Schwarz P Minimal Surface

[kieran.burr (Kieran)]

Hello everyone,
I’m particularly interested in the Schwarz P minimal surface, and I’ve been reproducing it using the various methods on other grasshopper threads. I’ve found using Mesh+ Schwarz P volumetric mesh to be the simplest and gives the cleanest output (gh file attached). My only issue is that I can’t constrain the outer rings to perfect circles, and I wonder if there is a way to do this? (see pics attached). I don’t mind whether the final output is a mesh or brep as long as there is good continuity between each face/surface.
Thanks for any help with this!
Kieran.

GH - Help (1).gh (24.6 KB)

[DanielPiker]

The true mathematically defined Schwarz P minimal surface actually doesn’t have perfectly circular sections.
(though they are very close - the radius varies by about 0.4%)

Here’s a simple relaxation with periodic boundaries that keeps the tangency:
SchwarzP.gh (15.4 KB)
(edit - uploaded the wrong file first time)

There’s an option there for if you want to force the sections on the unit cell to be circular.

[kieran.burr (Kieran)]

@DanielPiker

The true mathematically defined Schwarz P minimal surface actually doesn’t have perfectly circular sections.

Ahh that’s interesting, thank you for letting me know!
Also, thank you for the definition!

[DanielPiker]

Also here’s a NURBS version for if you want things really smooth

schwarz_P_Nurbs.3dm (281.0 KB)

[Ke_Ma]

Hi Daniel,

Could you please share how you create the NURBS version of Schwartz P surface? Now I have a mesh model where I can specify the box size, box scale, and number of mesh faces. However, when I use the “MeshToNURB” command, the quality depends on the mesh faces…

Thank you,
Ke Ma