Paneling a sphere or a parabolic dome with a regular pattern ?

Hello,

I’m trying to panel a regular shape (looking like a leaf :slight_smile: over the surface of a sphere and a parabolic dome; by that, I mean completely covering the surface by a closed network made up of that pattern. Unfortunately, I can’t manage to get it right. The problem seems similar to a geodesic dome, besides using a shape different than a tri or hex as a panel. Until now, I tried working with shrinkwrap and arrays, but the results are not very good. Any Ideas would be quite welcome. Thanks for your help,

qwerkus

Thanks for the tipp. Unfortunately, it only seems to shift the problem: you still need to fit the lattice to the sphere - and this time by hand, since shrinkwrap yelds the same problems as before.

Have you looked into dupliverts?

You can use duplication to scatter one object across the surface of another.

I’m trying to panel a regular shape (looking like a leaf :slight_smile: over the surface of a sphere and a parabolic dome; by that, I mean completely covering the surface by a closed network made up of that pattern

I interpret this to mean that you want to completely cover the surface of your dome with an arbitrary polygon. Mathematically this is known tessellation – a rich branch of mathematics in itself – but unfortunately not all n-gons can be used to form a periodic tessellation. A Google search for something like “mathematical tiling” or “mathematical tiling problem” will yield much more information about your issue.

Edit: also, check out this thread:
http://www.blenderartists.org/forum/showthread.php?344176-modeling-a-complex-coral-pendant-lamp

You can do with arrays or mirrors of your object that finally it is normal 6 sided box,each side full of your objects, apply all modifiers and join all together, then go to edit mode, remove doubles and To Sphere. It is a little bit distorted anyways.

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Thank you for your replies.

  1. Nice tipp JuhaW, but the distortions are too big for me.

  2. Dupliverts are a nice discovery. I’d never have scrolled down the object menu to find it, if not told here - thanks Atom. Yet, while it seems to solve the shrinkwrap distortion problem, getting a closed tiling via this option seems impossible.

  3. Thank you Sabba for clearing the terminology. It seems indeed a periodic tessalation problem, and the maths behind it are far from easy.
    a. Does anyone here know some example scripts about 3d surface periodic tiling ? The penrose scripts from the link are very intersting indeed, yet 2d - and not practicable for me.
    b. Do I understand this correctly, and the subsurf modifier IS a tri surface tessalation solution ?

Here is what I got using a mix of lattice and array, based on a geodesic (icosahedron) slice with dupliverts. I gives a general idea, but not quite there yet. Plus, the entire thing is supposed to shape a catenoidal dome, not a sphere.
Actually, it’s only a rhombus-tessalation - but I really don’t know where to start, to make it fit.