Results 1 
3 of
3
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
Abstract

Cited by 501 (0 self)
 Add to MetaCart
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floatingpoint arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick ” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
Star splaying: an algorithm for repairing Delaunay triangulations and convex hulls
 SCG ’05: PROCEEDINGS OF THE TWENTYFIRST ANNUAL ACM SYMPOSIUM ON COMPUTATIONAL GEOMETRY, ACM
, 2005
"... Star splaying is a generaldimensional algorithm that takes as input a triangulation or an approximation of a convex hull, and produces the Delaunay triangulation, weighted Delaunay triangulation, or convex hull of the vertices in the input. If the input is “nearly Delaunay” or “nearly convex” in a ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
Star splaying is a generaldimensional algorithm that takes as input a triangulation or an approximation of a convex hull, and produces the Delaunay triangulation, weighted Delaunay triangulation, or convex hull of the vertices in the input. If the input is “nearly Delaunay” or “nearly convex” in a certain sense quantified herein, and it is sparse (i.e. each input vertex adjoins only a constant number of edges), star splaying runs in time linear in the number of vertices. Thus, star splaying can be a fast first step in repairing a highquality finite element mesh that has lost the Delaunay property after its vertices have moved in response to simulated physical forces. Star splaying is akin to Lawson’s edge flip algorithm for converting a triangulation to a Delaunay triangulation, but it works in any dimensionality.
Averagecase Analysis of Algorithms for Convex Hulls and Voronoi Diagrams
, 1988
"... This thesis addresses the design and analysis of fastonaverage algorithms for two classic problems of computational geometry: the construction of convex hulls and Voronoi diagrams of finite point sets in Euclidean dspace. The main contributions of the thesis are: • A new algorithm for enumerating ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
This thesis addresses the design and analysis of fastonaverage algorithms for two classic problems of computational geometry: the construction of convex hulls and Voronoi diagrams of finite point sets in Euclidean dspace. The main contributions of the thesis are: • A new algorithm for enumerating the vertices of a convex hull that requires between O(n) and O(n 2) time on average for a set of n independent and identically distributed (i.i.d.) points. The exact running time depends on the input distribution. This algorithm is a useful preprocessing step for algorithms for the facetenumeration and faciallattice versions of the convexhull problem. • A new method for bounding the expected number of vertices of the convex hull of random points, new results on the asymptotic behavior of the expected number of vertices and facets of the convex hull of n i.i.d, points drawn from any of a wide variety of input distributions