We present an explicit formula for the mask of odd points n-ary, for any odd n 3, interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-point a-ary schemes introduced by Lian, 2008, and 2m 1 -point a-ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd point n-ar...

A set S of vertices of a graph G = (V, E) is a dominating set if every vertex of V (G) \ S is adjacent to some vertex in S. The domination number γ (G) is the minimum cardinality of a dominating set of G. The domination subdivision number sdγ (G) is the minimum number of edges that must be subdivided in order to increase the domination number. Velammal showed that for any tree T of order at lea...

In this paper, we investigate subdivision tree representations of arbitrary triangle meshes. By subdivision, we mean the recursive topological partitioning of a triangle into subtriangles. Such a process can be represented by a subdivision tree. We identify the class of regular triangle meshes, those that can be losslessly represented by a nontrivial subdivision tree, i.e. by a subdivision tree...

Let ∆ be a Euclidean n-simplex and let {∆j} denote a finite union of simplices which partition ∆. We assume that the partition is invariant under the affine symmetry group of ∆. A classical example of such a partition is the one obtained from barycentric subdivision, but there are plenty of other possibilities. (See §4.1, or else [Sp, p. 123], for a definition of barycentric subdivision.) Our p...

We present an algorithm for local subdivision of Powell-Sabin spline surfaces. The construction of such a spline is based on a particular PS-refinement of a given triangulation. We build the new triangulation on top of this PS-refinement by applying a √ 3-subdivision scheme on a local part of the domain. To avoid degeneration we introduce a simple heuristic for refinement propagation, driven by...

Subdivision surfaces were applied to the entire meshes in order to produce smooth surfaces refinement from coarse mesh. Several schemes had been introduced in this area to provide a set of rules to converge smooth surfaces. However, to compute and render all the vertices are really inconvenient in terms of memory consumption and runtime during the subdivision process. It will lead to a heavy co...

Subdivision rules have traditionally been designed to generate smooth surfaces from polygonal meshes. In this paper we propose to employ subdivision rules as a polygonal modeling tool, specifically to add additional level of detail to meshes. However, existing subdivision schemes have several undesirable properties making them ill suited for polygonal modeling. In this paper we propose a genera...