A quasi-Monte Carlo method for computing areas of point-sampled surfaces

CAD Computer Aided Design

Volumn 38, Issue 1, 2006, Pages 55-68

  Liu, Yu Shen ^a   Yong, Jun Hai ^a   Zhang, Hui ^a   Yan, Dong Ming ^b   Sun, Jia Guang ^a  

^a TSINGHUA UNIVERSITY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Area; Intersection; Point sampled surfaces; Quasi Monte Carlo methods

Indexed keywords

AREAS; CAUCHY-CROFTON FORMULAE; POINT-SAMPLED SURFACE; QUASI-MONTE CARLO METHODS;

ALGORITHMS; COMPUTATIONAL METHODS; MATHEMATICAL MODELS; ROBUSTNESS (CONTROL SYSTEMS);

MONTE CARLO METHODS;

EID: 26444619391     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cad.2005.07.002     Document Type: Article

References (28)

1. Adams B., Dutré P. Interactive boolean operations on surfel-bounded solids. In: Proceedings of SIGGRAPH'03; 2003. p. 651-656.
2. Adamson A., Alexa M. Ray tracing point set surfaces. In: Proceedings of Shape Modeling International 2003; 2003. p. 272-279.
3. Amenta N., Bern M., Kamvysselis M. A new Voronoi-based surface reconstruction algorithm. In: Proceedings of SIGGRAPH'98; 1998. p. 415-421.
4. Castro F., Sbert M. Application of quasi-Monte Carlo sampling to the multi-path method for radiosity. Proceedings of the Third International Conference on Monte Carlo and quasi Monte Carlo methods in scientific computing, Springer series Lecture Notes in Computational Science and Engineering, Springer Berlin, 1998.
5. Davies T., Martin R.R. Low-discrepancy sequences for volume properties in solid modelling, Proceedings of CSG, 98 (1998) p. 13.
6. Desbrun M., Meyer M., Schröder P., Barr A.H. Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of SIGGRAPH'99; 1999. p. 317-324.
7. Gärtner B. Fast and robust smallest enclosing balls. In: Proc. 7th Annual European Symposium on Algorithms (ESA). Volume 1643 of Lecture Notes in Computer Science, Springer-Verlag (1999), p. 325-338, 1999.
8. Hoppe H., DeRose T., Duchamp T., McDonald J., Stuetzle W. Surface reconstruction from unorganized point. In: Proceedings of SIGGRAPH'92; 1992. p. 71-78.
9. Jones T., Durand F., Desbrun M. Non-iterative, feature-preserving mesh smoothing. In: Proceedings of SIGGRAPH' 03; 2003. p 943-949.
10. T. Jones, F. Durand, and M. Zwicker Normal improvement for point rendering IEEE Comput Graph Appl 2004 53 56
11. L. Kobbelt, and M. Botsch A survey of point-based techniques in computer graphics Comput Graph 28 6 2004 801 814
12. Y.T. Lee, and A.A.G. Requicha Algorithms for computing the volume and other integral properties of solids, Part I Commun ACM 25 9 1982 635 641
13. Y.T. Lee, and A.A.G. Requicha Algorithms for computing the volume and other integral properties of solids, Part II Commun ACM 25 9 1982 642 650
14. X. Li, W. Wang, R.R. Martin, and A. Bowyer Using low-discrepancy sequences and the Crofton formula to compute surface areas of geometric models Comput Aided Design 35 9 2003 771 782
15. H. Niederreiter Quasi-Monte Carlo methods and pseudo-random numbers Bull Am Math Soc 84 6 1978 957 1041
16. H. Niederreiter Random number generation and quasi-Monte Carlo methods 1992 SIAM Philadelphia Philadelphia
17. Ohtake Y., Belyaev A., Alexa M., Turk G., Seidel H.P. Multi-level partition of unity implicits. In: Proceedings of SIGGRAPH'03; 2003. p. 463-470.
18. R. Osada, T. Funkhouser, B. Chazelle, and D. Dobkin Shape distributions ACM Transact Graph 21 4 2002 807 832
19. Pauly M., Kobbelt L., Gross M. Multiresolution modeling of point-sampled geometry. ETH Zurich Technical Report, #378, September 16, 2002. http://graphics.stanford.edu/∼mapauly/Pdfs/MultiresModeling.pdf.
20. Pauly M., Gross M., Kobbelt L. Efficient simplification of point-sampled surfaces. In: Proceedings of IEEE Visualization'02; 2002. p. 163-170.
21. Pauly M., Keiser R., Kobbelt L., Gross M. Shape modeling with point-sampled geometry. In: Proceedings of SIGGRAPH'03; 2003. p. 641-650.
22. Pauly M. Point primitives for interactive modeling and processing of 3D geometry. Ph. D thesis, ETH Zurich, Switzerland, 2003.
23. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery Numerical recipes in C 2nd ed 1992 Cambridge University Press
24. Rusin D. N-dim spherical random number drawing. In the Mathematical Atlas. http://www.math.niu.edu/∼rusin/known-math/96/sph.rand.
25. Schaufler G., Jensen H.W. Ray tracing point sampled geometry, In Proceedings of the 11th Eurographics Workshop on Rendering, (2000) 319-328
26. Taubin G. A signal processing approach to fair surface design. In: Proceedings of SIGGRAPH'95; 1995. p. 351-358.
27. H.G. Timmer, and J.M. Stern Computation of global properties of solid objects Comput Aided Design 12 6 1980 301 304
28. X. Wang Improving the rejection sampling method in quasi-Monte Carlo methods J Comput Appl Math 114 2 2000 231 246