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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 ..."
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Cited by 713 (0 self)
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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
The QuickHull algorithm in
"... > (right) of the line. In particular, for S upper we have S = S upper [ fu; vg with p 1 = u and p 2 = v; for S lower we set S = S lower [ fv; ug with p 1 = v and p 2 = u. Now we apply the following recursive method to S and (p 1 ; p 2 ): We determine the point pivot 2 S (called the pivot point) ..."
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> (right) of the line. In particular, for S upper we have S = S upper [ fu; vg with p 1 = u and p 2 = v; for S lower we set S = S lower [ fv; ug with p 1 = v and p 2 = u. Now we apply the following recursive method to S and (p 1 ; p 2 ): We determine the point pivot 2 S (called the pivot point) with the largest distance from line (p 1 ; p 2 ) (see Figure 2, left hand side), i.e. which maximizes the cross product #define cross(pivot,p1,p2) " ((x[p1]x[pivot])*(y[p2]y[pivot])  (y[p1]y[pivot])*(x[p2]x[pivot])) Obviously, pivot belongs to the conve
Finding Convex Hulls Using Quickhull on the GPU
, 2012
"... We present a convex hull algorithm that is accelerated on commodity graphics hardware. We analyze and identify the hurdles of writing a recursive divide and conquer algorithm on the GPU and divise a framework for representing this class of problems. Our framework transforms the recursive splitting s ..."
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step into a permutation step that is wellsuited for graphics hardware. Our convex hull algorithm of choice is Quickhull. Our parallel Quickhull implementation (for both 2D and 3D cases) achieves an order of magnitude speedup over standard computational geometry libraries.
AN ALGORITHM TO BUILD CONVEX HULLS FOR 3D OBJECTS
"... In this paper, a new algorithm based on the Quickhull algorithm is proposed to find convex hulls for 3D objects using neighbor trees. The neighbor tree is the data structure by which all visible facets to the selected furthest outer point can be found. The neighboring sequence of ridges on the oute ..."
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In this paper, a new algorithm based on the Quickhull algorithm is proposed to find convex hulls for 3D objects using neighbor trees. The neighbor tree is the data structure by which all visible facets to the selected furthest outer point can be found. The neighboring sequence of ridges
Convex Envelope Generation Using a Mix of Gift Wrap and QuickHull Algorithms
, 2012
"... The environment simulation is widely used nowadays. Training in many fields such as medicine and architecture heavily depends on virtual reality techniques. Since objects in real life do not have a deterministic shape it is not possible to have a geometric equation that might model them. Convex Hull ..."
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and compared. The first three algorithms are the Brute Force, the Gift Wrap and the QuickHull algorithm. The fourth one is a hybrid approach that combines the QuickHull and the Gift Wrap algorithms. Simulations were done in the medical environment, and algorithms are tested with the model of 3D wrist and knee
An Associative Implementation of Classical Convex Hull Algorithms
 Proceedings of Eighth IASTED International Conference on Parallel and Distributed Computing and Systems
, 1996
"... This paper will present the implementation and comparison of new parallel algorithms for the convex hull problem. These algorithms are a parallel adaptation of the Jarvis March and the Quickhull algorithms. The computational model selected for these algorithms is the associative computing model #ASC ..."
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Cited by 14 (4 self)
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This paper will present the implementation and comparison of new parallel algorithms for the convex hull problem. These algorithms are a parallel adaptation of the Jarvis March and the Quickhull algorithms. The computational model selected for these algorithms is the associative computing model
A Framework for MultiCore Implementations of Divide and Conquer Algorithms and its Application to the Convex Hull Problem ∗
"... We present a framework for multicore implementations of divide and conquer algorithms and show its efficiency and ease of use by applying it to the fundamental geometric problem of computing the convex hull of a point set. We concentrate on the Quickhull algorithm introduced in [2]. In general the ..."
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Cited by 3 (0 self)
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We present a framework for multicore implementations of divide and conquer algorithms and show its efficiency and ease of use by applying it to the fundamental geometric problem of computing the convex hull of a point set. We concentrate on the Quickhull algorithm introduced in [2]. In general
Parallelizing Two Dimensional Convex Hull on NVIDIA GPU and Cell BE
"... Multicore processors are a shift of paradigm in computer architecture that promises dramatic increase in performance. But they also bring complexity in algorithmic design. In this paper we describe the challenges and design issues involved in parallelizing two dimensional convex hull on both CUDA an ..."
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and Cell Brodband Engine (Cell BE). We have parallelized the quickhull algorithm for two dimensional convex hull. The major advantage of this algorithm is that interprocessor communication cost is highly reduced. 1.
Depends R (> = 2.5.0), magic Suggests testthat, rgl, R.matlab, tripack
, 2015
"... Description Makes the qhull library (www.qhull.org) available in R, in a similar manner as in Octave and MATLAB. Qhull computes convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthestsite Delaunay triangulations, and furthestsite Voronoi diagrams. I ..."
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. It runs in 2d, 3d, 4d, and higher dimensions. It implements the Quickhull algorithm for computing the convex hull. Qhull does not support constrained Delaunay triangulations, or mesh generation of nonconvex objects, but the package does include some R functions that allow for this. Currently
Load Balancing of Irregular Parallel DivideandConquer Algorithms in GroupSPMD Programming Environments
 Master’s Thesis, PELAB, Linköpings Universitet
, 2006
"... We study strategies for local load balancing of irregular parallel divideandconquer algorithms such as Quicksort and Quickhull in SPMDparallel environments such as MPI and Fork that allow to exploit nested parallelism by dynamic group splitting. ..."
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Cited by 6 (3 self)
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We study strategies for local load balancing of irregular parallel divideandconquer algorithms such as Quicksort and Quickhull in SPMDparallel environments such as MPI and Fork that allow to exploit nested parallelism by dynamic group splitting.
Results 1  10
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