(Originally posted in Stack Overflow, re-posting here since my question's probably a better fit here)
I'm going through Forsyth/Ponce and working through their reading on recreating a depth map from surface normals. The idea is that you do summation of partial derivatives across a path to calculate the shape, as explained in the textbook:
In the integration section, it goes over one "path" of calculating the depth map using the surface normal partial derivative matrices. It's been a while since I've done multivariate calculus, so my confusion is on why this specific integration represents one path, and how I can generate other paths with these same partial derivative matrices? I.e., what would another path look like (e.g. would I do a cumulative sum down the first two columns, then sum across all the rows?) Based on the line integral, the surface doesn't depend on the choice of the curve; I'm just not sure what this means in terms of the discrete summation using the partial derivatives.
Any help would be appreciated!