# Equilateral triangles

So I am trying to make a double curved surface out of equilateral triangles according to this post: polygon composition with hinges – Grasshopper
In this example you can drag the triangle to create a (curved) surface. Is there a way to, instead of dragging the triangles in a particular shape, to have the triangles generated to follow an already curved shape? So it kind of mimics the shape with its boundaries as accurate as possible. Any suggestion is helpful, thanks in advance.

ps.: attached file is the one out of the post mentioned above.
TriangulateSurface2.gh (14.1 KB)

They probably won’t be equilateral triangles if you want them to follow a curved surface.

There’s quite a lot of discussion on this on this forum… What tends to happen if you approximate a doubly curved surface with triangles is that they are nearly equilateral but not quite.

Similar discussions have been about trying to make a doubly curved surface from identical hexagons but in reality you need irregular hexagons and pentagons.

This is a rabbit hole of mesh theories and maths that I have followed for years but am still unqualified to explain!

What you are probably thinking is that you can make a load of equilateral triangles and then assemble them into a cool shape. Its way more complicated but really interesting.

I started with geodesic domes… the most basic is an icosohedron which is a 20 sided shape made of 20 equilateral triangles. All the points lie on a sphere. You can split these equilateral triangles by dividing their edges equally and projecting those points out onto a sphere but then the triangles are no longer equilateral.

Aah I see, sounds like something which is beyond my cabalities. Still a super interesting topic nevertheless. Thanks for your reply!