Subdividing Voronoi Cells

Hi all -

I've been struggling with the following:

I have a voronoi pattern with which I'd like to subdivide each cell into a split of sub cells, from the center point of the original cells. I then need to fillet (less important) and identify the center of each sub cell (more important).

The attached drawing describes the exact pattern I'm after, but after hours of attempting to replicate with Grasshopper/Geometry Gym I've had no luck. Unfortunately, my knowledge of Grasshopper is remedial, but any advice you could share would be extremely helpful. (i.e., a general explanation of how to access the individual cells and subdivide accordingly)

Thanks so much...

Attachments:

VoronoiSubdivided.png, 59 KB

Replies to This Discussion

Permalink Reply by Daniel Piker on March 13, 2011 at 2:13pm

No need for any plugins to do this.

You can explode a curve into its vertices and average them to get the centroid (the only thing you need to watch out for is that when you explode a closed curve, you'll get the start/end point twice, so you need to split it off first).

Attachments:

vorosubd.ghx, 293 KB

Permalink Reply by Anthony on March 13, 2011 at 2:19pm

Extremely helpful! Thank you Daniel.

Permalink Reply by David Rutten on March 13, 2011 at 2:20pm

Hi Anthony,

voronoi cells tend to sometimes have very short edge segments, this will result in very sharp triangles. Still, I think the attached is someway towards your goal.

As for the cell center points, I used the midpoint of the boundingbox. Another way to compute the center point would be to take the average of all corner points. Another way still would be to measure the Area Centroid.

David Rutten

david@mcneel.com

Poprad, Slovakia

Attachments:

VoronoiCellFracture.ghx, 87 KB

Permalink Reply by Danny Boyes on March 13, 2011 at 3:13pm

very nice use of the extrude to a point. I must remember that!

Permalink Reply by Danny Boyes on March 13, 2011 at 3:11pm

For what its worth here's my attempt (without offsetting and filleting)

Permalink Reply by Jon Mirtschin on March 14, 2011 at 4:41am

If you wish to continue using Geometry Gym, here's my quick attempt at this, you will need latest version of StructDrawRhino, http://www.geometrygym.com/downloads Some improvements to the definition (such as more parallel edges) should be possible without too much difficulty.

The filleting around short edges is certainly one good reason for using my routine (I've spent more than a couple of hours coding that aspect of it).

Permalink Reply by RWNB on March 14, 2011 at 1:32pm

dear danny,

i have taken your example as an opportunity
to try a certain urban parcelling.
output for this consideration are the voronoicells.
this results in the polysurface (development sites).
by the creation of the parcelling
i'm unfortunately not further with this.

maybe a little help

thanks

Attachments:

SubdivVoronoi.3dm, 119 KB
SubdivVoronoi.ghx, 421 KB

Permalink Reply by Danny Boyes on March 14, 2011 at 2:02pm

Hi Rassul,

I'm not sure that follow what you are trying to achieve.

Permalink Reply by RWNB on March 14, 2011 at 2:13pm

dear danny,

I have also the impression that it is a dead end.

Permalink Reply by Philipp S on March 16, 2014 at 10:23am

Hey Guys,

I am new in Grasshopper and I have a question to almost the same issue. I tried to subdivide 2D Voronoi cells into triangels like you did it before. In the next step I want to subdivide this created trangels into three new triangels by dividing the triangels by their center point. But I don't get the center point.

I hope you can help me.

Thank you very much.

Permalink Reply by Philipp S on March 19, 2014 at 9:10am

Nobody can help me? I'm sorry, but I don't know how to find the centerpoint. Maybe someone can help me now.

Attachments: