Voronoi relaxation (vorlax, voronax), kangaroo

Hi everyone,

I'm a "sunday grasshopper user", so forgive me if this topic has already been discussed on the forum.

I can't figure out how to obtain a relaxed voronoi diagram. Something of this sort (Andrea Mercurio's work):

Andrew Kudless used probably a similar approach to obtain his initial 2d diagram that he later mapped on the surface of his Chrysalis III project:

Vorlax on Surface from Andrew Kudless on Vimeo.

I know it must be a fairly uncomplicated Kangaroo simulation, but I just can't make this happen

I would be really grateful if someone could give me a hand.

Cheers and thanks in advance

Replies to This Discussion

Permalink Reply by Nik Willmore on March 1, 2016 at 12:26am

A custom Kangaroo 2 goal object written in simple Python. What a treasure. I had neglected this technique so far, being only vaguely aware of it.

http://www.grasshopper3d.com/group/kangaroo/forum/topics/scripting-...

Permalink Reply by Anders Holden Deleuran on March 1, 2016 at 1:37am

Not to take anything away from Marcus, but that isn't a custom goal written in Python. It uses the GHPython node-in-code functionality to call the Kangaroo2 components. It is however possible to implement the kangaroo2 assembly using GHPython AND to write custom goals. Just thought we needed to clear things up here to avoid further confusion ;)

Permalink Reply by Nik Willmore on March 1, 2016 at 2:37am

Oh, weird then. You likely saved me massive confusion when I need to learn this stuff from my teaser notes and files.

I just learned that to use Kangaroo 2 in Python from your links I must invoke EditPythonScript in Rhino then Tools>Options>Files and browse to C:>Users>Nik>AppData>Roaming>Grasshopper>Libraries to add it to the Python search path and restart Rhino.

Permalink Reply by Anders Holden Deleuran on March 1, 2016 at 2:46am

That just hard codes a path to the Grasshopper libraries folder for all RhinoPython environments (editPythonScript editor and GHPython). You can add the path "in script" as well if you prefer.

Permalink Reply by Nik Willmore on March 1, 2016 at 2:54am

Gave this error, using your TangentIncircles.gh example:

Permalink Reply by Anders Holden Deleuran on March 1, 2016 at 3:54am

See Giulio's post here.

Permalink Reply by Hyungsoo Kim on February 29, 2016 at 2:39pm

Hi.

This is a reproduction of first video clip using Kangaroo. Hope it is of some help. Best.

Attachments:

VoronoiRelaxation.gh, 21 KB

Permalink Reply by Nik Willmore on March 1, 2016 at 12:37am

Merely playing with line lengths won't also relax angles well, but will lead to crooked artifacts depending on goal length. Centroidal Voronoi I covered extensively here, using Lloyd's algorithm, which is simple finding a new center of each cell and making a new Voronoi from that. I also snuck a little bias into each cycle to get variation:

http://www.grasshopper3d.com/forum/topics/voronoi-diagram-and-bone-...

Attachments:

Centroidal Voronoi K New Aneneme Version.gh, 34 KB

Permalink Reply by Nik Willmore on March 1, 2016 at 12:44pm

Confusing at first, but you don't need the vector output component any more, I see. I've never used expressions. I switch to Python, but that hides the code.

Attachments:

Centroidal Voronoi L Expression Instead of Spaghetti.gh, 23 KB

Permalink Reply by Benoit Martel on March 1, 2016 at 4:12pm

Wow, guys you're all amazing. It's just the kind of help that I expected. Thank you Marcus, Hyungsoo and Nik, all of your advice and above all your files have been extremely helpful. I have no words to express my gratitude. I've been experimenting with your definitions (and still am), but let me extend my question.

Actually what I'm trying to achieve, is to recreate another project by Andrew Kudless, the spore lamp (I mentioned the Chrysalis at the beginning just because of the animation, which wasn't included in the Spore Lamp presentation).

Basically the spore lamp seems to me to be something like a preliminary study to the Chrysalis III project (I think it's a similar approach).

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 which then has been planarized, 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)

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 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-released?g...

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: Keep the cells planar in order to be able to loft them later and obtain those pyramidal forms, and assemble easily

Any ideas? Or maybe there's a completely different approach to that?

Attachments:

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

Permalink Reply by Ryan Whitby on March 4, 2016 at 4:20pm

Why do you need your initial vorinoi cells to be planar? If they are not planar you can extrude to a point and then truncate. Which would always produce planar faces. This would give you some more freedom for the patterning.

Permalink Reply by Benoit Martel on March 1, 2016 at 4:14pm

the relaxation files... part 1

Attachments: