A Class of Trigonometric Bernstein-Type Basis Functions with Four Shape Parameters

Abstract EN

In this work, a family of four new trigonometric Bernstein-type basis functions with four shape parameters is constructed, which form a normalized basis with optimal total positivity.

Based on the new basis functions, a kind of trigonometric Bézier-type curves with four shape parameters, analogous to the cubic Bézier curves, is constructed.

With appropriate choices of control points and shape parameters, the resulting trigonometric Bézier-type curves can represent exactly any arc of an ellipse or parabola.

The four shape parameters have tension control roles on adjusting the shape of resulting curves.

Moreover, a new corner cutting algorithm is also proposed for calculating the trigonometric Bézier-type curves stably and efficiently.