Weak Convex Decomposition by Lines-of-sight

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 wi...

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Bibliographic Details
Published in:Computer graphics forum Vol. 32; no. 5; pp. 23 - 31
Main Authors: Asafi, Shmuel, Goren, Avi, Cohen-Or, Daniel
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.08.2013
Subjects:
Algorithms
Computer graphics
Computer science
Concavity
Convexity
Decomposition
Line of sight
Spectral methods
Studies
Three dimensional models
Topology
United States > US
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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.
Bibliography:istex:03DE33ACDAEB28A4364FA659EF7CC62FB688BA67
ArticleID:CGF12169
ark:/67375/WNG-K63RDN7X-W
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.12169