A Method for Deducing Interpolating Subdivision Schemes from Approximating Subdivision Schemes and Blending Subdivisions

We present a method for deducing interpolating subdivision schemes from known approximating subdivision scheme which generates C² curves and blending subdivision schemes. We make use of the connection between the approximating subdivision schemes and interpolating subdivision schemes to produce a blending subdivision scheme that integrates interpolating and approximating subdivision schemes in a simple and efficient way. The basic idea is to use the specific linear combination of the displacements of the new vertices which are derived from approximating subdivision scheme to produce associated interpolating displacements for the new vertices therefore generating a corresponding interpolating subdivision scheme. The most importance is that such methods are deduced in premise of keeping the continuity of the original approximating subdivision schemes. In addition, our method has much lower computational complexity compared with the exiting methods and can be easily extended to the case of surface subdivision schemes.