Subdivision templates of numerical values are replaced by templates of matrices in this paper to allow the introduction of shape control parameters for the feasibility of achieving desirable geometric shapes at those points on the subdivision surfaces that correspond to extraordinary control vertices. Formulation of the matrix-valued subdivision surface is derived. Based on refinable bivariate ...

Subdivision schemes are commonly used to obtain dense or smooth data representations from sparse discrete data. E. g., B-splines 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 combinations of the initial control points. We present a new non-linear subdivision scheme for the refine...

A set S of vertices in a graph G(V,E) is called a total dominating set if every vertex v ∈ V is adjacent to an element of S. The total domination number of a graph G denoted by γt(G) is the minimum cardinality of a total dominating set in G. Total domination subdivision number denoted by sdγt is the minimum number of edges that must be subdivided to increase the total domination number. Here we...

Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases sharply with respect to subdivision depth. This paper presents an adaptive subdivision technique as a solution to this problem. Instead of subdivision depths of mesh faces, the adaptive subdivision process is driven by labels of ...

LetH be a multigraph, possibly containing loops. AnH-subdivision is any simple graph obtained by replacing the edges of H with paths of arbitrary length. Let H be an arbitrary multigraph of order k, size m, n0(H) isolated vertices and n1(H) vertices of degree one. In [10] it was shown that if G is a simple graph of order n containing an H-subdivision H and δ(G) ≥ n+m−k+n1(H)+2n0(H) 2 , then G c...

In this paper we extend the standard method to derive and optimize subdivision rules in the vicinity of extraordinary vertices (EV). Starting from a given set of rules for regular control meshes, we tune the extraordinary rules (ER) such that the necessary conditions for C continuity are satisfied along with as many necessary C conditions as possible. As usually done, our approach sets up the g...

Although previous studies have attempted to address the challenge of land subdivision, there is still a scarcity in the literature on how the extent of conformity to land subdivision planning regulations may be statistically and spatially analyzed. This study, therefore, explores the extent to which residential developers comply with land subdivision planning regulations in Kenya, a case study ...

Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.