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 internetâŚ
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.
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+ âm+ Map Crv to Crvâ, There is one for points as well.
BTW, I think the âsolutionâ button might be inhibiting the discussion. So many times there are more than one solutionsâŚ
Hi Michael,
Thanks a lot for your help! I didnât even know about this plugin. Itâs 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 doesnât 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 
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.
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).
Ok,
It is the last time I tell you how much you rock. Itâs becoming boring! 
from now on, it is implied!
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 didnât even know about this plugin. Itâs amazing!
It is one of my favorite 
