I have a large set of points in $n$-dimensional space and each point has a scalar associated with it. I would like to compute the gradient of the associated function.
If the points I'm considering were two-dimensional, I would do the following :
- generate Delaunay triangulation from the set of points
- assume the function is linear on each mesh element
- interpolate the gradient on each mesh element
If the points spaced out on a regular grid in $n$-dimensions, I would simply separate the dimensions, and compute the gradient in each direction.
But I don't know how to extend this to the $n$-dimensional case with points that are unevenly spread out. How can I interpolate a gradient on an irregular grid in $n$-dimensions?