A quadratic programming method for optimal degree reduction of Bézier curves with G^1-continuity  

作　　者：LU Li-zheng WANG Guo-zhao 

机构地区：[1]Institute of Computer Graphics and lmage Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2007年第10期1657-1662,共6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 Natural Science Foundation ofChina (No. 60473130);the National Basic Research Program(973) of China (No. G2004CB318000)

摘　　要：This paper presents a quadratic programming method for optimal multi-degree reduction of B6zier curves with G^1-continuity. The L2 and I2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applications of degree reduction of Bezier curves with their parameterizations close to arc-length parameterizations are also discussed.This paper presents a quadratic programming method for optimal multi-degree reduction of Bézier curves with G1-continuity. The L2 and l2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applica- tions of degree reduction of Bézier curves with their parameterizations close to arc-length parameterizations are also discussed.

关 键 词：Degree reduction Bezier curves Optimal approximation G^1-continuity Quadratic programming 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]