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November 24, 2005
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A quick experiment in the 4-dimensional rotation of a hypercube.

A hypercube (or tesseract) is the 4-dimensional analogue of a cube. It has 16 corners, 36 edges, and 24 sides. All corners are right angles although they may seem like acute or obtuse angles when seem from a different viewpoint, just as the corners of a cube may seem sharper or wider depending on your viewpoint.

Rotation is achieved through a simple 4x4 transformation matrix which allows the hypercube to be rotated along a single plane at a time. In 3-dimensional rotation, rotation usually occurs around a linear axis but 4-dimensional rotation occurs around a planar axis.

You can check/uncheck the box to see the hypercube with solid sides or empty sides. Click on "Perspective" to select different methods of display.
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:icondovsherman:
DovSherman Featured By Owner Nov 26, 2005  Professional Digital Artist
I was thinking about that but I'm not sure how the interface would work. In a 3-dimensional object, there are only three axes of rotation. But with a 4-dimensional object, there are SIX planes of rotation. So you'd need to be able to move your mouse in more than 3-dimensions to click-and-drag rotation. I'd have to do something more crude than a single click-and-drag like six slider controls.
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:icone-tahn:
e-tahn Featured By Owner Nov 24, 2005  Professional General Artist
sooo insane!!!
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:iconsorrowsdream:
sorrowsdream Featured By Owner Nov 24, 2005  Hobbyist Digital Artist
Wow.... Just Wow...Nicely done.
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:iconroux:
roux Featured By Owner Nov 24, 2005
@_@
i love such stuff
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