In numerical analysis, transfinite interpolation is a means to construct functions over a planar domain in such a way that they match a given function on the boundary. This method is applied in geometric modelling and in the field of finite element method.[1]
The transfinite interpolation method, first introduced by William J. Gordon and Charles A. Hall,[2] receives its name due to how a function belonging to this class is able to match the primitive function at a nondenumerable number of points.[3] In the authors' words:
We use the term ‘transfinite’ to describe the general class of interpolation schemes studied herein since, unlike the classical methods of higher dimensional interpolation which match the primitive function F at a finite number of distinct points, these methods match F at a non-denumerable (transfinite) number of points.
Transfinite interpolation is similar to the Coons patch, invented in 1967. [4]
With parametrized curves , describing one pair of opposite sides of a domain, and , describing the other pair. the position of point (u,v) in the domain is
where, e.g., is the point where curves and meet.
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