Extensions Of Bézier Curves And Surfaces With Multiple Shape Parameters

The thesis is composed of five chapters.At first, after reviewing the history of the curves and surfaces in CAGD, the author briefly introduces the main content. The second chapter are focused on the Bezier curve's definition and properties. The subdivision matrix of Bezier curve, its degree reduction by minimizing the distance function and degree elevation are presented.The third chapter introduces the extension of Bezier curve with one shape parameter by Han xuli and Liu zhi. By making a further study of it, the author presents the extension of Bezier curve with multiple shape parameters, whose shape can be adjusted totally or locally by changing the values of the shape parameters.In the fourth chapter, the Bezier surface is presented, including its definition and the conversion formula from the triangular Bezier surface to rectangular Bezier surface.At the last, the author presents the extension of Bezier surface with multiple shape parameters, and the changing of surface's shape by parameters is illustrated.