Banff Center, Calgary, Alberta, Canada
July 2, 2006 to July 5, 2006
S. Bereg , University of Texas at Dallas
M. L. Gavrilova , University of Calgary,Canada
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ISVD.2006.31
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.
S. Bereg, M. L. Gavrilova, "Robust Point-Location in Generalized Voronoi Diagrams", ISVD, 2006, 2010 International Symposium on Voronoi Diagrams in Science and Engineering, 2010 International Symposium on Voronoi Diagrams in Science and Engineering 2006, pp. 54-59, doi:10.1109/ISVD.2006.31