that star shapes are just awesome, as i told before, i like that they are just inside the menger when cutting diagonally,
i wonder how smooth the diagonal parts are, because the rasterization may lead to pixel-stepping !?
I'm mesmerised too.
There's no pixel-stepping.
I didn't do (for example) what bib does for creating 3d models, i.e. creating little cubes from a DE formula.
I created individually all the little cubes. And I computed the intersections for the cubes crossing the plane.
Computing cross sections of a cube is a pain in the ass, by the way
.
By the way, there is at least one more interesting shape hiding in that Menger sponge.
Starting from the whole cube, you can cut away a total of four "Triangle de Menger" pieces (2nd to last picture). You end up with a regular tetrahedron that has four identical faces, each looking like the equilateral face of of a "Triangle de Menger".
How do you "cut" a cube with fours planes and end up with a tetrahedron ?
I can see how to cut it with height planes and end up with an octahedron !
I'll try to create it I think it'll be worth it.
I've also spotted a mix between "Losange de Menger" and "Triangle de Menger" I have to render it.
February 09, 2010, 03:12:51 PM
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