Extensions Of Curves And Surfaces With Shape Parameters In CAGD

The technology of free-form curve and surface is the core of CAGD. The parameter curves and surfaces modeling are used very widely in CAD, and attract attentions from scholars and engineering technicians. In this paper we research a new technique in parameter curves and surfaces modeling—parameter curves and surfaces modeling with shape parameter.The paper is composed of five chapters.Firstly, we introduce the development history and background of parameter curves and surfaces modeling with shape parameter. The second chapter are focused on the B-Spline curve's definition and properties. Then we introduce the extension of B-Spline curve with shape parameter in the third chapter.In the fourth chapter, the Bernstein- Bézier surface over the triangular domain is presented, including its definition and properties. In the fifth chapter, we introduce the (n+1) degree triangular Bézier surface with a shape parameter by Wu Xiaoqin ,on this basis, a class of quasi-cubic-Bernstein basis functions with two shape parameters is presented , and the quasi-cubic-B-B parametric surfaces with two shape parameters over the triangular domain is defined based on it. Then the changing of surface's shape by parameters is illustrated. Finally, the extension of Bézier surface with multiple shape parameters by Wu Hongyi is introduced.