摘要
给出了m(m=1,2,3)次三角多项式样条曲线。与二次B样条曲线类似,曲线的每一段由相继的3 个控制顶点生成;对于等距节点,一次三角多项式样条曲线是C1连续、二次三角多项式样条曲线是G2连续、三次三角多项式样条曲线是C3连续,且讨论了3 种曲线对控制多边形的逼近及与二次B样条曲线的对比。还给出了一次三角多项式样条曲线表示椭圆和整圆的方法。通过加权混合可得到一类三角多项式样条曲线,曲线的形状随着次数m和形状参数λ的变化而改变。
Trigonometric polynomial spline curves of mth degree (m =1,2,3) are presented . Analogous to the quadratic B-spline curves, each trigonometric polynomial curve segment is generated by three consecutive control points. For equidistant knots, the trigonometric polynomial spline curves of first degree is C1 continuous, of second degree is G2 continuous and of third degree is C3 continuous. Moreover, all these kinds of curves approximate the control polygon and comparisons between trigonometric polynomial spline curves and quadratic B-spline curves are given. The first degree curve represents ellipse and circle precisely. A class of trigonometric polynomial spline curves is derived by their weighted blending. Its shape changes with degree m and shape parameter λ.
出处
《工程图学学报》
CSCD
北大核心
2005年第2期101-105,共5页
Journal of Engineering Graphics
基金
湖南省教育厅资助项目(04C215)
关键词
计算机应用
样条曲线
三角多项式
曲线设计
computer application
spline curve
trigonometric polynomial
curve design
