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On Minkowski sums of simplices
"... We investigate the structure of the Minkowski sum of standard simplices in Rr. In particular, we investigate the onedimensional structure, the vertices, their degrees and the edges in the Minkowski sum polytope. ..."
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We investigate the structure of the Minkowski sum of standard simplices in Rr. In particular, we investigate the onedimensional structure, the vertices, their degrees and the edges in the Minkowski sum polytope.
Pointbased Minkowski sum . . .
"... Minkowski sum is a fundamental operation in many geometric applications, including robotics, penetration depth estimation, solid modeling, and virtual prototyping. However, due to its high computational complexity and several nontrivial implementation issues, computing the exact boundary of the Min ..."
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Minkowski sum is a fundamental operation in many geometric applications, including robotics, penetration depth estimation, solid modeling, and virtual prototyping. However, due to its high computational complexity and several nontrivial implementation issues, computing the exact boundary
On the Fatness of Minkowski Sums
, 1999
"... Let A and B be two connected, closed, and bounded sets in E d . Let AB denote the Minkowski sum (that is, the vector sum) of A and B. We prove two results concerning the fatness of A B. First, we prove that fatness(A B) > min(fatness(A); fatness(B)): In addition, we show that if diam(A) > d ..."
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Let A and B be two connected, closed, and bounded sets in E d . Let AB denote the Minkowski sum (that is, the vector sum) of A and B. We prove two results concerning the fatness of A B. First, we prove that fatness(A B) > min(fatness(A); fatness(B)): In addition, we show that if diam(A) >
Minkowski Sum Selection and Finding
, 2008
"... Let P, Q ⊆ R2 be two npoint multisets and Ar ≥ b be a set of λ inequalities on x and y, where A ∈ Rλ×2, r = [ x y], and b ∈ Rλ. Define the constrained Minkowski sum (P ⊕Q)Ar≥b as the multiset ..."
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Let P, Q ⊆ R2 be two npoint multisets and Ar ≥ b be a set of λ inequalities on x and y, where A ∈ Rλ×2, r = [ x y], and b ∈ Rλ. Define the constrained Minkowski sum (P ⊕Q)Ar≥b as the multiset
Lattice points in Minkowski sums
"... Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact ..."
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Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact
Computing the Minkowski Sum of Prisms *
, 2006
"... Abstract. Within this paper we study the Minkowski sum of prisms ("Cephoids") in a finite dimensional vector space. For a vector a ∈ R n with positive components we writē a = ( ) and denote by = ā = {x ∈ R n  ā, x 1 , x 0} the associated prism. We provide a representation of a finite sum ..."
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Abstract. Within this paper we study the Minkowski sum of prisms ("Cephoids") in a finite dimensional vector space. For a vector a ∈ R n with positive components we writē a = ( ) and denote by = ā = {x ∈ R n  ā, x 1 , x 0} the associated prism. We provide a representation of a finite
Traveling the Boundary of Minkowski Sums
, 1997
"... We consider the problem of traveling the contour of the set of all points that are within distance 1 of a connected planar curve arrangement P, forming an embedding of the graph G. We show that if the overall length of P is L, there is a closed roundtrip that visits all points of the contour and has ..."
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and has length no longer than 2L + 2ß. This result carries over in a more general setting: if R is a compact convex shape with interior points and boundary length `, we can travel the boundary of the Minkowski sum P \Phi R on a closed roundtrip no longer than 2L + `.
Approximate Unions of Lines and Minkowski Sums
, 2004
"... We study the complexity of and algorithms to construct approximations of the union of lines and of the Minkowski sum of two simple polygons. We also study thick unions of lines and Minkowski sums, which are inflated with a small disc. Let b = D/ε be the ratio of the diameter of the region of interes ..."
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We study the complexity of and algorithms to construct approximations of the union of lines and of the Minkowski sum of two simple polygons. We also study thick unions of lines and Minkowski sums, which are inflated with a small disc. Let b = D/ε be the ratio of the diameter of the region
Results 1  10
of
373