Search Radius

[APMcClune]

Hello,

I was just wondering if anybody knew the units used for a search radius. I am using Cloud Compare to calculate the curvature and roughness of a point cloud but I wondered what the units of the search radius are. If I set this to 1 is this 1 metre or something different.

Thanks,
Andrew

[daniel]

The radius is expressed in the same units as your data. This is what we call 'implicit units' (i.e. CC doesn't make any assumption on your data's units nor provide any other mean of conversion apart from the 'Edit > Multiply/scale' method).

[APMcClune]

Thanks daniel,

Just wondering as well if you could tell me what the curvature value actually means? I have computed it over several point cloud but it has not given me the answer that I would be expected. I understand curvature is trying to fit a quadratic to the point but does the returned value actually mean?

Thanks,
Andrew

[daniel]

The (unsigned mean or gaussian) curvature is computed as suggested in "CURVATURE OF CURVES AND SURFACES – A PARABOLIC APPROACH" by ZVI HAR’EL (http://www.math.technion.ac.il/S/rl/docs/parabola.pdf).

We use equation 7.6 applied on a quadric: z = a.x + b.y + c.x^2 + d.x.y + e.y^2.

I double checked the formulas... and I realized that there was a mistake in the Gaussian curvature (a missing square in the lower part, so it should only change the scaling, not the ordering). The mean curvature seems right.

A new release should come out this evening with the gaussian curvature fixed.

[APMcClune]

Thanks for the reply Daniel and for clarifying how the curvature is calculated. I'm still not sure what the returned curvature value actually is. In the formula you listed by is the returned value Z? I guess the X and Y in the formula are the X and Y coordinates?

[daniel]

Well, the quadric that we best fit on the points has such an equation, but in practical x, y and z may be different from the cloud X, Y and Z default dimensions so as to get the best fit (i.e. we may have to switch X and Z for instance if the cloud is flat in the X dimension).

The returned value is K (or H) as described page 13 of Harel's article (i.e. the Gaussian curvature and the mean curvature).