한국컴퓨터그래픽스학회논문지 (Journal of the Korea Computer Graphics Society)

  • 제17권2호
  • /
  • Pages.45-53
  • /
  • 2011
  • /
  • 1975-7883(pISSN)
  • /
  • 2383-529X(eISSN)
한국컴퓨터그래픽스학회 (Korea Computer Graphics Society)
권호 표지

옥트리 기반의 적응적 사면체 요소망구성

Octree-Based Adaptive Tetrahedral Meshing

  • 투고 : 2010.04.15
  • 심사 : 2010.05.03
  • 발행 : 2011.06.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 양질의 이면각을 가진 사면체로 물체 내부를 채우는 볼륨 요소망 구성 방법을 제안한다. 본 논문에서 제안한 방법은 실행시간이 빠르고 안정적이며 구현이 쉬운 장점을 가지고 있다. 효율적인 공간 활용을 위해 옥트리를 사용함으로써 물체 내부에서 표면에 이르기까지 다양한 크기의 사면체를 활용할 수 있다. 최소 이면각을 최대화하고 최대 이면각을 최소화하는 양질의 요소망을 얻기 위하여 옥트리의 인접 셀들 사이의 레벨 차이를 제한하며, 옥트리 및 요소망 생성 속도를 높이기 위하여 정규 격자에서의 부호거리장을 사용한다. 본 논문에서 제안한 요소망 구성 방법은 유한요소법 기반의 변형체 시뮬레이션이나 사면체 기반의 유체 시뮬레이션 등에서 유용하게 활용될 수 있다.

This paper proposes a volume meshing method that fills the inside of an object with tetrahedra, of which dihedral angles are good. The suggested method is fast, stable and easy to implement It can also utilize an octree structure to space-efficiently fill an object with graded tetrahedra by reducing the total number of tetrahedra. To obtain a high-quality mesh with good dihedral angles, we restrict the octree such that any pair of neighboring cells only differs by one level. To efficiently construct a restricted-octree and generate a volume mesh from the octree, we utilize a signed distance field of an object on its bounded workspace. The suggested method can be employed in FEM-based simulation of large elasto-plastic deformation and tetrahedral-mesh-based simulation of fluid flow.

키워드

참고문헌

  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. https://doi.org/10.1137/S0097539796314124
  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. https://doi.org/10.1016/S0022-0000(05)80059-5
  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. https://doi.org/10.1145/355483.355487
  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. F. Labelle and J. R. Shewchuk, "Isosurface stuffing: Fast tetrahedral meshes with good dihedral angles," ACM Transactions on Graphics (Proc. SIGGRAPH 2007), vol. 26, no. 3, p. 57, 2007.
  11. J. Brerentzen and H. Aaenas, "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. https://doi.org/10.1080/10867651.1998.10487487
  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. https://doi.org/10.1073/pnas.93.4.1591