Research For Approximation Problems Of The Circular Arcs And Sphere

Circular arcs and sphere are very important and basic object of geometric research in CAGD and CAM.The Modern CAD/CAM systems can not deal with the parameter equation and the implicit equation of circle and the sphere.Therefore,people can only use the parametric polynomial and parametric rational polynomial to approximate the circular arc,the circle,the spherical surface and the sphere enabling the Modern CAD/CAM systems to deal with them.Approximation and representation of circular arcs and sphere have been hot question.In the thesis,based on the Legendre expansion of function, using Legendre polynomial to approximate circular arcs and sphere,approximation function of the circular arcs and sphere are obtained in Legendre polynomial.Then,the arbitrary order Bézier polynomial approximation of circular arcs and sphere are obtained by transformation between Legendre and Bernstein polynomial,and we also use this method to obtain Bézier polynomial approximation of ellipse and ellipsoid.Finally,some examples are given to show the effectiveness of these methods,and the results are also compared with other methods.