Suppose that you have a number of large point clouds and you want to observe whether they contain any valuable information or meaningful surfaces. To decrease the cost of surface reconstruction, you may ignore some point clouds with specific distribution, for instance, random distribution. How do you pick the point clouds with meaningful point orders and which ones do you avoid to reconstruct?
Two ideas:
Pick several locations and explore covariance matrix there. If the surface is well approximated by a plane in the neighbourhood, one of eigen values of the matrix will very small. The size of the neighbourhood used for analysis depends on smoothness of the surface.
Split the space into voxel grid. Count voxels containing at least one point. Then half size of voxels and count again. After several such measurements you will be able to approximate dependency of voxel number on voxel size. For surface-like distribution it should be number~(1/size)^2, for uniform distribution around volume it will be closer to (1/size)^3.