A class of quasi-cubic B-spline with two parameters

Abstract

A class of quasi-cubic B-spline base functions with two parameters is presented and the corresponding curves and surfaces defined by the introduced base function in this paper. The curves inherit some characteristic with traditional cubic B-spline curves, and it can represent exactly some quadratic curves such as the arc of circle, arc of ellipse, arc of parabola and some transcendental curves such as sine curve without using rational form. The corresponding tensor product surfaces can also represent precisely some quadratic surfaces and transcendental surfaces, such as sphere, cylindrical surfaces and helix tube. Its shape can be adjusted totally and can interpolate some control points without solving system of equations through changing the value of the parameters. Further more, these curves are C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> continuous totally in proper condition. Examples are given to illustrate that the curve can be used as an efficient new model for geometric design in the fields of CAGD.