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Convex hull algorithms
About: Convex hull algorithms is a research topic. Over the lifetime, 106 publications have been published within this topic receiving 11324 citations.
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TL;DR: This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm, and provides empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory.
Abstract: 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 two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond 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 used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous 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.
5,050 citations
TL;DR: P can be chosen to I&E the centroid oC the triangle formed by X, y and z and Express each si E S in polar coordinates th origin P and 8 = 0 in the direction of zu~ arhitnry fixed half-line L from P.
1,741 citations
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.
Abstract: The convex hulls of sets of n points in two and three dimensions can be determined with O(n log n) operations. The presented algorithms use the “divide and conquer” technique and recursively apply a merge procedure for two nonintersecting convex hulls. Since any convex hull algorithm requires at least O(n log n) operations, the time complexity of the proposed algorithms is optimal within a multiplicative constant.
731 citations
692 citations
450 citations