带形状参数的TC-Coons曲面

TC-Coons patch with shape parameters

为了能够灵活地调控双三次Coons曲面的形状,对双三次Coons曲面进行改进,构造了一组由4个含形状参数λ的函数组成的三角混合函数组,称之为TC-Hermite基。TC-Hermite基具有端点性质、对形状参数λ的单调性、形状可调性等性质,基于TC-Hermite基,构造了一种新的带形状参数的Coons曲面,并称之为TC-Coons曲面。TC-Coons曲面不仅可以通过形状参数调整其形状,而且还可以精确表示球面、圆环面等二次曲面。另外还讨论了TC-Coons曲面片在几何造型方面的应用。

In order to flexibly control the shape of the bi-cubic Coons patch and improve the bi-cubic Coons patch,we construct a triangular mixing function group consisting of four functions with shape parameterλ,named TC-Hermite basis.The TC-Hermite basis has properties of endpoints,monotonicity of parameterλ,adjustability of shape etc..Based on the TC-Hermite basis,we also construct a new Coons patch with shape parameters,called TC-Coons patch.The TC-Coons patch not only adjusts its shape through shape parameters,but also accurately represents quadratic surfaces,such as sphere and torus.Furthermore,the application of the TC-Coons patch in geometric modeling is also discussed.