An Extension of Doo-Sabin Subdivision Algorithm Based on the Dynamic Scheme

We present a new dynamic convexity preserving subdivision scheme based on the b-i quadratic uniform trigonometric polynomial B-spline.This scheme can be considered as an extension of the Doo-Sabin scheme in the dynamic case.The subdivision rules based on the geometric interpretation of the tensor product scheme,and it can reproduce the surfaces of revolution.Furthermore,we can control the shape of the limit surface by modifying the shape parameter.The convergence of the scheme is proved in the paper by the traditional discrete Fourier technigue and the eigenvalue method.