Suppose we are given a set of sample points in $\mathbb{R}^3$. I don't have any knowledge about the surface, but we may assume that it is smooth. I want to approximate the gradient of each sample point based on the smoothness of the surface (I can find the Taylor expansion around a small neighbourhood of the sample point) and the location of other sample points. Also, the sample data cannot be mapped to a regular grid. How should I go about doing this?
Any help would be appreciated!