curvature metaball

What is a good way to find the curvature at a specific point on a metaball?

I'm looking for a mean curvature value as can be obtained from a surface by the surface curvature component.

I know metaballs created by grasshopper aren't surfaces but a collection of lines. Maybe combining the curvature of lines intersecting at one point can result in the curvature of the metaball at that point?

Replies to This Discussion

Permalink Reply by Wiet Mazairac on August 26, 2010 at 12:48pm

My definition.
I have to calculate a few curvature circles too. If I set it at 8 or 16 at every point I get the results from above. There is an error in it. Sometimes I get two sectioncurves on 1 plane. I posted another topic on that. I fixed it by culling the second curve, it works, but it's a little strange.
I was planning of making some sort of roof. The definition is made with that in mind. The multi metaball scattered through space can't be processed by this definition, but that might be easy to change.

Attachments:

metab_curv_upload.ghx

edit: my def is not as well organized as yours :)

Permalink Reply by Jacek Jaskólski on August 29, 2010 at 12:42pm

Hmm...

I haven't managed to get to the core of your definition, but from what I understand you don't want to compute the exact mean curvature and you're fine with the coarse and innacurate result you get by checking a few section curves... is that right?

However, I'd still be interested to find out a way to calculate the curvatures precisely.
Since the metaball is a representation of an equipotential surface in an electric field, maybe a physycist would know how to do it. I have one or two in the family so I'll be checking on that soon... :)