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The divider set of explicit parametric geometry
Ugail, Hassan Aggarwal, A. Bakopoulos, Y. Kotsios, S.
Ugail, Hassan
Aggarwal, A.
Bakopoulos, Y.
Kotsios, S.
Publication Date
2008
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Copyright © [2008] IEEE. Reprinted from International Conference on Cyberworlds, 2008. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Bradford's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubspermissions@ ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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Abstract
In this paper we describe a novel concept for classification
of complex parametric geometry based on the concept
of the Divider Set. The Divider Set is an alternative concept
to maximal disks, Voronoi sets and cut loci. The Divider
Set is based on a formal definition relating to topology
and differential geometry. In this paper firstly we discuss
the formal definition of the Divider Set for complex
3-dimensional geometry. This is then followed by the introduction
of a computationally feasible algorithm for computing
the Divider Set for geometry which can be defined
in explicit parametric form. Thus, an explicit solution form
taking advantage of the special form of the parametric geometry
is presented. We also show how the Divider Set can
be computed for various complex parametric geometry by
means of illustrating our concept through a number of examples
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Citation
Ugail H, Aggarwal A, Bakopoulos Y et al (2008) The divider set of explicit parametric geometry. In: International Conference on Cyberworlds, 2008. IEEE Computer Society: 232-239. ISBN: 9780769533810.
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