Transfinite interpolation
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].
The transfinite interpolation method, first introduced by William J. Gordon and Charles A. Hall, 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.
In the authors' words:
Transfinite interpolation is similar to the Coons patch, invented in 1967.
Formula
With parametrized curves, describing one pair of opposite sides of a domain, and, describing the other pair. the position of point in the domain is
where, e.g., is the point where curves and meet.