Cubic spline curves with shape control

Abstract

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than β-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like v-spline of Nielson[9], β-splines[1], γ-splines of Boehm[3] and weighted v-splines[6]. The method for evaluating these generalized β-splines is suggested by a transformation to Bézier form. © 1994.