Signed mean curvature can differentiate these cases if k>0.
What is a signed mean curvature?
Rhino _CurvatureAnalysis command supports only: Gaussian, Mean, Max radius, Mean radius.
Mean curvature is usually defined as the average of the minimum and maximum curvature. Curvature can be either positive or negative. Therefore mean curvature as usually defined can be either positive or negative.
CurvatureAnalysis shows the absolute value of curvature which is always positive. In this discussion “signed mean curvature” means as usually defined which can be positive or negative rather than the absolute value.
Thank you for the explanation @davidcockey !
But I still do not understand which curvature type should be used for visually making a difference between the convex and concave shapes of the surface?
If Guassian curvature is negative then the surface is anticlastic or saddle-like at that location and convex/concave do not apply.
If Guassian curvature is positive then the surface is synclastic or dome/bowl like at that location and signed mean curvature can be used for differentiating between convex and concave. However the CurvatureAnalysis command currently only shows the magnitude of the mean curvature but not the sign so it does not help. The Curvature command can be used to examine which way a surface is curved at a point.
Thank you for the clarification David!
Sorry for taking me too long to see this reply.