Space subdivision to speed-up convex hull construction in E3
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This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E3, based on "spherical" space subdivision.About:
This article is published in Advances in Engineering Software.The article was published on 2016-01-01 and is currently open access. It has received 10 citations till now. The article focuses on the topics: Convex hull & Convex set.read more
Citations
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Journal ArticleDOI
LPCN: Least polar-angle connected node algorithm to find a polygon hull in a connected euclidean graph
Farid Lalem,Ahcène Bounceur,Madani Bezoui,Massinissa Saoudi,Massinissa Saoudi,Reinhardt Euler,M. Tahar Kechadi,M. Tahar Kechadi,Marc Sevaux,Marc Sevaux +9 more
TL;DR: A new algorithm is proposed that chooses for a current node and among its neighbors in the graph the nearest polar angle node with respect to the node found in the previous iteration and modified to obtain a procedure of the given complexity.
Proceedings ArticleDOI
Reducing the Number of Points on the Convex Hull Calculation Using the Polar Space Subdivision in E2
TL;DR: A new algorithm to speed up any planar convex hull calculation is presented, based on a polar space subdivision, which enables a fast and very efficient reduction of the given points, which cannot contribute to the final convex Hull.
Proceedings ArticleDOI
CudaPre2D: A Straightforward Preprocessing Approach for Accelerating 2D Convex Hull Computations on the GPU
TL;DR: A straightforward preprocessing approach to discard the points that locate inside a convex polygon formed by 16 extreme points that achieves the speedups of about 4x ~ 5x on average and 5x ~ 6x in the best cases over the cases where the proposed approach is not used.
Book ChapterDOI
Diameter and Convex Hull of Points Using Space Subdivision in E 2 and E 3
TL;DR: Surprisingly, the experiments proved, that in the case of the space subdivision the reduction of points is so efficient, that the “brute force" algorithms for the convex hull and its diameter computation of the remaining points have nearly no influence to the time of computation.
Journal ArticleDOI
CudaCHPre2D: A straightforward preprocessing approach for accelerating 2D convex hull computations on the GPU
TL;DR: This paper presents a straightforward preprocessing approach by discarding the points locating in a convex polygon formed by 16 extreme points, which achieves speedups of approximately 4 ×∼5× on average and 5 ∼6× in the best cases over the cases where the proposed approach is not used.
References
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Journal ArticleDOI
The quickhull algorithm for convex hulls
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.
Book
Meshfree Approximation Methods with MATLAB
TL;DR: In this article, the authors provide the salient theoretical results needed for a basic understanding of mesh-free approximation methods, such as radial basis function and moving least squares method, and a good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs.
Proceedings ArticleDOI
Applications of random sampling in computational geometry, II
TL;DR: Asymptotically tight bounds for a combinatorial quantity of interest in discrete and computational geometry, related to halfspace partitions of point sets, are given.
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.
Journal ArticleDOI
Optimal output-sensitive convex hull algorithms in two and three dimensions
TL;DR: This work presents simple output-sensitive algorithms that construct the convex hull of a set of n points in two or three dimensions in worst-case optimalO (n logh) time and O (n) space, whereh denotes the number of vertices of the conveX hull.