Browse > Article

Tetrahedral Meshing with an Octree-based Adaptive Signed Distance Field  

Park, Seok-Hun (Kwangwoon University)
Choi, Min-Gyu (Kwangwoon University)
Publication Information
Journal of the Korea Computer Graphics Society / v.18, no.1, 2012 , pp. 29-34 More about this Journal
Abstract
High-quality tetrahedral meshes are crucial for FEM-based simulation of large elasto-plastic deformation and tetrahedral-mesh-based simulation of fluid flow. This paper proposes a volume meshing method that exploits an octree-based adaptive signed distance field to fill the inside of a polygonal object with tetrahedra, of which dihedral angles are good. The suggested method utilizes an octree structure to reduce the total number of tetrahedra by space-efficiently filling an object with graded tetrahedra. To obtain a high-quality mesh with good dihedral angles, we restrict the octree in such a way that any pair of neighboring cells only differs by one level. In octree-based tetrahedral meshing, the signed distance computation of a point to the surface of a given object is a very important and frequently-called operation. To accelerate this operation, we develop a method that computes a signed distance field directly on the vertices of the octree cells while constructing the octree using a top-down approach. This is the main focus of the paper. The suggested tetrahedral meshing method is fast, stable and easy to implement.
Keywords
volume meshing; tetrahedral mesh; octree; signed distance field;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 S.-W. Cheng and T. K. Dey, "Quality meshing with weighted delaunay refinement," in Proc. Thirteenth Annual Symposium on Discrete Algorithms, 2002, pp. 137-146.
2 S. A. Mitchell and S. A. Vavasis, "Quality mesh generation in higher dimensions," SIAM Journal on Computing, vol. 29, no. 4, pp. 1334-1370, 2000.   DOI
3 B. S. Baker, E. Grosse, and C. S. Rafferty, "Nonobtuse triangulation of polygons," Discrete and Computational Geometry, vol. 3, no. 2, pp. 147-168, 1998.
4 L. P. Chew, "Guaranteed-quality triangular meshes," Department of Computer Science, Cornell University, Tech. Rep. TR-89-983, 1989.
5 M. Bern, D. Eppstein, and J. R. Gilbert, "Probably good mesh generation," Journal of Computer and System Sciences, vol. 48, no. 3, pp. 384-409, 1994.   DOI
6 S.-W. Cheng, T. K. Dey, H. Edelsbrunner, M. A. Facello, and S.-H. Teng, "Sliver exudation," Journal of the ACM, vol. 47, no. 5, pp. 883-904, 2000.   DOI
7 L. P. Chew, "Guaranteed-quality delaunay meshing in 3D," in Proc. Thirteenth Annual Symposium on Computational Geometry, 1997, pp. 391-393.
8 X.-Y. Li and S.-H. Teng, "Generating well-shaped delaunay meshes in 3D," in Proc. Twelfth Annual Symposium on Discrete Algorithms, 2001, pp. 28-37.
9 F. Labelle, "Sliver removal by lattice refinement," in Proc. Twenty-Second Annual Symposium on Computational Geometry, 2006, pp. 347-356.
10 C. W. Kim, S. H. Park, and M. G. Choi, "Octree-based adaptive tetrahedral meshing," Journal of The Korea Computer Graphics Society, vol. 17, no. 2, pp. 45-53, 2011.   DOI
11 J. Bærentzen and H. Aænas, "Generating signed distance fields from triangle meshes," Information and Mathematical Modelling, Technical University of Denmark, Lyngby, Denmark, Tech. Rep. IMM-TR-2002-21, 2002.
12 C. H. Sequin, "Procedural spline interpolation in unicubix," in Proc. Third USENIX Computer Graphics Workshop, 1986, pp. 63-83.
13 G. Thurmer and C. Wuthrich, "Computing vertex normals from polygonal facets," Journal of Graphics Tools, vol. 3, no. 1, pp. 43-46, 1998.   DOI
14 J. A. Sethian, "A fast marching level set method for monotonically advancing fronts," in Proc. National Academy of Sciences, vol. 93, no. 4, 1996, pp. 1591-1595.   DOI
15 D. Green and D. Hatch, "Fast polygon-cube intersection testing," in Graphics Gems V. Academic Press Professional Inc., 1995, pp. 375-379.