Here’s what I took out from the extensive discussion in this thread and the many others that were linked from it. It is a request for a curvature analysis display mode that focuses on visually finding the areas that form concave dips, convex bumps, or are planar for some tolerance, in a surface.

Actually fulfilling that request will need trial and error, and there will be ample time to adjust it depending on your feedback, either now or later when there are actually images to show.

RH-75092 CurvatureAnalysis: Make a mode for analyzing bumps above/below tangent plane

Plus two other requests for things that were discussed here and are more straightforward:

RH-75093 CurvatureAnalysis: Make a signed mean curvature display mode

RH-75094 Zebra: Make a mode that displays dots instead of vertical or horizontal stripes

They were invented for this thread and do not need to be used again. I just felt like it was the easiest way to make sure we all had the same non-standard definition of these concave areas that should show up in the new display mode. And to highlight the fact that with these definitions, concave + convex + planar areas will leave two other types of local regions uncolored.

@gustojunk I still do not understand why or how you would use Zebras (or dots) to find areas with single curvature. Gaussian curvature is the usual tool for this.

I think those terms are really on point, specific, useful. Imho.

Looking at some “threshold” to distinguish flat from non-flat, having negative, zero, positive curvature for 2 directions (min and max curvature), we have 5 “levels”:
-2 double convex
-1 single convex (conic, cylinder, developable)
0 flat
+1 single concave
+2 double concave
A gradient with 5 colors would be best.

Making a guess:
Zebra stripes width should be constant at any view angle, while looking flat surfaces. (probably isn’t currently) Each stripe should be equal to a tot amount of normal angle change.
Concave/convex curvature should translate in decreasing/increasing in stripe width.

If dots/leopard instead of stripes/zebras, we should have circles while looking at planes and bigger/smaller circles while looking at concave/convex spherical surfaces (where min/max curvature are equal).
(note this implies with parallel projection view we shouldn’t view circles with flat surfaces, camera lens length take a role in the size of circles, maybe).

Back to your question: developable/conic/single curvature surfaces should have elliptical dots with smaller diameter equal to circle diameters on flat surfaces.

Derivative and stuff…

Just mumbling. I might be wrong on multiple levels.

Hi @pierrec, sorry for being prescriptive of how to implement what I need. It does not have to be dots or zebras. I simply want a clear way to know looking at a model where in the topology the form is (as described by Riccardo):

Enabling curvature graph on ALL edges of a SubD is not ok.
With big SubDs, it kills performance and clogs the viewport with countless graphs/hairs.
Using History=on, extracting some edge, and doing curvature graph on those edges only, is faster (performance-wise) and way more useful (and analyzing only what the user want, not everything)

Please consider making it possible to select SubD edges for curvature analysis.

PS Even curvature analysis would be super if applied only on some SubD faces, faster computation, hopefully.

This follows the same logic of ‘all or nothing’ also used for SubD cage/smooth mode. It’s a simple and elegant way for programming, UX and user understanding.

It is also however, extremely simplistic and limiting for those working on complex projects/variants//models where having hundreds of parts and millions of polygons is the norm, and this current design/programming limitation renders Rhino unfit to do our work.