Metaball "Zero-Charge" Lines

Hello, can anyone help me with a clever way to generate the seam lines of "zero charge" in the attached metaball diagram? The metaballs are generated with the standard component, and the streamlines are generated using [uto]'s flowL plug-in.

Thanks!

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Taxonomy 120226 004.jpg, 150 KB

Replies to This Discussion

Permalink Reply by David Rutten on March 3, 2012 at 11:56pm

A metaball connects all points of equal charge. Points with zero charge would be at infinity if you have only positively (or only negatively) charged seed points. Zero charge points can only occur in valid world space if you have a mixture of both positively and negatively charged seed points. Grasshopper itself does not allow for negative charges though.

I think you need to come up with a different definition of the points you want to connect.

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Eli Meltzer on March 4, 2012 at 7:45am

I think that more accurately, I am looking for the set of points with Electric Potential V = 0, as in this diagram

Permalink Reply by Daniel Piker on March 4, 2012 at 8:39am

Eli - using the tool I posted here (http://www.grasshopper3d.com/profiles/blogs/rheotomic-surfaces-and-...), you can take the contour of the mesh at Z=0, which corresponds to an electric potential of zero

Permalink Reply by Eli Meltzer on March 4, 2012 at 8:28pm

Thank you Daniel, perhaps you could give me a bit of instruction in the use of your component. From what I can tell, I only have sources (or maybe sink), but your component seems to require both. Is this correct?

Permalink Reply by Daniel Piker on March 5, 2012 at 3:36pm

Hi Eli - If you want to use only sources, connect the null object (there should be one in that definition) to the Sinks input. (It just seems to be an oddity of clusters that makes this necessary)

Permalink Reply by Eli Meltzer on March 5, 2012 at 10:06pm

I see, this works for charges of opposite signs, however, in my case all the charges are positive ... which brings us back to David's initial concern about how (in)accurately I have defined the points I am looking for. I can't seem to find the name of this line, but in a vector field, or in this case, an electric field, of all like charges you can see that there are some lines that all the streamlines approach as a limit, that pass through the points where the electric field = 0, and those are the lines, or set of points, that I am looking for

Permalink Reply by to] on March 6, 2012 at 1:23am

What you are looking for is the weighted voronoi in this case if all points are on the same dz.

We have written something like that, but we still have minor bugs in it which we have to polish until we can release it.

but you an look into that topic

Permalink Reply by David Rutten on March 6, 2012 at 2:36am

Is it? Voronoi diagrams are only affected by points in the immediate neighbourhood, but a field can be affected by a strong charge very far away. Maybe I'm wrong, I don't fully understand the maths behind the different kinds of weighted voronoi diagrams...

David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Hannes Löschke on March 6, 2012 at 2:47am

From a physical point of view, the field of only positive charges approaches 0 only at inifity.

You want to find the local minima of the field. I don't know if weighted Voronoi, as to] mentioned, does exactly that but seems a pretty good approximation.

Permalink Reply by Daniel Piker on March 6, 2012 at 2:51am

It sounds like maybe what you are looking for are the separatrices of the vector field, which connect the critical points

Permalink Reply by Eli Meltzer on March 6, 2012 at 10:38am

Yes, this is correct; specifically they are hyperbolic seperatrices. From what I can tell weighted voronoi still only takes into account the closest members of the set (although I have difficultly to find the difference between multiplicatively weighted and additively weighted).

To find the critical point seems simple enough; I think that this is the set of points where E = 0, or in other words, where the sum of all the force vectors with magnitude q/r^2 = 0; and, when all the charges are equal, where the sum of 1/r^2 = 0.

Permalink Reply by Daniel Piker on March 6, 2012 at 1:19pm

Using the definition I posted above you could find the critical points manually by adjusting the 'Move R' slider until the lines met.

It should also be fairly easy to check with a script at least which cell they are occurring in. Because these points are exactly the saddle points of the surface, we can check the corners of a cell and see if we have one pair of diagonally opposite points higher than the other pair.

Once we have the critical points, we can take contours at those heights to get the separatrices.

Also, I'm not sure how they were generated, but I'm pretty sure the streamlines in the image you posted above are physically incorrect for electrostatics. They shouldn't gather at the critical point like that - I believe this is more realistic: