摘要
基于PH曲线的定义以及平面曲线的复数表示,探讨了7次Bézier曲线是PH曲线的充要条件.根据速端曲线的2个分量的最大公因式的次数,7次PH曲线被自然地分类4类;针对每一类7次PH曲线,分别用控制多边形的几何量表出了它们的几何性质.此外,为了避免引入坐标系,提出一种降阶的算法,利用控制多边形的几何量来求解速端曲线的2个分量的最大公因式.
Based on the definition of PH curve and complex representation of planar curve,the sufficient and necessary conditions for septic Bézier curve are explored to possess Pythagorean Hodograph.Septic PH curves are divided into four categories on the basis of the degree of greatest common divisor of two components of their hodograph.Concerning each type of septic PH curves,their geometric properties are expressed in terms of geometric magnitudes of control polygon.Besides,in order to avoid introducing coordinate system,an order reduction method is proposed to compute the greatest common divisor of hodograph using geometric magnitudes of control polygon.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2014年第3期378-384,共7页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(60933008
61272300)
关键词
PH曲线
控制多边形
几何性质
最大公因式
septic PH curve
control polygon
geometric property
greatest common divisor
