Understanding Voronoi!

Rigging
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I’ve recently regained my interest in math and fun stuff like it (Thanks Kahn Academy!), and todays concept was voronoi algorithms/diagrams/regions/panties.
I read about it on a few different places and got the gist of it. I started thinking and doing simple drawings in my notepad. But I couldn’t verify that I had understood it so I tried to explain what I had drawn to some of my more technical friends. I am certain they now believe I am drunk.

What I was trying to say was, if I have a square plane and put a point in the middle, what would the voronoi regions look like. I wanted to hear if they described what I had gotten.
They did not. They told me off. Apparently you can’t calculate it with just one point and yada yada.

I obviously meant a point in the middle and the corners are points as well. It will give you a rotated square touching all sides of the plane.

Now, why am I rambling about this here? Partly because I’m happy I got it and I’m one step closer to writing a shatter script. But mostly because I found this nifty tool online to test it! I felt a warm geeky pride go through my body when I clicked out the dots and saw the lines be drawn just where I expected :slight_smile:

The java applet is at the bottom

(Mods, if this is to rambly and off topic, feel free to move/delete the thread)

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I remember reading about voronoi patterns a year or so back but I couldn’t remember what they were, but once I clicked the link it all came back to me. I think it’s quite simple to explain in that between each point, an area must be divided between them equally, and as you add in points, this area must be divided amoungst them.

Anyway, thanks for the link and that little bit of info today. I always love to see examples of maths in nature (I really like vhart’s videos on Youtube for that reason)!

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@Demno: Hi! I wrote an article about the creation of voronoi polygon using maxscript…it will be published before this summer in a book about game development tools. If you can’t wait and need help, just write a line :slight_smile:

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in the meantime, there’s always this site http://www.cgal.org/
(and the associated book) albeit on a more academic approach.

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Great posts on voronoi for shattering and blue noise on Jose’s blog:

http://www.joesfer.com/?tag=voronoi