On a Bernstein-Like Trigonometric Basis without Shape Parameters for Cubic Bézier Curves

Abstract

In this paper, we introduce a new trigonometric blending basis of Bernstein type without shape parameters for the construction of Bézier-like curves. Fundamental properties of the new basis are rigorously established, including non-negativity, partition of unity, and endpoint interpolation.

A theoretical comparison with the classical Bernstein basis is provided, highlighting similarities in geometric behavior and differences in approximation capability. We used to assess practical performance, least-squares curve fitting and several numerical examples are presented. These results indicate that the proposed parameter-free trigonometric basis offers an effective alternative to classical Bernstein polynomials, combining strong geometric properties with improved approximation quality for curve modeling applications.