voronoi/facet dome pattern relaxation on a sphere surface

Hello,

I'm trying to model something similar to the Andrew Kudless's spore lamp project. I already posted a question about the voronoi diagram relaxation here, but didn't get any response so far concerning how to do that on a sphere.

So I know already all the different approches of how to get a relaxed voronoi pattern on a free-form open surface, but still don't know how to obtain the same elegant effect on a sphere (or an ellipsoid closed surface, whatever), or how to relax the facet dome cells.

Andrew stated on his site that he used kangaroo for this project, so the Spore Lamp consists in my opinion either of a relaxed voronoi 3d diagram (b-rep, b-rep intersection) on a sphere the cells of which have been planarized later on, or more likely it is a sort of relaxed facet dome.

The trick is to:

1. obtain a nicely-balanced voronoish diagram (or facet dome cells) on a sphere

2. keep each cell/polyline planar (or force them with kangaroo to be planar) in order to move scale and loft them later on.

Here is what I have by now.(files: matsys spore lamp attempt)

That's the closest appearance that I got so far (simple move scale and loft of facet dome cells with the amount of transformations being proportional to the power of the initial cell area: bigger cell = bigger opening etc.) - with no relaxation of the diagram. But it's obviously not the same thing as the matsys design.

Here are some of my attempts of facet dome relaxation, but well, it's certainly still not the right approach, and most importantly I don't know how to keep or force the cells to be planar after the relaxation.

1. pulling vertices to a sphere - no anchor points. That obviously doesn't make sense at all, but the relaxation without anchor points gives at the beginning a pattern that is closer to what I am looking for. (files: relaxation 01)

2. pulling vertices to a sphere - two faces of the initial facet dome anchored (files: relaxation 02)

3. pulling vertices to the initial geometry (facet dome) no anchor points (files: relaxation 03)

The cell pattern of the lamp kinda looks like this:

You can find it here: http://www.grasshopper3d.com/forum/topics/kangaroo-0-095-releasedgr...

Done with Plankton (of course without the "gradient increase" appearance), but in fact not, I took a look at Daniel Parker's Plankton example files, and it's not quite the same thing. Also the cells aren't planar...

The last problem is that during the relaxation attempts that I did, the biggest initial cells became enormous, and it's not like that in the elegant project by Andrew Kudless, that I'd like to achieve.

So to sum up:

Goal no 1: Obtain an elegant voronoi /facet dome cell pattern on a sphere (or an ellipsoid surface, whatever).

Goal no 2: How to keep the cells planar in order to be able to loft them later, obtain those pyramidal forms, and assemble easily

Have you got any ideas? Or maybe there's a completely different approach to that?

Cheers, and thanks in advance

Attachments:

matsys spore lamp attempt (03.2016).3dm, 902 KB
matsys spore lamp attempt (03.2016).gh, 17 KB

Replies to This Discussion

Permalink Reply by Benoit Martel on March 2, 2016 at 12:31pm

relaxation files part 1

Attachments:

relaxation 01.3dm, 170 KB
relaxation 01.gh, 15 KB

Permalink Reply by Benoit Martel on March 2, 2016 at 12:32pm

relaxation files part 2

Attachments:

relaxation 02.3dm, 169 KB
relaxation 02.gh, 15 KB

Permalink Reply by Benoit Martel on March 2, 2016 at 12:33pm

relaxation files part 3

Attachments:

relaxation 03.3dm, 170 KB
relaxation 03.gh, 16 KB

Permalink Reply by Benoit Martel on March 3, 2016 at 1:41am

Oh yeah, almost there. At first glance it tells me that the final cells are indeed planar, so that's really cool. Gonna experiment with it this evening. You're really great buddy, I'd buy you a bear. Thank's a lot

Permalink Reply by Benoit Martel on March 3, 2016 at 3:05am

bear :) Too quick fingers

Permalink Reply by Nik Willmore on March 3, 2016 at 2:10am

Permalink Reply by Nik Willmore on March 3, 2016 at 12:15pm

The problem with Python, I realized last week, was that if you build separate little components, to get them to play nice without using the sticky variables you delighted in, which destroys their utility on the usual Grasshopper canvas, you have to read in and then recreate Grasshopper trees. That's not impossible, but really a drag. There's no auto-conversion, LIKE THERE SHOULD BE, of Python lists of lists into Grasshopper data trees, or any automatic reading in of data trees into python arrays (lists of lists), LIKE THERE SHOULD BE.

Doing everything in Python is a damn good idea, thus.

Permalink Reply by Benoit Martel on March 3, 2016 at 3:30am

Oh, you're right, I did that:

However these not cells but simple lines. But thanks anyway, your help is priceless. Will play with that this evening. Does anyone know how to force these cells to be planar?

Permalink Reply by Benoit Martel on March 3, 2016 at 11:57am

Just back home and start "trying" :) Thanks once more for your help blud (and most importantly for the time you spent to help me)!

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