I am trying to identify unknown breaks in multidimensional continuous piecewise functions.
I have a dataset with values p for each point(x,y,z) that I am attempting to fit a continuous piecewise function to
$$ p = f(x,y,z) $$ where $ f(x,y,z)$ is a continuous piecewise function with an unknown number of breaks.
I have read a number of methods for identifying breakpoints in 1D piecewise functions however I have yet to find information on a more generalized method that will work with higher dimensions.
You can try a clustering approach: sample the function at random points with a density above the typical domain size. Give each sample a distinct domain id. Now examine the line between nearest neighbors and identify their domain ids if the function along the line has no breaks. Rinse, repeat until convergence.