A trigonometric extension of Bézier curve and surface which automatically satisfy G2 continuity

In order to make the curve and surface meet with relatively high smooth under relatively simple conditions, we can modify the shape of the curves and surfaces without changing the control points at the same time. So the low order Bézier basis function with shape parameters is constructed. Based on the basis functions, the curves and surfaces of arbitrary order trigonometric Bézier are defined by linear combination. The basic properties of the curves are discussed, and the conditions of the smooth blending of curves and surfaces are also discussed. According to the blending condition, the piecewise curves and surfaces can be constructed. The blending curves and surfaces will not be changed the continuity of curve and surface by modifying the control points and parameters of the method, and can automatically meet with the GP2 Pcontinuity. The numerical results show the validity of the method.