ReMESH USER MANUAL - imati-cnr - Consiglio Nazionale delle
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1. V g Figure 2 A scheme of all of the possible relationships between topological entities in a triangle mesh Let v be a vertex VV v is the set of all the vertices which are connected to v through an edge VE y is the set of all the edges which are incident at v VT v is the set of all the triangles of which visa vertex Let e be an edge EV e is the set containing the two ending vertices of e ET e is the set of the triangles of which e is an edge Notice that since we consider only manifold triangle meshes possibly with boundary each set ET e contains either two elements when e is an internal edge or one element when e is a border edge The set EE e is the set of the edges bounding the triangles of which e is an edge excluding e itself Thus if e is an internal edge the set EE e contains four edges while if e is on the boundary EE e 2 Let be a triangle The set TV t is the set of the three vertices of t TE t is the set of the three edges bounding and finally TT t is the set of the triangles sharing an edge with 1 Moreover a topological relation may map each element of its domain into a set of constant or variable cardinality Hence when dealing with closed triangle meshes one can classify the relationships in e Constant relations These relations map edges and triangles into sets of neighboring elements with constant cardinality Specifically EV e 2 EE e 4 ET e 2 TV t 32. 14 15 16 17 18 19 20 21 Attene M Falcidieno B Rossignac J and Spagnuolo M 2003 Edge Sharpener Recovering sharp features in triangulations of non adaptively re meshed surfaces Proceedings of the 1 Eurographics Symposium on Geometry Processing 63 72 Attene M Falcidieno B Rossignac J and Spagnuolo M 2005 Sharpen amp Bend Recovering curved sharp edges in triangle meshes produced by feature insensitive sampling IEEE Transactions on Visualization and Computer Graphics 11 2 181 192 Attene M Falcidieno B Spagnuolo M and Rossignac J 2003 SwingWrapper Retiling triangle meshes for better EdgeBreaker compression ACM Transactions on Graphics 22 4 982 996 Barequet G and Sharir M 1995 Filling Gaps in the Boundary of a Polyhedron Computer Aided Geometric Design 12 2 207 229 Botsch M and Kobbelt L P 2001 A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes In Proceedings of Vision Modeling and Visualization Bruzzone E and De Floriani L 1990 Two Data Structures for Constructing Tetrahedralizations The Visual Computer 6 5 266 283 De Floriani L Falcidieno B and Pienovi C 1985 Delaunay based Representation of Surfaces defined over Arbitrarily Shaped Domains Computer Vision Graphics and Image Processing 32 127 140 Forrest A R 1987 Computational geometry and software engineering Towards a geometric computing environment Techn
3. GUI Configuration ReMesh provides some facilities for interactively setting visualization parameters of the scene being rendered After setting these parameters each user can store their configuration to a file for future use Current settings are saved in a hidden file placed in the user s home dir and are automatically applied when ReMESH will be launched in the future These settings include windows position size and visibility backgroud color of the render area material settings of the rendered mesh Save Current This button saves the current configuration to a file in the user s home directory The next time ReMESH is launched by the same user it will start with the configuration saved Load Last This button restores the last saved configuration Load Default Restores the default configuration of the GUI 11 ReMESH M Attene Settings gt Material Editor The material editor is a widget through which the user can control a number of settings about the material properties of the mesh es being displayed According to OpenGL s definition of materials the user may control material reaction to ambient diffuse specular and emissive lightening as well as surface shininess and transparency Through the menu button Edit a material list is provided from which the user may choose a pre defined set of material properties While chaning parameters the effects are interactively shown in the main scene unless ma
4. TE 3 and TT t 3 e Variable relations These relations are vertex based and the cardinality of the set may vary depending on which vertex is being mapped VV VE and VT In the design of a data structure however it is useful to extend the concept of constant relation to the case of manifold triangle meshes with boundary In fact although the cardinality of some The set VV v is also known as the link of v 15 ReMESH M Attene image sets is no longer constant it can assume a finite number of values Specifically the cardinality of the EE may be 2 or 4 the one of the ET may be 1 or 2 and the one of the TT may be 0 1 2 or 3 All the others are still properly constant 8 2 A non redundant data structure Clearly a data structure coding all the relations depicted in Figure 2 is redundant Conversely when dealing with manifold triangle meshes with boundary the scheme depicted in Figure 3 meets all of the requirements discussed above 6 T Figure 3 Scheme of relations from which it is possible to derive all of the other non stored relations in optimal time The dotted line representing the VE indicates that such a relation is only partially stored In Figure 3 the VE is indicated with a dotted line meaning that such a relation is only partially stored From now on we denote with VE such a restricted VE VE v maps v into one of its incident edges The complete VE v can be computed starting from the VE v b
5. gt Normal noise This operation distributes Gaussian noise over the vertices in the normal direction The amount of noise can be selected by the user in the pop up dialog as a percentage of the model s bounding ball radius Works on the entire mesh Algorithms gt Refine This feature increases the number of vertices up to a user selected value Vertices are inserted one by one Each of them is inserted in the mid point of the currently longest edge of the mesh If a selection is active only edges belonging to the selection are split Algorithms gt Optimize This feature iteratively swaps edges to locally maximize the minimum angle If the mesh is flat and non overlapping the method converges to a 2D Delaunay triangulation of the vertices Otherwise convergence is not guaranteed and the method quits after 10 iterations If a selection is active only edges belonging to the selection are swapped 4 Checking and Repairing a mesh The problem of robustness of geometric algorithms has received a lot of attention from more than 15 years 8 9 and it remains a vibrant area of research When designing a geometric algorithm in 9 ReMESH M Attene fact a researcher uses the theory of real numbers and their exact arithmetic Such a framework is often referred to as the Real Arithmetic Model or more compactly the RAM At implementation time however real numbers have to be approximated with finite precision representations and the er
6. is desirable that all of the following requirements are satisfied e The structure must be complete that is it must be possible to extract all of the entities and relationships which are not explicitly stored without ambiguity e The structure should be non redundant that is if an entity or a relationship can be computed in optimal time then it should not be explicitly coded in the data structure M Attene ReMESH e Each relationship which is not explicitly stored must be computable in optimal time that is the number of operations required must be linear in the number of elements of the relationship 8 1 Scheme of the relationships A topological relation is essentially a function which associates to each element o of a given type a vertex an edge or a triangle the set of all the elements of another given type having a topological connection with o For example if V is the set of vertices of a triangle mesh M V E T then the set of pairs VE v Y ve V Y c E and Y ge Y v c 9 is the topological relationship which relates each vertex with the set of all the edges incident at it Clearly the set of pairs VE may be viewed as a function VE V gt fo E which maps each element of V into a subset of E Let M V E T be a manifold triangle mesh The following Figure 2 depicts all of the possible relationships between elements of M Notice that a good data structure should not store them all in order to avoid redundancy Cy
7. region are projected on the plane and edges are iteratively swapped up to convergence which is guaranteed on planar and simple domains Finally the vertices are moved back to their original positions This operation is particularly useful to improve the quality of nearly flat regions The selection must be simple and its Gauss map must be entirely contained in a semi sphere Modelling gt Selection gt Remove Remove all the triangles belonging to the selected region s This is equivalent to pressing the Delete button on the keyboard Modelling gt Flip Normals When the user selects this button all the triangles of the mesh are inverted Modelling gt Fill Holes When selected this button pops up a dialog where the user can select a threshold number n Then all the boundary loops made of at most n edges are patched using the same strategy as in the interactive operation Triangulate Holes If the refine toggle is set after triangulation new vertices are inserted in the patched holes so as to reproduce the sampling density of neighboring regions If the smooth button is set too the newly inserted vertices are moved so as to produce a tangentially continuous patch with respect to its boundary If a selection exists this button limits its action to the selected region Only completely selected boundaries are filled Modelling gt Sharp edge tagging This feature allows the user to automatically tag as sharp see the in
8. the others a slider for the selection of the target number of vertices When settled with the parameters the user clicks on the OK button to actually perform the simplification Also non interactive operations include all of the actions which do not require the specification of a particular element of the mesh such as global modifications or operations which rely on a prior specification of a selection 3 Local and Global Editing In this section we describe the set of operations that can be performed interactively on the triangle mesh and produce a modification Sometimes it is easier to interact with the mesh if its edges are explicitly rendered to switch to such a kind of rendering the GUI Config gt settings window includes a toggle button labeled hidden line Local editing operations are accessible through two windows the Modelling and the Algorithms Modelling gt Transform gt Normalize Scene This operation computes the bounding box of the scene and normalizes it Specifically it performs a uniform scaling and a translation of the mesh so that it fits into the cube 0 1 0 1 0 1 This operation is particularly useful to avoid numerical overflows due to extreme values of the original coordinates Modelling gt Transform gt Transform Scene This button pops up a dialog containing a number of controls for setting affine transformations to the whole geometry Notice that while the visualization of the scene being trans
9. M Attene ReMESH Istituto di Matematica Applicata e Tecnologie Informatiche Consiglio Nazionale delle Ricerche Genova ITALY ReMESH Version 1 2 An interactive and user friendly environment for remeshing surface triangulations MARCO ATTENE USER MANUAL ReMESH M Attene Index 1T ReEMESH ara as ete Ve sap i else daa AS ts sale A pees GAS Ay eke a eee eS 3 A ol sorrento TC ACID pa at is oacreecse lle 3 TD Navigating THE SCENE 218 ener iui ili 4 2 Overview OF the featufeS ac clean 4 2 1 Interactiveoperationis ricalcolo 4 2 2 Selections and cut n Paste Perno scarl usi 5 PEOIA REI OLS E1 E TO a EEEE RIINA a 5 So Local and Global Edita aaa ea ASI e IAA E EAS EEE A ari 5 4 Checking and Repairing atmmeshi forse ia 9 3 Sra tT ATO cee arr ts a E a cede aces Gadetede nsw neloashemece N 11 COP a n a ile 12 T Manifold triangle mesh snrninicdr enneren a a e a a aa T i 14 8 A data structure for manifold triangle Meshes 14 8 1 Scheme Of th relationships icerir iaa E E E E OEE E aR 15 8 2 A non redundant data structure eolie 16 Bibliography nenene bes Selene ipsa eat class tee Pa ea alata gtd ha a a oars aaa eatin antl 18 M Attene ReMESH Research and software development involving geometry processing are often slowed down by the absence of suitable models for testing and benchmark purposes In particular when dealing with triangle meshes a researcher may need to check the behavior of a new algorithm
10. Roty and Dolly control respectively the rotation around the X axis the one around the Y axis and the dolly These actions however can also be carried out through direct interaction of the mouse in the canvas Further navigation parameters can be controlled through the buttons on the right of the window Some aspects of the scene such as the background color and pictorial properties of the surface material shading can be selected by clicking the button labeled GUI Config gt settings 2 Overview of the features Besides navigation and visualization tasks the user can perform a number of editing operations that we conveniently subdivide into two classes 2 1 Interactive operations This kind of actions can be performed through mouse clicks directly on the surface Notice that clicks and drags can also be used to navigate the scene In order to establish the behavior of mouse events in the canvas without ambiguity two buttons are provided the little arrow and the hand on the top right corner of the window for switching between viswalization and interactive modes At start up the mode is set to visualization the pointer has the shape of a hand and mouse events are M Attene ReMESH used for navigating the scene The user can switch to the interactive mode by clicking on the arrow button and can go back to visualization by clicking on the little hand Interactive operations include triangle removal vertex insertion edge swapping s
11. ases the toolbox provides a command line option to set the value of e to zero but subsequent processing must take into account possible failures All of the check and repairing tasks can be performed by the user after selecting a new value for e This can be useful when the model being edited is known to become the input for a less robust system At run time the Check amp Repair window provides an interactive slider to set the value for e The same window provides a number of buttons for further operations dealing with robustness issues in particular the following controls are provided 1 Check Connectivity This action performs a sequence of consistency tests on the connectivity graph of the mesh Notice that in normal conditions it should always pass all of the tests However it has been incorporated to help the developer of a new plug in to check the status of the structure at any time 2 Check Geometry This action looks for coincident vertices coincident edges degenerate triangles and overlapping adjacent triangles according to the current value of s If one of these situations is verified the camera is automatically moved to a viewpoint suitable for showing the flaw so that the user can analyze what went wrong and choose to perform some manual editing for a possible correction Also the user can rely on the automatic correction approaches provided 3 Glue Boundaries This action looks for coincident edges and if possible merge
12. ated by the vertices of co is an Euclidean k simplex e The collection X of all the simplexes generated by f as described above fulfills condition 2 of the definition of Euclidean Simplicial Complex Thus an embedding of an abstract simplicial complex is fully defined by mapping its vertices into points in the Euclidean space In R an abstract simplicial complex endowed with an embedding f describes a triangle mesh M V E T where V E and T are the sets of 0 1 and 2 simplexes respectively and each element of V can be mapped to R through f 16 An element of V is called a vertex an element of E is called an edge and an element of T is called a triangle Furthermore we call connectivity of M the combinatorial structure of X while we call geometry of M the function f that associates a 3D point to each vertex of V The set X c R defined as the union of all the Euclidean k simplexes generated by the vertices of f o for each o e is called the geometric realization of amp We say that a triangle mesh is manifold possibly with boundary if X is a two dimensional manifold possibly with boundary 8 A data structure for manifold triangle meshes The definition of a data structure for boundary representations such as triangle meshes requires the coding of topological entities with the associated geometric information and of a suitable subset of the topological relationships between such entities In particular it
13. ation loads a triangle mesh from file and inserts it in the current scene without removing the existing mesh es Notice that no geometrical check is performed on the newly loaded mesh that may consequently have degenerate elements To automatically remove all the degeneracies of the current meshes use the buttons provided in the Check amp Repair window The same file formats supported when launching ReMESH are supported here Save as out wrl The file out wrl is the default filename for work in progress models If ReMesh was launched from the directory MY PATH then this button creates the file MY PATH out wrl and saves the current mesh in it Notice that if the file already exists ReMesh automatically overwrites it without asking confirmation because again this file should be considered a work in progress M Attene ReMESH Save as This button pops up a file selector from which the user may choose the name of an existing file to overwrite or may specify a new file name for the current model If the file exists confirmation will be asked before overwriting The FORMAT is chosen based on the filename extension according to the following table wrl gt ASCII VRML 1 0 iv gt Open Inventor 2 1 off gt Object File Format ply gt Stanford s PLY format 0bj gt Wavefront s OBJ stl gt Stereolithography tri gt IMATI ver tri If no extension is provided ReMESH automatically appends w
14. ce is not oriented ReMESH assigns an orientation to one triangle for each connected component and propagates the orientation to neighboring triangles once all of the triangles have been visited the mesh is cut along edges having non consistently oriented incident triangles Possible isolated vertices are removed automatically Once the loader is settled with the topology and the structure is properly filled the tool performs some geometrical checks and corrections removal of degenerate triangles identification of edges having coincident end points These corrections can be prevented by passing the additional parameter nocheck to the command line Finally the graphical user interface GUI starts up and shows the model encoded in the data structure some information about the model number of vertices handles boundaries and a set of controls and parameters to be used for the editing see Figure 1 If the user wants to operate on more models at the same time the Append button may be used to load a triangle mesh from file and to insert it in the current scene without removing the existing mesh es Notice that no geometrical check is performed on the newly loaded mesh that may consequently have degenerate elements To automatically remove all the degeneracies of the current meshes use the buttons provided in the Check amp Repair window To load multiple models at once and perform a global geometric correction just pass all thei
15. ed through dense and non adaptive samplings Works on the entire mesh Algorithms gt Simplify This button pops up a dialog containing a set of parameters for the simplification The user can set the desired number of vertices and choose whether to prevent mesh inversion taking into account that in this case the processing time grows lightly As a rule of thumb the prevent invertion should be used when the surface is densely sampled on large flat regions It is important to consider that due to topological constraints it cannot be guaranteed that the target number of vertices is reached The simplification strategy implemented uses the quadric error metrics introduced by Garland Setting the multiple choice parameter to a value greater than zero makes the method use a faster but less precise algortihm the higher is this value the slower and more precise is the simplification Works on the entire mesh Algorithms gt Marching Cubes This operation remeshes the model using a marching cubes like pattern The user must select the size of the grid and the process is performed according to the Marching Intersections paradigm This functionality is particularly useful to find a single component approximation of a set of nearly adjacent meshes Vertices of the new mesh can be forced to coincide with vertices of the grid In their turn vertices of the grid can be forced to be integer values Works on the entire mesh Algorithms
16. edral angles degenerate triangles and so on No new vertex is inserted Modelling gt Interaction gt Fill Holes This is as Interaction gt Triangulate Holes but refines and smooths the resulting patch so as to reproduce the sampling density of neighboring regions and to have a tangential continuity with the surrounding mesh 17 Modelling gt Interaction gt Flip shell When the user clicks on a triangle that triangle along with all the other triangles in the same connected component are reversed that is their orientations and therefore their normals are inverted Modelling gt Interaction gt Selects shell When this toggle is set the connected component containing the triangle clicked is selected ReMESH M Attene Modelling gt Interaction gt Select SB region Selects all the triangles belonging to a sharply bounded region Specifically the surface point the user clicks on is used as a seed to grow the selected region up to edges tagged as sharp Modelling gt Interaction gt Tag Sharp Features When this toggle is set the behavior of the clicks is similar to the case of select triangles except for the fact that here the user selects edges instead of triangles To visualize the selected edges it is necessary to turn on the per tag mode from the GUI config gt settings window These edges will receive particular treatment during some other processes e g Algorithms gt Bender Modellin
17. formed is interactive vertex coordinates are actually transformed only when the dialog is closed Modelling gt Transform gt Transform Shells This button pops up a dialog in which each connected component shell is bounded by a sensitive box Each such box can be interactively manipulated through clicks and drags and the corresponding shell is transformed accordingly Dragging a face of the box corresponds to translate 5 ReMESH M Attene the shell Dragging an edge of a box makes the corresponding shell rotate Dragging a vertex of the box causes a uniform scale of the shell Modelling gt Transform gt Redistribute Shells All the connected components are normalized and placed on a virtual sphere Particularly useful to work with several models having very different sizes and positions is space Modelling gt Selection gt Grow Adds to the current selection all the triangles having at least one selected vertex Modelling gt Selection gt Shrink Removes from the current selection all the triangles having at least one vertex on the border of the selection Modelling gt Selection gt Invert Toggles the selection status of the triangles Modelling gt Selection gt Re triangulate Performs a re triangulation of the currently selected region using a Delaunay like approach Specifically a common plane is computed as the average of the planes of the triangles selected then the vertices of the
18. g gt Region radius Its functionality is deprecated Currently its only scope is to show a numerical feedback of the radius selected interactively by the user Algorithms gt Split all edges This button splits all the edges at their middle points The geometry of the mesh does not change but the number of triangles is quadruplicated All the edges are split unless a selection is active in this latter case only the edges belonging to the selected area s are split Algorithms gt Loop subdivide This button performs a subdivision step using Loop s scheme Boundary treatment is provided while no special rule is implemented to manage sharp edges If a selection is active the subdivision works on it only Algorithms gt Bender This button performs a subdivision step using Bender a modified Butterfly scheme in which both boundaries and sharp edges are treated properly 2 If a selection is active the subdivision works on it only Algorithms gt Sqrt 3 Subdivide This button performs a subdivision step based on Kobbelt s approximant sqrt 3 scheme No support is provided for boundaries and sharp edges If a selection is active the subdivision works on it only Algorithms gt Laplacian Smooth This button pops up a dialog where the user can select the number of Laplacian smoothing iterations to be performed on the mesh At each iteration each vertex is moved towards the center of mass of its neighbors The amount of move
19. he user clicks on is removed from the mesh The process takes care of maintaining a coherent data structure possibly by duplicating non manifold vertices that can be created due to the removal Modelling gt Interaction gt Swap edges When the user clicks on or nearby an edge that edge is swapped Also in this case the toolbox takes care of not performing illegal swaps i e boundary edges or resulting incoherent topology Modelling gt Interaction gt Insert vertices When this toggle is set a new vertex is inserted in the point of the surface the user clicks on If such a point is inside a triangle the insertion is performed through a triangle split operation If it is on or nearby an edge an edge split operation subdivides that edge If it is on or nearby a vertex that vertex is snapped to the position of the point In all of the cases the term nearby is quantified by the Acos tolerance chosen by the user in the Check amp Repair window Such a threshold prevents the creation of nearly degenerate triangles that would be produced by splitting a triangle with a point too close to one of its edges Modelling gt Interaction gt Triangulate Holes When this toggle is set the user can click on a boundary edge to start a triangulation routine that tries to fill the corresponding hole The triangulation approach is based on a number of heuristics inspired from 20 4 which try to minimize bad behaviors such as extreme dih
20. hell selection and many others that can be selected from a list of Interaction buttons in the Modeling window 2 2 Selections and cut n paste operations Clicking using the middle mouse button sets the center of a spherical selection that can be used for processing sub regions of the mesh By holding the middle nutton and dragging the mouse it is possible to specify the radius of the selection All the triangles having all the three vertices within the sphere are selected and shown using a different color Holding the shift key before clicking adds the new selection to the existing one Holding the ctrl key before clicking removes the new selection from the existing one Holding both the shift and ctrl keys before clicking intersects the new selection with the existing one Clicking without dragging selects a new region with the same radius of the last one Selected triangles can be removed by pressing the Delete key while in interactive mode The usual shortcuts CTRL C CTRL X and CTRL V can be used to perform copy cut and paste operations respectively The clipboard consists of the selected and copied cut triangles 2 3 Other operations Besides interactive operations there are several other actions available for the user in which some parameters are required In such a case a new dialog style window containing controls on the parameters is shown For example if the user wants to simplify the mesh the corresponding dialog shows among
21. iques for Computer Graphics 23 37 Fortune S 1996 Robustness issues in geometric algorithms In Proceedings of the 1 Workshop on Applied Computational Geometry WACG 96 9 14 Garland M and Heckbert P S 1997 Surface simplification using quadric error metrics In Proceedings of ACM SIGGRAPH 97 209 216 Gu ziec A Taubin G Lazarus F and Horn B 2001 Cutting and stitching Converting sets of polygons to manifold surfaces IEEE Transactions on Visualization and Computer Graphics 7 2 136 151 Guibas L Salesin D and Stolfi J 1989 Epsilon geometry building robust algorithms from imprecise computations ACM Symposium on Computational Geometry 5 208 217 Guskov I and Wood Z 2001 Topological noise removal In Proceedings of Graphics Interface 01 19 26 Hatcher A 2002 Algebraic Topology Cambridge University Press UK Kobbelt L 2000 Sgrt 3 subdivision In Proceedings of ACM SIGGRAPH 00 103 112 Lee A W F Sweldens W Schr der P Cowsar L and Dobkin D 1998 MAPS Multiresolution adaptive parameterization of surfaces In Proceedings of ACM SIGGRAPH 98 95 104 Liepa P 2003 Filling Holes in Meshes In Proceedings of the Eurographic Symposium on Geometry Processing 200 206 Loop C 1987 Smooth subdivision surfaces based on triangles Master s thesis University of Utah USA Department of Mathematics Rocchini C Cignoni P Ganovelli F Montani C Pingi P and Scopign
22. ment is controlled by the parameter Neighbors weight 100 means that in one iteration each vertex is placed exactly in the center of mass of its neighbors Tagged sharp edges are smoothed using a one dimensional support If a selection is active the subdivision works on it only Algorithms gt Uniform Remesh This button strives to uniformize the vertex distribution on the model The number of vertices in the new mesh can be specified in the dialog along with the number of relaxation steps Sharp edges and boundaries are handled properly Although a selection may be active this feature works on the entire mesh in any case Algorithms gt Open to Disk This operation performs a topological cut along edges in order to make the mesh homeomorphic to M Attene ReMESH a disk Edges and vertices belonging to the cuts are properly duplicated Algorithms gt Spherize Iterative flattening of regions with high gaussian curvature Tips and sharp concavities are greedily smoothed Works on the entire mesh Algorithms gt Feature Recover When selecting this button an Edge Sharpener filter is run 1 A dialog is popped up from which the user may select threshold values default values are provided Note that a zero value of the parameter threshold normal angle implies that the algorithm automatically computes this value based on an averaging of the angles throughout the whole surface Default values are safe for rough meshes obtain
23. nual was chosen from the Edit menu Background Color This is another set of controls to define the color of the background of the scene being rendered These controls are not interactive that is the user is required to select OK to show the result Per face color This button toggles the status per face color which defines wether the mesh must be rendered with a single material color throughout the whole surface or with different colors for different triangles When this toggle is set ReMesh shows selected triangles using a brighter color with respect to the remaining surface Notice that this feature may slightly impact on the rendering performances Per tag color As ReMesh supports edge tagging this button allows the user to display edges currently tagged as sharp using a different color red Notice that this feature may slightly impact on the rendering performances Show Edges This button toggles between the default flat shading and the hidden line flat shading More visualization options may be selected through the proper pull down menu by right clicking into the rendering area This menu includes the old hidden line visualization mode Visualization modes Per face Per tag and Show edges may be also toggled through the buttons placed on the top left of the canvas 6 File Operations This menu contains buttons to add meshes to the current scene and to save the current scene to a file Append This oper
24. o R 2001 Marching Intersections an efficient resampling algorithm for surface management In Proceedings of Shape Modeling International SMI 01 296 305 Schroeder W Zarge J and Lorensen W E 1992 Decimation of triangle meshes In Proceedings of ACM SIGGRAPH 92 65 70 Zorin D Schr der P and Sweldens W 1996 Interpolating subdivision for meshes with arbitrary topology In Proceedings of ACM SIGGRAPH 96 189 192
25. on several particular cases In most situations the test model is easily conceivable in mind but at actual design time its formalization turns out to be a much harder task than expected Also simple modifications over an existing triangle mesh may become a tedious work without a suitable interactive environment In order to simplify the remeshing of existing models we have developed ReMESH to interactively edit manifold triangle meshes mostly through user friendly actions such as mouse clicks and drags 1 ReMESH ReMESH incorporates a wrapper for loading several file formats including the web standard VRML 2 0 the older VRML 1 0 the OpenInventor file format iv the Object File Format off Stanford s PLY Wavefront s OBJ Stereolithography stl and the SWM which is the compressed format produced by the SwingWrapper encoder 3 In all of the cases however the parser assumes that the file has one section describing the vertex coordinates and one section describing the faces only simply connected faces are allowed and are automatically triangulated further information transformations colors is ignored While loading a data structure such as the one described in appendix B is initialized Some file formats however may represent sets of polygons which are non manifold and or non orientable In this case the loader runs the Cutting amp Stitching algorithm 11 to make the mesh manifold If the resulting manifold surfa
26. oved from the mesh unless their removal would corrupt the topology in this case the user must manually remove these elements see Check Geometry above Note that in extreme cases very large or wire like cylinders connecting two bodies this action may also cause topological modifications Remove Overlapping Triangles This action removes all of the triangles which form an excessive dihedral angle with one of the neighbors A dihedral angle is excessive if it is less than e of more than n e Remove Tiny Handles This action looks for small handles and tunnels referred to as topological noise in 13 and selects them The threshold size for handles to be removed is controlled through the spherical selection tool which helps the user in having a visual idea of that size Select Boundary Triangles This features selects all the triangles having at least one vertex on the boundary This may be useful for example to erode range maps in which the boundary typically incorporates most of the measurement distortion Select Intersecting Triangles This selects all the intersecting triangles and works both on self intersections and on intersections of disconnected components If a selection was alredy present the test is performed for selected triangles only and results in a sub selection Acos tolerance Controls the value of g Notice that a zero value makes the tool non robust Allowed values for e range from 0 to arcsin 0 00499 5
27. r filenames to the command line 1 1 Point and Click Help To obtain information about a widget of the toolbox first click on Help and while the cursor looks like a hand click on the desired widget to pop up a help dialog If no dialog is displayed it means that no help is available for that widget ReMESH M Attene C grayloc_10kv wrl i Yertices 9998 Edges 30042 Triangles 20028 Boundaries 0 Handles 9 Shells 1 w GE Modelling Algorithms Check amp Repair Snapshot wW W 0 CC tt A oomme fi _ Rotx Roty Meee GUI Config Undo Help File Ea Quit Figure 1 Screenshot of the graphical user interface of the remeshing tool 1 2 Navigating the scene The graphical part of the toolbox is built upon SGI s Open Inventor toolkit and most of the facilities for navigating the scene have been inherited from it For self containedness however we briefly sketch them here The canvas and all of the controls in its window are part of an Examiner viewer component of Open Inventor It allows the user to rotate the view around a point of interest using a virtual trackball This viewer also allows the user to translate the camera in the viewer plane as well as dolly move forward and backward to get closer to or further away from the point of interest The viewer also supports seek to quickly move the camera to a desired point With reference to Figure 1 the three wheels labeled Rotx
28. rl to the filename and saves it as an ASCII VRML 1 0 model 13 ReMESH M Attene 7 Manifold triangle meshes Let V be a nonempty set An abstract simplicial complex 14 is a collection of finite nonempty subsets of V such that every v e V belongs to and if A is an element of then so is every nonempty subset of A Each element of V is called a vertex of X An element o of of cardinality k 1 is called a k simplex and k is the order of o hence a 0 simplex is a vertex A d simplex o is said to be incident at a k simplex t if t Co Let Vs be a set of d 1 affinely independent points in the 3 dimensional Euclidean space R with d lt 3 The subset o of R formed by the points x that can be expressed as the convex combination of the points v of Vo d d x x with Sl 1 20 i 0 i 0 is called an Euclidean d simplex generated by Vs and the points of V are called the vertices of o Any Euclidean s simplex t generated by a set V C Vo of cardinality s lt d is called an s face of o A finite collection of simplexes is an Euclidean simplicial complex iff the following conditions hold 1 For each simplex o e all faces of o belong to 2 For each pair of simplexes o and 1 either o A t or o A Tis a face of both o and t Let V be a nonempty set and let X be an abstract simplicial complex on V An embedding of into R is a function f V gt R such that e For every k simplex o in the set o gener
29. ror introduced cannot always be neglected In the context of our remeshing toolbox such an error may perturb the geometry and thus cause the creation of degenerate elements self intersecting surfaces and a number of other flaws Although a slight error in the geometry may be simply interpreted as noise when performing computations such a slight modification may cause a wrong branching in the process pipeline and as a consequence it may cause a topological inconsistence or a failure of the algorithm In order to deal with robustness we chose to implement a strategy based on the Epsilon Geometry introduced in 12 The toolbox provides the possibility for the user to choose a threshold angle s In all of the internal computations including the loading step the toolbox prevents the creation of triangles with angles smaller than or bigger than n e Such a prevention is carried out through swapping and contraction of short edges inspired from ideas of 5 The default value of is arcsin 10 by experiment this value proved to be a good compromise between precision and robustness Even if the strategy implemented does not guarantee robustness in all of the cases we have found that it avoids nearly all of the most common problems when dealing with remeshing Furthermore it is worth to be considered that if the input model has many degenerate faces according to the value of the corrected mesh may be strongly distorted To cope with this c
30. s them This is particularly useful to topologically join several connected components that are usually created by geometric modeling tools 4 Remove Smallest Components This action scans the data structure and removes all of the connected components but the one with the largest number of triangles This is useful for eliminating typical tiny disconnected sheets from models coming from marching cubes or other sorts of polygonization algorithms 5 Orient Normals This action scans the data structure and for each connected component orients the triangle normals consistently If a connected component is closed triangle normals are oriented so that the outer surface is visible i e normals point outwards the enclosed solid 6 Duplicate non manifold vertices This action checks for non manifold vertices and for each one M Attene ReMESH 10 11 12 of them creates a copy of the vertex for each connected component in its original VT The incidence relations of the neighboring edges are then updated with the new vertices so as to have a single component VT for each copy Notice that this operation is purely topological that is the geometry of the surface is not modified As for the Check Connectivity button however this should have no effect in normal conditions Remove Degenerate Triangles This button performs a removal of possible degenerate triangles According to the current value of e all of the degenerate triangles are rem
31. teractive operation Tag Sharp Edges all of the edges in which the normals of the two incident triangles form an excessive angle The threshold value is selected through a dialog and defaults to PI 4 45 degrees Modelling gt Join Boundaries This feature requires the user to click on two vertices belonging to two different boundary loops Starting from such a pair the algorithm joins the two loops with new triangles Such newly inserted M Attene ReMESH triangles remain selected for possible further processing The two boundaries can be just connected that is only two triangles are added to chenge the topology If the boundaries are to be filled completely as opposed to being just connected the user may choose whether to refine the patch by inserting additional vertices or to smooth it by moving additional vertices towards positions that make the patch fairly smooth with respect to the original geometry Modelling gt Interaction gt Select triangles When this toggle is set each triangle the user clicks on is marked as selected and subsequent operations requiring a selection will act only on these triangles If the user clicks on a previously selected triangle it changes its state to unselected In order to display selected triangles using a different color it is possible to switch to per face color mode from the GUI config gt settings window Modelling gt Interaction gt Remove triangles Each triangle t
32. y turning around v through successive applications of the coded relations keeping track of the already traversed triangles In particular the initial VE is initialized as the VE then choose one triangle of the ET VT v let it be 7 and choose the edge e of TE such that v e EV e and e VE Now add e to the set VE and repeat the same operations by considering e as the new VE If v is not on the boundary the process terminates when e becomes equal to the original VE v If v is on the boundary e may become a boundary edge In this case the process continues by considering the unconsidered triangle of ET VE v and turns in the opposite sense An example of this process is depicted in the following Figure 4 ROS la Qa Bos gt lt b ACR Figure 4 Reconstruction of the VE relation starting from the VE Note that this process requires a number of operations that is linearly proportional to the number of elements of the final VE therefore it is optimal All the other relations which are not explicitly stored in the data structure may be derived in optimal time as follows M Attene ReMESH e VE v construction described above e VV v weEEV e e e VE v and w v e VT v te ET e e e VE v e EE e f e TE t t e ET e and f e e TV t ve EV e e e TE t e TT ye ET e e e TE t andy t ReMESH M Attene Bibliography 1 2 3 4 5 6 7 8 9 10 11 12 13
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