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 ...

In this paper, we introduce two generalizations of midpoint subdivision and analyze the smoothness of the resulting subdivision surfaces at regular and extraordinary points. The smoothing operators used in midpoint and mid-edge subdivision connect the midpoints of adjacent faces or of adjacent edges, respectively. An arbitrary combination of these two operators and the refinement operator that ...

The domination subdivision number sdγ(G) of a graph G is the minimum number of edges that must be subdivided to increase the domination number of G. We present a simple characterization of trees with sdγ = 1 and a fast algorithm to determine whether a tree has this property.

Subdivision schemes provide efficient algorithms both for the design and processing of arbitrary control meshes. Theoretically, these techniques are often considered as an elegant algorithmic way to approximate a desired surface from a given surface. In practice, controlling the accuracy of control meshes with regard to the limit surface remains difficult. In this paper, from a bound of the dis...

PURPOSE We analyzed the clinical data of T3 colorectal cancer patients to assess whether T3 subdivision correlates with node (N) or metastasis (M) staging and stage-independent factors. METHODS Five hundred fifty-five patients who underwent surgery for primary colorectal cancer from January 2003 to December 2009 were analyzed for T3 subdivision. T3 subdivision was determined by the depth of i...

We show that the Wyman’s solution may be obtained from the fourdimensional Einstein’s equations for a spherically symmetric, minimally coupled, massless scalar field by using the continuous self-similarity of those equations. The Wyman’s solution depends on two parameters, the mass M and the scalar charge Σ. If one fixes M to a positive value, say M0, and let Σ 2 take values along the real line...

In this paper we shall study the initial functions in a subdivision scheme in a Sobolev space. By investigating the mutual relations among the initial functions in a subdivision scheme, we are able to study in a relatively uniied approach several questions related to a subdivision scheme in a Sobolev space such as convergence, error estimate and convergence rate of a subdivision scheme in a Sob...

In this article, the objective is to introduce an algorithm to produce the quaternary m-point (for any integer ) approximating subdivision schemes, which have smaller support and higher smoothness, comparing to binary and ternary schemes. The proposed algorithm has been derived from uniform B-spline basis function using the Cox-de Boor recursion formula. In order to determine the convergence an...