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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 Bezier-type curves with four shape parameters, analogous to the cubic Bezier curves, is constructed. With appropriate choices of control points and shape parameters, the resulting trigonometric Bezier-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 Bezier-type curves stably and efficiently.

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