Minimal surfaces

Ah, okay I see.
It’s true that making a starting mesh isn’t always easy, however you are going to relax it.
One advantage of the relaxation with remeshing though, is that as long as your starting mesh has the right topology, it doesn’t matter too much the quality of the triangles, they won’t distort the result.

Anyway, perhaps this discussion is diverging a bit, so to get back to the original topic of this sculpture-
This page by the same artist gives some clues. It doesn’t cover this stone piece specifically, but some relevant ideas are covered:
https://www.mi.sanu.ac.rs/vismath/nat/index.html

According to the description of the piece here: http://www.ams.org/publicoutreach/math-imagery/2009-Exhibition
‘The form is based on the shape of the soap film minimal surface on a configuration of a wire trefoil knot’

Figure 8b in the first link shows a Seifert surface that looks similar to the piece we are talking about. It’s a trefoil knot, but arranged so that instead of the usual 3 leaf arrangement, it has 2-fold rotational symmetry.

To make a starting mesh for a Seifert surface, we can draw a polyline of the knot, then fill in the areas in plan with faces, which turn vertical wherever the curve crosses itself:



Once we subdivide/remesh/relax this, we get something like this:

Which starts to look a little like the sculpture.

However… a minimal surface is something with zero thickness, and the sculpture doesn’t look like simply an offset of this. What’s more, if you try and trace the sharp edge of the sculpture around, it doesn’t actually look like it is knotted at all (which is why my initial thought was that it looked like some boolean operation on linked tori). So there is something else going on there…
image

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