I want to do scattered interpolation in Matlab, but scatteredInterpolant does not do quite what I want.
scatteredInterpolant allows me to provide a set of input sampling positions and corresponding sample values. Then I can query the interpolated values by supplying a set of positions:
F = scatteredInterpolant(xpos, ypos, samplevals)
interpvals = F(xgrid, ygrid)
This is sort of the opposite of what I want. I already have a fixed set of sample positions, xpos/ypos, and output grid, xgrid/ygrid, and then I want to vary the sample values. The use case is that I have many quantities sampled at the same sampling positions, that should all be interpolated to the same output grid.
I have an idea how to do this for nearest neighbor and linear interpolation, but not for more general cases, in particular for natural neighbor interpolation.
This is what I want, in mock code:
G = myScatteredInterpolant(xpos, ypos, xgrid, ygrid, interp_method)
interpvals = G(samplevals)
In terms of what this means, I suppose G should hold a (presumably sparse) matrix of weights, W, and then G(samplevals) basically does W * samplevals, where the weights in the matrix W depends on the input and output grid, as well as the interpolation method (nearest neighbor, linear, natural neighbor). Calculating the matrix W is probably much more expensive than evaluating the product W * samplevals, which is why I want this to be reused.
Is there any code in Matlab, or in a similar language that I could adapt, that does this? Can it somehow be extracted from scatteredInterpolant in reasonable processing time?