带形状参数的三次TC-Bézier曲线  

Cubic TC-Bézier curves with shape parameter

作　　者：马素静[1] 刘旭敏[1] 

机构地区：[1]首都师范大学信息工程学院,北京100037

出　　处：《计算机工程与设计》2009年第5期1151-1153,共3页Computer Engineering and Design

基　　金：北京市教委重点基金项目(KZ200710028014);北京市自然科学基金项目(4062009;4082009)。

摘　　要：针对自由曲线曲面设计中的形状控制问题,构造了带形状控制参数的三次TC-Bézier曲线。具有明确的几何意义,的值越大曲线越逼近控制多边形。同时证明了几种有实际应用价值的曲线(椭圆弧、花瓣)可以用带形状参数三次TC-Bézier曲线的形式精确表示。还给出了带参数三次TC-Bézier曲线间的1拼接条件及在曲面造型中的应用实例。造型实例表明,该曲线在计算机辅助几何设计中具有重要的应用价值。For the problem of shape controlling in curves and surfaces design with free form, cubic TC-Bézier curves with shape parameter is constructed. Parameter λ affects geometric property of curves, the larger is λ, the curve comes more near the control polygon. Then it is demonstrated that many valuable curves can be expressed by TC-Bézier curves. And then G^t condition of cubic TC-Bézier curves and example in surface modeling are presented. The modeling examples illustrate that the new curve is very valuable for computer aided geometric design.

关 键 词：形状参数 TC-Bézier曲线 椭圆弧 拼接 曲面造型 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]