Coons Patches Of Half-antiperiodic Trigonometric Hermite Interpolation

In this paper,we have studied a new type Coons patch constructed by the trigonometric Hermite interpolation for two points with two multiplicities.It presents an extension of Coons patch.In the first,we introduced trigonometric interpolation and discussed mainly trigonometric and paratrigonometric Hermite interpolation .The convergence of the paratrigono-metric Hermite interpolation bases were constructed.Secondly,we introduced the Coons patch and the nature of the blending function.We summarized two papers about constructing trigonometric blending function of Coons patches.One was the bases of {1, t, cos t, sin t} and another was the bases of {1, sin πt,cos πt, sin 2πt, cos 2πt, ..}.Afterthat,we provided the result of this paper that constructing the blending function by the trigonometric Hermite interpolation for two points with two multiplicities,and obtained the bases of {sin 1/2t, cos 1/2t, sin 3/2t, cos 3/2t}. Finally, we show the quality by the images of two examples.