1992 John D Hobby A user s manual for MetaPost Computing Science Technical Report no 162 AT amp T Bell Laboratories Murray Hill New Jersey April 1992 Available as http cm bell labs com cs cstr 162 ps gz Adobe Systems Inc PostScript Language Ref erence Manual Addison Wesley Reading Mas sachusetts second edition 1990 Donald E Knuth METAFONT the Program Addison Wesley Reading Massachusetts 1986 Volume D of Computers and Typesetting Leslie Lamport TEX A Document Prepara tion System Addison Wesley Reading Mas sachusetts 1986 U S Bureau of the Census Statistical Abstracts of the United States 1992 Washington D C 112th edition 1992 Edward R Tufte Visual Display of Quanti tative Information Graphics Press Box 430 Cheshire Connecticut 06410 1983 John D Hobby Bell Laboratories Room 2C 458 700 Mountain Ave Murray Hill NJ 07974 0636 hobby research bell labs com TUGboat Volume 22 2001 No 1 2
4. pattern and the color is redpart p greenpart p bluepart p If the line is not dashed dashpart p returns an empty picture The same part extraction operators work when filled p is true except that dashpart p is not meaningful in that case For text compo nents textual p is true textpart p gives the text that got typeset fontpart p gives the font that was used and xpart p ypart p xxpart p xypart p yxpart p yypart p tell how the text has been shifted rotated and scaled The redpart greenpart and bluepart operators also work for text components When clipped p or bounded p is true pathpart p gives the clipping or setbounds path and the other part extraction operators are not meaningful Such non meaningful part extractions do not generate errors they return null values in stead the trivial path 0 0 for pathpart nullpen for penpart an empty picture for dashpart zero for redpart greenpart bluepart and the null string for textpart or fontpart One final operator for extracting information from a picture is length picture primary This returns the number of components that a for within iteration would find B 3 Other New Features The marith mp and sarith mp packages use num bers of magnitude 4096 or more Since such numbers can cause overflow problems in MetaPost s linear equation solving and path fitting algorithms they are normally allowed only as intermediate results This limitation is rem
5. a line is ignored Placing a setcoords command between two gdraw commands graphs two functions in different coordinate systems as shown in Figure 6 Whenever you give a setcoords command the interpreter examines what has been drawn selects appropriate x and y ranges and scales everything to fit Every thing drawn afterward is in a new coordinate system that need not have anything in common with the old coordinates unless setrange commands enforce similar coordinate ranges For instance the two setrange commands force both coordinate systems to have x ranging from 80 to 90 and y starting at 0 When you use multiple coordinate systems you have to specify where the axis labels go The default is to put tick marks on the bottom and the left side of the frame using the coordinate system in 50 TUGboat Volume 22 2001 No 1 2 100 Standard 4 draw begingraph 2 3in 2in setcoords log log 10 gt glabel 1ft btex Seconds etex OQUT glabel bot btex Matrix size etex Seconds OUT gdraw matmul d dashed evenly 0 1 glabel ulft btex Standard etex 8 gdraw matmul d 0 01 glabel 1rt btex Strassen etex 7 j endgraph 20 50 100 200 500 Matrix size Figure 5 Timings for two matrix multiplication algorithms with the corresponding MetaPost input draw begingraph 6 5cm 4 5cm setrange 80 0 90 whatever glabel bot btex Year etex OUT glabel lft btex vbox hbox Emissions in hb
6. bot btex Age in years etex OUT gdraw agepopm d in the input for Figure 1 generates Figure 3 This improves the graph by adding axis labels and using a new data file agepopm d where the populations have been divided by one million to avoid large numbers We shall see later that simple transformations such as this can be achieved without generating new data files All flavors of TEX can handle multi line labels via the hbox within vbox arrangement used above but TEX users will find it more natural to use the tabular environment 9 Troff users can use nofill mode btex nf Population in millions etex 2 2 Coordinate Systems The graph macros automatically shift and rescale coordinates from data files gdraw paths and glabel locations to fit the graph Whether the range of y coordinates is 0 64 to 4 6 or 640 000 to 4 600 000 they get scaled to fill about 88 of the 48 TUGboat Volume 22 2001 No 1 2 we J 4x106 0 fe a S OO bag 3x 10 e 2x106 4 ba 10 0 20 40 60 80 Figure 2 The 1991 age distribution plotted with bullets 44 3 Population in millions 3 1 0 20 40 60 80 Age in years Figure 3 An improved version of the 1991 age distribution graph height specified in the begingraph statement Of course line widths labels and plotting symbols are not rescaled The setrange command controls the shifting and rescaling pr
7. field s2 Figure 9 shows how to use augment to read multiple column data and make multiple paths Paths p2 p3 p4 p5 give cumulative totals for columns 2 through 5 and pictures lab2 through lab5 give corresponding labels The expression image unfill bbox lab j draw lab j executes the given drawing commands and returns the resulting picture unfill bbox lab j puts TUGboat Volume 22 2001 No 1 2 defaultfont cmr7 draw begingraph 3in 2in 53 glabel 1lft btex vbox hbox Life hbox expectancy etex OUT glabel bot btex Per capita G N P thousands of dollars etex OUT setcoords log linear gdata countries d s glabel s3 s1 s2 endgraph 80 Gre SPH Jawi cken oe as Lus Cze ai bnn A SKo USS AS PMor I rz Life P or InpgAP expectancy 60 Ninn Egy ch T eZ sud 50 E Wep Uga Nig Moz 0 1 0 2 05 1 2 5 10 20 Per capita G N P thousands of dollars Figure 8 A scatter plot and the commands that generated it down a white background and draw lab j puts the label on the background The gfill command is just like gdraw except it takes a cyclic path and fills the interior with a solid color The color is black unless a withcolor clause specifies another color See the manual 6 for explanations of for loops arrays colors and path construction operators like cycle and reverse 3 Manipulating Big Numbers MetaPost inherits a fixed point numb
8. format autogrid otick bot endfor 2 4 Processing Data Files The most general tool for processing data files is the gdata command gdata string expression variable commands It takes a file name a variable v and a list of commands to be executed for each line of the data file The commands are executed with i set to the input line number and strings v1 v2 v3 set to the input fields on the current line A null string marks the end of the v array 3 The manual 6 explains how vardef defines functions and mlog computes logarithms 52 TUGboat Volume 22 2001 No 1 2 vardef newy expr y 256 75 y mlog y enddef draw begingraph 3in 2in glabel 1ft btex vbox hbox Population hbox in millions etex OUT gdraw ttimepop d for y 5 10 20 50 100 150 200 250 grid 1ft format g y newy y withcolor 85white endfor autogrid grid bot withcolor 85white frame 1llft endgraph 250 200 150 100 Population in millions 50 20 i a a 1800 1850 1900 1950 2000 Figure 7 Population of the United States in millions versus time with the population re expressed as p 75 Inp The MetaPost input shown above the graph assumes a data file ttimepop d that gives year p 75 Inp pairs Using a glabel command inside of gdata gen erates a scatter plot as shown in Figure 8 The data file countries d begins 20 910 75 7 US 1 831 66 7 Alg where the last
9. In addition to the usual MetaPost drawing options the list can contain a plot picture clause to plot a specified picture at each data point The drawing and labeling commands are closely related to a set of similarly named com mands in plain MetaPost The gdrawarrow and gdrawdblarrow commands are included to maintain this relationship gdotlabel label suffix p location This is like glabel except it also puts a dot at the location being labeled gdraw p Draw path p or if p is a string read co ordinate pairs from file p and draw a polygonal line through them gdrawarrow p This is like dgraw p except it adds an arrowhead at the end of the path gdrawdblarrow p This is like dgraw p except it adds an arrowhead at each end of the path gfill p Fill cyclic path p or read coordinates from the file named by string p and fill the resulting polygonal outline 56 glabel label suffix p location If p is not a picture it should be a string Typeset it using defaultfont then place it near the given location and offset as specified by the label suffix The location can be x and y coordinates a pair giving x and y a numeric value giving a time on the last path drawn or OUT to label the outside of the graph A 3 Grids Tick Marks and Framing auto x or y Generate default x or y coordinates for tick marks autogrid axis label command axis label command Draw default axis labels using the specified c
10. ads a data file and returns a path where all the coordinates are in Mlog form An internal variable Gpaths determines whether gdraw and gfill expect paths to be given in Mlog form For example this graphs the data in agepop91 d with y coordinates divided by one million interim Gpaths log gdraw Mreadpath agepop91 d shifted 0 6 Mten 4 Typesetting Numbers The graph package needs to compute axis labels and then typeset them The macro format string expression numeric or string expression does this You must first input graph or input format to load the macro file The macro takes a format string and a number to typeset and returns a picture containing the typeset result Thus format g 2 2 yields 4 and format 3g 6 022e23 yields 6 021028 A format string consists of TUGboat Volume 22 2001 No 1 2 e an optional initial string not containing a per cent sign a percent sign an optional numeric precision p one of the conversion letters e f g G an optional final string The initial and final strings are typeset in the default font usually cmri0 and the typeset number is placed between them For the e and g formats the precision p is the number of significant digits allowed after rounding for f and G the number is rounded to the nearest multiple of 10 If the precision is not specified the default is p 3 The e format always uses scientific notation and the f format uses
11. er system from Knuth s METAFONT 8 Numbers are expressed in multiples of 2716 and they must have absolute value less than 32768 Knuth chose this system because it is perfectly adequate for font design and it is guaranteed to give identical results on all types of computers Fixed point numbers are seldom a problem in MetaPost because all computations are based on coordinates that are limited by the size of the paper on which the output is to be printed This does not hold for the input data in a graph drawing application Although graphs look best when coordinate axes are labeled with numbers of reasonable magnitude the strict limits of fixed point arithmetic would be inconvenient A simple way to handle large numbers is to include the line input sarith and then use binary operators Sadd Ssub Smul and Sdiv in place of and These operators are inefficient but very flexible They accept numbers or strings and return strings in exponential notation with the exponent marked by e e g 6 7e 11 means 6 7 x 10711 The unary operator Sabs string finds a string that represents the absolute value Binary operators Sleq and Sneq perform numeric comparisons on strings and return boolean results The operation Scvnum string finds the numeric value for a string if this can be done without overflowing MetaPost s fixed point number system If the string does not contain e it is much more efficient to use the prim
12. field in each line gives the label to be plotted Setting defaultfont in the first line of input selects a small font for these labels Without these labels no gdata command would be needed Replacing the gdata command with gdraw countries d plot btex circ etex would change the abbreviated country names to open circles Both gdraw and gdata ignore an optional initial on each input line parse data fields separated by white space and stop if they encounter an input line with no data fields Leading percent signs make graph data look like MetaPost comments so that numeric data can be placed at the beginning of a MetaPost input file It is often useful to construct one or more paths when reading a data file with gdata The augment command is designed for this augment path variable coordinates If the path variable does not have a known value it becomes a path of length zero at the given coordi nates otherwise a line segment to the given coordi nates is appended to the path The coordinates may be a pair expression or any combination of strings and numerics as explained at the beginning of Section 2 2 If a file timepop d gives t p pairs augment can be used like this to graph newy p versus t path p gdata timepop d s augment p s1 newy scantokens s2 gdraw p MetaPost s scantokens primitive interprets a string as if it were the contents of an input file This finds the numeric value of data
13. g commands B 1 Reading and Writing Files A new operator readfrom file name returns a string giving the next line of input from the named file The file name can be any primary expression of type string If the file has ended or cannot be read the result is a string consisting of a single null character The preloaded plain macro package introduces the name EOF for this string TUGboat Volume 22 2001 No 1 2 After readfrom has returned EOF additional reads from the same file cause the file to be reread from the start The opposite of readfrom is the command write string expression to file name This writes a line of text to the specified output file opening the file first if necessary All such files are closed automatically when the program terminates They can also be closed explicitly by using EOF as the string expression The only way to tell if a write command has succeeded is to close the file and use readfrom to look at it B 2 Extracting Information from Pictures MetaPost pictures are composed of stroked lines filled outlines pieces of typeset text clipping paths and setbounds paths A setbounds path gives an artificial bounding box as is needed for TEX output A picture can have many components of each type They can be accessed via an iteration of the form for symbolic token within picture expression loop text endfor The loop text can be anything that is balanced with respect t
14. hatever whatever gdraw agepopm d endgraph 354 Population in millions 2 1s 40 60 80 Age in years Figure 4 The 1991 age distribution graph and the input that creates it does the job Any fixed or floating point repre sentation is acceptable as long as the exponent is introduced by the letter e Coordinate systems need not be linear The setcoords command allows either or both axes to have logarithmic spacing coordinate setting gt setcoords coordinate type coordinate type coordinate type log linear log linear A negative coordinate type makes x or y run backwards so it is largest on the left side or bottom of the graph Figure 5 graphs execution times for two matrix multiplication algorithms using setcoords log log to specify logarithmic spacing on both axes The data file matmul d gives timings for both algorithms 20 007861 standard MM size seconds 30 022051 40 050391 60 15922 80 4031 120 1 53 160 3 915 240 18 55 320 78 28 480 279 24 20 006611 Strassen size seconds 30 020820 40 049219 60 163281 80 3975 120 1 3125 160 3 04 240 9 95 320 22 17 480 72 60 A blank line in a data file ends a data set Sub sequent gdraw commands access additional data sets by just naming the same data file again Since each line gives one x coordinate and one y coordinate commentary material after the second data field on
15. iles Seis ley Ability to handle numbers outside the usual range ra Arbitrary plotting symbols 8 Drawing filling and labeling commands for graphs In addition to these items the user also has access to all the features described in the MetaPost user s manual 6 These include access to almost all the features of PostScript ability to use and manipulate typeset text ability to solve linear equations and TUGboat Volume 22 2001 No 1 2 data types for points curves pictures and coordi nate transformations Section 2 describes the graph macros from a user s perspective and presents several examples Sections 3 and 4 discuss auxiliary packages for ma nipulating and typesetting numbers and Section 5 gives some concluding remarks Appendix A sum marizes the graph drawing macros and Appendix B describes some recent additions to the MetaPost language that have not been presented elsewhere 2 Using the Graph Macros A MetaPost input file that uses the graph macros should begin with input graph This reads a macro file graph mp and defines the graph drawing commands explained below The rest of the file should be one or more instances of beginfig figure number graphics commands endfig followed by end The following graphics commands suffice to generate the graph in Figure 1 from the data file agepop91 d draw begingraph 3in 2in gdraw agepop91 d endgraph Each line of agepop91 d gi
16. itive operation scantokens string The above operators are based on a low level package that manipulates numbers in Mlog form 4 The argument to a unary operator need not be paren thesized unless it is an expression involving binary operators 54 TUGboat Volume 22 2001 No 1 2 draw begingraph 3in 2in glabel 1ft btex vbox hbox Quadrillions hbox of BTU etex OUT path p numeric t gdata energy d t 0 augment p1 1 0 for j 2 upto 5 t t scantokens j augment p j 1 endfor picture lab lab2 btex coal etex lab3 btex crude oil etex lab4 btex natural gas etex labd btex hydroelectric etex for j 5 downto 2 gfill p jl l reverse p j 1 cycle withcolor 16j white glabel 1ft image unfill bbox lab j draw lab j 7 length p j endfor endgraph 60 40 Quadrillions of BTU 20 o hydroelectric natural gas crude oil 1900 1920 1940 1960 Figure 9 A graph of U S annual energy production and the commands that generated it A number zv in Mlog form represents 9724 16 2 ae H 7 where u Any value between 1 61 x 10728 and 3 88 x 1055 can be represented this way There is a constant Mten such that k Mten represents 10 for any integer k in the interval 29 55 The main reason for mentioning Mlog form is that it allows graph data to be manipulated as a MetaPost path The function Mreadpath file name re
17. o for and endfor The symbolic token is a loop variable that scans the components of the picture in the order in which they were drawn The component for a clipping or setbounds path includes everything the path applies to Thus if a single clipping or setbounds path applies to everything in the picture expression the whole picture could be thought of as one big component In order to make the contents of such a picture accessible the for within iteration ignores the enclosing clipping or setbounds path in this case Once the for within iteration has found a picture component there are numerous operators for identifying it and extracting relevant informa tion The operator stroked primary expression tests whether the expression is a known picture whose first component is a stroked line Similarly the filled and textual operators return true if the first component is a filled outline or a piece of typeset text The clipped and bounded operators test whether the argument is a known picture that starts with a clipping path or a setbounds path This is true if the first component is clipped or bounded or if the entire picture is enclosed in a clipping or setbounds path There are also numerous part extraction opera tors that test the first component of a picture If p is a picture and stroked p is true pathpart p is the 57 path describing the line that got stroked penpart p is the pen that was used dashpart p is the dash
18. ocess by specifying the minimum and maximum graph coordinates setrange coordinates coordinates where coordinates pair expression numeric or string expression numeric or string expression The first coordinates give min Ymin and the second give max Ymax The lines x Tmin r Tmax Y Ymin and y Ymax define the rectangular frame around the graph in Figures 1 3 For example an adding a statement setrange origin whatever whatever to the input for Figure 3 yields Figure 4 The first coordinates are given by the predefined pair constant origin and the other coordinates are left unspecified Any unknown value would work as well but whatever is the standard MetaPost representation for an anonymous unknown value Notice that the syntax for setrange allows coordinate values to be given as strings Many commands in the graph package allow this option It is provided because the MetaPost language uses fixed point numbers that must be less than 32768 This limitation is not as serious as it sounds because good graph design dictates that coordinate values should be of reasonable magnitude 2 11 If you really want x and y to range from 0 to 1 000 000 setrange origin 1e6 1e6 TUGboat Volume 22 2001 No 1 2 draw begingraph 3in 2in 49 glabel 1ft btex vbox hbox Population hbox in millions etex OUT glabel bot btex Age in years etex OUT setrange origin w
19. oes the same for y An empty argument suppresses labeling for that axis Otherwise the label suffix tells which side of the graph gets the numeric label Be careful to use bot or top for the x axis and 1ft or rt for the y axis Use otick for outward tick marks itick for inward tick marks and grid for grid lines The option list tells how to draw the tick marks or grid lines Grid lines tend to be a little overpowering so it is a good idea to give a withcolor option to make them light gray so they do not make the graph too busy 2 3 Explicit Grids and Framing In case autogrid is not flexible enough axis label commands generate grid lines or tick marks one at a time The syntax is grid or tick label suffix label format numeric or string expression option list where grid or tick and label suffix are as in autogrid and label format is either a format string like g or a picture containing the typeset numeric label The axis label commands use a macro format format string numeric or string expression to typeset numeric labels Full details appear in Sec tion 4 but when the format string is g it uses decimal notation unless the number is large enough or small enough to require scientific notation The example in Figure 7 invokes format explicitly so that grid lines can be placed at trans formed coordinates It defines the transformation 51 newy y y 75 lny and shows that this f
20. ommands for the x and y axes An axis label command may be empty or it may be itick otick or grid followed by a label suffix frame label suffix option list Draw a frame around the graph or draw the part of the frame specified by the label suffix grid label suffix f z Draw a grid line across the graph from the side specified by the label suffix and label it there using format string f and coordinate value z If f is a picture it gives the label itick label suffix f z This is like grid except it draws an inward tick mark otick label suffix f z This is like grid except it draws an outward tick mark A 4 Miscellaneous Commands augment variable coordinates Append coor dinates to the path stored in variable format f x Typeset x according to format string f and return the resulting picture gdata f variable commands Read the file named by string f and execute commands for each input line using the variable as an array to store data fields init_numbers s m 2x t e Provide five pictures as templates for future format operations s is a leading minus m is a sample mantissa x follows the mantissa t is a leading minus for the exponent e Mreadpath f Read a path for the data file named by string f and return it in Mlog form A 5 Arithmetic on Numeric Strings It is necessary to input sarith before using the following macros Sabs x Compute z and return a numeric
21. oved when the internal vari able warningcheck is zero In earlier versions of MetaPost the limitation could be removed for vari ables but explicit constants were always restricted to be less than 4096 For completeness we also mention one other new feature of MetaPost Version 0 60 When TREX material is included in a picture via the btex etex feature the thickness of horizontal and vertical rules gets rounded to exactly the right number of pixels i e interpreting MetaPost output according to the PostScript scan conversion rules 7 makes the pixel width equal to the ceiling of the unrounded width In fact a similar relationship holds for all line widths The generated PostScript sets line 58 widths by first transforming to device coordinates and rounding appropriately References 1 Jon L Bentley and Brian W Kernighan Grap a language for typesetting graphs In Unix Research System Papers volume II pages 109 146 AT amp T Bell Laboratories Murray Hill New Jersey tenth edition 1990 William S Cleveland The Elements of Graph ing Data Hobart Press Summit New Jersey 1985 William S Cleveland A model for studying display methods of statistical graphics with discussion Journal of Computational and Statistical Graphics 3 to appear William S Cleveland Visualizing Data Hobart Press Summit New Jersey to appear John D Hobby Introduction to MetaPost In EuroT X 92 Proceedings
22. ox thousands of hbox metric tons hbox heavy line etex OUT gdraw lead d withpen pencircle scaled 1 5pt autogrid otick 1ft setcoords linear linear setrange 80 0 90 whatever glabel rt btex vbox hbox Micrograms hbox per cubic hbox meter of air hbox thin line etex OUT gdraw lead d autogrid otick bot otick rt endgraph 0 5 60 0 4 Emissions in 49 0 3 Micrograms thousands of per cubic metric tons 0 2 meter of air heavy line 29 4 thin line 0 1 0 0 80 82 84 86 88 90 Year Figure 6 Annual lead emissions and average level at atmospheric monitoring stations in the United States The MetaPost input is shown above the graph TUGboat Volume 22 2001 No 1 2 effect when the endgraph command is interpreted Figure 6 uses the autogrid otick 1ft to label the left side of the graph with the y co ordinates in effect before the setcoords command This suppresses the default axis labels so another autogrid command is needed to label the bottom and right sides of the graph using the new coordinate system The general syntax is autogrid axis label command axis label command option list where axis label command gt empty grid or tick label suffix grid or tick grid itick otick The label suffix should be 1ft rt top or bot The first argument to autogrid tells how to label the x axis and the second argument d
23. pulated in various ways such as measuring the bounding box and providing a white background We have seen how to generate shaded regions and control line width color and styles of dashed lines Numerous other variations are possible The 55 full MetaPost language 6 provides many other potentially useful features It also has enough computing power to be useful for generating and processing data A Summary of the Graph Package In the following descriptions italic letters such as w and h denote expression parameters and words in angle brackets denote other syntactic elements Unless specified otherwise expression parameters can be either numerics or strings An option list is a list of drawing options such as withcolor 5white or dashed evenly a label suffix is one of 1ft rt top bot ulft urt 11ft lrt A 1 Graph Administration begingraph w h Begin a new graph with the frame width and height given by numeric pa rameters w and h endgraph End a graph and return the resulting picture setcoords tz ty Set up a new coordinate system as specified by numeric flags tz ty Flag values are linear and 1log setrange coordinates coordinates Set the lower and upper limits for the current coor dinate system Each coordinates can be a single pair expression or two numeric or string expressions A 2 Drawing and Labeling All of the drawing and labeling commands can be followed by an option list
24. s shown in Figure 2 Fol lowing the plot option with a withpen option would cause the line to reappear superimposed on the plotting symbols The glabel and gdotlabel commands add labels to a graph The syntax for glabel is glabel label suffix string or picture expression location option list where location identifies the location being labeled and label suffix tells how the label is offset relative to that location The gdotlabel command is identical except it marks the location with a dot A label suffix is as in plain MetaPost empty centers the label on the location 1ft rt top bot offset the label horizontally or vertically and ulft urt 11ft lrt give diagonal offsets The location can be a pair of graph coordinates a knot number on the last gdraw path or the special location OUT Thus gdotlabel top btex 50 0 etex 50 0 2 Troff users should replace btex bullet etex with btex bu etex would put a dot at graph coordinates 50 0 and place the typeset text 50 0 above it Alterna tively glabel ulft Knot3 3 typesets the string Knot3 and places it above and to the left of Knot 3 of the last gdraw path The knot number 3 is the path s time parameter 6 Section 8 2 The location OUT places a label relative to the whole graph For example replacing gdraw agepop91 d with glabel 1ft btex vbox hbox Population hbox in millions etex OUT glabel
25. string TUGboat Volume 22 2001 No 1 2 x Sadd y Compute x y and return a numeric string Scvnum x Return the numeric value for string x x Sdiv y Compute z y and return a numeric string 8 Sleq y Return the boolean result of the compar ison g lt y 8 Smul y Compute x y and return a numeric string 8 Sneq y Return the boolean result of the compar ison x y 8 Ssub y Compute x y and return a numeric string A 6 Internal Variables and Constants Autoform Format string used by autogrid De fault 4g Fe_base What precedes the exponent when typeset ting a power of ten Fe_plus Picture of the leading plus sign for positive exponents Gmarks Minimum number of tick marks per axis for auto and autogrid Default 4 Gminlog Minimum largest smallest ratio for loga rithmic spacing with auto and autogrid De fault 3 0 Gpaths Code for coordinates used in gdraw and gfill paths linear for standard form log for Mlog form Mten The Mlog form for 10 0 B New Language Features The graph mp macros and the arithmetic routines in marith mp and sarith mp use various language features that were introduced in Version 0 60 of the MetaPost language We summarize these features here because they are not covered in existing docu mentation 6 5 Also new is the built in macro image drawing commands that was used in Section 2 4 to find the picture produced by a sequence of drawin
26. unction increases almost linearly 3 This is a little like using logarithmic y coordinates except that y is mapped to y 75 lny instead of just In y Figure 7 uses the command frame label suffix option list to draw a special frame around the graph In this case the label suffix is 11ft to draw just the bottom and left sides of the frame Suffixes lrt ulft and urt draw other combinations of two sides suffixes 1ft rt top bot draw one side and empty draws the whole frame For example frame dashed evenly draws all four sides with dashed lines The default four sided frame is drawn only when there is no explicit frame command To label an axis as autogrid does but with the labels transformed somehow use auto x or auto y for positioning tick marks or grid lines These macros produce comma separated lists for use in for loops Any x or y values in these lists that cannot be represented accurately within MetaPost s fixed point number system are given as strings A standard macro package that is loaded via input sarith defines arithmetic operators that work on numbers or strings Binary operators Sadd Ssub Smul and Sdiv do addition subtraction multiplication and division One possible application is rescaling data Fig ure 4 used a special data file agepopm d that had y values divided by one million This could be avoided by replacing gdraw agepopm d by gdraw agepop91 d for u auto y otick 1ft
27. ves an age followed the estimated number of Americans of that age in 1991 10 2 1 Basic Graph Drawing Commands All graphs should begin with begingraph width height and end with endgraph This is syntactically a picture expression so it should be preceded by draw and followed by a semicolon as in the example The width and height give the dimensions of the graph itself without the axis labels The command gdraw expression option list draws a graph line If the expression is of type string it names a data file otherwise it is a path that gives the function to draw The option list is zero or more drawing options withpen pen expression withcolor color expression dashed picture expression 1 See the user s manual 6 for explanations of draw commands and syntactic elements like picture expression TUGboat Volume 22 2001 No 1 2 47 4x108 5 3x106 4 2x106 4 106 MR 0 20 40 60 80 Figure 1 A graph of the 1991 age distribution in the United States that give the line width color or dash pattern as explained in the User s Manual 6 In addition to the standard drawing options the option list in a gdraw statement can contain plot picture expression The picture expression gives a plotting symbol to be drawn at each path knot The plot option suppresses line drawing so that gdraw agepop91 d plot btex e etex generates only bullets a
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