Hot: Hodge-optimized triangulations

ACM Transactions on Graphics

Volumn 30, Issue 4, 2011, Pages

  Mullen, Patrick ^a   Memari, Pooran ^a   De Goes, Fernando ^a   Desbrun, Mathieu ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Discrete Exterior Calculus; Discrete Hodge Star; Optimal Transport; Optimal triangulations

Indexed keywords

DELAUNAY TRIANGULATION; DISCRETE EXTERIOR CALCULUS; DISCRETE HODGE STAR; FUNCTIONALS; OPTIMAL TRANSPORT; OPTIMAL TRIANGULATION; ORTHOGONALITY; POWER DIAGRAMS; PRIMAL-DUAL; VORONOI;

INTERACTIVE COMPUTER GRAPHICS; OPTIMIZATION; STARS;

TRIANGULATION;

EID: 80051883892     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/1964921.1964998     Document Type: Article

References (35)

1. ALLIEZ, P., COHEN-STEINER, D., YVINEC, M., AND DESBRUN, M. 2005. Variational tetrahedral meshing. ACM Trans. On Graphics (SIGGRAPH) 24, 3 (July), 617-625.
2. AUCHMANN, B., AND KURZ, S. 2006. A geometrically defined discrete Hodge operator on simplicial cells. IEEE Trans. Magn. 42, 4, 643-646.
3. BATTY, C., XENOS, S., AND HOUSTON, B. 2010. Tetrahedral embedded boundary methods for accurate and flexible adaptive fluids. Computer Graphics Forum (Eurographics) 29 (May), 695- 704(10).
4. BOSSAVIT, A. 1998. Computational Electromagnetism. Academic Press, Boston.
5. CGAL, 2010. Computational Geometry Algorithms Library (release 3.8). http://www.cgal.org.
6. CHENG, S.-W., DEY, T. K., AND LEVINE, J. 2008. Theory of a practical Delaunay meshing algorithm for a large class of domains. In Algorithms, Architecture and Information Systems Security, B. Bhattacharya, S. Sur-Kolay, S. Nandy, and A. Bagchi, Eds., vol. 3 of World Scientific Review, 17-41.
7. DESBRUN, M., KANSO, E., AND TONG, Y. 2007. Discrete differential forms for computational modeling. In Discrete Differential Geometry, A. Bobenko and P. Schröder, Eds. Springer.
8. DU, Q., FABER, V., AND GUNZBURGER, M. 1999. Centroidal voronoi tessellations: Applications and algorithms. SIAM Rev. 41 (December), 637-676. (Pubitemid 30536738)
9. EDELSBRUNNER, H. 1987. Algorithms in Combinatorial Geometry. Springer-Verlag.
10. ELCOTT, S., TONG, Y., KANSO, E., SCHRöDER, P., AND DESBRUN, M. 2007. Stable, circulation-preserving, simplicial fluids. ACM Trans. on Graphics 26, 1 (jan), 4.
11. FISHER, M., SPRINGBORN, B., BOBENKO, A. I., AND SCHRöDER, P. 2006. An algorithm for the construction of intrinsic delaunay triangulations with applications to digital geometry processing. In ACM SIGGRAPH Courses, 69-74.
12. GLICKENSTEIN, D. 2005. Geometric triangulations and discrete Laplacians on manifolds. Arxiv preprint math/0508188.
13. GRADY, L. J., AND POLIMENI, J. R. 2010. Discrete Calculus: Applied Analysis on Graphs for Computational Science. Springer.
14. HAURET, P., KUHL, E., AND ORTIZ, M. 2007. Diamond Elements: a finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity. Int. J. Numer. Meth. Engng. 72, 3, 253-294. (Pubitemid 47559589)
15. HIRANI, A. N. 2003. Discrete Exterior Calculus. PhD thesis, Caltech.
16. LéVY, B., AND LIU, Y. 2010. Lp Centroidal Voronoi Tesselation and its Applications. ACM Trans. on Graph. 29, 4.
17. LIPMAN, Y., AND DAUBECHIES, I. 2010. Surface Comparison With Mass Transportation. In ArXiv preprint 0912.3488.
18. LIU, Y., WANG, W., Lé VY, B., SUN, F., YAN, D., LU, L., AND YANG, C. 2009. On Centroidal Voronoi Tessellation - energy smoothness and fast computation. ACM Trans. on Graph. 28, 4.
19. MéMOLI, F. 2011. A spectral notion of Gromov-Wasserstein distances and related methods. Journal of Applied and Computational Harmonic Analysis 30, 3, 363-401.
20. MEYER, M., DESBRUN, M., SCHRö DER, P., AND BARR, A. H. 2003. Discrete differential-geometry operators for triangulated 2-manifolds. In Visualization and Mathematics III, Springer- Verlag, H.-C. Hege and K. Polthier, Eds., 35-57.
21. MUNKRES, J. R. 1984. Elements of Algebraic Topology. Addison- Wesley.
22. NOCEDAL, J., AND WRIGHT, S. J. 1999. Numerical optimization. Springer Verlag.
23. OKABE, A., BOOTS, B., SUGIHARA, K., AND CHIU, S. N. 2000. Spatial tessellations: Concepts and applications of Voronoi diagrams, 2nd ed. Probability and Statistics. Wiley.
24. PEDOE, D. 1988. Geometry, a comprehensive course, 2nd ed. Dover Publications.
25. PEROT, J. B., AND SUBRAMANIAN, V. 2007. Discrete calculus methods for diffusion. Journal of Computational Physics 224, 59-81.
26. PINKALL, U., AND POLTHIER, K. 1993. Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2(1), 15-36.
27. RAJAN, V. 1994. Optimality of the Delaunay triangulation in Rd. Discrete and Computational Geometry 12, 1, 189-202.
28. SHEWCHUK, J. 2002. What is a Good Linear Element? Interpolation, Conditioning, and Quality Measures. In Proc. of the 11th Int. Meshing Roundtable, 115-126.
29. SIEGER, D., ALLIEZ, P., AND BOTSCH, M. 2010. Optimizing voronoi diagrams for polygonal finite element computations. In Proceedings of the 19th International Meshing Roundtable. 335-350.
30. TOURNOIS, J., WORMSER, C., ALLIEZ, P., AND DESBRUN, M. 2009. Interleaving delaunay refinement and optimization for practical isotropic tetrahedron mesh generation. ACM Trans. Graph. 28 (July), 75:1-75:9.
31. VANDERZEE, E., HIRANI, A. N., GUOY, D., AND RAMOS, E. 2010. Well-centered triangulation. SIAM Journal on Scientific Computing 31, 6, 4497-4523.
32. VILLANI, C. 2009. Optimal Transport: Old and New. Fundamental Principles of Mathematical Sciences, 338. Springer-Verlag.
33. WARDETZKY, M., MATHUR, S., Kä LBERER, F., AND GRINSPUN, E. 2007. Discrete laplace operators: no free lunch. In Symposium on Geometry processing, 33-37.
34. WARREN, J., SCHAEFER, S., HIRANI, A., AND DESBRUN, M. 2007. Barycentric coordinates for convex sets. Advances in Computational Mathematics 27, 3, 319-338.
35. WILSON, S. O. 2007. Cochain algebra on manifolds and convergence under refinement. Topology and its Applications 154, 9, 1898-1920.