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Adopting a recurrence technique, generalized trigonometric basis (or GT-basis, for short) functions along with two shape parameters are formulated in this paper. These basis functions carry a lot of geometric features of classical Bernstein basis functions and maintain the shape of the curve and surface as well. The generalized trigonometric Bezier (or GT-Bezier, for short) curves and surfaces are defined on these basis functions and also analyze their geometric properties which are analogous to classical Bezier curves and surfaces. This analysis shows that the existence of shape parameters brings a convenience to adjust the shape of the curve and surface by simply modifying their values. These GT-Bezier curves meet the conditions required for parametric continuity ( , , , and ) as well as for geometric continuity ( , , and ). Furthermore, some curve and surface design applications have been discussed. The demonstrating examples clarify that the new curves and surfaces provide a flexible approach and mathematical sketch of Bezier curves and surfaces which make them a treasured way for the project of curve and surface modeling.

A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications