This is a problem that I have been stewing in for quite some time now, I need an equation I can understand to find surface normals. I'll try describing an example problem, with an analogy.
Imagine a hilly landscape. There is a flat "grid", or x-y chart, flat at sea level. "z" is the height of the land, where at sea level z=0. Below is a visualization, imagine looking down from a helicopter. x and y are labeled, numbers at each x,y is z, or height of the land.
4|| 1| 3| 1| 0| 1|
3|| 1| 2| 4| 3| 2|
2|| 0| 5| 3| 7| 6|
1|| 0| 2| 1| 2| 0|
0|| 8| 0| 0| 0| 0|
|| 0| 1| 2| 3| 4|---X
So each (x,y,z) coordinate is a point, not a plane, but I need to calculate a normal for each point. This is only a small example, the real program has a much larger data set, and I eventually need to have an equation I can put down in programming code. I have looked online at many different websites, but my inexperience with vectors, and certain symbols I've never seen has left me bewildered. I'd appreciate any and all details, proofs or explanations.