The Two Types Of Construction And Application Of Mixed-coons Surface With Shape Parameters

In the modeling methods of free curves and surfaces,coons surface patch as a method of generating for interpolating surface has the profound meanings.Particularly,bicubic coons surface patch has been applied on the project widely.This paper studies the expandings of coons surface patches in application.In this paper two blending spaces composed by polynomial basis function and trigonometric basis function are given first, then two classes of blending functions with shape parameters are construncted builted on the two blending spaces separately,and the properties and the optimal problem of the two blending functions are analyzed,then two kinds of coons surface patches are constructed based on them separately,The constructed surface patches combine the merits of polynomial interpolating surface and trigonometric interpolating surface.Furthermore,the construncted surfaces not only inherit the most properties of bicubic coons surface patches, but also can adjust the inner shape by meas of changing the value of the shape parameters while keeping their boundary conditions unchanged.Therefore,they are fiter for the technology about free surfaces design. Specially,the resulting surface patches can accurately represent torus,ellipsoid,sphere and so on.Contrarilly,the traditional polynomial surface patches can only approache to the quadratic surface patches approximately. In addition,First-class surface patch,for example,the G1 smooth splice of the two surface patches is studyed and three kinds of genometrical condition for G1 smooth splice are given in the paper.And the relevant algorithems and examples are provided.Therefore,this kinds of coons surface patch are more practical in surface modeling methods.