Manipulating Shape and Producing Geometuic Contnuity in ß-Spline Curves

This article examines some of the desirable features of ß-splines that make them particularly suitable for computer-aided design. First, a theoretical analysis is presented regarding the effects upon the shape of a design curve when the bias and tension parameters are allowed to vary in certain ways. Second, the concept of geometric continuity is discussed, and conditions are derived upon the control vertices to ensure that the design curve has second-order geometric continuity. Illustrations of ,ß-spline curves are presented to support the theoretical conclusions.