Journal ArticleDOI
Finding extreme points in three dimensions and solving the post-office problem in the plane
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TLDR
By use of geometric transforms, the post-office problem for a finite set of points in two dimensions and certain two-dimensional point location problems are reduced to the former problem and thus also optimally solved.About:
This article is published in Information Processing Letters.The article was published on 1985-07-10. It has received 34 citations till now. The article focuses on the topics: Closest pair of points problem & Smallest-circle problem.read more
Citations
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Journal ArticleDOI
Voronoi diagrams—a survey of a fundamental geometric data structure
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Book
Algorithms in Combinatorial Geometry
TL;DR: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.
Book ChapterDOI
Determining the Separation of Preprocessed Polyhedra - A Unified Approach
TL;DR: The emphasis is the uniform treatment of polyhedra separation problems, the use of hierarchical representations of primitive objects to provide implicit representations of composite or transformed objects, and applications to natural problems in graphics and robotics.
Journal ArticleDOI
Finding minimal enclosing boxes
TL;DR: It is proven that at least two adjacent box sides are flush with edges of the hull of the convex hull, and this characterization enables the anO(n3) algorithm to find all minimal boxes for a set ofn points.
Book
Visibility Problems for Polyhedral Terrains
Richard Cole,Micha Sharir +1 more
TL;DR: An O(n@l"4(n)log n)-time algorithm is presented that preprocesses L and @s into a data-structure of size O(o(log^2n) time ray Shooting queries, which supports fast ray shooting queries.
References
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Journal ArticleDOI
Optimal Search in Planar Subdivisions
TL;DR: This work presents a practical algorithm for subdivision search that achieves the same (optimal) worst case complexity bounds as the significantly more complex algorithm of Lipton and Tarjan, namely $O(\log n)$ search time with $O(n)$ storage.
Proceedings ArticleDOI
Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams
Leonidas J. Guibas,Jorge Stolfi +1 more
TL;DR: Two algorithms are given, one that constructs the Voronoi diagram of the given sites, and another that inserts a new site in O(n) time, based on the use of the Vor onoi dual, the Delaunay triangulation, and are simple enough to be of practical value.
Journal ArticleDOI
Convex hulls of finite sets of points in two and three dimensions
Franco P. Preparata,S. J. Hong +1 more
TL;DR: The presented algorithms use the “divide and conquer” technique and recursively apply a merge procedure for two nonintersecting convex hulls to ensure optimal time complexity within a multiplicative constant.