Local Modifications Of The Bézier Spline Curves

In CAGD. we often adjust the shape of curves or change the site of curves. This thesis mainly discusses the question of local modifications of the Bezier spline curves in Computer Aided Geometry Design. It is composed of four chapters.In the first chapter, we introduce the concept and properties of the Bezier curves. The question of continuity and modification of the Bezier curves is given. And we introduce the context and produce of the question of the taffeta curve with given tangent polygon.In the second chapter, a class of polynomial blending functions of degree n+1 is presented. Based on the functions, we present polynomial curves with some shape parameters. The generated curves are similar with the degree n Bezier curves. By changing the value of the shape parameter, we can adjust the approaching degree of the curves to their control polygon and manipulate the degree n Bezier curves from both sides.In the third chapter, we present a class of C2-continuous spline curves of degree 4 with some shape parameter. The segmented curves are all shape preserving to given polygon. By changing the value of the shape parameter, we can adjust the approaching degree of the curves to their control polygon. The results have definite geometric meanings that are useful for shape modification and representation of curves.In the forth chapter, we proposes an approach of constructing planar piecewise Bezier curve of 3rd 4th and 6th degree with all edges tangent to a given control polygon and the curve segments are joined together with C1 C2 and C3-continuity. The segmented Bezier curves are all shape-preserving to their tangent polygon. This chapter gives the admissible scope of the inner control points of the next two curves in order to guarantee it's continuity at the common joining end. The local modifications for these curves are possible. It can locally or globally approximates the tangent polygon.The author acquires three main results, i.e. an approach of constructing polynomial curves with some shape parameters, C2-continuous spline curves of degree 4 with some shape parameter, and planar piecewise Bezier curve of 3 4th and 6th degree with given control polygon and the curve segments are joined together with C1 C2 and C3-continuity.