Optimal multi-degree reduction of C-Bézier surfaces with constraints

Abstract

We propose an optimal approach to solve the problem of multi-degree reduction of C-Bézier surfaces in the norm L₂ with prescribed constraints. The control points of the degree-reduced C-Bézier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the C-Bézier basis. With prescribed boundary constraints, this method can be applied to piecewise continuous patches or to a single patch with the combination of surface subdivision. The resulting piecewise approximating patches are globally G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.

Keywords

C-Bézier surfaces / Degree reduction / Boundary constraints

RIGHTS & PERMISSIONS

Zhejiang University and Springer-Verlag GmbH Germany