Construction of generalized developable Bézier surfaces with shape parameters

Abstract

In this paper, we propose a novel method for constructing generalized developable Bézier surfaces with shape parameters. The generalized developable Bézier surfaces are designed by using control planes with generalized Bernstein basis functions, and their shapes can be adjusted by changing their shape parameters. When the shape parameters take on different values, a family of developable surfaces, which retain the characteristics of developable Bézier surfaces, can be constructed. In addition, we derive the necessary and sufficient conditions for G 1 continuity, Farin‐Boehm G 2 continuity, and G 2 Beta continuity between 2 adjacent generalized developable Bézier surfaces. Finally, some properties of the new developable surfaces are discussed, and the influence rules of shape parameters on the new developable surfaces are studied. The modeling examples show that the proposed method is effective and so can greatly improve problem‐solving abilities in engineering appearance design by adjusting the position and shape of developable surfaces.