A novel generalization of Bézier curve and surface (Q929920)

A novel approach to Bézier curves and surfaces modelling is presented. This approach lies in a generalization of the classical Bernstein polynomials by introducing a sequence of shape parameters into these basis functions. These additional shape parameters are associated with the legs of the control polygon and allow changing the shape of the curve or surface without moving the control points. The excellent geometric properties of this generalized so-called quasi-Bézier (q-Bézier) curves and surfaces are preserved -- e.g. terminal property, symmetry, independence of the choice of coordinates, convex hull property. The influence of different choices of the particular shape parameters on the resulting shape of the q-Bézier curve is shown in many figures. The problems of continuity between two q-Bézier curves and closed q-Bézier curves are solved, too.