Multi-degree reduction of tensor product Bézier surfaces with conditions of corners interpolations  

作　　者：陈国栋 王国谨 

出　　处：《Science in China(Series F)》2002年第1期51-58,共8页中国科学（F辑英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 69973041) Natural Science Foundation of Zhejiang Province (Grant No. 698025) and the Foundation of State Key Basic Research 973 Project (Grant No. G1998030600).

摘　　要：This paper studies the multi-degree reduction of tensor product B(?)zier surfaces with any degree interpolation conditions of four corners, which is urgently to be resolved in many CAD/CAM systems. For the given conditions of corners interpolation, this paper presents one intuitive method of degree reduction of parametric surfaces. Another new approximation algorithm of multi-degree reduction is also presented with the degree elevation of surfaces and the Chebyshev polynomial approximation theory. It obtains the good approximate effect and the boundaries of degree reduced surface can preserve the prescribed continuities. The degree reduction error of the latter algorithm is much smaller than that of the first algorithm. The error bounds of degree reduction of two algorithms are also presented .This paper studies the multi-degree reduction of tensor product B(?)zier surfaces with any degree interpolation conditions of four corners, which is urgently to be resolved in many CAD/CAM systems. For the given conditions of corners interpolation, this paper presents one intuitive method of degree reduction of parametric surfaces. Another new approximation algorithm of multi-degree reduction is also presented with the degree elevation of surfaces and the Chebyshev polynomial approximation theory. It obtains the good approximate effect and the boundaries of degree reduced surface can preserve the prescribed continuities. The degree reduction error of the latter algorithm is much smaller than that of the first algorithm. The error bounds of degree reduction of two algorithms are also presented .

关 键 词：corner interpolation multi-degree reduction APPROXIMATION tensor product surfaces. 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]