Command Error: CurvatureAnalysis - Max Radius

The Max Radius option in CurvatureAnalysis does not work properly for regions of surfaces where the Guassian curvature is negative. It shows red representing the top of the scale in those regions, independent of the scale and the actual maximum radius. The Max Radius option appears to be working properly in regions where the Guassian curvature is non-negative, displaying the color code corresponding to the principal radius of curvature with the largest magnitude (ignoring sign of the curvature).

The Min Radius option appears to be working as expected, displaying the color code corresponding to the principal radius of curvature with the smallest magnitude (ignoring sign) everywhere.

The attached file contains examples of surfaces with Guassian curvature non-negative everywhere, surfaces with Guassian curvature non-negative in some regions and negative in others, and surfaces with Guassian curvature negative everwhere (except for isolated points or lines). Curvature Shapes 11.3dm (937.2 KB)

This problem occurs in both V5 and V6 WIP. I posted it here in hope that it will be corrected in V6 before it is released.

Perhaps I should note that the cylinder shows always displays the top of the scale color for Max Radius even though the Guassian curvature is zero, ie non-negative. That is correct because the cylinder is a developable surface with one of the principal curvatures zero everywhere, and zero curvature has infinite radius.

@pascal Can this problem receive some attention, at least be put on the stack? I need the Max Radius option functioning properly to use when evaluating almost developable warped surfaces.

Hi David - thanks, yep, I see that it is not what I expect at least… I’ll poke some more.

@davidcockey - here’s Mikko’s comment:

“Saddle shaped surfaces that have negative gaussian curvature always have infinite maximum radius of curvature. It’s easiest to understand by starting from the two principal curvatures: Think about measuring the surface curvature at that point into all other directions too. There is always one direction where the signed curvature isn’t positive or negative and the radius of curvature center isn’t on either side of the surface, and that’s where the curvature is zero and radius of curvature infinite.”


Torus_Curvature-Analysis.3dm (116.5 KB)

hello Pascal and David
sorry to go back to this older issue:
Totally accept and understand Mikko’s Answer quoted by Pascal.

Before i came across this same issue today - i always thought that the _curvatureAnalysis Tool just uses min and max Radius as a more easy to read description for the two principal curvature-Values.
… but ok it really looks at the Radius-Range as pointed out by Mikko
… and this is worthless for saddle-like surfaces as pointed out by David and as it is shown in the attached Torus-Example.

But there are cases, where the range / domain of two principal curvature matter.
And the nice thing about curvature is - that 0 (infinite Radius) is inbetween the negative minimum value and the positive maximum value of the curvature.

Imagine a sattle-like surface - and i want to mill it with a mill-bit that as a Diameter (R-body), and a Radius-Knife.(R-cut) and R-body is bigger then R-cut:

now i would love to analyse the areas i can access with this tool.

therefore we would need two additional options for the _curvatureAnalysis:
–>Range of minimal principal curvature (which is not the same as maximal Radius - as Mikko points out)
–>Range of maximal principal curvature (which is not the same as minimal Radius)

hope this makes sence.
would love to see this very helpful feature / option.