Multi-degree reduction of triangular Bézier surfaces with boundary constraints

Given a triangular Bézier surface of degree nn, the problem of multi-degree reduction by a triangular Bézier surface of degree mm with boundary constraints is investigated. This paper considers the continuity of triangular Bézier surfaces at the three corners, so that the boundary curves preserve endpoints continuity of any order αα. The l2l2- and L2L2-norm combined with the constrained least-squares method are used to get the matrix representations for the control points of the degree reduced surfaces. Both methods can be applied to piecewise continuous triangular patches or to only a triangular patch with the combination of surface subdivision. And the resulting piecewise approximating patches are globally C0C0 continuous. Finally, error estimation is given and numerical examples demonstrate the effectiveness of our methods.