Research On Quintic Trigonometric Bézier Curve And Surface With Shape Parameter

Curve surface design is an important research subject in computer aided geometric design (CAGD) and computer graphics (CG). Now Non- uniform rational B-spline (NURBS) method can express not only free curve and surface, but also some traditional analytical model, such as cone curve, etc. However, there are some limitations in shape design and analysis about NURBS, such as increased number of derivative, weight factor selection inconvenience, cannot transcend express curve, such as cycloid, spirals, etc. In addition, in the plane design and most mechanical parts processing, often meet with pure by quadratic curve arc shape, and traditional polynomial cannot accurately express. So is trying to seek new trigonometric function space curve surface modeling method. This thesis summarized about trigonometric polynomial curve surface and triangular spline polynomial curve surface. Firstly blending functions with shape parameters are constructed by the deployment of sine and cosine function. The blending functions presented are to be proved the function of linear independence. The properties of blending functions are discussed, such as positive, unit of decomposition and so on. Then using blending functions, we define the parameters of the curve, and the properties of the curve are discussed, such as the endpoint interpolation properties, symmetry, convex hull, and so on. The parametric curves have similar features to five degree the Bézier curve, therefore we call the curve for five degree triangular Bézier curve. By the method of tensor product, using the base function, We define the double five degree triangular Bézier surface and discuss its properties. Lastly, the condition of continuously joining is given for two five degree triangular Bézier curves.