Is there a way to create uniform, evenly sized voronoi pieces in H13?

[magneto]

That sounds like stippling

http://www.joesfer.com/?p=108

 

Does that also apply to 3d? I assume that growing on an arbitrary 3d surface might be alot harder than 2d. Not sure if the extension to 3d would be straight forward to implement.

 

the only way i can think of how you would get perfect equidistant points is to use a circle packing. but if you don´t want any approximation this could become quite challenging on arbitrary 3D meshes if it´s done right...

 

Circle packing would still require iterations, right? Also isn't circle packing very similar to point cloud and minimum position approach where points repel each other using a radius? I assume the difference is circle packing uses strictly 2d distances on the surface instead of 3d distances?

 

Thanks

[SpencerL]

Remesh SOP > Divide SOP

 

Remesh SOP creates evenly sized equilateral triangles followed by a Divide SOP and tick on 'compute dual' will give you voronoi cells.  

 

You can take it a step further and get the center pts of those cells to plug into a voronoi fracture

uniformVoronoiCells_v1.hip

[petz]

Does that also apply to 3d? I assume that growing on an arbitrary 3d surface might be alot harder than 2d. Not sure if the extension to 3d would be straight forward to implement.

 

 

Circle packing would still require iterations, right? Also isn't circle packing very similar to point cloud and minimum position approach where points repel each other using a radius? I assume the difference is circle packing uses strictly 2d distances on the surface instead of 3d distances?

 

Thanks

 

no, no, a real circle packing has nothing to do with repelling points. that would be more like a rough approximation. but as i said before, for exact circle packings on 3d surfaces rather heavy math is involved...

Edited February 5, 2014 by petz

[magneto]

Remesh SOP > Divide SOP

 

Remesh SOP creates evenly sized equilateral triangles followed by a Divide SOP and tick on 'compute dual' will give you voronoi cells.  

 

You can take it a step further and get the center pts of those cells to plug into a voronoi fracture

 

Thanks SpencerL, I tried it by creating points at the center of the voronoi cells but some points still end up inside the surface. I used the Ray SOP's Minimum Position but the points still seem to bunch up at certain places of the surface.

 

I made a comparison of it with the relaxation method, top and bottom respectively:

 

 

Still an interesting approach

 

no, no, a real circle packing have nothing to do with repelling points. that would be more like a rough approximation. but as i said before, for exact circle packings on 3d surfaces rather heavy math is involved...

 

Thanks petz. Do you know any good papers or examples of it online? When I search, lots of grasshopper links show up.

 

But the videos I found still seem to show them do this iteratively like this one:

 

 

Even if it's math intensive, it wouldn't hold you back

[petz]

 

But the videos I found still seem to show them do this iteratively like this one:

well, that is NOT a circle packing!

i guess it is just a spring based model what could easily be done in houdini by using a triangular mesh with pre-assigned restlength and some vex/vops inside a sop-solver. but at the end i don´t think it would be more correct than what christian did in his otl, probably with more iterations.

 

 

Thanks petz. Do you know any good papers or examples of it online? When I search, lots of grasshopper links show up.

do a search for kenneth stephenson and you´ll find plenty of scientific papers for circle packings in 2d and some for 3d

 

 

Even if it's math intensive, it wouldn't hold you back

oh, actually it does! i tried it once but after all i gave up because it became rather "academic" and i thought it wasn´t worth the work for what i needed it. a good approximation was enough at the end...

Edited February 5, 2014 by petz