한국게임학회 논문지 (Journal of Korea Game Society)

  • 제19권6호
  • /
  • Pages.99-106
  • /
  • 2019
  • /
  • 1598-4540(pISSN)
  • /
  • 2287-8211(eISSN)
한국게임학회 (Korea Game Society)
권호 표지
DOI QR코드

DOI QR Code

두 타원체 사이의 최단 접근 거리를 구하는 안정적이며 효율적인 방법

A Robust and Efficient Method to Compute the Closest Approach Distance between Two Ellipsoids

  • 최민규 (광운대학교 컴퓨터과학과)
  • Choi, Min Gyu (Dept. of Computer Science, Kwangwoon University)
  • 투고 : 2019.11.12
  • 심사 : 2019.12.06
  • 발행 : 2019.12.20
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 두 타원체 사이의 중심 간 방향으로의 최단 접근 거리를 구하는 방법을 다룬다. 이는 타원체 사이의 충돌 검사 및 반응에 있어서 핵심 기술이다. 외부에서 서로 접하는 두 타원체의 중심 사이의 거리와 접촉점, 접촉방향에 관한 조건식을 세우고, 해를 포함하는 구간을 유지하는 이분법과 도함수를 이용하는 Newton 방법의 혼합을 통해 최단 접근 거리를 항상 안정적이며 효율적으로 구할 수 있게 한다. 또한 다양한 실험을 통해 제안된 방법의 안정성 및 효율성을 보인다.

This paper addresses a method to compute the closest approach distance between two ellipsoids in their inter-center direction. This is the key technique for collision detection and response between ellipsoids. We formulate a set of conditions with the inter-center distance, the contact point and the contact normal vector of the two externally-contacting ellipsoids. The equations are solved robustly and efficiently using a hybrid of Newton's method and the bisection method with root bracketing. We demonstrate the robustness and efficiency of the proposed method in various experiments.

키워드

참고문헌

  1. M. Muller and N. Chentanez, "Solid simulation with oriented particles", ACM Transactions on Graphics, Vol. 30, No. 4, Article 92, 2011.
  2. M. G. Choi, "Real-time simulation of ductile fracture with oriented particles", Computer Animation and Virtual Worlds, Vol. 25, pp. 455-463, 2014. https://doi.org/10.1002/cav.1601
  3. M. G. Choi and J. Lee, "As-rigid-aspossible solid simulation with oriented particles", Computers and Graphics, Vol. 70, pp. 1-7, 2018. https://doi.org/10.1016/j.cag.2017.07.027
  4. M. G. Choi, "A practical method to compute the closest approach distance of two ellipsoids", Journal of Korea Game Society, Vol. 19, No. 1, pp. 5-14, 2019. https://doi.org/10.7583/JKGS.2019.19.1.5
  5. W. Wang, J. Wang, and M.-S. Kim, "An algebraic condition for the separation of two ellipsoids", Computer Aided Geometric Design, Vol. 18, No. 6, pp. 531-539, 2001. https://doi.org/10.1016/S0167-8396(01)00049-8
  6. Y.-K. Choi, J.-W. Chang, W. Wang, M.-S. Kim, and G. Elber, "Continuous collision detection for ellipsoids", IEEE Transactions on Visualization and Computer Graphics, Vol. 15, No. 2, pp. 311-324. 2009. https://doi.org/10.1109/TVCG.2008.80
  7. X. Jia, Y.-K. Choi, B. Mourrain, and W. Wang, "An algebraic approach to continuous collision detection for ellipsoids", Compuer Aided Geometric Design, Vol. 28, pp. 164-176, 2011. https://doi.org/10.1016/j.cagd.2011.01.004
  8. L. Gonzalez-Vega and E. Mainar, "Solving the separation problem for two ellipsoids involving only the evaluation of six polynomials", In Proc. Milestones in Computer Algebra 2008.
  9. J. W. Perram and M. S. Wertheim, "Statistical Mechanics of Hard Ellipsoids. I. Overlap Algorithm and the Contact Function", Journal of Computational Physics, Vol. 58, 409-416, 1985. https://doi.org/10.1016/0021-9991(85)90171-8
  10. J. W. Perram, J. Rasmussen, E. Præstgaard, and J. L. Lebowitz, "Ellipsoid contact potential: Theory and relation to overlap potentials", Physical Review E, Vol. 54, No. 6, pp. 6565-6572, 1996 https://doi.org/10.1103/PhysRevE.54.6565
  11. L. Paramonov and S. N. Yaliraki, "The directional contact distance of two ellipsoids: Coarse-grained potentials for anisotropic interactions", Journal of Chemical Physics, Vol. 123, No. 19, Article 194111, pp. 1-11, 2005.
  12. X. Zheng and P. Palffy-Muhoray, "Distance of closest approach of two arbitrary hard ellipses in two dimensions", Physical Review E, Vol. 75, Article 061709, pp. 1-6, 2007.
  13. X. Zheng, W. Iglesias and P. Palffy-Muhoray, "Distance of closest approach of two arbitrary hard ellipsoids", Physical Review E, Vol. 79, Article 057702, pp. 1-4, 2009.
  14. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd edition, Cambridge University, 2007.
  15. K. B. Petersen and M. S. Pedersen, "The Matrix Cookbook", Technical University of Denmark, 2012.