LOOP subdivision surface of progressive interpolation
渐进插值的LOOP曲面细分*

Subdivision surfaces can not deal with the open and closed mesh with the same method. This paper presented a new method based on interpolating LOOP subdivision surfaces. Gave a triangular mesh M, the main idea was to iteratively upgrade the vertices of M to generate a new control mesh such that limit surface of would interpolate M. The new vertex was bound through the constraint solving of its adjacent vertices. It could be shown that the iterative process was convergent for LOOP subdivision surfaces. As new vertex was generated by constraint solving of its adjacent vertices, essentially it was a local method.Hence, the method was well-defined. The new method has the advantages of both a local method and a global method, it can handle meshes of any size and any topology while generating smooth interpolating subdivision surfaces that faithfully resemble the shape of the given meshes.The meshes considered here can be open or closed.