New extension of cubic TC-Bézier curves

A set of cubic trigonometric polynomial function with two parameters is presented as an extension of cubic Bernstein basis functions.The quality of the new basis is analyzed.Based on the new basis,the trigonometric polynomial curve with two shape parameters is defined.The new curve not only holds many applied geometrical qualities of Bezier curve,but also can rectify the shape.When the control polygon is fixed,different approximation to the control polygon with the changing of shape parameters α and β are given.The circle and ellipse is represented with this curve accurately.G1 and G2 condition of cubic TC-Bezier curves and examples in surface model are presented,which is more useful in free curve and surface design.