The Survey Of Curves And Surfaces With Adjustable Parameters

Parameter curve and surface design is the core of computer aided geometer design(CAGD),treatment the problem of the curve and surface modeling by adjusting the parameters in computer aided geometric design has been the concern of many experts and scholars. This paper focuses on the problem that how to adjust the parameters of the binary quadratic Bézier surface on the triangle must occur to achieve an effect of deformation. The method used by the transformation matrix with adjustable parameters to increase the number of control points, and adjust the position of control points by changing the adjustable parameters to achieve the purpose of adjusting the surface shape.To The binary quadratic Bézier surface on the triangle, the number of adjustment parameters has been defined is nine,α,β,γ,τ,μ,ν,δ1 ,δ2 ,δ3, whichα,β,γ,τ,μ,νis the parameters of affecting the boundary control points of the surface,δ1 ,δ2 ,δ3is the parameters of internal control points of the surface. According to the different range of parameters, we can adjust the shape of Bézier surface on the triangle.The main work is as follows:At first, we study a border of Bézier surface on the triangle, to the defined parameters matrix, the parameters of affect a boundary has two. According to the different range of parameters, we can obtain 9 different types of surface.Furthermore, we study three borders of Bézier surface on the triangle, each boundary has 9 types, a total of 729 kinds.Finally, we study the internal of Bézier surface on the triangle, according to the corresponding area of the sign of area coordinates to determine the location of control points, a total of 7 kinds. So we can obtain 5103 kinds of different types of surface by changing the value of the parameters.The paper researchs on several curves and surfaces with some shape parameters and discusses the geometric meaning of the shape parameters and the impact of shape parameters to curves and surfaces. The adjustable parameters control both the overall shape of the curve, but also local control. Because of the invariance of the function base, weak the restrictions on the range of parameters, increase the freedom of parametric curves and surfaces. So it can adjust the curves and surfaces very well.