关键词: 张量积Bé, zier曲面, 降多阶, 角点插值, 逼近

Abstract: A matrix formula of the multi-degree reduction of tensor product Bézier surface approximation error is presented based on least squares normal[(L2)]. It gives the explicit representation of control points of the reduced multi-degree tensor product Bézier surface, through minimizing the distance function between the original Bézier surface and the reduced multi-degree tensor product Bézier surface over unit square [[0,1]×[0,1]]. During the multi-degree reduction process, it is considered that the constraint of high-order interpolations over corners. Examples show that the proposed approach has better approximation of the reduced surfaces than that of current methods. An iterative algorithm for degree reduction of Bézier surfaces is given.

Key words: tensor product Bézier surface, multi-degree reduction, corner interpolation, approximation