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

Support Modeling
1

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

2

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.

3

Have you looked into dupliverts?

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

4

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:

5

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.

Attachments

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6

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 ?

7

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.

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