Minimalismus II: voronoiBall

Build­ing this con­struct with ana­lyt­i­cal geom­e­try would’ve been a night­mare: a sphere divided in Voronoi cells. So we cheated. The cells are cre­ated by expand­ing a thou­sand ran­dom points from each cen­ter a small step at a time. Each step the dis­tance of the mov­ing point to all cen­ters is cal­cu­lated. If the cen­ter of ori­gin is no longer the clos­est, the point stops mov­ing. The algo­rithm takes as many steps as nec­es­sary to bring all points to a stop, or until the points cross a bound­ary sur­face (in this case a sphere).

The sta­tic point cloud for each cen­ter is then ren­dered as a con­vex hull. Just like in the Delau­nay flock, I used the QuickHull3D pack­age for the cal­cu­la­tion of the con­vex hull. The result­ing image is only an approx­i­ma­tion, but I find the rough edges rather nice.

voronoi ball

voronoi ball

voronoi ball

voronoi ball

voronoi ball

This entry was posted on Sunday, February 22nd, 2009 at 21:27 and is filed under Blog, Portfolio, Processing and tagged with , , , , . You can follow any responses to this entry through the RSS 2.0 feed.

4 Responses to “Minimalismus II: voronoiBall”

  1. subblue says:
    February 23, 2009 at 00:32

    Very impres­sive. I guess a tech­nique like this would be good for sim­u­lat­ing the shat­ter­ing of a 3D object.

  2. Frederik says:
    February 23, 2009 at 00:35

    Thanks! If you could find an effi­cient way to keep the cells con­fined to a cer­tain bound­ary sur­face, it would def­i­nitely make a nice shat­ter technique.

  3. introspector says:
    February 24, 2009 at 22:12

    nice!

    thanks for show­ing me how to use this quickhull3d package.

  4. Frederik says:
    February 25, 2009 at 00:24

    Hi Corneel, you’re wel­come ;-) Some­how I man­aged to miss your autopoiesis sketch, amaz­ing stuff!

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