Finding Self-intersections of a Triangular Mesh by Using Visibility Maps

가시 정보를 이용한 삼각망의 꼬임 찾기

  • 박상철 (아주대학교 산업정보시스템공학부)
  • Published : 2004.12.01

Abstract

This paper presents an algorithm for the triangular mesh intersection problem. The key aspect of the proposed algorithm is to reduce the number of triangle pairs to be checked for intersection. To this end, it employs two different approaches, the Y-group approach and the space partitioning approach. Even though both approaches have the same objective of reducing the number of triangular-triangular intersection (TTI) pairs, their inherent characteristics are quite different. While the V-group approach works by topology (reduces TTI pairs by guaranteeing no intersection among adjacent triangles), the space partitioning approach works by geometry (reduces TTI pairs by guaranteeing no intersection among distant triangles). The complementary nature of the two approaches brings substantial improvement in reducing the number TTI pairs.

Keywords

References

  1. Choi, B. K. and Jerard, R. B., Sculptured Surface Machining, Kluwer, 1998
  2. Woo, T. C., 'Visibility maps and spherical algorithms,' Computer-Aided Design, Vol. 26, No. 1, pp. 6-16, 1994 https://doi.org/10.1016/0010-4485(94)90003-5
  3. 박상철, 최병규, '점열곡선의 꼬임을 효율적으로 찾는 알고리즘,' 한국CAD/CAM학회 논문집, 제4권, 제3호, pp. 190-199, 1999
  4. Volino, P. and Thalmann, N. M., 'Collision and self-intersection detection: efficient and robust solutions for highly deformable surfaces,' Proceedings of Eurographics Workshop on Animation and Simulation, pp. 55-65, 1995
  5. Tomas, M. and Prosolvia, C. A. B., 'A fast triangle-triangle intersection test,' Journal of Graphics Tools, Vol. 2, No. 2, pp. 25-30, 1997 https://doi.org/10.1080/10867651.1997.10487472
  6. Jimenez, P., Thomas, F. and Torras, C., '3D collision detection: a survey,' Computers and Graphics, Vol. 25, No. 2, pp. 269-285, 2001 https://doi.org/10.1016/S0097-8493(00)00130-8
  7. Shamos, M. I. and Hoey, D. J., 'Geometric intersection problems,' in Proc. 17th Annu. Conf. Foundation of Computer Science, pp. 208-215, Oct 1976