Curvature range

I am playing around with the vedo library a bit and find it super helpful to work with surfaces. In particular, I turn point clouds into surfaces with recoSurface() and then measure curvatures with the addcurvatureScalar() function and the Gaussian curvature method.

The visualized surface looks like this:

According to the definition of the curvature method, the algorithm takes into account the edges connecting an individual vertex with its neighbours. I was wondering if it was possible to increase the range within which points will be considered as neighbours and thus calculate the curvature in a bit more global fashion? Because for a sufficiently large amount of points, any surface will appear locally flat (as in the screenshot), but I’m more interested in the larger-scale curvatures.

Do you have a suggestion on how to do this? Any tips are greatly appreciated 😃

[jo-mueller]

There goes 😃 I’m not so seasoned on visualizing with vedo, though.

[jo-mueller]

Hey @marcomusy ,

thanks for the super-fast reply!

One could be to smooth out your mesh surface to make the neighbor vertices more representative of the average region around them.

This was my first idea as well, aside from averaging the curvatures of neighboring vertices. But this would lead me a bit to the problem that the curvature would then depend more on the number of remaining points on the surface rather than the “true” curvature. If possible, I would like to keep the surface density of vertices constant; I currently do this with the densify() function.

There is also the possibility to explicitly fit a sphere to a 3d point cloud

This is a brilliant idea! I could then iterate over all the vertices on the surface, extract all neighbors within a defined range and fit a sphere to these. I’ll try this and let you know 👍