Numerically calculating the divergence of a set of oriented points

Say I have a set of oriented points at locations $\vec{v_i}$ with each some direction $\vec{n_i}$, in practice they represent the normals of some surface that has been non uniformly sampled. How would I calculate the divergence of this vector field? Standard finite-difference methods would obviously not work because there is no grid.

Can I perhaps assume a grid and use nearest neighbours to infer the vector field at each point (I think it's called "splatting")? The discretized vector field would then have at each point a weighted average of nearby points. This would then allow me to use standard FD-methods to calculate (or rather estimate) the divergence at each gridpoint. Is this a common method, or are there better methods?