2D interpolation with dependent variables

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Hello,
I have a matrix E(Nx*Ny) that depends of the coordinates K(Nx*Ny) and I would like to interpolate E on new coordinates Ki(Nx*Ny).
K is not uniformly spaced (in both axis), and can not be expressed as a vector product of independent vectors.
Ki is uniformly spaced and can be expressed as a vector product of two vectors.
It seems that interp2 and scatteredInterpolant are not working in this case because both require a format with independant coordinates for the axis.
I already have something that works with interp1 and a loop on each Nx, but I would try to speed it up.
Is there a solution ? Thank you.

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