G2 continuity conditions for generalized Bézier-like surfaces with multiple shape parameters

Abstract

Abstract In order to tackle the problem of shape design and shape adjustment of complex surfaces in engineering, continuity conditions between generalized Bézier-like surfaces with multiple shape parameters are studied in this paper. Firstly, the geometric model of the generalized Bézier-like surfaces is built by blending a number of Bézier-like curves with independent shape parameters. Secondly, based on the terminal properties and linear independence of Bernstein-like basis functions, the conditions for G2 continuity between two adjacent generalized Bézier-like surfaces are derived, and then simplified by choosing appropriate shape parameters. Finally, some properties and applications of the smooth continuity between generalized Bézier-like surfaces are discussed. The modeling examples show that the proposed method is effective and easy to implement, which can greatly improve the ability to construct complex surfaces by using the generalized Bézier-like surfaces.

Keywords

• Bernstein-like basis functions
• generalized Bézier-like surfaces
• shape parameter
• G2 continuity conditions