Trigonometric Polynomial With A Shape Parameter Coons

The key application of Coons surface was mainly the shape of internal control since it was established. In addition to the corner conditions, the control function is another factor to affect the shape of Coons surface. This article first introduces the ways of several Coons surface's construction whose control functions are based on polynomial-based structure. Bi-cubic Coons patch is the most common application form.Because of good calculus feature of trigonometric functions , we attempt to construct control functions of Bi-cubic Coons patch with trigonometric functions in this paper. A kind of blending functions with shape parameters is constructed based on cubic trigonometric polynomial functions. Then the method of generating cubic trigonometric polynomial Coons patch is discussed and then we give bi-cubic trigonometric polynomial Coons patch's formula with shape parameters. The constructed surface has the same structure to the bi-cubic Coons patch, and the difference is: two different directions have different parameters:λ₁ andλ₂. For a given matrix of information of the border, it can help us to obtain surfaces of different shapes by changing the values of the parameters. This approach has the advantage of breakthroughs in the past when a fixed boundary curve is given , the shape of surface can only be limited changed through changing the twisted vector. Further more, by selecting a special border information matrix when control functions are not changed, we can accurately acquire torus, ellipsoid and so on. It has many valuable applications.