We discuss the solution of cornea curvature using a meshless method based on radial basis functions (RBFs). A full two-dimensional nonlinear thin membrane model is introduced and solved using the multiquadratic and inverse multiquadratic RBFs. This method does not rely on radial symmetry or other simplifying assumptions in respect of the cornea shape. The results show good agreement with published corneal data and allow back calculations for estimating certain physical properties of the cornea, such as tension, elasticity coefficient and Young’s modulus. All calculations and generation of graphics were performed using the R language programming environment \cite{Rct-15} and RStudio the integrated development environment (IDE) for R \cite{Rst-15}, both of which are open source and free to download.

Part II of this paper demonstrates how the method has been used to provide a very accurate fit to a cornea measured data set.