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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
Convex hull
, 2009
"... Real RAM Model. A memory cell stores a real number. Any single arithmetic operation or comparison can be computed in constant time. In addition, sometimes also roots, logarithms, other analytic functions, indirect addressing (integral), or oor and ceiling are used. This is a quite powerful (and some ..."
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Real RAM Model. A memory cell stores a real number. Any single arithmetic operation or comparison can be computed in constant time. In addition, sometimes also roots, logarithms, other analytic functions, indirect addressing (integral), or oor and ceiling are used. This is a quite powerful (and somewhat unrealistic) model of computation. Therefore we have to ensure that we do not abuse its power. Algebraic Computation Trees (BenOr [1]). A computation is regarded a binary tree. The leaves contain the (possible) results of the computation. Every node v with one child an operation of the form +, −, , /, p,... is associated to. The operands of this operation are constant, input values, or among the ancestors of v in the tree. Every node v with two children a branching of the form> 0, 0, or = 0 is associated to. The branch is with respect to the result of v's parent node. If the expression yields true, the computation continues with the left child of v; otherwise, it continues with the right child of v. a − b ≤ 0 a − c b − c
Dynamic planar convex hull
 Proc. 43rd IEEE Sympos. Found. Comput. Sci
, 2002
"... In this paper we determine the amortized computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage o ..."
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Cited by 66 (1 self)
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In this paper we determine the amortized computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage
Convex Hull Algorithms
, 2008
"... The objective of this work is comparing algorithms for the planar convex hull problem. We implemented three convex hull algorithms, as well as a clever preprocessing technique. We were interested in evaluating the work required to implement these algorithms and validate the efficiency results predi ..."
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The objective of this work is comparing algorithms for the planar convex hull problem. We implemented three convex hull algorithms, as well as a clever preprocessing technique. We were interested in evaluating the work required to implement these algorithms and validate the efficiency results
Implementation of Convex Hull algorithm for
"... this report an associative algorithm for the Convex Hull is presented. The algorithm was generated and checked by means of the ARTVM simulator. But first let us overview the ARTVM architecture ..."
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this report an associative algorithm for the Convex Hull is presented. The algorithm was generated and checked by means of the ARTVM simulator. But first let us overview the ARTVM architecture
Convex hull realizations of the multiplihedra
, 2007
"... . We present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the n th polytope in the sequence known as the multiplihedra. This answers the open question of whether the multiplihedra could be realized as convex polytopes. ..."
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Cited by 17 (6 self)
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. We present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the n th polytope in the sequence known as the multiplihedra. This answers the open question of whether the multiplihedra could be realized as convex polytopes.
FAST APPROXIMATION OF CONVEX HULL
"... The construction of a planar convex hull is an essential operation in computational geometry. It has been proven that the time complexity of an exact solution is Ω(NlogN). In this paper, we describe an algorithm with time complexity O(N + k2), where k is parameter controlling the approximation qua ..."
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The construction of a planar convex hull is an essential operation in computational geometry. It has been proven that the time complexity of an exact solution is Ω(NlogN). In this paper, we describe an algorithm with time complexity O(N + k2), where k is parameter controlling the approxi
Formalizing Convex Hulls Algorithms
 IN TPHOLS’01
, 2001
"... We study the development of formally proved algorithms for computational geometry. The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally ..."
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Cited by 15 (3 self)
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We study the development of formally proved algorithms for computational geometry. The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally
Convex hulls; Bivariate density;
"... Convex hull drawing is a wellknown computational geometry problem and there is a multitude of algorithms available for solving it. Even though links between computational geometry and statistics have ..."
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Convex hull drawing is a wellknown computational geometry problem and there is a multitude of algorithms available for solving it. Even though links between computational geometry and statistics have
Extended Convex Hull
, 2000
"... In this paper we address the problem of computing a minimal Hrepresentation of the convex hull of the union of k Hpolytopes in R^d. Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull. Efficient wrapping is done by projecting the polytopes onto t ..."
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Cited by 8 (0 self)
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In this paper we address the problem of computing a minimal Hrepresentation of the convex hull of the union of k Hpolytopes in R^d. Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull. Efficient wrapping is done by projecting the polytopes onto
Results 1  10
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