Wolfram|Alpha Spikey

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titanmiller

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Description

I did this to see how accurate of a point cloud I could get with a complicated geometric shape.

Affectionately known as the "Wolfram|Alpha spikey," this 3D object has many interesting mathematical properties. It is a polyhedron with 60 identical faces, 62 verticies and 120 edges, known as a rhombic hexecontahedron. Its 20 outer points form the verticies of a regular dodecahedron; its 12 inner points form the verticies of a regular icosahedron. Each of its faces is a golden rhombus, with four equal sides, and diagonals with lengths in the golden ration of ~1.618. One might think that such an elegant geometrical object must have been known since antiquity, but in fact is seems to have first been explicitly constructed only in 1940, and rediscovered several times even more recently. It can however be produced by stellating the rhombic triacontahedron which was constructed by Kepler around 1611. When 12 of these triacontahedra are packed together (as in some natural quasicrystals), they leave a gap in the center that is in the shape of the Wolfram|Alpha log.
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Views 417
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Photos 127
Date Created 1/15/2011

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Comments

(2)
NateLawrence Over 1 year ago
The shape poses absolutely no challenge for Photosynth, however the severe lack of any real non-repeating texture (think unique speckled pattern over the entire surface of the spikey) makes its point cloud less than what it could be.

By contrast, you may notice that the texture of the wall behind the polyhedron lights up in the point cloud. Generally speaking plain white surfaces are not the most synthy subjects, simply because they tend to overexpose easily, but in this case your photos are largely exposed such that the wall's texture is within detection range for Photosynth's feature descriptor algorithms. My brother once synthed a brilliant white snowman, so it's more than possible to tackle white subjects, given reasonable exposure.
NateLawrence Over 1 year ago
Although the paper that the spikey is constructed of has texture, it is largely not in tight enough focus or of large enough scale in the frame for Photosynth to track it and its repetitiveness would likely prove problematic, even if you had closer shots of the spikey's surface.

Spraying the spikey all over with a subtle dusting of paint with a toothbrush or similar brush capable of flicking the paint in speckles would likely bring out the surface of the spikey in full force, given good crisp shots of the speckles.

In any case, I hope I'm not coming off as a know it all but rather a voice of some experience with Photosynth. I'm fond of Wolfram|Alpha's logo and was pleased to see it around these parts.

Cheers!
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