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A tetrahedral mesh generator that does isosurface stuffing with an acute tetrahedral tile.
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Quartet ******* A tetrahedral mesh generator based on Jonathon Shewchuk's isosurface stuffing algorithm in combination with the A15 acute tetrahedral tile. written by: Robert Bridson (www.cs.ubc.ca/~rbridson) Crawford Doran (www.crawforddoran.com) -------------------------------------- Overview ========== Quartet converts a watertight triangle mesh into a high-quality uniform tetrahedral mesh that closely approximates the geometry, up to the curvature implied by the specified grid sampling (dx). Optionally, the tetrahedral mesh can be warped to match sharp features on the input, and also improved by a quality optimization pass. Building Quartet ================= 1) It may be necessary to edit Makefile.defs in order to ensure that platform-specific variables are set correctly. These include the compiler, linker, and all flags associated with them, including libraries. 2) Run 'make depend' 3) Run 'make' and/or 'make release' ('make' is equivalent to 'make debug') Running Quartet ================== Quartet is run from the command line with the following syntax: quartet <input.obj> <dx> <output.tet> [-f <feature.feat>] [-a <angle_threshold>] [-s <surface.obj>] [-i] [-o] - <input.obj> is the OBJ file containing the surface to be converted to a tetrahedral mesh. - <dx> is the grid spacing used in the isosurface stuffing algorithm. The generated tetrahedra will be approximately this size. - <output.tet> is a path to the file where the resulting tetrahedral mesh will be saved. The optional flags have the following effects: -f <features.feat> -- The given file <features.feat> contains lists of points and edges indicating sharp corners and ridges in the input. The output mesh will resolve these features as well as possible. -a <angle_threshold> -- Auto-detects sharp features in the input. Edges with a dihedral angle smaller than <angle_threshold> degrees will be resolved in the output as well as possible. In addition, these features will be written to a file called 'auto.feat' (which can then be fed to the -f option in future executions). -s <surface.obj> -- The boundary of the resulting tetrahedral mesh is written to <surface.obj>. This is largely for convenience of visualizing the result. -i -- Intermediate stages of the mesh generation process are saved to disk in files named 'N_*_.tet' where N is the numbering of the steps. -o -- Perform quality optimization on the resulting tetrahedral mesh. Example inputs can be found in the 'meshes' directory. For the inputs with sharp features, corresponding .feat files are provided. Example usages: quartet dragon.obj 0.01 dragon_01.tet -o -s dragon.obj quartet fandisk.obj 0.1 fandisk_1.tet -f fandisk.feat quartet block.obj 0.5 block_5.tet -a 110.0 -o Running view_tet ================== We have included an OpenGL viewer application for visualizing resulting tet meshes. The viewer is called view_tet, and can be called with the following syntax: view_tet <input.tet> [-s] [-f <features.feat>] [-p (x|y|z)<cutting-plane-pos>]* [-w <num_tets>] Here, <input.tet> is the TET file produced by quartet containing the tet mesh. The optional flags have the following effects: -s -- Assume that <input.tet> is actually <input.obj> and read it in as a surface mesh from an OBJ file. -f <features.feat> -- Displays the sharp features in the file <features.feat> alongside the mesh. -p (x|y|z)<cutting-plane-pos> -- Specifies a plane to cut the mesh so the viewer can see "inside" of it. The plane is specified by which coordinate axis is its normal and its position along that axis. Multiple planes can be specified with multiple occurrences of this flag. -w num_tets -- Draw the mesh so that the <num_tets> worst-quality tetrahedra are highlighted. Example usages: view_tet block.tet -p x0.0 view_tet dragon.obj -s view_tet fandisk.tet -f fandisk.feat -w 10 Once view_tet is running, the viewer can be controlled with the following inputs: Shift+LeftMouseButton -- Rotate camera Shift+RightMouseButton -- Zoom camera Shift+MiddleMouseButton -- Pan camera Source Code overview ====================== The following files make up the quartet source: Utilities / Data Structures: util.h - a bunch of small useful functions vec.h - a convenience wrapper around fixed-length arrays (for vectors in 3D etc.) array3.h - a convenience wrapper around STL vectors to get 3D arrays sdf.h/cpp - a signed-distance-field data structure for working with level sets read_obj.h/cpp - code to read in a Wavefront .OBJ file trimesh.h/cpp - a simple half-edge triangle mesh data structure tet_mesh.h/cpp - an index-based tetrahedral mesh data structure. Maintains incidence relationships as necessary for fast adjacency queries. features.h/cpp - Data structures representing sharp features of a triangle mesh and aggregations of those features (called FeatureSets) Meshing Functions: geometry_queries.h/cpp - some simple and not-so-simple geometric operations needed for creating signed distance functions from triangle meshes. Uses Jonathan Shewchuk's robust geometric predicates code, found in predicates.cpp (http://www.cs.cmu.edu/~quake/robust.html). make_signed_distance.h/cpp - code for robustly creating a fairly accurate signed distance function of a watertight triangle mesh, sampled on a regular 3D grid. make_tet_mesh.h/cpp - code to create a quality tetrahedral mesh of the interior of a level set tet_quality.h/cpp - functions for measuring quality of tetrahedra based on various metrics match_features.h/cpp - code to restore desired sharp features onto a tetrahedral mesh optimize_tet_mesh.h/cpp - code to improve the overall quality of a given tetrahedral mesh. Uses as much data from the meshing step (ie: sdf, sharp features, etc.) as possible. main.cpp - quartet command-line program Viewer Application: gluvi.h/cpp - code for creating a simple generic OpenGL viewer application view_tet.cpp - view_tet main code file for viewing tet meshes