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Tetrahedra-based Volumetric Meshes.md

Below I collected relevant links and papers more or less pertaining to the subject of tetrahedral meshes. It's an ever-growing list.

Relevant links:

http://en.wikipedia.org/wiki/Types_of_mesh http://en.wikipedia.org/wiki/Tetrahedron http://en.wikipedia.org/wiki/Simplicial_complex

A C++ library that deals with tetrahedral and other volumetric meshes http://www.openvolumemesh.org/

The data structure from "Half-edges redux" could be expanded similarly to OVM for one more indirection. https://fgiesen.wordpress.com/2012/04/03/half-edges-redux/

Mesh Generation (slides) Gives Euler-Poincaré metrics for tet meshes, typical valences, a whole range of methods for tetrahedralization and refinement. http://perso.uclouvain.be/vincent.legat/teaching/documents/meca2170-jfr-cours3.pdf

The Linear Tetrahedron Course paper about tetrahedra, discussing properties, use cases and associated formulas for metrics, transformations, etc. http://www.colorado.edu/engineering/CAS/courses.d/AFEM.d/AFEM.Ch09.d/AFEM.Ch09.pdf

(Vaguely) related research links:

  • An Unified Approach for 2D and 3D Rasterization voxelization of tetrahedra as analog to rasterization of triangles. http://virtual.inesc.pt/siacg02/papers/10.pdf

  • OpenVolumetricMesh-An Efficient Data Structure for Tetrahedral and Hexahedral Meshes Data structure for both cubic and tetrahedral volumes. Elevates the face structure to a half-face structure analog to half-edges. Volume mesh operations are then well-defined. http://openvm.org/data/OVM.pdf

  • TransCut: Interactive Rendering of Translucent Cutouts Renders tetrahedral meshes with subsurface scattering in real time, provides non-destructive cutting to look inside the mesh http://research.microsoft.com/en-us/um/people/stevelin/papers/tvcg13.pdf

  • Half-Edge Multi-Tessellation: A Compact Representation for Multi-Resolution Tetrahedral Meshes Discusses techniques to store different LOD levels of a volume in a single structure for adaptive mesh extraction. ftp://ftp.disi.unige.it/person/DanovaroE/pdf/3dpvt.pdf A newer summary is here

  • The Half-Edge Tree: A Compact Data Structure for Level-of-Detail Tetrahedral Meshes ftp://ftp.disi.unige.it/person/MagilloP/PDF/het-short.pdf

  • Progressive Simplicial Complexes Describes a format to store simplices at varying levels of detail http://groups.csail.mit.edu/graphics/pubs/sigg97-psc.pdf

  • Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes Uses deformable simplical complexes to animate fluids https://www.cs.ubc.ca/~rbridson/docs/misztal-sca2012-multiphaseDSC.pdf

[LD08] Accelerating Ray Tracing using Constrained Tetrahedralizations Tetrahedralizes space around an object to skip space while raytracing http://people.cs.kuleuven.be/~ares.lagae/publications/LD08ARTCT/LD08ARTCT.pdf

Multiple papers on Sparse Voxel Octree Cone Tracing & related stuff:

Books

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