AN APPROXIMATING SUBDIVISION SCHEME BY CUTTING AND UPHEAVING THE CORNER OF CONTROL POLYGON

摘要

In this paper, we aim at generating a stationary subdivision algorithm over arbitrary topology networks by either cutting or upheaving the corner of control polygon in order to approximate the control nets. We consider of the two basic curve subdivision schemes: Chaikin algorithm and 4-point interpolatory algorithm. We combine these two schemes together and propose a new curve and surface subdivision scheme. So the curves and surfaces generated by our proposed algorithm are more approximating the control polygon model than those generated only by Chaikin algorithm. And the speed of shrinkage of our scheme is also faster than the one of 4-point scheme. The limit curve or surface is C1 continuous and the refinement process is simple and effective.