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, β-splines, γ-splines of Boehm and weighted v-splines. The method for evaluating these generalized β-splines is suggested by a transformation to Bézier form. © 1994.
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