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This is interesting. I was trying to compute curvature for points using 8 of their neighbors after thinning a .las file that's not dense enough for most ground-finding algorithms to work - it ends up leaving a lot of "spikes" where the trees are. I was trying to figure out why I couldn't partition the convex and concave features with the curvature calculations (if all the "spike" points have the highest positive curvature values it makes them easy to filter out). Then I read in this thread that curvature is unsigned. darn. There goes my chance of using it.

I have a question regarding the curvature analysis. Is it possible to set a normal direction in order to determine a sign for the Gaussian curvature?

A positive Gaussian curvature implies that the surface is synclastic/spherical. In some applications it is useful to know if the Gaussian curvature is negative or positive.

Not sure about this. I'll have to review how the algorithm works...

Indeed, that would be super useful to know if the curvature is positive is negative with respect either to the local normal (if known), or to the vertical direction (e.g., a +Z orientation). You could do much more advanced point cloud segmentation with this info.