Planarising a Curving Voronoi Surface

Replies to This Discussion

Permalink Reply by Canhui Chen on April 26, 2015 at 8:06pm

Hi Rawr

yes, the planarization force example on the LMS will do it for you.

it's not just for hexagons, it works with all types of polygons, explode each voronoi cells and plug their verticies  you should be fine

Permalink Reply by Rawrson on April 26, 2015 at 11:07pm

I tried and its not working and im not sure why :\

I also tried it in the one you did before for the original shape and it didn't work either

Attachments:

• B4 2 Planarise voronoi.3dm, 828 KB
• B4 2 Planarise voronoi.gh, 18 KB

Permalink Reply by Canhui Chen on April 27, 2015 at 3:21am

Hi Rawr,

I took a look, compared to hexagon, it seems kangaroo doesn't plagiarize voronoi very well.

I did some test. the script is really sensitive to all the parameters of the forces such as planarizing strength/spring stiffness and even the unit of your 3DM file setting. 

sometimes the same pattern that can be planarized in one file would stop working once something else is modified. and sometimes the force can't even planarize one single cell.

I think you can find some idea from the following post:

http://www.grasshopper3d.com/forum/topics/planar-polygons-by-using-...

 'Reply by Daniel Piker on December 17, 2013 at 10:25am

Making the faces of a polygonal mesh planar is not always possible without dramatically changing the shape of either the polygons or the surface.

When the target surface has only positive Gaussian curvature it makes things somewhat easier, but the surface in your file also has regions of negative Gaussian curvature.

To approximate a surface of negative curvature with a discrete mesh, we need the angles around some of the vertices to sum to less than 360°. This is impossible to do in a mesh with 3 hexagons around each vertex without making some of these hexagons non-convex.

There are a few possible approaches, but I would say how to automatically cover an arbitrary surface with nicely shaped planar hexagons is still an unsolved problem.'

I have uploaded some test files for you to look at. 

Attachments:

• Planarizing voronoi response.3dm, 243 KB
• Planarizing voronoi response.gh, 34 KB

Permalink Reply by Daniel Piker on April 27, 2015 at 3:40am

Try using the new version of Kangaroo for this. It is much faster and more stable, and works on the example curves you gave. An example attached (requires Kangaroo 2.01 or later).

However, I still think that starting from random Voronoi cells on a doubly curved surface and just trying to planarize them directly is not a very robust method. Sometimes it will work, but without something else guiding their shape the polygons are likely to often end up in some ugly shapes.

Attachments:

• VoronoiPlanarize.gh, 27 KB

Permalink Reply by Canhui Chen on April 27, 2015 at 8:01am

Hi Daniel,

Thank you very much for replying to this discussion,

I did some test Rawr's voronoi file again with the Kangaroo 2.01 script you attached,

and I did it cell by cell and see if Kangaroo would planarize any single polygon. My finding is that new Kangaroo can planarize some cells but not all. 

May I ask what is the factor that determines whether it can be planarize or not? And what should we avoid in the making of polygons?

Thanks in advance, your help would be much appreciated.

I have attached some images and the files.

 

Attachments:

• VoronoiPlanarize testing.gh, 15 KB
• B42Planarisevoronoi testing.3dm, 861 KB

Permalink Reply by Canhui Chen on April 27, 2015 at 3:23am

Permalink Reply by Canhui Chen on April 27, 2015 at 3:31am

Here are some advice:

work on your design, see if you can simplify it to create a smoother/simpler initial geometry that would allow the planarization force to work better.  

I don't what the design intend is, but the original voronoi cells faces are already planar, which can be trimmed easily and made buildable, and you can use plane to cut each cell's face and although they won't match up with all adjacent cell's edges, but it will sit nicely within the voronoi cell faces. and as an architect, you always have the option of designing  and developing your details to embrace these constraints instead of fighting it. 

hope that helps

Permalink Reply by Rawrson on April 27, 2015 at 8:37pm

Thanks Canhui for your help! :D Real life saver

Reason I need to make them surfaces are for further deconstruction into panels and possibly 3d printing depending on when i can finish and fablab.