Quantum Trigonometric Bézier Curves

In order to construct quantum trigonometric B\'ezier curves with shape parameter, one parameter family of trigonometric Bernstein basis functions are introduced. We study the total positivity of the basis functions to analyze the shape preserving properties of the quantum trigonometric B\'ezier curves. We also showed that quantum trigonometric B\'ezier curves can be evaluated by two different recursive evaluation algorithms. Finally, we have defined rational counterpart of quantum trigonometric B\'ezier curves and show that the rational quantum trigonometric B\'ezier curves posses nice shape preserving properties.