CTH B-spline curves and its applications

A method of generating cubic blending spline curves based on weighted trigonometric and hyperbolic polynomial is presented in this paper. The curves inherit nearly all properties of cubic B-splines and enjoy some other advantageous properties for modeling. They can represent some conics and some transcendental curves exactly. Here weight coefficients are also shape parameters, which are called weight parameters. The interval [0,1] of weight parameter values can be extended to [ e−1) 2 (e−1)2−π , e−1)π (e−1)2π2−8e ]. Not only can the shape of the curves be adjusted globally or locally, but also the type of some segments of a blending curve can be switched by taking different values of the weight parameters. Without solving system of equations and letting certain weight parameter be (e−1) (2−π) 2(e−1)2−2π , the curves can interpolate corresponding control points directly.