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


  • 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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