Multi-degree Reduction Of Bézier Curves And Surfaces

In order to compress information and data storage, and facilitate the data exchange between different modeling tools in CAD/CAM systems, degree reduction of Bezier curves and surfaces are widely used in the area of CAGD, which tries to approximate a given curve or surface of certain degree by another one of lower degree, such that the given error is satisfied. In this thesis, we discuss the problem of degree reduction of Bezier curves and surfaces. The main innovative results are as follows.A matrix formula of the multi-degree reduction of tensor product Bezier surface approximation error is presented based on least squares normal (L2). We give the explicit representation of control points3f the reduced multi-degree tensor product Bezier surface Qm1,n1(u, v), through minimizing the distance function between Pm,n(u,v) and Qm1,n1(u,v)(n1≤n-1,m1≤m-1) over unit square [0,1]×[0,1].During the multi-degree reduction process, we consider 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. Finally, an iterative algorithm for degree reduction of Bezier surfaces is given.