A 4-Point Subdivision Scheme with Four Parameters for Surface Design

This paper extends the classical4-point interpolating subdivision scheme,and brings forward a new 4-point subdivision scheme with four parameters for curve design,which can be controlled by choosing the parameters appropriately.At the same time,we extend it to surface design,and its uniform convergence is investigated.In addition,some sufficient conditions for curve C⁰ to C³ continuity and those for surface continuity of the subdivision scheme are provided.