The Connection of Bi-Cubic T-Bézier Surfaces and its Modeling Application

T-Bezier curves and surfaces whose basis functions are constructed from the trigonometric polynomials, have properties similar to those of Bezier curves and surfaces. But they have more wide representations which can express arcs, cylinders and other transcendental curves and surfaces. In this paper, we discuss one kind of bi-cubic T-Bezier surfaces and provide the sufficient conditions of G¹ continuity and G² continuity between two adjacent T-Bezier surfaces. In the end of this paper, we use the bi-cubic T-Beizer surfaces to construct some fabric modelings.