Construction of B\'{e}zier-like Curves with Energy Constraints

Abstract:

      In this paper, we present a class of novel Bernstein-like basis functions, which is an extension of classical Bernstein basis functions. The properties of this group of bases are analyzed and the B\'{e}zier-like curve with two shape parameters $h_1$, $h_2$ is defined. The basis functions and B\'{e}zier-like curves have properties similar to cubic Bernstein basis functions and cubic B\'{e}zier curves, respectively. Furthermore, we construct B\'{e}zier-like curves with energy constraints and consider the $C^1$ and $G^1$ Hermite interpolation with minimal energy. Finally, some representative examples show the applicability and effectiveness of the proposed method.