Research On Some Kinds Of Curves With Shape Parameters

In this paper ,we analyze and investigate 3 type of curves with shape parameters which are generally used in CAGD(Computer Aidied Geometric Design): Extension of quartic Bezier curve with parameters, a class of trigonometric interpolation curves, trigonometric curves with given tangent polygons.The thesis is composed of four chapters.The first chapter, we review the background of the parameter curves and surfaces modeling in CAGD, and briefly introduce Bezier, B-spline and non-polynomial curves and surfaces modeling, which include C-curves etc.The second chapter introduces the status of extensions of B6zier curves and construct a class of degree 5 basis functions of containing three shape control parameters. It is extension of quartic Bernstein basis functions. Properties of this new basis are analyzed and a polynomial curve with three shape parameters is defined based on it. The curve not only inherits the outstanding properties of quartic curve, but also is adjustable in shape and fit close to the control polygon. The parameters have obvious geometric meaning. Some examples illustrate that an effective method to design curve and surface has been obtained by using the curve defined in this paper.The third chapter firstly presents the status of shape preserving polynomial interpolation Curves.secondly ,we construct a class of trigonometric interpolation curve with a parameter. The control points of the trigonometric polynomial curves are computed by a set of the points {V_i}_i=1ⁿ.The kind of trigonometric interpolation curves is C^2m-1-continuous and is shape preserving and can be modified not only locally but also totally.The fourth chapter firstly introduces the status of polynomial spline curves with given tangent polygon and C-B-Spline curve which is tangent to the given polygon is described.At last, we give a class of trigonometric curves with parameters which is tangent to the given control polygons and it can be modified not only locally but also totally.Finally, in the fifth chapter, we make a summary and give expections.