The Nature Of A Class Of Conformal Curve, Constructed And Applied Research

In the Computer Aided Geometric Design basic functions have a basic and determining action. In this paper we discuss the properties and characteristic of therational Bezier curves and Said-Ball curves. We also research the construction ofthe puartic and fifth rational Bezier function and how to adjust for shape preserving.The first chapter, prolegomenon,we simply introduces the provenience and development of the Computer Aided Geometric Design and the newest research of the convex preserving and shape preserving and some properties and characteristic of spline curves. The second chapter, the conformal curves having weight factor, is divided four parts. In the first three part we research the construction of conformal rational Bezier curves, the properties of shape preserving, convergence, the shape preserving way of quartic and fifth rational Bezier curves and design a quarticcomposite conformal rational Bezier curve which can reach C1 continuity . In the fourth part we research the condition of the cubic and quartic Said -Ball curves ,give the way of judging conformal condition and shape preserving algorithm. The third chapter is the figure example and application part. All figures are yielded by conformal way in this paper. The figure examples are very good and the shape preserving can also be reached. In the last chapter, the appendix part, all programs are edited by matlab code and in this paper all figures are yielded by these programs. These programs are accurate and correct through enough correction and debugging.