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Primal Dividing and Dual Pruning: Output-Sensitive Construction of 4-d Polytopes and 3-d Voronoi Diagrams (1997)
| Citations: | 38 - 3 self |
BibTeX
@MISC{Chan97primaldividing,
author = {Timothy Chan and Jack Snoeyink and Chee-keng Yap},
title = {Primal Dividing and Dual Pruning: Output-Sensitive Construction of 4-d Polytopes and 3-d Voronoi Diagrams},
year = {1997}
}
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Abstract
In this paper, we give an algorithm for output-sensitive construction of an f-face convex hull of a set of n points in general position in E 4 . Our algorithm runs in O((n + f)log 2 f) time and uses O(n + f) space. This is the first algorithm within a polylogarithmic factor of optimal O(n log f + f) time over the whole range of f . By a standard lifting map, we obtain output-sensitive algorithms for the Voronoi diagram or Delaunay triangulation in E 3 and for the portion of a Voronoi diagram that is clipped to a convex polytope. Our approach simplifies the "ultimate convex hull algorithm" of Kirkpatrick and Seidel in E 2 and also leads to improved output-sensitive results on constructing convex hulls in E d for any even constant d > 4.
Keyphrases
output-sensitive construction voronoi diagram primal dividing 4-d polytopes 3-d voronoi diagram dual pruning convex hull delaunay triangulation euclidean d-dimensional space convex polytope point set whole range outputsensitive algorithm standard lifting map general position polylogarithmic factor first algorithm ultimate convex hull algorithm output-sensitive result many practical situat introduction geometric structure f-face convex hull
