Closed Adjustable Spline Curve With Given Tangent Polygon

This thesis is composed of five chapters.In the first chapter, we briefly introduces the background and the main content of this thesis. The second chapter is focused on the definition and properties of the Bézier spline curves. And we introduce Bézier curves of degree 4 contains one shape parameter are all adjustable and shape persevering to the given polygon. Based on the chapter two, the third chapter proposes closed adjustable quartic Bézier curves contains two shape parameters with given tangent polygon.In the forth chapter, we introduces the generalized Ball curves of 3rd,4th degree contains one shape parameter with all edges tangent to a given tangent polygon and the curve segments are joined together with C~1and C~2-continuity. The generalized Ball curve of 5th degree with C~3continuity contains no shape parameter, so it can not be adjustable. Based on the chapter four, the fifth chapter proposes closed adjustable generalized Ball curves of 3rd,5th degree contains two shape parameters with all edges tangent to a given tangent polygon and the curve segments are joined together with C~1and C~2continuity. The generalized Ball curve with C~3continuity contains one shape parameter, it can be adjustable.The local modifications for these curves are possible, it can locally or globally approximates the tangent polygon. The examples illustrate the availability of this kind of curves.