nodename » Delaunay http://nodename.com/blog Wed, 11 Apr 2012 20:39:41 +0000 en hourly 1 http://wordpress.org/?v=3.0 Blobs in Games: Polygon Map Generation, by Amit Patel http://nodename.com/blog/2010/10/02/blobs-in-games-polygon-map-generation-by-amit-patel/ http://nodename.com/blog/2010/10/02/blobs-in-games-polygon-map-generation-by-amit-patel/#comments Sat, 02 Oct 2010 23:20:07 +0000 alan http://nodename.com/blog/?p=670 Amit Patel has published a great article on map generation based upon Voronoi polygons. He generates the Voronoi polygons using my as3delaunay library. But the polygons are just the beginning of his process…

Try the demo! And — yum — see the . . . → Read More: Blobs in Games: Polygon Map Generation, by Amit Patel]]> Amit Patel has published a great article on map generation based upon Voronoi polygons. He generates the Voronoi polygons using my as3delaunay library. But the polygons are just the beginning of his process…

Try the demo! And — yum — see the source code!

]]> http://nodename.com/blog/2010/10/02/blobs-in-games-polygon-map-generation-by-amit-patel/feed/ 1 Roll Over, Delaunay: Voronoi Library Goes Open-Source http://nodename.com/blog/2009/12/03/roll-over-delaunay-voronoi-library-goes-open-source/ http://nodename.com/blog/2009/12/03/roll-over-delaunay-voronoi-library-goes-open-source/#comments Thu, 03 Dec 2009 04:28:55 +0000 alan http://nodename.com/blog/?p=377 . . . → Read More: Roll Over, Delaunay: Voronoi Library Goes Open-Source]]> A few people have asked for the code for my Voronoi Toy. I haven’t made the entire program public yet, but I have released the underlying as3delaunay library, which I originally ported from Steven Fortune’s C implementation of his plane-sweep algorithm.

In addition to the Voronoi diagram and the Delaunay triangulation, the library also provides the convex hull, minimum and maximum spanning trees, and several other related geometric entities.

You can download the source and compile it, or just get the compiled swc from the downloads page.

So far I have had two users, JakeTastic (Voronoi shattering complete!) and Li (Faster Voronoi Noise); thanks to them both for jumping on, and to Jake also for finding the two bugs :-)

There’s no documentation yet, but there is a test suite which incorporates an example of using the library for nearest-site queries, and there’s also a mailing list, where I’ve archived Fortune’s paper and his C code, as well as a growing page of interesting links related to Voronoi/Delaunay.

The library is hosted on github, so YOU can conveniently modify, fix, or enhance it!

Roadmap for possible enhancements:
Generalize to support weighted Voronoi diagrams, both additive and multiplicative (This is described in Fortune’s paper)
Generalize to use an arbitrary polygon as a boundary
… what else?

]]> http://nodename.com/blog/2009/12/03/roll-over-delaunay-voronoi-library-goes-open-source/feed/ 17 Mona Voronita http://nodename.com/blog/2009/05/18/mona-voronita/ http://nodename.com/blog/2009/05/18/mona-voronita/#comments Tue, 19 May 2009 02:39:45 +0000 alan http://nodename.com/blog/?p=139 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 . . . → Read More: Mona Voronita]]> 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!

]]> http://nodename.com/blog/2009/05/18/mona-voronita/feed/ 2 The Name of the Node: Image Fill with Spanning Trees http://nodename.com/blog/2009/05/12/the-name-of-the-node/ http://nodename.com/blog/2009/05/12/the-name-of-the-node/#comments Tue, 12 May 2009 18:31:19 +0000 alan http://nodename.com/blog/?p=118 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 . . . → Read More: The Name of the Node: Image Fill with Spanning Trees]]> 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.

]]> http://nodename.com/blog/2009/05/12/the-name-of-the-node/feed/ 3 Relaxing in the Plane: A Voronoi Toy http://nodename.com/blog/2009/05/11/a-voronoi-toy/ http://nodename.com/blog/2009/05/11/a-voronoi-toy/#comments Tue, 12 May 2009 01:43:11 +0000 alan http://nodename.com/blog/?p=68 . . . → Read More: Relaxing in the Plane: A Voronoi Toy]]> 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.)

]]> http://nodename.com/blog/2009/05/11/a-voronoi-toy/feed/ 9 Have you seen this man? http://nodename.com/blog/2008/10/12/have-you-seen-this-man/ http://nodename.com/blog/2008/10/12/have-you-seen-this-man/#comments Mon, 13 Oct 2008 03:40:14 +0000 alan http://nodename.com/blog/?p=66 . . . → Read More: Have you seen this man?]]> He supports an expansion of stem-cell research. He’s made nuclear nonproliferation a priority. He favors combating global warming with a “cap and trade” system. He supported a bill to expand the government’s eavesdropping authority and to protect telephone companies that cooperated with the program from being sued. He embraces the idea of continuing Bush’s faith-based initiative. He said he was picked last on a sports team as a boy. He said it taught him to work hard and persevere. His favorite childhood Halloween costume was a pirate.


Click on the image to open AstroMorpher in a new window (requires Flash Player 10).

The program uses Nicolas Barradeau’s Delaunay triangulation code.

Download the source archive, which can be imported as a project into Flex Builder 3, or just opened normally to read the code.

Work with Flash 10 in Flex Builder 3

]]> http://nodename.com/blog/2008/10/12/have-you-seen-this-man/feed/ 3