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

Yu Shen Liu*, Jun Hai Yong, Hui Zhang, Dong Ming Yan, Jia Guang Sun

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


A novel and efficient quasi-Monte Carlo method for computing the area of a point-sampled surface with associated surface normal for each point is presented. Our method operates directly on the point cloud without any surface reconstruction procedure. Using the Cauchy-Crofton formula, the area of the point-sampled surface is calculated by counting the number of intersection points between the point cloud and a set of uniformly distributed lines generated with low-discrepancy sequences. Based on a clustering technique, we also propose an effective algorithm for computing the intersection points of a line with the point-sampled surface. By testing on a number of point-based models, experiments suggest that our method is more robust and more efficient than those conventional approaches based on surface reconstruction.

Original languageEnglish (US)
Pages (from-to)55-68
Number of pages14
JournalCAD Computer Aided Design
Issue number1
StatePublished - Jan 2006
Externally publishedYes

Bibliographical note

Funding Information:
We would like to thank Wenping Wang for many helpful discussions, and Piqiang Yu and Jean-Claude Paul for some valuable comments during our work. The authors appreciate the comments and suggestions of the anonymous reviewers. The research was supported by Chinese 973 Program (2004CB719400), and the National Science Foundation of China (60403047). The second author was supported by the project sponsored by a Foundation for the Author of National Excellent Doctoral Dissertation of PR China (200342), and SRF for ROCS, SEM (041501004).


  • Area
  • Intersection
  • Point-sampled surfaces
  • Quasi-Monte Carlo methods

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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