Roughness calculation

[ekincia86]

We have been using CC to try to quantify the abrasion of surfaces during shearing and found the roughness parameter quite useful, however, we could not find the mathematical formulation for this and how the kernel proposed by the software is determined from the point cloud. Any help or guidance with this would be much appreciated.

[daniel]

As we discussed by email, I just add my first answer for the records:

the roughness calculation is very simple (as explained here: https://www.cloudcompare.org/doc/wiki/i ... =Roughness). But it's not easy to write it as an equation.

<< for each point, the 'roughness' value is equal to the distance between this point and the best fitting plane computed on its nearest neighbors. >>

The 'kernel' is simply the neighborhood radius (around each point, inside which we extract the 'neighbors').

Then the distance is the orthogonal distance to the best fit plane.

[beauthetford]

Hello, I have a follow up question about the CC "roughness" calculation:
For the roughness "up direction", the user can specify a vector in R3. How is this up direction incorporated into the roughness calculation exactly? Perhaps, is the resulting roughness of a given point the magnitude of a component of the orthogonal distance from the point to the best-fit plane, in the direction of the specified "up" vector? I.e., the projection of the orthogonal vector onto the up direction vector?

Thank you
Beau

[daniel]

Yes, the roughness calculation is based on the differences of height between the central point and the average height of its neighbors. So here the 'height' is computed along the specified 'vertical' orientation.