looking for WEIGHTED voronoi

Hi all !

does anyone have a definition for weighted voronoi diagram (this is like a voronoi diagram, only the points have different weights = different degrees of influence) ?

https://www.youtube.com/watch?v=A0YPHFUq3GQ
somebody has done it, so i'm guessing maybe it's around here..

i would really need it fast since i need it for my thesis project and days are running by oh so fast...

thanks again!

Replies to This Discussion

Permalink Reply by Matt on February 1, 2011 at 4:13pm

Jacek,

This looks very nice and direct. When I am using your definition I get jagged lines and the approximation misses at times. Is there a way to tweak the definition to get results like what you have posted?

Permalink Reply by Jacek Jaskólski on February 2, 2011 at 11:55am

Matt,

The AW-Voronoi diagramm is "scale-aware" so the reason for the jagged output lines is probably that the weights are set too high in relation to the distances of the points.

See this example:

1. When the weights are too large, the circles intersect, and the diagram is corrupt:

(to see the circles enable preview on the circle component)

(to manipulate with the scale insert a multiply component and a slider, as shown above)

2. If you adjust the weights so that they don't intersect, you'll get a reasonable result:

3. To enhance the solution, lower the "precision factor" (here set from 1.0 to 0.25) which controls the number of divisions of the circles:

Keep in mind that the definition is just a sketch, a proof of concept rather...

Permalink Reply by Andrei Raducanu on April 17, 2010 at 8:32am

thanks to Jacek Jaskólsk for the great input!

Permalink Reply by Stephen Yoshida on April 4, 2016 at 10:44pm

I have been toying with this lately and have run into some issues. Namely the intersection command no longer calculates intersections for all combinations of breps.

I found two solutions to this:

A visual basic script c/o DR found here
A boolean union of all the cones with a simple project onto surface.

This shouldn't have taken me a day to work through given how stupid the solution was so hopefully it will work better for you reading this in the future.