Research On Model Of Trigonometric Polynomial Curves In Cagd

In CAD/CAM modeling system, as a union mathematical model, NURBS has become a standard in industrial product manufacturer field because it not only represents free curves and surfaces, but also it also represents some traditional geometric curves. But for its weight parameters, parameterize, continuity and the complexity of its description and calculation, its preponderance is difficult to exert current curves and surfaces modeling. For resolve this problem, more and more scholars try to find new modeling methods in the space of trigonometric functions.This paper first introduce some typical curves and surfaces modeling in CAGD and some extension of B-spline.(1) By analyzing the characters of Bezier, we construct trigonometric polynomial curves in the space of trigonometric functions, which assume the characters of Bezier curves. Its representatives are simple and direct. We call it as TC- Bezier. It has a shape parameter, so we can adjust its shape by changing its shape parameter. It can represent the circle and ellipseaccurately. We present G~1 condition of TC- Bezier curves.(2) We present k -Degree T-Bezier basis function and reparametrize it on the interval [0,1],representation of ellipse and cardioid and G~1 condition of T-Bezier curves based on the analysisof T-Bezier basis function and terminal properties. The results have definite geometric meanings that are useful for surface modeling.(3) We presents G~1 of C-B-spline curves and C-Bezier curves. Using C-Bezier curvesrepresents the semicircle and semi-ellipse and G~1 condition with C-B-spline curves to resolve the representation of semicircle and semi-ellipse in C-B-spline surface modeling.(4) We present an encryption algorithm based on amalgamation-coeffecient-matrix. By this algorithm, we can encrypt the cubic B-spline curves and surface with amalgamating the coefficient-matrix of basis function for cubic B-spline and cubic Bezier.In this paper last we present a simple vase modeling system based TC-Bezier curves, withit, users can conveniently design a vase model according with their request.