Resamlpe/ warp 2D images at a non-uniform resampling grid

I have a 'regular' 2D rectilinear intensity image, (i.e.)

x = linspace(-12,12,24); c = 25;
y = (1/(c*(2*pi)^.5))*exp(-(x.^2/2/c^2));
spot = y2'*y2;
figure; imagesc(spot); title('spot');

I wish to resample this at a specific grid points with non-uniform spacing (i.e.

[X,Y] = meshgrid([1 2 4 8 16 19],[1 2 4 8 16 19]).

and form a new image. The meshgrid index could be the index location. The resulting image will be still rectangular, but properly interpolated and warped. I bet there is a neat transformation technique I could use.. Thank you for your help