Research On Bézier-Type Curve And Surface With Shape Parameters

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 definition,properties and joint condition of Bézier curve, and introduces the main research conclusion on Bézier curve and surface with parameter recent years. The Bézier curve with parameter presented by Wu Xiaoqin is introduced first in the third chapter, and then, the author improves the curve with more parameters, and discussed the joint condition and the effect of parameters. Extensions of Cubic Bézier Expand Curve with C2 Constraint are discussed at last.In the fourth chapter, the author presents a class of Bézier-type curve with parameter in spaceΓ2 = {1,sin t ,cos t}, and the conic curve such as circle, ellipse, parabola are exactly denoted with TC-Bézier curve. So TC- Bézier curve has more expressive ability than the curve in spaceΓ1 = {1, t , t 2 , t 3 , t4}.The surface modeling using shape parameter is discussed at last.In the fifth chapter, the author presents a class of Bézier-type curve with parameter in spaceΓ3 = {1, t ,sinh t ,cosh t}, and the conic curve such as hyperbola, catenary are exact denoted by H-Bézier curve. And then , the surface modeling using shape parameter is discussed.In the end, the author summarizes full text, innovations and theories, actual meaning, and prospects the research work of aftertime.