NON-UNIFORM QUADRATIC WEIGHTED TRIGONOMETRIC HYPERBOLIC SPLINE CURVES
非均匀的二次三角双曲加权样条曲线

A method of generating quadratic blending spline curves based on weighted trigonometric and hyperbolic polynomials is presented in this paper, which shares many important properties of quadratic non-uniform B-splines. Here weight coefficients are also shape parameters, which are called weight parameters. The interval 0,1] of weight parameter values can be extended to -2.6482 ,3.9412]. Taking different values of the weight parameter, one can not only totally or locally adjust the shape of the curves but also change the type of some segments of a curve among trigonometric or hyperbolic polynomials. Without using multiple knots or solving system of equations and letting one or several weight parameter be -2.6482, the curve can interpolate certain control points or control polygon edge directly. Moreover, it can represent ellipse (circle) and hyperbola exactly.