It has been shown that one triangulation of a set of points can be converted to any other triangulation of the same set of points by a sequence of edge flip operations. In this paper we consider a tesselation of a set of points consisting of convex cells, a convex subdivision, and explore the notion of flipping edges from one convex subdivision of the points to another, where both subdivisions ...

A non-uniform 3-point ternary interpolatory subdivision scheme with variable subdivision weights is introduced. Its support is computed. The C and C convergence analysis are presented. To elevate its controllability, a modified edition is proposed. For every initial control point on the initial control polygon a shape weight is introduced. These weights can be used to control the shape of the c...

We present an adaptive subdivision scheme for unstructured tetrahedral meshes inspired by the √ 3-subdivision scheme for triangular meshes. Existing tetrahedral subdivision schemes do not support adaptive refinement and have traditionally been driven by the need to generate smooth three-dimensional deformations of solids. These schemes use edge bisections to subdivide tetrahedra, which generate...