A New Scheme of Interpolation Subdivision Surface by Using the Bezier Curve

Abstract

To achieve more realistic surface design, this paper proposes a new scheme of interpolation subdivision surface, which is extended from interpolation subdivision of Bezier curve. Different from the previous interpolation subdivision schemes, the normal vectors are used to generate a circle from a triangle which results in only 3 vertices and 3 edges. This improvement not only makes a curve smooth, but also can produce sharp angles during subdivision. Furthermore, we make new contributions in the subdivision surface scheme compared to the existing methods. The proposed scheme in this paper avoids solving a large system of linear equations, which can greatly reduce the cost of calculation. Due to the usage of the normal vectors, there is also no need to consider the meshes adjacent to the target. Since it has no change on the topology of the mesh and no update of the vertices, this scheme can also be realized in parallel and thus achieve fast implementation. Finally, examples of subdivision surface by this scheme are illustrated, and the comparison with the results by existing method is also discussed to show the advantages of this scheme.