Click on the image to see 1000 Voronoi points in motion. Keyboard controls as in the Voronoi Toy.

If the popup won’t go away when you click the X, click in the movie and hit “s” to stop the moving points.

I couldn’t resist, Frank!

Jim Armstrong, the Flash community’s primary math whiz, has encouraged me in the past, and today he did so publicly. I’m very grateful for this recommendation.

Here’s the crass part: I’m available for contract or permanent work, locally or remotely. I live in New York City. CV, references, and samples of my work are available. Please hit the Contact link to get in touch.

See you in Minneapolis?

And we’ll now return to tech talk…

I’ve rendered some images using the Voronoi Toy from my last post.

I’ve used my logo 結 (as in 結點 “node”) as the input image, run Sakri Rosenstrom’s image segmentation algorithm on it, dropped 10,000 random points into the segments, and drawn the minimum spanning tree of each set of points, thus creating a sort of space-filling tree.

The idea for this kind of fill comes from Mario Klingemann’s presentation at FITC.

Click on each image for a larger version.

relax, v.
10. Chiefly Physics. To return towards a state of equilibrium. (OED)

Here’s the planar analog of my earlier post Distributing Points on the Sphere. This time I’ve ported Steve Fortune’s C implementation of his sweepline algorithm for Voronoi diagrams, and applied Lloyd’s algorithm to change the input values (the point locations) iteratively so the output function (the stress or energy) approaches a minimum. Lloyd’s algorithm works by repeatedly computing the Voronoi diagram and moving each point to the centroid of its region. Soon the points converge to an even distribution. You can see this in action by starting the app by clicking on the image, and then pressing the “r” key.

While I was at it I built out some more of the basic Voronoi-related geometric structures: the Delaunay triangulation, the convex hull, the onion, and the minimum spanning tree.

I’ve had fun playing with this app, changing the display options while moving, adding, or removing points. I hope you enjoy it.

(The app is built for Flash Player 10.)