Constrained multi-degree reduction of rational Bézier curves using reparameterization  

作　　者：CAI Hong-jie WANG Guo-jin 

机构地区：[1]Institute of Computer Images and Graphics, State Key Laboratory of CAD ＆ CG, Zhejiang University, Hangzhou 310027, China

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2007年第10期1650-1656,共7页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：Project supported by the National Basic Research Program (973) of China (No. 2004CB719400);the National Natural Science Founda-tion of China (Nos. 60673031 and 60333010);the National Natural Science Foundation for Innovative Research Groups of China (No. 60021201)

摘　　要：Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bezier curves to the algorithms of constrained multi-degree reduction for rational Bezier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bezier curves, which are used to make uniform the weights of the rational Bezier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of ＂cancelling the best linear common divisor＂ and ＂shifted Chebyshev polynomial＂, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduc- tion for polynomial Bézier curves to the algorithms of constrained multi-degree reduction for rational Bézier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bézier curves, which are used to make uniform the weights of the rational Bézier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of "cancelling the best linear common divisor" and "shifted Chebyshev polynomial", the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.

关 键 词：Rational Bezier curves Constrained multi-degree reduction Reparameterization 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] O29[自动化与计算机技术—计算机科学与技术]