Gyroid Approximation

Hello,

I'm trying to approximate de gyroid minimal surface using a technique that uses curves inside a cube to create a "unit cell" of the gyroid and then makes an assembly.

My problem is that I cannot get rid of discontinuities arisen from the connections between that unit cells. And I cannot create a minimal surface from that.

I'm not an expert in these kind of surfaces. So I can't figure out a better way to do that.

My guess is that my curves aren't the right kind of curves to be used to make the unit cell surface. Or, as I'm using the "patch" component, it could be that this component is not the right method to create the surface.

I've tried to create that with two types of curves: the arc and the interpolated curves with tangents.

Those do not work properly. So how could I make a minimal surface from this? What I'm doing wrong? Is there a better way to assembly the gyroid as NURBS?

Attached definition below.

Thank you.

Attachments:

Gyroid.gh, 46 KB

Replies to This Discussion

Permalink Reply by Dimitrios Polychron on December 2, 2014 at 12:30am

Uendel,

the grasshopper file uploaded will not work with my version of Grasshopper, wish I could help tho. The image you have included with the primitive surface used in the Gyroid was incredibly helpful for me to visualize the form, and I thank you for that. would it be possible to include a baked rhino file for further visualization?

BTW you can always use a command within rhino called MERGE FACES, or MERGE EDGES...It works well with surfaces that have proper tangents, but when the tangents are not PERFECT, it won't work...

Is it possible to make your smallest unit slightly larger? whether by lofting a larger set of curves together or just patching a wireframe? Then you would have less tangents and therefore less creases.

Permalink Reply by Igor on December 2, 2014 at 12:33pm

Gyroid cos(x) * sin(y) + cos(y) * sin(z) + cos(z) * sin(x)=0

From this definition the shape of edge for example at z=Pi will be y=arcsin(sin(x)/cos(x)) 0<x<=Pi. If Patch tool correct make trimmed surface from such edges (tangent trimmed surfaces each ather at the edges) you will create right Gyroid.

IMHO.....

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