多形状参数的二次非均匀三角多项式曲线

Quadratic Non-Uniform Trigonometric Polynomial Curve with Multiple Shape Parameters

提出了一类带多个形状参数的二次非均匀三角多项式曲线,它是同类型单形状参数曲线的推广,具有二次非均匀B样条曲线的绝大多数性质。根据形状参数的不同取值,人们既能整体地又能局部地调控这类曲线的形状。并且无须采用重节点技术或解方程组,就能直接插值某些控制点或控制边。此外,它还能直接表示椭圆与抛物线。

The quadratic non-uniform trigonometric polynomial curve with multiple shape parameters is an extension to the same type with single shape parameter. Taking different values of the shape parameters, one can globally or locally adjust the curve shape. Without using multiple knots or solving system of equations, the curve can interpolate certain control point or certain control polygon edge directly. It can also represent ellipse and parabola.