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Topic: Two rotating coins
Replies: 0

 cfish92 Posts: 2 Registered: 6/18/13
Two rotating coins
Posted: Jun 18, 2013 7:48 PM

I'm not sure I'll be able to clearly define the problem, but here goes.

(L)
-+-
(L)

(L) is a coin with an L on it.
The L is just to give you an idea of the orientation of the coin.

-+- represents the x, y, and z axes. The x axis runs horizontally along the screen, y vertically, and z runs into/out of the screen.

Rotating a coin 180 degrees around its x axis will result in the coin looking like is has a backwards 7 on it.
Rotating it 180 degrees around its y axis will result in the coin looking like it has a backwards L on it.
Rotating it 180 degrees around its z axis will result in the coin looking like it has a 7 on it.

There are two coins, L1 and L2. L1 is centered at (0,1,0), and L2 at (0,-1,0). They won't move from these positions, just rotate around their centers.

Now for the problem. I need a method to systematically go through every possible orientation of the coins, to some arbitrary precision, P. I already have a method to do this, but I want one that doesn't check duplicate orientations. The method that does check duplicates is as follows.

For every 1/P P-degree rotations of L1 around its x axis, rotate L1 P degrees around its y axis.
For every 1/P P-degree rotations of L1 around its y axis, rotate L1 P degrees around its z axis.
For every 1/P P-degree rotations of L1 around its z axis, rotate L2 P degrees around its x axis.
For every 1/P P-degree rotations of L2 around its x axis, rotate L2 P degrees around its y axis.
For every 1/P P-degree rotations of L2 around its y axis, rotate L2 P degrees around its z axis.
After 1/P P-degree rotations of L2 around its z axis, I've seen every possible orientation of the coins relative to one another.

An example of the duplicates encountered by this method is seen when both coins are rotated any amount around their respective y axes and 0 degrees around their respective x and z axes.

Hopefully that was clear? I have a feeling the solution is something simple, but maybe just hard to figure out. I have no idea where to start, but I'm sure this kind of problem has been solved before. Can anyone help or point me in the direction of some writing on the subject?