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89
Excluding Subdivisions of Infinite Cliques
, 1989
"... For every infinite cardinal κ we characterize graphs not containing a subdivision of K_κ. ..."
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Cited by 2 (1 self)
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For every infinite cardinal κ we characterize graphs not containing a subdivision of K_κ.
Finite Subdivision Rules
 Conform. Geom. Dyn
, 2001
"... . We introduce and study finite subdivision rules. A finite subdivision rule is a finite list of instructions which determines a subdivision of a given planar tiling. Given a finite subdivision rule and a planar tiling associated to it, we obtain an infinite sequence of tilings by recursively sub ..."
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Cited by 33 (8 self)
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. We introduce and study finite subdivision rules. A finite subdivision rule is a finite list of instructions which determines a subdivision of a given planar tiling. Given a finite subdivision rule and a planar tiling associated to it, we obtain an infinite sequence of tilings by recursively
A Nonlinear Subdivision Scheme for Triangle Meshes
 Vision, Modeling and Visualization 2000
, 2000
"... Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E. g., Bsplines are smooth curves or surfaces that can be constructed by infinite subdivision of a polyline or polygon mesh of control points. New vertices are computed by linear combinat ..."
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Cited by 10 (2 self)
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Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E. g., Bsplines are smooth curves or surfaces that can be constructed by infinite subdivision of a polyline or polygon mesh of control points. New vertices are computed by linear
Improved Triangular Subdivision Schemes
, 1998
"... In this article we improve the butterfly and Loop's algorithm. As a result we obtain subdivision algorithms for triangular nets which can be used to generate G 1  and G 2  surfaces, respectively. Keywords: Subdivision, interpolatory subdivision, Loop's algorithm, butterfly algorithm ..."
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Cited by 24 (8 self)
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produced by these algorithms are piecewise polynomial and at ordinary points curvature continuous. At extraordinary points however, the curvature is zero or infinite. In general, singularities at extraordinary points is an inherent phenomenon of subdivision, see [13, 12, 9]. The smoothness of a subdivision
Refining Triangle Meshes by NonLinear Subdivision
, 2001
"... Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E. g., Bsplines are smooth curves or surfaces that can be constructed by infinite subdivision of a polyline or polygon mesh of control points. New vertices are computed by linear combinat ..."
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Cited by 7 (0 self)
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Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E. g., Bsplines are smooth curves or surfaces that can be constructed by infinite subdivision of a polyline or polygon mesh of control points. New vertices are computed by linear
Interpolatory subdivision schemes with infinite masks originated from splines
"... A generic technique for the construction of diversity of interpolatory subdivision schemes on the base of polynomial and discrete splines is presented in the paper. The devised schemes have rational symbols and infinite masks but they are competitive (regularity, speed of convergence, computational ..."
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Cited by 16 (11 self)
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A generic technique for the construction of diversity of interpolatory subdivision schemes on the base of polynomial and discrete splines is presented in the paper. The devised schemes have rational symbols and infinite masks but they are competitive (regularity, speed of convergence, computational
Spectra of the subdivisionvertex and subdivisionedge corona
, 2013
"... The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge of G. Let G1 and G2 be two vertex disjoint graphs. The subdivisionvertex corona of G1 and G2, denoted by G1 G2, is the graph obtained from S(G1) and V (G1) copies of G2, all vertexdisjoint, b ..."
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Cited by 3 (1 self)
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The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge of G. Let G1 and G2 be two vertex disjoint graphs. The subdivisionvertex corona of G1 and G2, denoted by G1 G2, is the graph obtained from S(G1) and V (G1) copies of G2, all vertex
Variational Surface Modeling
 Computer Graphics
, 1992
"... We present a new approach to interactive modeling of freeform surfaces. Instead of a fixed mesh of control points, the model presented to the user is that of an infinitely malleable surface, with no fixed controls. The user is free to apply control points and curves which are then available as handl ..."
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Cited by 186 (4 self)
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We present a new approach to interactive modeling of freeform surfaces. Instead of a fixed mesh of control points, the model presented to the user is that of an infinitely malleable surface, with no fixed controls. The user is free to apply control points and curves which are then available
Spectra of subdivisionvertex and subdivisionedge joins of graphs
, 2012
"... Let G = (V (G), E(G)) be a graph with vertex set V (G) and edge set E(G). The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge of G. Let G1 and G2 be two vertex disjoint graphs. The subdivisionvertex neighbourhood corona of G1 and G2, denoted by G ..."
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Cited by 4 (0 self)
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(respectively, G1G2) in terms of the corresponding spectra of G1 and G2. As applications, these results enable us to construct infinitely many pairs of cospectral graphs, and using the results on the Laplacian spectra of subdivisionvertex neighbourhood coronae, new families of expander graphs are constructed
Necessary Conditions for Subdivision Surfaces
, 1997
"... Subdivision surfaces are considered which consist of tri or quadrilateral patches in a mostly regular arrangement with finitely many irregularities. A sharp estimate on the lowest possible degree of the patches is given. It depends on the smoothness and flexibility of the underlying subdivision sch ..."
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Cited by 13 (4 self)
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Subdivision surfaces are considered which consist of tri or quadrilateral patches in a mostly regular arrangement with finitely many irregularities. A sharp estimate on the lowest possible degree of the patches is given. It depends on the smoothness and flexibility of the underlying subdivision
Results 1  10
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89