The gyroid is a favourite surface of mine and I’ve played with it a lot over the years.
Generating it as a level set mesh like in the tutorial you link is very heavy though.
I agree remeshing would be of limited use here if you’re ultimately after a surface - you could improve the triangle quality compared to the isosurface, but you’d still have a mesh with lots of triangles.
For other triply periodic minimal surfaces, like the Schwarz P and D surfaces, there are well known quad representations which can be used as a basis for a subdivision surface.
The gyroid is trickier though as it doesn’t have any straight lines or reflectional symmetry (which I think is also one of the things that make it such a fascinating object).
I actually discovered a few years ago a discretization of the gyroid into only 2 shapes of planar quad, which as far as I could find has never been documented before.
(Note that creating a simple planar quad form like this is not an easy or automated process - it took me years to find this one)
gyroidplanarquadunit.3dm (63.8 KB)
This can be used as the basis for a SubD version of the surface
If you array this unit with the box shown as the unit cell, join it (and run AlignVertices to make sure all vertices are connected), you can then convert it into a SubD to get a file which is lightweight and smooth.
