Pythagorean-Hodograph C-曲线  

Pythagorean-Hodograph C-Curve

作　　者：陈文喻[1] 曹娟[1] 汪国昭[1] 

机构地区：[1]浙江大学数学系计算机图象图形研究所

出　　处：《计算机辅助设计与图形学学报》2007年第7期822-827,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60473130);国家"九七三"重点基础研究发展规划项目(2004CB31800)

摘　　要：给出了Pythagorean-hodograph(PH) C-曲线的定义、平面四阶C-曲线是PH曲线的充分必要条件及平面四阶PHC-Bézier曲线的几何构造方法.最后证明了高于四阶的平面PHC-曲线只能是直线或者多项式PH曲线.The definition of Pythagorean-hodograph C-curve is given and a necessary and sufficient condition for a fourth-order plane C-curve to be a PH C-curve is obtained. A new geometric construction approach of fourth-order PH C-Bézier curves is also proposed. Finally, it is proved that higher order （〉4） PH C-curves are either straight lines or polynomial PH curves.

关 键 词：Pythagorean-hodograph(PH) C-曲线 C-BÉZIER 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]