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#ActualRavyne

Posted 05 November 2013 - 12:33 PM

Its not really that there's no rotation necessarily. The vectors are co-linear only if they point in exactly the same direction or exactly opposite directions. In the first case, no rotation is needed to get from a to be since they're the same, in the second case you need to rotate 180 degrees -- what the cross product is really telling you here is that all axes of rotation are equally good -- there is no shortest rotation from a to b, so the choice is arbitrary. You can handle that particular rotation as a special case and choose a fixed axis (probably the one linearly independent of the two primary axes of play, if applicable), choose any suitable axis of rotation at random, or one which best reflects any constraints of the physical object in question, if applicable.

 

[edit] Strikethrough: Realized a fixed axis isn't going to cut it for arbitrary rotations.


#1Ravyne

Posted 04 November 2013 - 02:58 PM

Its not really that there's no rotation necessarily. The vectors are co-linear only if they point in exactly the same direction or exactly opposite directions. In the first case, no rotation is needed to get from a to be since they're the same, in the second case you need to rotate 180 degrees -- what the cross product is really telling you here is that all axes of rotation are equally good -- there is no shortest rotation from a to b, so the choice is arbitrary. You can handle that particular rotation as a special case and choose a fixed axis (probably the one linearly independent of the two primary axes of play, if applicable), choose an axis of rotation at random, or one which best reflects any constraints of the physical object in question, if applicable. 


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