Polygonal mapping

Hi all,
Does anybody know an easy way to map geometry from and to polygonal surfaces?
I am working on a muqarnas dome and I am trying to map a pattern on various irregular polygon cells (3/4/5/6/7-gons).
I (think I) am pretty familiar with paneling tools but it is based on quads. Is there a way to work with polygonal mapping like the picture bellow?

The idea is to design a pattern on a regular polygon and then map it on an irregular polygon of equal sides.

any help will be appreciated


this is the closest thing I found so far in the entire internet…

Is it another one of these things that seem simple but are very difficult?

A typical thing to do (and seems so in the geometry of that Muqarnas) is to break your geometry down into a quad or triangle.

TriMap.gh (10.9 KB)

In the link you posted you can see they are also breaking down into triangles.

and actually Mesh+ has this for Mesh and curves using the same method as that article. The key is that the polylines typologies must match (same number of sides).


Search as well: Non Affine Transformations, QuadrilateralDistortion


but of course we are talking about meshes.
I was breaking down the methodology and thought about transforming the control points of curves so as to recreate them within the new polygon.

There is a component for that also in M+ “m+ Map Crv to Crv”, There is one for points as well.

BTW, I think the ‘solution’ button might be inhibiting the discussion. So many times there are more than one solutions…

Hi Michael,
Thanks a lot for your help! I didn’t even know about this plugin. It’s amazing!
still though, Map Crv to Crv only seems to work with polylines. It completely distorts curves and arcs.
I tried using map Pt to Crv to transform the control points but that doesn’t work either and it becomes complicated fast.
Do you have any advice?

remapping.gh (27.6 KB)

as for the triangular mapping, it also becomes complicated when you have a shape that extends beyond the comprising triangles (for example, some of the shapes I want to recreate, do not have polar but single symmetry thus each half extends over three triangles)

Oh great Lord, I never disregard your wisdom :slight_smile: and please keep it coming.
But following your previews advice, I try not to think like an academic (at least until the opportune moment!)

If your curves are to be transformed into shapes of degree 3 or higher afterward, then you should rebuild degree 1 or 2 curves to degree 3 or higher in advance.

remapping_re.gh (33.0 KB)


When you know a thing or two about Dark Matters notify:

The Mother Goose C# thingy is the answer to all questions (4*4 trans Matrices etc etc).


It is the last time I tell you how much you rock. It’s becoming boring! :joy:
from now on, it is implied!

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Side note: you can also use fit curve set to degree 3 to try and maintain the arc shapes.

Hi Michael,
Thanks a lot for your help! I didn’t even know about this plugin. It’s amazing!

It is one of my favorite :smiley: