In this paper, a class of quasi-quintic trigonometric Bezier´ curve with two shape parameters, with a tension parameter, are presented. The new basis functions share the properties with Bernstein basis functions, so the generated curves inherit many properties of traditional Bezier´ curves. The presence of shape parameters provides a local control on the shape of the curve which enables the designer to control the curve more than the ordinary Bezier´ curve. These type of functions are useful for constructing trigonometric Bezier curves and surfaces, they can be applied to construct continuous shape preserving interpolation spline curves with shape parameters. To better visualize objects and graphics a tension parameter is included. In this work we constructed the Trigonometric Bezier curves followed by a construction of the shape preserving interpolation spline curves with local shape parameters and a tension parameter.
