I have function surface given by f(x,y) values (plus x and y). I know normal at each point and neighbourhood points as well. Is it possible to use this information to calculate Gaussian and Mean curvature? I have almost no knowlegde of this kind of math, so some kind of "5-years old" explanation would be good.
I have found, that Gaussian map can be used to calculate what I want - http://mathworld.wolfram.com/GaussMap.html. But again, I have not found, how to construct this or manipulate it.
You can find formulae for the curvatures of a graph here. These are in terms of the first and second derivatives of the function, so you just need to replace these smooth derivatives with approximations using your data set. If your data points are laid out on a regular lattice then you can just use the standard finite difference formulae, while if they are not I guess you will need to use some form of interpolation - this should be a very common problem in finite element analysis, which you probably know more about than I do.