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6,578
Partial Results on Convex Polyhedron Unfoldings
, 2004
"... This paper is submitted for credit in the Algorithms for Polyhedra course at the University of Waterloo. We discuss a longstanding open problem in computational geometry and prove some partial results. 1 ..."
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This paper is submitted for credit in the Algorithms for Polyhedra course at the University of Waterloo. We discuss a longstanding open problem in computational geometry and prove some partial results. 1
Cutting a convex polyhedron out of a sphere
, 2009
"... Given a convex polyhedron P of n vertices inside a sphere Q, we give an O(n³)time algorithm that cuts P out of Q by using guillotine cuts and has cutting cost O((log n)²) times the optimal. ..."
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Cited by 1 (1 self)
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Given a convex polyhedron P of n vertices inside a sphere Q, we give an O(n³)time algorithm that cuts P out of Q by using guillotine cuts and has cutting cost O((log n)²) times the optimal.
HOW TO CUT OUT A CONVEX POLYHEDRON
, 2009
"... It is known that one can fold a convex polyhedron from a nonoverlapping face unfolding, but the complexity of the algorithm in [MP] remains an open problem. In this paper we show that every convex polyhedron P ⊂ R d can be obtained in polynomial time, by starting with a cube which contains P and ..."
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Cited by 1 (0 self)
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It is known that one can fold a convex polyhedron from a nonoverlapping face unfolding, but the complexity of the algorithm in [MP] remains an open problem. In this paper we show that every convex polyhedron P ⊂ R d can be obtained in polynomial time, by starting with a cube which contains P
On Computing Fréchet Distance of Two Paths on a Convex Polyhedron ∗
"... We present a polynomial time algorithm for computing Fréchet distance between two simple paths on the surface of a convex polyhedron. 1 ..."
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We present a polynomial time algorithm for computing Fréchet distance between two simple paths on the surface of a convex polyhedron. 1
Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons
 Theory of Probability and Its Applications
, 1995
"... We consider the problem of existence and uniqueness of semimartingale reflecting Brownian motions (SRBM's) in convex polyhedrons. Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the polyhedron the process behaves like a Brownian motion with a con ..."
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Cited by 66 (15 self)
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We consider the problem of existence and uniqueness of semimartingale reflecting Brownian motions (SRBM's) in convex polyhedrons. Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the polyhedron the process behaves like a Brownian motion with a
The Skorokhod oblique reflection problem in a convex polyhedron
 Georgian Math. J
, 1996
"... Abstract. The Skorokhod oblique reflection problem is studied in the case of ndimensional convex polyhedral domains. The natural sufficient condition on the reflection directions is found, which together with the Lipschitz condition on the coefficients gives the existence and uniqueness of the solu ..."
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Cited by 1 (0 self)
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Abstract. The Skorokhod oblique reflection problem is studied in the case of ndimensional convex polyhedral domains. The natural sufficient condition on the reflection directions is found, which together with the Lipschitz condition on the coefficients gives the existence and uniqueness
ON FACES OF A CONVEX POLYHEDRON IN R3 WITH A SMALL NUMBER OF SIDES
"... Abstract. For any convex polyhedron P ⊂ R3 and for any natural number k, let Fk(P) denote the number of all faces of P with exactly k sides. It is well known that Fk(P) ≥ 2 for at least one k. We consider the question whether Fk(P) ≥ 3, for at least one k, and present a solution to it. Some relate ..."
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Abstract. For any convex polyhedron P ⊂ R3 and for any natural number k, let Fk(P) denote the number of all faces of P with exactly k sides. It is well known that Fk(P) ≥ 2 for at least one k. We consider the question whether Fk(P) ≥ 3, for at least one k, and present a solution to it. Some
A Complete and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron
 IN PROC. 3RD WORKSHOP ALGORITHMS DATA STRUCT
, 1993
"... A polyhedron is any set that can be obtained from the open halfspaces by a finite number of set complement and set intersection operations. We give an efficient and complete algorithm for intersecting two threedimensional polyhedra, one of which is convex. The algorithm is efficient in the sense ..."
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Cited by 17 (1 self)
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A polyhedron is any set that can be obtained from the open halfspaces by a finite number of set complement and set intersection operations. We give an efficient and complete algorithm for intersecting two threedimensional polyhedra, one of which is convex. The algorithm is efficient in the sense
Research on Convex Polyhedron Collision Detection Algorithm Based on Improved Particle Swarm Optimization
"... Abstract—A convex polyhedron collision detection algorithm based on the shortest distance is proposed, which uses convex Bounding Volume Hierarchies to express convex polyhedron. Thus the distance problem of two convex polyhedrons is come down to a nonlinear programming problem with constraints. Th ..."
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Abstract—A convex polyhedron collision detection algorithm based on the shortest distance is proposed, which uses convex Bounding Volume Hierarchies to express convex polyhedron. Thus the distance problem of two convex polyhedrons is come down to a nonlinear programming problem with constraints
Results 1  10
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6,578