Surface splines generalization and large deflection interpolation

The generalized method based on the standard IPS (infinite plate spline) is established for vector value function interpolation, and the numerical scheme for structure configuration characters is deducted through a simple differential geometry method. The data fitting method between arbitrary dimension spaces is carried out by the further generalization of TPS (thin-plate spline). The transformation matrix defines a mapping from the original structure configuration to the set of displacement, or to the final configuration. Through the interpolation, the tangent mapping can be obtained as well to calculate the tangent or normal vectors of the configuration. This method provides a general interpolation scheme not limited to the structural and aerodynamic interface, but also applicable to interpolate any smooth data and curve/surface reconstruct.