@davidcockey thank you for the detailed reply!
It looks like the whole confusion is caused due to _CurvatureAnalysis command, which for some reason threats negative mean curvature values as positive - like you noticed, it shows the absolute mean curvature value.
I posted this question to another Rhino user on different forum who is skillful in programming. He used some Rhino Common command which evaluates the Mean curvature at particular point. This Rhino Common command:
http://developer.rhino3d.com/api/RhinoCommonWin/html/P_Rhino_Geometry_SurfaceCurvature_Mean.htm
He then evaluated the Mean curvature at a couple of points and made an analysis mesh from it with a legend. That is the number 3) photo:
Number 1) photo is a surface for which he performed the Mean analysis. When _Curvature command is applied to the two red points of that surface, they show the same results as the 3) photo (the same results for “Mean curvature”).
Photo 2) has been made by using Rhino’s _CurvatureAnalysis command.
As you already mentioned, for some reason: negative mean curvature values are always threated as positive, which is what caused the confusion.
So can we conclude:
If I use the _Curvature command, or that SurfaceCurvature.Mean Rhino Common programming command, and if the following values are returned:
- negative Mean curvature values: then that part of the surface is bowl-like - concave (viewed from the side of the surface normal)
- positive Mean curvature values: then that part of the surface is saddle-like - convex (viewed from the side of the surface normal)
- zero Mean curvature value: then that part of the surface is flat in both directions
Is this incorrect?
Here is the .3dm file with all three mentioned images:
Thank you.