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2010 International Symposium on Voronoi Diagrams in Science and Engineering (2006)
Banff Center, Calgary, Alberta, Canada
July 2, 2006 to July 5, 2006
ISBN: 0-7695-2630-6
pp: 54-59
Y. Zhang , University of Texas at Dallas
S. Bereg , University of Texas at Dallas
M. L. Gavrilova , University of Calgary,Canada
ABSTRACT
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.
INDEX TERMS
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CITATION
Y. Zhang, S. Bereg, M. L. Gavrilova, "Robust Point-Location in Generalized Voronoi Diagrams", 2010 International Symposium on Voronoi Diagrams in Science and Engineering, vol. 00, no. , pp. 54-59, 2006, doi:10.1109/ISVD.2006.31
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