Abstract. Based on the viewpoint of topological and geometrical operator, a novel class of subdivision schemes named semi-stationary subdivision is proposed for freeform surface design in this talk. Compared with traditional stationary methods, the main advantage of the semi-stationary subdivision is that an appropriate parameter-changing manner is given during the subdivision iterations. It makes the user able to work with easier shape control. It can also generate local revolving surfaces, directional and/or bumpy effects. For the practical and theoretical importance, the convergent properties of degree three subdivision schemes are strictly analyzed by employing DFT and matrix computing techniques to deal with the dynamic subdivision transform matrix. Also, its basic algorithms are generalized in several aspects, including selection of the multi-nucleus functions, disposing and interpolation of boundary. Due to the simplicity in both mathematical theory and practical implementation, the similarity to Catmull-Clark subdivision surface, and G2 continuity except irregular points, our method is promised to be much valuable in Computer Aided Design and computer graphics.

Keywords: solid modeling, subdivision surface, geometry continuity, convergence.