True minimal surface in Kangaroo

I'd been aware for some time that simply treating edges of a mesh as springs and relaxing doesn't give a true minimal surface, especially if the meshing density is not even.
The next version of Kangaroo now has a properly area based surface minimization which does not have this dependency on the meshing, and gives true minimal surfaces*, as tested against known analytical solutions
(*well, of course a true minimal surface is continuous not made up of flat triangles, but as the mesh is refined it converges to one).

For many practical purposes this actually doesn't really matter, because we often don't even want tensile structures to be true minimal surfaces, and in many cases a minimal surface with the desired topology and boundaries does not even exist (for example, if the circles of the catenoid are too far apart), but still, it's nice to have the option of mathematical correctness (and as far as I have tested the ones I could find, none of the other Grasshopper plugins do).

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Comment by Jon on May 6, 2014 at 5:43am: i have to say, that the example file was sorted perfectly! thx daniel!

Comment by Ángel Linares on May 6, 2014 at 5:04am: Thanks for the work and for your clarity exposing the theory behind :)

Comment by Daniel Piker on May 6, 2014 at 4:55am: Hi Frank, this functionality is already in the current release of Kangaroo, and the definition shown above is included in the new example files zip, in the tensile folder.

Diederik - sorry for missing your question before. This uses the cotan weighted discrete Laplace-Beltrami operator, for which the earliest reference I know of is Duffin's 1959 paper “Distributed and lumped networks”, but I think it is more commonly associated with Pinkall and Polthier 93 “Computing discrete minimal surfaces and their conjugates”.