NDLI: Computing the Voronoi cells of planes, spheres and cylinders in $R^{3}$

Content Provider	ACM Digital Library
Author	Elber, Gershon Hanniel, Iddo
Abstract	We present an algorithm for computing the Voronoi cell for a set of planes, spheres and cylinders in $R^{3}.$ The algorithm is based on a lower envelope computation of the bisector surfaces between these primitives, and the projection of the trisector curves onto planes bounding the object for which the Voronoi cell is computed, denoted the base object. We analyze the different bisectors and trisectors that can occur in the computation. Our analysis shows that most of the bisector surfaces are quadric surfaces and five of the ten possible trisectors are conic section curves. We have implemented our algorithm using the IRIT library and the CGAL 3D lower envelope package. All presented results are from our implementation.
Starting Page	47
Ending Page	58
Page Count	12
File Format	PDF
ISBN	9781605581064
DOI	10.1145/1364901.1364911
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-06-02
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Constructive solid geometry Skeleton Medial axis
Content Type	Text
Resource Type	Article

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Computing the Voronoi cells of planes, spheres and cylinders in $R^{3}$