Weighted Nu splines with local support basis functions

Abstract

A constructive approach has been adopted to build B-spline like basis for cubic spline curves with the same continuity constraints as those for interpolatory weighted v-splines. These are local basis functions with local support and having the property of being positive everywhere. The design curves and surfaces, constructed through these functions, possess all the ideal geometric properties like partition of unity, convex hull, and variation diminishing. The method provides not only a variety of very interesting shape control like point, and interval tensions but, as a special case, also recovers the cubic B-spline method. In addition, it also provides B-spline like design curves and surfaces for weighted splines, v-splines and weighted v-splines. The method for evaluating these splines is suggested by a transformation to Bézier form.