Rational Coons Surface With A Shape Parameter Constructor

Methods of Coons surfaces is the technology about free curves and surfaces design which was adopted by Coons in 1964, and it has been evaluated high by the academic community. Comparing to Bézier surfaces and B-spline surfaces, the expression of Coons surfaces are more simple. It can adjust the shapes of the entire surfaces through changing the control function instead of amending every point. Coons bicubic surface has been applied on the project. Coons bicubic surfaces are analyzed with expansion in this paper. The paper focuses on the problem as follows:Firstly, the research background is introduced in the chapter one, and the main contents of this thesis are given. Secondly in the chapter two we present the definition of Coons surface and Coons bicubic surface. Thirdly a new type Coons patch called C-Coons patch constructed by C-Hermite blending functions is discussed in the chapter three. C-Coons patch presents an extension of bicubic Coons patch. Its shape depends on two parameters a,β, and the limiting case forα,βâ†'0 is bicubic Coons patch.At last two classes of rational blending functions with a parameter A are presented in the chapter four. The properties of this new basis are analyzed. Based on the rational blending functions, we defined two kinds of rational Coons surfaces with shape control parameters, which are named RBF₁-Coons surface and RBF₂ -Coons surface. These surfaces not only inherit the most properties of Coons surfaces, but also can adjust their shapes through changing the values of parameters. We also discuss the effect of two parametersλ₁ andλ₂ on the interior concavity and convexity of the generated surfaces.