Abstract:  In order to solve the lack of shape adjustability of the traditional Coons surface and the inability to accurately represent ellipsoid, elliptical cone, and elliptical cylinder etc., a set of rational hybrid basis functions is constructed in rational space, which is named R-Hermite basis. Firstly, the properties of R-Hermite basis are illustrated. Secondly, based on the R-Hermite basis, a rational Coons surface with two shape parameters is constructed by using the tensor product method, and it is called R-Coons surface, which not only has the good properties of traditional Coons surface, but also has shape adjustability. Finally, the method that can accurately represent ellipsoid, elliptical cone and elliptical cylinder is given, and some examples are illustrated to prove the effectiveness of the method.

Key words: R-Hermite basis, R-Coons surface, shape parameter, elliptical cone