Calculate mean curvature from osculating circles compared to surface curvature component

Grasshopper
#1

Curvature-gaussian-mean.gh (60.2 KB)

Hi

Was just reading up on principle curvature and curvature measuring on wikipedia to understand the concepts better: https://en.wikipedia.org/wiki/Principal_curvature

Tried to make a simple test (attached) where the mean and gaussian curvatures are calculated from the osculating circles instead of using the surface curvature component.

I was wondering if anybody here can explain why the mean curvature I get from the ‘surface curvature component’ differs from calculating it from the radii of the osculating circles (i.e. averaging the reciprocal of the radii of the osculating circles). The sign is different when the value is otherwise the same, but it looks as if the numbers are completely different when the osculating circles are on each side of the surface.

best regards
jacob

Edge Continuity Radius Value
Principle curvature
#2

Hi Jacob,
You need to take into account the signs of the principal curvatures.
Here’s a modification of your definition that does this by taking the dot product with the surface normal
Curvature-gaussian-mean2.gh (61.6 KB)
edit - cleaned up the def a little

1 Like
#3

Thanks a lot Daniel!