Bezier surfaces on circle and fan-shaped domain

Chunfeng Liu, Xiaolong Zhang,

Abstract

The Bernstein basis in Cartesian coordinate system rotated around z can be the rotating Bernstein basis in cylindrical coordinate system, so it can get rotating Bezier surface in cylindrical coordinate system. As this surface has good symmetry, the shape of the rules is not common in geometric modeling, in order to deal this problem we introduce new parameters  constitute tensor product type Bernstein basis in cylindrical coordinate system, and gives the tensor Bezier surface in unit circle domain which has it nature and de Casteljau algorithm. But there will be a gap in Bezier surfaces, so we popularized Bezier method on circular area to any type on the tensor Bezier surface on fan-shaped area.