Designing of curves and surfaces using cubic splines with geometric characterization

A constructive approach has been adopted to build interpolatory and B-spline like 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 ν-spline of G.M. Nielson (1974), β-splines, γ-splines of W. Boehm (1995) and weighted ν-splines. The curve schemes have also been generalized to produce smooth surfaces with local shape control. The local shape control has been achieved by introducing variable shape parameters