The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.02 - Feb. (2014 vol.20)
pp: 223-237
Jonathan Bronson , University of Utah, Salt Lake City
Joshua A. Levine , University of Utah, Salt Lake City
Ross Whitaker , University of Utah, Salt Lake City
ABSTRACT
We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach.
INDEX TERMS
Lattices, Materials, Topology, Geometry, Finite element analysis, Joining processes, Biological system modeling, adaptive meshing, Lattices, Materials, Topology, Geometry, Finite element analysis, Joining processes, Biological system modeling, guaranteed meshing, Tetrahedral meshing, multimaterial, multilabel, biomedical, conformal meshing, watertight, mesh quality
CITATION
Jonathan Bronson, Joshua A. Levine, Ross Whitaker, "Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees", IEEE Transactions on Visualization & Computer Graphics, vol.20, no. 2, pp. 223-237, Feb. 2014, doi:10.1109/TVCG.2013.115
REFERENCES
[1] N. Amenta, S. Choi, T.K. Dey, and N. Leekha, “A Simple Algorithm for Homeomorphic Surface Reconstruction,” Int'l J. Computational Geometry & Applications, vol. 12, nos. 1/2, pp. 125-141, 2002.
[2] M. Bern, P. Chew, D. Eppstein, and J. Ruppert, “Dihedral Bounds for Mesh Generation in High Dimensions,” Proc. Sixth Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 189-196, 1995.
[3] BioMesh3D, “Quality Mesh Generator for Biomedical Applications,” Scientific Computing and Imaging Inst. (SCI).
[4] J. Bloomenthal and K. Ferguson, “Polygonization of Non-Manifold Implicit Surfaces,” Proc. ACM SIGGRAPH, pp. 309-316, 1995.
[5] J.-D. Boissonnat and S. Oudot, “Provably Good Sampling and Meshing of Surfaces,” Graphical Models, vol. 67, no. 5, pp. 405-451, 2005.
[6] D. Boltcheva, M. Yvinec, and J.-D. Boissonnat, “Feature Preserving Delaunay Mesh Generation from 3d Multi-Material Images,” Computer Graphics Forum, vol. 28, no. 5, pp. 1455-1464, 2009.
[7] L. Branets and G.F. Carey, “Condition Number Bounds and Mesh Quality,” Numerical Linear Algebra with Applications, vol. 17, no. 5, pp. 855-869, 2010.
[8] J. Bronson, J. Levine, and R. Whitaker, “Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees,” Proc. 21st Int'l Meshing Roundtable (IMR), Page to Appear, 2012.
[9] J.R. Bronson, J.A. Levine, and R.T. Whitaker, “Particle Systems for Adaptive, Isotropic Meshing of CAD Models,” Proc. 19th Int'l Meshing Roundtable (IMR), pp. 279-296, Oct. 2010.
[10] S. Cheng, T. Dey, and J. Shewchuk, Delaunay Mesh Generation. CRC Press, 2012.
[11] S.-W. Cheng, T.K. Dey, H. Edelsbrunner, M.A. Facello, and S.-H. Teng, “Sliver Exudation,” Proc. 15th Ann. Symp. Computational Geometry, pp. 1-13, 1999.
[12] S.-W. Cheng, T.K. Dey, and E.A. Ramos, “Delaunay Refinement for Piecewise Smooth Complexes,” Discrete & Computational Geometry, vol. 43, no. 1, pp. 121-166, 2010.
[13] S.-W. Cheng, T.K. Dey, E.A. Ramos, and T. Ray, “Sampling and Meshing a Surface with Guaranteed Topology and Geometry,” SIAM J. Computing, vol. 37, no. 4, pp. 1199-1227, 2007.
[14] N. Chentanez, B.E. Feldman, F. Labelle, J.F. O'Brien, and J.R. Shewchuk, “Liquid Simulation on Lattice-Based Tetrahedral Meshes,” Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation (SCA), pp. 219-228, Aug. 2007.
[15] L.P. Chew, “Constrained Delaunay Triangulations,” Proc. Third Ann. Symp. Computational Geometry (SCG '87), pp. 215-222, 1987.
[16] L.P. Chew, “Guaranteed-Quality Mesh Generation for Curved Surfaces,” Proc. Ninth Ann. Symp. Computational Geometry, pp. 274-280, 1993.
[17] M. Dannhauer, B. Lanfer, C.H. Wolters, and T.R. Knsche, “Modeling of the Human Skull in EEG Source Analysis,” Human Brain Mapping, vol. 32, no. 9, pp. 1383-1399, 2011.
[18] T.K. Dey, F. Janoos, and J.A. Levine, “Meshing Interfaces of Multi-Label Data with Delaunay Refinement,” Eng. with Computers, vol. 28, no. 1, pp. 71-82, Jan. 2012.
[19] T. Etiene, L. Nonato, C. Scheidegger, J. Tienry, T. Peters, V. Pascucci, R. Kirby, and C. Silva, “Topology Verification for Isosurface Extraction,” IEEE Trans. Visualization & Computer Graphics, vol. 18, no. 6, pp. 952-965, June 2012.
[20] L.A. Freitag and C. Ollivier-Gooch, “Tetrahedral Mesh Improvement Using Swapping and Smoothing,” Int'l J. Numerical Methods in Eng., vol. 40, no. 21, pp. 3979-4002, 1997.
[21] P. Frey and P. George, Mesh Generation. John Wiley & Sons, 2010.
[22] A. Fuchs, “Automatic Grid Generation with Almost Regular Delaunay Tetrahedra,” Proc. Seventh Int'l Meshing Roundtable (IMR), pp. 133-147, 1998.
[23] A. Guéziec and R.A. Hummel, “Exploiting Triangulated Surface Extraction Using Tetrahedral Decomposition,” IEEE Trans. Visualization & Computer Graphics, vol. 1, no. 4, pp. 328-342, Dec. 1995.
[24] S. Institute, “SCIRun: A Scientific Computing Problem Solving Environment,” Scientific Computing and Imaging Inst. (SCI), http:/www.scirun.org, 2012.
[25] S. Institute, “Cleaver: A MultiMaterial Tetrahedral Meshing Library and Application,” Scientific Computing and Imaging Inst. (SCI), http://www.sci.utah.edu/softwarecleaver. 2012.
[26] B.M. Isaacson, L.B. Brunker, A.A. Brown, J.P. Beck, G.L. Burns, and R.D. Bloebaum, “An Evaluation of Electrical Stimulation for Improving Periprosthetic Attachment,” J. Biomedical Materials Research Part B: Applied Biomaterials, vol. 97B, no. 1, pp. 190-200, 2011.
[27] T. Ju, F. Losasso, S. Schaefer, and J. Warren, “Dual Contouring of Hermite Data,” Proc. ACM 29th Ann. Conf. Computer Graphics and Interactive Techniques (SIGGRAPH '02), pp. 339-346, 2002.
[28] B.M. Klingner and J.R. Shewchuk, “Aggressive Tetrahedral Mesh Improvement,” Proc. 16th Int'l Meshing Roundtable (IMR), pp. 3-23, 2007.
[29] F. Labelle and J.R. Shewchuk, “Isosurface Stuffing: Fast Tetrahedral Meshes with Good Dihedral Angles,” Proc. ACM SIGGRAPH, 2007.
[30] Y. Liu, P. Foteinos, A. Chernikov, and N. Chrisochoides, “Multi-Tissue Mesh Generation for Brain Image,” Proc. 19th Int'l Meshing Roundtable (IMR), pp. 367-384, Oct. 2010.
[31] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Proc. ACM SIGGRAPH, pp. 163-169, 1987.
[32] B. Merriman, J.K. Bence, and S.J. Osher, “Motion of Multiple Junctions: A Level Set Approach,” J. Computational Physics, vol. 112, no. 2, pp. 334-363, 1994.
[33] M.D. Meyer, R.T. Whitaker, R.M. Kirby, C. Ledergerber, and H. Pfister, “Particle-Based Sampling and Meshing of Surfaces in Multimaterial Volumes,” IEEE Trans. Visualization & Computer Graphics, vol. 14, no. 6, pp. 1539-1546, Nov. 2008.
[34] N. Molino, R. Bridson, J. Teran, and R. Fedkiw, “A Crystalline, Red Green Strategy for Meshing Highly Deformable Objects with Tetrahedra,” Proc. 12th Int'l Meshing Roundtable (IMR), pp. 103-114, 2003.
[35] G.M. Nielson and R. Franke, “Computing the Separating Surface for Segmented Data,” Proc. IEEE Visualization, pp. 229-233, 1997.
[36] C. Paige and M. Saunders, “Solution of Sparse Indefinite Systems of Linear Equations,” SIAM J. Numerical Analysis, vol. 12, no. 4, pp. 617-629, 1975.
[37] A.A. Pasko, V. Adzhiev, A. Sourin, and V.V. Savchenko, “Function Representation in Geometric Modeling: Concepts, Implementation and Applications,” The Visual Computer, vol. 11, no. 8, pp. 429-446, 1995.
[38] J.-P. Pons, F. Ségonne, J.-D. Boissonnat, L. Rineau, M. Yvinec, and R. Keriven, “High-Quality Consistent Meshing of Multi-Label Data Sets,” Proc. 20th Int'l Conf. Information Processing in Medical Imaging (IPMI), pp. 198-210, 2007.
[39] J. Ruppert, “A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation,” J. Algorithms, vol. 18, no. 3, pp. 548-585, 1995.
[40] J.R. Shewchuk, “Tetrahedral Mesh Generation by Delaunay Refinement,” Proc. 14th Ann. Symp. Computational Geometry, pp. 86-95, 1998.
[41] J.R. Shewchuk, “What Is a Good Linear Element? Interpolation, Conditioning, and Quality Measures,” Proc. Int'l Meshing Roundtable (IMR), pp. 115-126, 2002.
[42] J.R. Shewchuk, “General-Dimensional Constrained Delaunay and Constrained Regular Triangulations I: Combinatorial Properties,” Discrete and Computational Geometry, vol. 39, pp. 580-637, 2005.
[43] H. Si, “TetGen: A Quality Tetrahedral Mesh Generator and Three-Dimensional Delaunay Triangulator,” http:/tetgen.berlios.de/, 2013.
[44] CGAL, “Computational Geometry Algorithms Library,” http:/www.cgal.org, 2013.
[45] J. Tournois, C. Wormser, P. Alliez, and M. Desbrun, “Interleaving Delaunay Refinement and Optimization for Practical Isotropic Tetrahedron Mesh Generation,” ACM Trans. Graphics, vol. 28, no. 3,article 75, 2009.
[46] J.K. Triedman, M. Jolley, J. Stinstra, D.H. Brooks, and R. MacLeod, “Predictive Modeling of Defibrillation Using Hexahedral and Tetrahedral Finite Element Models: Recent Advances,” J. Electrocardiology, vol. 41, no. 6, pp. 483-486, 2008.
[47] J. Wang and Z. Yu, “Feature-Sensitive Tetrahedral Mesh Generation with Guaranteed Quality,” Computer-Aided Design, vol. 44, no. 5, pp. 400-412, 2012.
[48] J. Williams and J. Rossignac, “Tightening: Curvature-Limiting Morphological Simplification,” Proc. ACM Symp. Solid and Physical Modeling (SPM), 2004.
[49] D.-M. Yan, B. Lévy, Y. Liu, F. Sun, and W. Wang, “Isotropic Remeshing with Fast and Exact Computation of Restricted Voronoi Diagram,” Computer Graphics Forum, vol. 28, no. 5, pp. 1445-1454, 2009.
[50] M.A. Yerry and M.S. Shephard, “Automatic Three-Dimensional Mesh Generation by the Modified-Octree Technique,” Int'l J. Numerical Methods in Eng., vol. 20, pp. 1965-1990, 1984.
[51] Z. Yu, M.J. Holst, and J.A. McCammon, “High-Fidelity Geometric Modeling for Biomedical Applications,” Finite Elements in Analysis and Design, vol. 44, no. 11, pp. 715-723, 2008.
[52] N. Zhang, W. Hong, and A. Kaufman, “Dual Contouring with Topology-Preserving Simplification Using Enhanced Cell Representation,” Proc. IEEE Visualization (VIS '04), pp. 505-512, 2004.
[53] Y. Zhang, C. Bajaj, and B.-S. Sohn, “3d Finite Element Meshing from Imaging Data,” Computer Methods in Applied Mechanics and Eng., vol. 194, no. 4849, pp. 5083-5106, 2005.
[54] Y. Zhang, T. Hughes, and C.L. Bajaj, “Automatic 3d Mesh Generation for a Domain with Multiple Materials,” Proc. Int'l Meshing Roundtable (IMR), pp. 367-386, 2007.
[55] Y. Zhang and J. Qian, “Resolving Topology Ambiguity for Multiple-Material Domains,” Computer Methods in Applied Mechanics and Eng., vol. 247/248, pp. 166-178, 2012.
164 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool