I know the values for a function v[x,y] on an irregular grid of (x,y) points. Call the table storing all these points xyvtriples. Because of the irregular grid, the Mathematica function Interpolation only works as
interpolatedvfunc = Interpolation[xyvtriples, InterpolationOrder -> 1];
But what I really need are the partial derivatives of interpolatedfunc with respect to each argument, and for those partials to be continuous, which won't happen due to the edges produced by InterpolatioOrder -> 1.
Is there any way around this? I can make a very fine grid of (x,y) points to (I hope) counter any problems with forcing a spline like interpolation if I can somehow force this to happen.