Why is the “mean curvature” displayed and reported by CurvatureAnalysis “unsigned”, ie always the positive absolute value, rather than the usual “signed” version which is reported by Curvature and returned by the Rhino Common SurfaceCurvature.Mean property http://developer.rhino3d.com/api/RhinoCommo…

This is probably best answered by @GregArden .

Mathematically speaking the normal, principle, mean, min and max curvatures can be positive or negative numbers and the sign depends on the choice of unit surface normal. That is these numbers are not a property of the surface by itself , but are a property of the surface together with an orient…

Hi Greg, I understand the approach you took on that. This is also expressed in the Rhino Help: Displays the absolute value of the mean curvature. It is useful for finding areas of abrupt change in the surface curvature. Unfortunately this only works well on synclastic surfaces i.e. where the Gauss…

[image] Jess: Mathematically this is correct in a sense of mean curvature (edit: more or less: red should be negative), but it does not help me to find the areas with most change of the surface curvature like indicated in the help file. I don’t know what “areas with most change of the surfac…

@jess I disagree with your interpretation AnticlasticSrf.jpg: [image] Jess: But if you inspect the mean curvature on an anticlastic surface (overall negative curvature) like the hyperbolic surface below, then it appears that the center of the surface has no curvature, while the edges (which are…

[image] jim: the help file says mean curvature helps locate areas of abrupt change of curvature. I assume that means that when the color bands are close together that indicates rapid changes in curvature. If you analyze a surface with a mix of negative and positive mean curvature, then the ra…

[image] GregArden: I do not understand what a designer is looking for when looking at mean curvature. Seems to me If one is interested in anticlastic vs synclastic characteristics then Gausian curvature is the right tool and mean curvature is the wrong tool. Discussion of what mean curvatu…

Hi Greg, [image] GregArden: I disagree with your interpretation AnticlasticSrf.jpg: Oops, sorry - this belongs to my description of the synclastic surface: [image] Jess: synclastic surfaces i.e. where the Gaussian curvature is positive at any point on the surface. it should read: an…

Hi Greg, [image] GregArden: The information we are missing is wether the red areas have mean curvature of the same sign or opposite sign. Just to complete the image sequence, this is what the hyperbolic surface would look like including negative mean curvature: [image] [image] GregArde…

Why "Unsigned" Mean Curvature in CurvatureAnalysis?

Rhino Rhino for Windows

davidcockey (David Cockey) December 2, 2016, 7:24pm 9

Discussion of what mean curvature shows and what it does not show in this thread.

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Why "Unsigned" Mean Curvature in CurvatureAnalysis?

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