Generalized geometric cubic splines

Abstract

A constructive approach has been adopted to build interpolatory and freeform cubic spline curves with a more general continuity than -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 -spline of G.M. Nielson (1974), -splines, -splines of W. Boehm (1995) and weighted -splines. A discussion, for the conversion of complex continuity constraints into simple ones, has also been made for the practical implementation point of view