# Curvature of function given by points

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.

• Do you have $f(x, y)$ itself, or just its value at some finite number of points? In the former case, this is just working out the Gaussian and mean curvature for a graph surface; in the latter case, since these are local properties, you can't say anything at all without some more information. Nov 4, 2014 at 12:43
• @Travis I have only points, f(x,y) is unknown. What more info do I need to calculate curvature. I could also use only estimate value, not 100% accurate. In my case, speed is important, precision is second. Nov 4, 2014 at 13:31
• The curvatures will depend on the derivatives of $f$, so you need some information about how much the derivatives vary. Otherwise, the function $f$ could be very wild in between your sample points. Nov 4, 2014 at 13:33
• @Travis I am taking it as the sampling points are direct neighbouring values, eg. my sampling is detailed enough. There is no wildness in non-sampled points. Nov 4, 2014 at 13:42