Abstract: This paper discusses the method for constructing arbitrary rational and non rational parametric cubic and quadric conical curves by the use of controling parameters which contain types,kinds and shape factors.It put forward the unified mathematical models of representing irregular as well as regular,rational and non rational parametric curves,and discusses the relationship between the controling parameters,weight factors and curves,along with the property of variations curves.It provides a simple convenient audio visual mathematical method with substantial content and powerfull descriptive ability for CAGD(Computer Aided Geometrical Design).