An optimization method for rational Bézier curve design  

作　　者：HAN Xuli SHUAI Jun HAN Jing 

机构地区：[1]School of Mathematics and Statistics, Central South University

出　　处：《Computer Aided Drafting,Design and Manufacturing》2012年第4期41-45,共5页计算机辅助绘图设计与制造（英文版）

基　　金：Supported by Natural Science Foundation of China(No.10871208,No.60970097)

摘　　要：Adjusting weights as a shape control tool in rational B6zier curve design is not easy because the weights have a global in- fluence. The curve could not approximate control polygon satisfactorily by an interactive manner. In order to produce a curve close enough to control polygon at every control vertex, an optimization model is established to minimize the distance between rational B6zier curve and its control points. This optimization problem is converted to a quadratic programming problem by separating and recombining the objective function. The new combined multi-objective optimization problem is reasonable and easy to solve. With an optimal parameter, the computing process is discussed. Comparative examples show that the designed curve is closer to control polygon and preserves the shape of the control polygon well.Adjusting weights as a shape control tool in rational B6zier curve design is not easy because the weights have a global in- fluence. The curve could not approximate control polygon satisfactorily by an interactive manner. In order to produce a curve close enough to control polygon at every control vertex, an optimization model is established to minimize the distance between rational B6zier curve and its control points. This optimization problem is converted to a quadratic programming problem by separating and recombining the objective function. The new combined multi-objective optimization problem is reasonable and easy to solve. With an optimal parameter, the computing process is discussed. Comparative examples show that the designed curve is closer to control polygon and preserves the shape of the control polygon well.

关 键 词：curve design OPTIMIZATION rational B6zier curve shape modification quadratic programming 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O185[自动化与计算机技术—计算机科学与技术]