CAH B-Spline Curves and Its Applications

Abstract： A kind of quasi-cubic uniform B-spline curves (briefly CAH B-spline curves) unified by algebraic and hyperbolic polynomial using weight method is presented in this paper. Here weight coefficients are called weight parameters. The interval [0, 1] of weight parameter values can be extended to [-62.1748, 12.6061]. The curves can include cubic B-spline curve as special case and reach the both sides of cubic B-spline curve. Not only can the shape of the curve be adjusted totally or locally, but also the type of some segments of a blending curve can be switched by taking different values of the weight parameters. If letting weight parameters be 31.0739, the curve can interpolate certain control points directly without solving system of equations. The defined curves can be used to precisely represent some conics and transcendental curves with the weight parameter and the positions of the control points chosen properly.