منابع مشابه
Approximation by Bases on Polygonal Complexes
We consider the approximation properties of a class of bases defined on refined polygonal complexes. This class includes many bases used in geometric modeling for surfaces of arbitrary topology, subdivision surfaces in particular. We show that under moderately weak assumptions, the approximation rate of the bases in our class is no worse than the approximation rate of these bases restricted to ...
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This paper provides a theoretical foundation of a thinning method due to Kovalevsky for 2D digital binary images modelled by cell complexes or, equivalently, by Alexandroff T0 topological spaces, whenever these are constructed from polygonal tilings. We analyze the relation between local and global simplicity of cells, and prove their equivalence under certain conditions. For the proof we apply...
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Regular polygonal complexes in euclidean 3-space E3 are discrete polyhedra-like structures with finite or infinite polygons as faces and with finite graphs as vertex-figures, such that their symmetry groups are transitive on the flags. The present paper and its predecessor describe a complete classification of regular polygonal complexes in E3. In Part I we established basic structural results ...
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A polygonal complex in euclidean 3-space E3 is a discrete polyhedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number r > 2 of faces surround each edge. It is said to be regular if its symmetry group is transitive on the flags. The present paper and its successor describe a complete classification of regular polygonal complex...
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In this paper we introduce a class of polygonal complexes for which we can define a notion of sectional combinatorial curvature. These complexes can be viewed as generalizations of 2-dimensional Euclidean and hyperbolic buildings. We focus on the case of non-positive and negative combinatorial curvature. As geometric results we obtain a Hadamard-Cartan type theorem, thinness of bigons, Gromov h...
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ژورنال
عنوان ژورنال: Publicacions Matemàtiques
سال: 2013
ISSN: 0214-1493
DOI: 10.5565/publmat_57213_07