## Primal Dividing and Dual Pruning: Output-Sensitive Construction of 4-d Polytopes and 3-d Voronoi Diagrams (1997)

Citations: | 31 - 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}

}

### Years of Citing Articles

### OpenURL

### 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 outputsensitive 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. 1 Introduction Geometric structures induced by n points in Euclidean d-dimensional space, such as the convex hull, Voronoi diagram, or Delaunay triangulation, can be of larger size than the point set that defines them. In many practical situat...