Yes, 0.8 is indeed larger than 0.663

This means there is not a stable soap film between those rings.

Yes, 0.8 is indeed larger than 0.663

This means there is not a stable soap film between those rings.

Thanks, that was it. Just for others reading this. Above I flipped the ratio numbers.

Is it possible that this does not exactly correspond to a physical catenoid? I did a quick physical test with the original radius 40, distance 60 and was able to produce the soap film while pulling apart the rings. Why could that be?

Secondly, why is it related to mesh resolution? With a denser mesh, I can achieve more distance?

Sorry, for bugging you.

I meant to say separation/*diameter*.

Still, diameter 80, separation 60 is I believe theoretically not stable without volume constraint.

Do you have a photo of this 0.75 ratio soap catenoid?

As for the resolution, if the equilibrium shape is stable but close to an unstable one, small differences in momentum could carry it past the stable point, especially if the starting shape is far from the equilibrium one.

If you need to find a minimal surface which is just on the brink of stability, you could start with an anchor strength 1 on all internal points and gradually slide it down to zero.

Think of it like trying to find this dip in the energy landscape. If it starts too high or goes too fast it can easily roll past the local minimum.

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Thanks for the clarification regarding the ratios. I’ll take a photo tomorrow, need a second person to do so.

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It sounds like you were maybe trying to do this by hand and eyeballing the distances? which could explain a misreading like this.

There’s a well established limit theoretically and confirmed experimentally though, which is why I’m quite confident that you made some mistake in your measurement (you might get a longer catenoid momentarily, but as it’s unstable I think it won’t last more than a fraction of a second).

Here’s an example showing that Kangaroo’s LiveSoap does indeed agree with the theoretical value and pop the catenoid into two disks (the Goldschmidt solution) right on cue at the predicted ratio

catenoid_stability.gh (13.5 KB)

The above is for actual minimal surfaces, but if you want you can also generate stable tensile surfaces which are not minimal in Kangaroo by using EdgeLengths with a LengthFactor of zero. This will let you stretch it into any ratio you like without it popping. The shape won’t be a minimal surface, but it will all be in tension.

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Hi Daniel,

thanks for the papers, links and all the clarifications. It is greatly appreciated!

Please find the photos of the soap film test below: For the first test (no photos) I indeed eyeballed the diameter along the yard stick. For the second test when I did the photos, I calculated the exact circumference. The diameter in the first test was slightly too wide. After adjusting the circumference, it was only possible to get to approx. 50 mm (.625 ratio). Which is pretty much the theoretical ratio of .663 - my shaking hands ;).

Edit: Just for others reading this: As mentioned by Daniel above, with physical tests you can get to ratios above .663 dynamically, but the films are not stable. This added to the exaggerated result from the first test.

The earlier collapse of coarser meshes makes total sense after your explanation with the dip in the fitness landscape.

What’s most relevant for us is to achieve the CMC property of the surface. You mentioned minimization of edge lengths for tensile structures? Would this also achieve CMC? As far as I understood http://www.polthier.info/articles/s3diri/s3diri_preprint.pdf it is not sufficient.

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Nice experiments.

I confess I’ve never actually tried this with measurements physically myself, so it’s nice to see confirmation.

I imagine getting much closer to the theoretical limit would require strict laboratory conditions, as it’s the equivalent in my green sketch above of trying to balance the ball on a vanishingly small bump on the side of a steep hill, so little vibrations would tip it over.

Area minimization with a volume constraint (as with LiveSoap with ‘UseVolume’ on) should produce CMC surfaces. Minimizing edge lengths alone indeed won’t give CMC surfaces.

Some shapes are a bit easier to achieve as stable CMC surfaces - for example, with minimal surfaces most shapes with handles or tunnels collapse, but the additional volume constraint can make some of these stable.

However, lots of the spatially interesting CMC surfaces such as the ones in that Polthier paper you link are unfortunately not physically stable (despite being true CMC solutions). These critical point solutions are a bit like geodesics between 2 points on a sphere. Generally there will be 2 different arcs between them on the same great circle, both these arcs are geodesic, but an elastic cable would only be stable on the shorter one.

These unstable solutions aren’t as easy to model with Kangaroo - it will generally be like physical modelling, so ones that pop there will pop in simulation.

Finding CMC surfaces within fixed boundaries is relatively easy, but anything closed tends to just pop to a sphere, and trying to find something periodic with handles, the handles quickly pop.

Sometimes it is possible though. For instance, if you know some symmetry properties of the correct solution, enforcing these can sometimes be enough to stabilise it without distorting it from CMC.

I am interested in finding better ways to simulate the unstable minimal and CMC solutions though. For discrete quad versions you can use the Koebe polyhedron method I was talking about recently over in this thread.

For something more general it might require some changes to the solver though.

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