Modeling of Schwartz P minimal surface using NURBS

Hello everyone!

I’m trying to modeling Schwartz P minimal surface using NURBS. I first built up the meshes and used the mesh vertices as interpolation points for NURBS surfaces. However, the quality seems not so good under smoothness and curvature check. Therefore, I’m wondering if there is a direct way of doing this.

In particular, I noticed that in a previous post, @DanielPiker shared a “NURBS version”, which is surprisingly very smooth! Daniel, would you mind sharing some instructions on how you build up this?

I appreciate any comments and replies!

Ke

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This may or may not be helpful for what you want, but some time ago someone here (I think MagicTeddy?) posted the method below and I used it to make a couple of things like this:

test.gh (28.0 KB)

Hello Quan,

Thank you for your help! I tried your suggestion and the smoothness and curvature looks great if a proper level of mesh refinement is chosen.

Best regards,
Ke

Hi Birk,

Thank you for sharing this! The modeling technique is surprising and new to me. I may need quadrilateral patches. Is it possible to break the patch into 3 quadrilateral patches?

Best regards,
Ke

Is it possible to break the patch into 3 quadrilateral patches?

I don’t understand your question - quadrilateral implies 4. If you combined only 3 you’d have a big gap.

Do you mean "is there a way to convert the quad patch into a tri patch, where only 3 are needed to make a complete closed surface? If so my answer is “I don’t know” because I have never tried to analyze how the quad patch is actually created. My guess is there is a way to do it - maybe.

Hi Birk,

Oh I’m sorry I didn’t make my question clear. So in the file you shared, the “patch” component gives us a surface with 6 boundaries. I mean to know if it’s possible for us to build only 1/3 of it and use some transformation operations to get the surface (as the picture below shows). I think I get your point and I will give it a try.

Thank you,
Ke