Artifacts caused by simplicial subdivision

2006 ◽  
Vol 12 (2) ◽  
pp. 231-242 ◽  
Author(s):  
H. Carr ◽  
T. Moller ◽  
J. Snoeyink
Keyword(s):  
Simplicial Subdivision

Subdivisions of Simplicial Complexes Preserving the Metric Topology

2012 ◽  
Vol 55 (1) ◽  
pp. 157-163 ◽  
Author(s):  
Kotaro Mine ◽  
Katsuro Sakai
Keyword(s):  
Simplicial Complex ◽  
Simplicial Complexes ◽  
Simplicial Subdivision ◽  
Metric Topology ◽  
The One

AbstractLet |K| be the metric polyhedron of a simplicial complex K. In this paper, we characterize a simplicial subdivision K′ of K preserving the metric topology for |K| as the one such that the set K′(0) of vertices of K′ is discrete in |K|. We also prove that two such subdivisions of K have such a common subdivision.

scholarly journals Goldberg-Coxeter Construction for $3$- and $4$-valent Plane Graphs

10.37236/1773 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Mathieu Dutour ◽  
Michel Deza
Keyword(s):  
Finite Index ◽  
Plane Graph ◽  
Mathematical Journal ◽  
Index Subgroup ◽  
Plane Graphs ◽  
Circuit Structure ◽  
Simplicial Subdivision ◽  
Finite Index Subgroup ◽  
Algebraic Formalism

We consider the Goldberg-Coxeter construction $GC_{k,l}(G_0)$ (a generalization of a simplicial subdivision of the dodecahedron considered by Goldberg [Tohoku Mathematical Journal, 43 (1937) 104–108] and Coxeter [A Spectrum of Mathematics, OUP, (1971) 98–107]), which produces a plane graph from any $3$- or $4$-valent plane graph for integer parameters $k,l$. A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face; a central circuit in a $4$-valent plane graph $G$ is a circuit of edges, such that no two consecutive edges belong to the same face. We study the zigzag (or central circuit) structure of the resulting graph using the algebraic formalism of the moving group, the $(k,l)$-product and a finite index subgroup of $SL_2(\Bbb{Z})$, whose elements preserve the above structure. We also study the intersection pattern of zigzags (or central circuits) of $GC_{k,l}(G_0)$ and consider its projections, obtained by removing all but one zigzags (or central circuits).

SPLINE APPROXIMATIONS ON MANIFOLDS

2006 ◽  
Vol 04 (03) ◽  
pp. 383-403 ◽  
Author(s):  
YU. K. DEMYANOVICH
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Smooth Manifold ◽  
Compact Set ◽  
Simple Method ◽  
Manifold With Boundary ◽  
Local Approximations ◽  
Simplicial Subdivision

A method of construction of the local approximations in the case of functions defined on n-dimensional (n ≥ 1) smooth manifold with boundary is proposed. In particular, spline and finite-element methods on manifold are discussed. Nondegenerate simplicial subdivision of the manifold is introduced and a simple method for evaluations of approach is examined (the evaluations are optimal as to N-width of corresponding compact set).

On Rational Subdivisions of Polyhedra with Rational Vertices

1977 ◽  
Vol 29 (2) ◽  
pp. 238-242 ◽  
Author(s):  
W. M. Beynon
Keyword(s):  
Convex Polytopes ◽  
Rational Points ◽  
Short Paper ◽  
Simplicial Subdivision

This short paper is devoted to the proof of a single theorem, which, in its simplest form, asserts that if Q is a polyhedron in Rn which can be expressed as the union of finitely many convex polytopes whose vertices are at rational points in Rn, and if is a simplicial subdivision of Q﹜ then there is an isomorphic simplicial subdivision ” of Q in which all vertices are at rational points.

Sign in / Sign up

Export Citation Format

Share Document