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91
On Traces of dstresses in the Skeletons of Lower Dimensions of Piecewiselinear dmanifolds
, 2001
"... We show how a dstress on a piecewiselinear realization of an oriented (nonsimplicial, in general) dmanifold in R d naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of selfstresses in spatial frameworks. The mappings w ..."
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Cited by 2 (0 self)
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We show how a dstress on a piecewiselinear realization of an oriented (nonsimplicial, in general) dmanifold in R d naturally induces stresses of lower dimensions on this manifold, and discuss implications of this construction to the analysis of selfstresses in spatial frameworks. The mappings
Discrete Morse Theory for Manifolds with Boundary
, 2012
"... We introduce a version of discrete Morse theory specific for manifolds with boundary. The idea is to consider Morse functions for which all boundary cells are critical. We obtain “Relative Morse Inequalities ” relating the homology of the manifold to the number of interior critical cells. We also ..."
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Cited by 14 (8 self)
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, there are exponentially many combinatorial types of simplicial dmanifolds (counted with respect to the number of facets) that admit discrete Morse functions with at most k critical interior (d − 1)cells. (This connects discrete Morse theory to enumerative combinatorics/ discrete quantum gravity.) (3) The barycentric
CONSTRUCTING SIMPLICIAL BRANCHED COVERS
, 2007
"... Branched covers are applied frequently in topology most prominently in the construction of closed oriented PL dmanifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d ≤ 4. On the other hand, Izmestiev and Joswig described how ..."
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Branched covers are applied frequently in topology most prominently in the construction of closed oriented PL dmanifolds. In particular, strong bounds for the number of sheets and the topology of the branching set are known for dimension d ≤ 4. On the other hand, Izmestiev and Joswig described
Fractal Structure of 4D Euclidean Simplicial Manifold
, 2003
"... The fractal properties of fourdimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to make more unambiguous measurement of the fractal dimension, we ..."
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The fractal properties of fourdimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to make more unambiguous measurement of the fractal dimension, we
Progressive lossless compression of arbitrary simplicial complexes
 ACM Trans. Graphics (Proc. ACM SIGGRAPH 2002
, 2002
"... Efficient algorithms for compressing geometric data have been widely developed in the recent years, but they are mainly designed for closed polyhedral surfaces which are manifold or “nearly manifold”. We propose here a progressive geometry compression scheme which can handle manifold models as well ..."
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Cited by 76 (0 self)
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Efficient algorithms for compressing geometric data have been widely developed in the recent years, but they are mainly designed for closed polyhedral surfaces which are manifold or “nearly manifold”. We propose here a progressive geometry compression scheme which can handle manifold models as well
Simplicial manifolds, bistellar flips and a 16vertex triangulation of the Poincaré homology 3sphere
 Math
, 2000
"... We present an algorithm based on bistellar operations that provides a useful tool for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16vertex triangulation of the Poincaré homology 3sphere; we construct an infinite series of nonPL ddimensional spheres with ..."
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Cited by 47 (15 self)
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We present an algorithm based on bistellar operations that provides a useful tool for the construction of simplicial manifolds with few vertices. As an example, we obtain a 16vertex triangulation of the Poincaré homology 3sphere; we construct an infinite series of nonPL ddimensional spheres
Update operations on 3D simplicial decompositions of nonmanifold objects
, 2004
"... We address the problem of updating nonmanifold mixeddimensional objects, described by threedimensional simplicial complexes embedded in 3D Euclidean space. We consider two local update operations, edge collapse and vertex split, which are the most common operations performed for simplifying a sim ..."
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Cited by 3 (3 self)
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We address the problem of updating nonmanifold mixeddimensional objects, described by threedimensional simplicial complexes embedded in 3D Euclidean space. We consider two local update operations, edge collapse and vertex split, which are the most common operations performed for simplifying a
Topological Decompositions for 3D Nonmanifold Simplicial Shapes
, 2007
"... Modeling and understanding complex nonmanifold shapes is a key issue in several applications including formfeature identification in CAD/CAE, and shape recognition for Web searching. Geometric shapes are commonly discretized as simplicial 2 or 3complexes embedded in the 3D Euclidean space. The t ..."
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Modeling and understanding complex nonmanifold shapes is a key issue in several applications including formfeature identification in CAD/CAE, and shape recognition for Web searching. Geometric shapes are commonly discretized as simplicial 2 or 3complexes embedded in the 3D Euclidean space
Classification of simplicial triangulations of topological manifolds
 Ann. of Math
"... In this note we announce theorems which classify simplicial (not necessarily combinatorial) triangulations of a given topological «manifold M, n> 7 (> 6 if dM = 0) , in terms of homotopy classes of lifts of the classifying map r: M —• BTOP for the stable topological tangent bundle of M to a c ..."
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Cited by 23 (0 self)
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In this note we announce theorems which classify simplicial (not necessarily combinatorial) triangulations of a given topological «manifold M, n> 7 (> 6 if dM = 0) , in terms of homotopy classes of lifts of the classifying map r: M —• BTOP for the stable topological tangent bundle of M to a
Voxelization of Solids Using Simplicial Coverings
, 2004
"... Rasterization of polygons in 2D is a well known problem, existing several optimal solutions to solve it. The extension of this problem to 3D is more difficult and most existing solutions are designed to obtain a voxelization of the solid. In this paper a new approach to rasterize and voxelize solids ..."
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solids in 3D is presented. The described algorithms are very simple, general and robust. The 3D algorithm is valid to be used in the new 3D displays, and it can also be used to voxelize solids delimited by planar faces (with or without holes, manifold or nonmanifold). The proposed methods are very
Results 1  10
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91