Approximating tensor product Bézier surfaces with tangent plane continuity

Abstract

We present a simple method for degree reduction of tensor product Bézier surfaces with tangent plane continuity in L 2 -norm. Continuity constraints at the four corners of surfaces are considered, so that the boundary curves preserve endpoints continuity of any order α . We obtain matrix representations for the control points of the degree reduced surfaces by the least-squares method. A simple optimization scheme that minimizes the perturbations of some related control points is proposed, and the surface patches after adjustment are C ∞ continuous in the interior and G 1 continuous at the common boundaries. We show that this scheme is applicable to surface patches defined on chessboard-like domains.