DOI QR코드

DOI QR Code

Precise Sweep Volume Computation Accelerated by GPU

GPU 가속을 이용한 정밀밀한 스웹 볼륨 경계 계산

  • 이현호 (아주대학교 미디어학과) ;
  • 경민호 (아주대학교 미디어학과)
  • Received : 2014.11.27
  • Accepted : 2015.02.03
  • Published : 2015.03.01

Abstract

We present a robust GPU algorithm constructing a sweep volume boundary for a triangular mesh model. Sweeping geometric entities of a triangular mesh object is first approximated to a set of triangles, the envelope of which becomes the outer boundary of the sweep volume. We find the envelope by computing the arrangement of the triangle set and extracting its outmost boundary. To ensure robustness of the algorithm, we adopt random perturbation of sweep vertices and the interval arithmetic using multi-level precisions. The algorithm is implemented to perform most computation on GPU, and as a result it runs two orders of magnitude faster than other algorithms.

본 논문에서는 삼각형 메시의 스웹 볼륨 표면을 정밀하고 안정적으로 계산하는 GPU 알고리즘을 제안한다. 삼각형 메시의 기하 요소들을 스웹하여 근사적으로 삼각형 집합을 생성하고, 이 집합의 엔벨롭을 계산하면 스웹 볼륨의 최외곽 경계 표면을 얻을 수 있다. 엔벨롭을 찾기 위하여 우리는 삼각형 집합의 공간 분할을 계산하고 그 분할의 최외곽 경계를 추출하였다. 알고리즘의 안정성을 확보하기 위하여 우리는 스웹 정점들을 초기에 랜덤 섭동하는 방법과 다중 정밀도 구간 연산 기법을 적용하였다. 전체 알고리즘은 대부분의 계산을 GPU에서 처리하도록 구현되었고, 결과적으로 기존 알고리즘에 비해 수십~수백 배의 성능을 보여준다.

Keywords

References

  1. Young J. Kim Gokul Varadhan Ming C. Lin Dinesh Manocha, "Fast Swept Volume Approximation of Complex Polyhedral Models", Proc. of ACM Symposium on Solid Modeling and Applications, 11-22, 2003
  2. Xinyu Zhang, Young J. Kim, Dinesh Manocha, "Reliable sweep", SIAM/ACM Joint Conference on Geometric and Physical Modeling, p 373-378, 2009
  3. Campen, M. and Kobbelt, L., "Polygonal Boundary Evaluation of Minkowski Sums and Swept Volumes", Computer Graphics Forum, 29, 2010.
  4. Sacks, E., Milenkovic, V., and Kyung, M.-H., "Controlled linear perturbation", Computer-Aided Design, 43(10), pp. 1250-1257, 2011. https://doi.org/10.1016/j.cad.2011.06.015
  5. Pottmann, H., Leopoldseder, S., "Geometries for CAGD", In G. Farin, J. Hoschek, and M. S. Kim, editors, Handbook of Computer Aided Geometric Design, pp. 43-73, Elsevier, 2002.
  6. Abrams, S., Peter K. Allen, "Computing swept volmues", Journal of Visualization and Computer Animation, 11, 1997
  7. J.R. Rossignac, J.J. Kim, S.C. Song, K.C. Suh, C.B. Joung, "Boundary of the volume swept by a free-form solid in screw motion", Computer-Aided Design 39, 9, 745-755, 2006 https://doi.org/10.1016/j.cad.2007.02.016
  8. J.J. Kim, C.B. Jung, K.C. Seo, M.W. Kang, "Swept Volumes Generated by Polyhedral Objects Through Screw Motions", Transactions of the Society of CAD/CAM Engineers / v.7 no.4, pp.211-218, 2002
  9. Abdel-Malek, K., Blackmore, D., and Joy, K., "Swept volumes: foundations, perspectives and applications", International Journal of Shape Modeling, 2004.
  10. von Dziegielewski, A., Hemmer, M., and Shomer, E., "High Precision Conservative Surface Mesh Generation for Swept Volumes", In Proc. of IEEE International Conference on Robotics and Automation, 2012.
  11. M.H. Kyung, J.G. Kwak, J.J. Choi, "Robust GPU-based intersection algorithm for a large triangle set", Journal of the Korea Computer Graphics Society, vol. 17, no. 3, pp. 9-20, 2011.
  12. Fogel, E., and Halperin, D., CGAL Arrangement and Their Applications: A Step-by-Step Guide(Geometry and Computing), Springer, 2012.