Research On Non-uniform Spline Curves With Multiple Shape Parameters Over Three-Point

The thesis is composed of six chapters.In the first chapter, the author briefly introduces the background and the main content of this thesis. The second chapter focuses on the B-spline curve's definition and properties. The third chapter introduces the extension of quadratic non-uniform B-spline curve. At first, the author introduces the non-uniform cubic polynomial curves with local shape parameters presented by Han xuli. And then, the quadratic trigonometric polynomial curve with a shape parameter presented by Han xuli is introduced.In the fourth chapter, the author presents the cubic non-uniform polynomial curve with multiple shape parameters, which is an extension to the cubic polynomial curves with local shape parameters. It possesses the characteristics of quadratic non-uniform B-spline curve. Its shape can be adjusted totally or locally by changing the values of the shape parameters. The curves can also interpolates certain control points or certain control polygon edges directly.In the fifth chapter, the quadratic non-uniform trigonometric polynomial curve with multiple shape parameters is presented , which is an extension to the same type with single shape parameter. Taking different values of the shape parameters, one can globally or locally adjust the curve shape. Without using multiple knots or solving system of equations, the curve can interpolate certain control points or certain control polygon edges directly. It can also represent ellipse and parabola.In the end, the author summarizes full text, innovations and theories, actual meaning, and prospects the research work of aftertime.