Weak convex decomposition by lines-of-sight

Shmuel Asafi, Avi Goren, Daniel Cohen-Or

Research output: Contribution to conferencePaperpeer-review


We define the convexity rank of a set of points to be the portion of mutually visible pairs of points out of the total number of pairs. Based on this definition of weak convexity, we introduce a spectral method that decomposes a given shape into weakly convex regions. The decomposition is applied without explicitly measuring the convexity rank. The method merely amounts to a spectral clustering of a matrix representing the all-pairs line of sight. Our method can be directly applied on an oriented point cloud and does not require any topological information, nor explicit concavity or convexity measures. We demonstrate the efficiency of our algorithm on a large number of examples and compare them qualitatively with competitive approaches.

Original languageEnglish
Number of pages9
StatePublished - 3 Jul 2013
Event11th Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP 2013 - Genova, Italy
Duration: 3 Jul 20135 Jul 2013


Conference11th Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, SGP 2013

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Modelling and Simulation


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