A Novel Generalization of Bezier-like Curves and Surfaces with Shape Parameters

Bezier curves and surfaces with shape parameters have received more attention in the field of engineering and technology in recent years because of their useful geometric properties as compared to classical Bezier curves, as well as traditional Bernstein basis functions. In this study, the generalized Bezier-like curves (gBC) are constructed based on new generalized Bernstein-like basis functions (gBBF) with two shape parameters. The geometric properties of both gBBF and gBC are studied, and it is found that they are similar to the classical Bernstein basis and Bezier curve, respectively. Some free form curves can be modeled using the proposed gBC and surfaces as the applications.