Methods to interpolate surfaces from gradient field?

[grumpymrgruff]

I have a 2D regular grid of vectors representing average headings on a 2D spatial domain. These are generated by stochastic simulation of chemical-sampling and gradient-estimation techniques for a robotic search algorithm seeking a chemical source.

Without going into a lot of detail, I would like to treat this grid of robot headings as an approximation of a gradient field. Ideally, I want to interpolate the function from its gradient and use it to determine basins of attraction where my search algorithm converges to "true" chemical sources.

What I don't know is if their are any standard methods for estimating a 2D function given a grid of gradient data.

Does anyone know of any? Or perhaps I'm over-complicating things and there are simpler ways to estimate the basins of attraction (areas and morphologies) from this regular grid of vector data?

Thanks!

 

[Stephen Tashi]

A similar question was answered on stackexchange: http://math.stackexchange.com/questions/1340719/numerically-find-a-potential-field-from-gradient