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

polygonal

this is the closest thing I found so far in the entire internet…
https://www.andrew.cmu.edu/user/vasua/FinalAssignmentWriteup/FinalAssignmentWriteup.html

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).

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Search as well: Non Affine Transformations, QuadrilateralDistortion

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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)

edit:
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)

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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).

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Ok,
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: