Indentification Of Singularities And Inflection Points On Parametric Curves

The geometric characters of curves and surfaces is very important in study of geometric design. Singularities and inflection points are the geometric characters, it is very useful to study their existence in parametric curves and spline curves.This thesis introduce the main results of planar parametric segment ,rational segment and C-curves. Then we use the method of planar cubic B-spline and Bézier curve to discuss the existence of singularities and inflection points in barycentric coordinate space. The superiorty of the barycentric coordinate is in application we only need to calculate the area of some simply triangles,it is easy to operate on computer.The whole paper consists of six chapters. In the first chapter, introduce the general situation of the parametric curves and arragement of the whole paper. In the sceond chapter, introduce the singularities and inflection points anaysis of the planar parametric curves, it is the basis of my work. In the third chapter, introduce the singularities and inflection points of the rational curves, mainly about the results of the Li and Cripps, Monterde. In the forth chapter, introduce the main results of Guozhao Wang and Zhenglin Ye. The fifth chapter is my work that discuss the existence of singularities and inflection points in barycentric coordinate. The last chaper is the conclusion of the paper.