I'm looking for guidance on how to determine the desired output resolution, when interpolating a surface from irregularly-spaced point samples.
I have a series of boreholes taken across a city, and the density of the samples varies considerably – sometimes boreholes are located within ~5m of each other, while in other locations they are ~1km apart.
What techniques should I use to determine the applicable cell-size, when interpolating a surface from these points? Does the optimal cell-size depend on the interpolation method?
I'd like the highest resolution which is supported by the dataset. eg I assume that a 1m grid is no more accurate than a ~10m grid – but how do I determine that number?
Best Answer
You are interpolating the unknown z=f(x,y) from scattered data. Interpolation (surface reconstruction) on highly irregular point clouds of moderate size is best done with globally, non-compactly supported radial basis functions (RBF, thin plate spline, multiquadric). Implementations are available for SciPy, Matlab, C++ TPS.
One could then easily, for moderate datasets, rasterize by evaluating in each "pixel" or cell the fitted RBF interpolant function for plotting or multiscale analysis by choosing different resolutions.