摘要
给出了带有参数λ的二次三角多项式样条曲线。与三次B样条曲线类似,曲线的每一段由相继的4个控制顶点生成。对于等距节点,在一般情形下,曲线达到了C1连续,而当λ=1时,曲线达到了C3连续。λ有明确的几何意义,λ越大,曲线越逼近控制多边形。还给出了用此种曲线表示椭圆和整圆的方法,在相同的控制顶点下,可生成一簇椭圆弧和圆弧。
Analogous to the cubic B-spline curves, each trigonometric polynomial curve segment is generated by four consecutive control points. For equidistant knots, the trigonometric polynomial spline curves are C^1 continuous, but when the shape parameter λ=1, the curves are C^3 continuous. Parameter λ affects geometric property of curves, the larger is λ the curve comes more near the control polygon. The way to represent ellipse and circle precisely is also given. It could generate a family of ellipse and arcs based on the same control points.
出处
《工程图学学报》
CSCD
北大核心
2006年第1期92-97,共6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
形状参数
computer application
spline curve
trigonometric polynomial
shape parameter
