α-B Spline Interpolation Curves And Surface With Shape Parameters

The thesis is composed of five chapters.In the first chapter, the author briefly introduces the background and the main content of this thesis. The second chapter is focused on the B-spline curve's definition and properties. The third chapter introduces the extension of B-spline curve. At first, the author introduces uniform B-spline curve with one shape parameter presented by Han xuli;and then, the uniform B-spline curve with multiple shape parameters and its properties, which is constructed by Zhang li and Wu hongyi, are presented;at last, the a -B spline: linear singular blending B-spline curve presented by K. F. Loe is introduced. The fourth chapter introduces the α-Bspline interpolation curve and its properties, which is presented by Pan yongjuan and Wang guojin.In the last chapter, the author presents the extension of α -Bspline interpolation curve. Several α -B spline interpolation curves with multiple shape parameters are constructed by introducing new shape parameters. Then C or C continuity of these curves are presented, and the total or local modification of these curves' shapes is illustrated. In the end of this chapter, the author points out that the α -B spline interpolation curve can be extended to surface.