多形状参数的二次双曲多项式曲线

Quadratic Hyperbolic Polynomial Curves with Multiple Shape Parameters

给出了带多个形状参数的二次双曲多项式基函数,该基函数具有二次非均匀B样条基的绝大多数性质。基于这种基函数,建立了一种带多个形状参数的二次双曲多项式曲线,该类曲线对于非均匀节点为C1连续。根据形状参数的不同取值,曲线的形状既能整体又能局部地变化。并且毋需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,它还能精确表示双曲线。

Quadratic hyperbolic polynomial basis functions with multiple shape parameters are presented in this paper, which possess the most properties of quadratic non-uniform B-spline basis functions. Based on the basis functions, quadratic hyperbolic polynomial curves with multiple shape parameters are constructed. These curves are C^- continuous with a non-uniform knot vector . With different values of the shape parameters, the shapes of the curves can be adjusted totally or locally,, Without using multiple knots or solving equations, the curves can be interpolated given certain control points or control polygon edges directly. And hyperbolic polynomial curves can represent hyperbolas exactly.