Orientation of Best Fit Plane for Roughness Calculation

[civengrgmu]

Hello,

I apologize for this question, because I know the 'roughness' calculation has been discussed many times.

I understand that the roughness value for a point is the orthogonal distance to the best fit plane of the local neighborhood, but here is my question:

Is the best fit plane established to be orthogonal to the surface normal vector at that point (calculated off of the same neighborhood, for example)? In other words, does the roughness "vector" have the same orientation as the surface normal vector at the point?

Thanks

[daniel]

No, we don't consider the points normals (and it's not a requirement to have normals to compute roughness). We use the neighbor points and 'best-fit' the plane on these points.

[civengrgmu]

OK - thanks. I apologize for the late follow up question:

How is the best fit plane calculated? Am I correct to assume that it's through a PCA on the local neighborhood?

[daniel]

Yes, PCA (from the eigenvalues and eigenvectors of the cross covariance matrix ;)