Abstract:

In order to improve the disadvantages of the cubic Bspline curve,its  shape is fixed to its control polygon. It cannot describe the conic section except the parabola, and the shape parameters and the trigonometric functions are combined. A trigonometric curve with shape parameters is defined. Its structure is similar to the cubic Bspline curve. The new curve not only inherits the major advantages of the cubic Bspline curve, but also can express ellipse with shape adjustability. Besides, the continuity and approximability of the new curve is better than the cubic Bspline curve. For equidistant knots, the new curve is C3continuous, and it is C5 continuous under special conditions. Using the tensor product method, the curve can be extended to the surface. The surface has properties similar to the curve. The way to represent the ellipse surface using the new surface is given.

Key words: computer application;trigonometric basis;spline curve;shape parameter, continuity