Subdivision Surfaces Based on Planar Hexagon Edge-Cutting

It is difficult to extend corner-cutting subdivision curve methods to edge-cutting subdivision surface gen-eration. In this paper, we propose a planar hexagonal edge-cutting subdivision scheme which can generate interpolatory and convexity preserving inscribed smooth surfaces for convex polyhedral initial meshes through only edge-cutting by planes. The method is a new extension of the corner-cutting subdivision curves. First, the conditions of initial parameter for edge-cutting are given to avoid over cutting. Next, the method for adjusting edge-cutting points is presented for making the new edge parallel to the old edge. Then, the formulae for calculating new vertices are obtained. After that, two methods for generating a nat-ural boundary and a normal boundary are also given. The initial meshes of numerical examples include regular tetrahedron, cube and its variants. The results show that our edge-cutting method possesses the same main properties as the interpolatory convexity preserving subdivision and has some advantages over the latter.