Proportional Hexagon on circurum Strip-Surface

I am trying to apply Hexagon-Pattern (lunchbox addon) onto a Surface as shown.

The Problem is the Proportion of Hexagon Shape. Namely the deformation of hexagon is getting larger in the area of the center.
How can I keep hexagon in nice proportion( approx. 1 to 1 in UV direction)
It would be appreciated if there are any elegant way to fix the issue.

GH file uploaded.

Proportional (7.6 KB)


you either don’t use a mapping based on surface parameterization or you change the parameterization of the surface below which is actually harder in my opinion. Lunchbox is way too trivial for many use-cases. You need to create this pattern differently, ideally by being able to control the locations of the rows.

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I agree with @TomTom that using the surface parametrization would be a harder way to go about this than creating the pattern separately.
For example, make a spiral with polar coordinates, take the Voronoi cells, then trim them to fit your surface. (6.8 KB)


wow, brilliant method! Althoug I was think about circle-packing or rheotomic approach…