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It seems that computing a Voronoi diagram with mathematical accuracy for a real-time animation is not really feasible. I found this Processing hack that takes advantage of graphic acceleration to draw an approximate Voronoi diagram. It works by drawing 3D cones at the points of interest of the diagram and rendering a top view — the regions are drawn automatically as the Voronoi edges sit on the intersections between the cones.

Using this hack, it is possible to make a real-time Voronoi diagram animation, albeit with a limited number of points and a restricted applet area. This video was rendered with 364 particles (= sum of powers of 3 from 0 to 5).

View HD video at Vimeo.

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Voronoi diagrams display areas of influence of a set of points in a plane. And they can also be used to create beautiful, organic images.

But even though constructing a Voronoi diagram geometrically seems easy, computing it efficiently can be quite hard. I’m still trying to figure out both Fortune’s and Bowyer-Watson algorithms, but as a first and quick exercise I implemented a naive algorithm with Processing and generated a short animation.

A beta version of Flash Player 10 (codename Astro) was released this week, along with a new build of the free Flex SDK 3 that allows developers to test the new Flash Player capabilities.

The following demo is a simple implementation of Cover Flow that takes advantage of the 2.5D API — all DisplayObjects now have x, y, and z properties (position, rotation, scale).

Use the arrow keys to navigate:

I developed a Cover Flow clone with Papervision3D 1.5 for the Quatro Arquitetura website a few months ago, and adapting it to the new FP10 API was really easy. Download the source code. You’ll also need Tweener.

Following the Generator.x group on Flickr I came across Apophysis, an open-source fractal flame editor (there’s a dedicated Apophysis Flickr group too). It is so easy to create beautiful images with it — too easy, one might say. The following is my first Apophysis flame (adjusted brightness/contrast in Photoshop).