Spectra of subdivision-vertex and subdivision-edge neighbourhood coronae

Effect of edge-subdivision on vertex-domination in a graph

Let G be a graph with ∆(G) > 1. It can be shown that the domination number of the graph obtained from G by subdividing every edge exactly once is more than that of G. So, let ξ(G) be the least number of edges such that subdividing each of these edges exactly once results in a graph whose domination number is more than that of G. The parameter ξ(G) is called the subdivision number of G. This not...

Vertex-Rounding a Three-Dimensional Polyhedral Subdivision

Adaptive Subdivision of Catmull-Clark Subdivision Surfaces

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 ...

N-Sided Hole Filling and Vertex Blending Using Subdivision Surfaces

To fill an N-sided hole on a NURBS surface and to blend a corner formed by NURBS surfaces, we propose a regular N-sided open uniform quadratic subdivision surface derived by applying the open uniform quadratic subdivision scheme to a regular N-sided control mesh which is confined to the hole or to the region of the vertex blend. Boundary conditions such as C and G-continuity required for the ho...

REVERSE LOOP SUBDIVISION FOR GEOMETRY AND TEXTURES

Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke. We apply this mas...