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3rd International Symposium on Voronoi Diagrams in Science and Engineering (ISVD'06)
Robust Point-Location in Generalized Voronoi Diagrams
Banff Center, Calgary, Alberta, Canada
July 02-July 05
ISBN: 0-7695-2630-6
S. Bereg, University of Texas at Dallas
Y. Zhang, University of Texas at Dallas
M. L. Gavrilova, University of Calgary,Canada
We address the problemof robust point-locationin a generalized -dimensional Voronoi diagram. The exact point location requires the solution for expressions of degree four. A natural question is what can be done using expression of smaller degree. We apply polyhedral metrics for this task. In general dimensions two Minkowski metrics can be used L_1(Manhattan metric) and l_r00. The approximation factor is \sqrt d and the computation uses expressions of degree one. We also show that a polygonal metric can be applied in two dimensions. The compuation involves only calls of the algorithm ESSA for detecting the sign of a sum using floating-point arithmetic.
Citation:
S. Bereg, Y. Zhang, M. L. Gavrilova, "Robust Point-Location in Generalized Voronoi Diagrams," isvd, pp.54-59, 3rd International Symposium on Voronoi Diagrams in Science and Engineering (ISVD'06), 2006
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