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I would like your help regarding rotations. Assuming we have a group of "n" planar surfaces within the following 3-dimensional system (image below), where the Red, Green and Blue planes are the xz, yz and xy Axes planes respectively. These planar surfaces are at random positions and have random orientations, sizes, and shapes.

System

Now imagine that we rotate all these planes as a group in all ways possible (for example 360{dimension1}*360{dimension2}*360{dimension3} = 46656000 times (assuming that our chosen rotational precision is the magnitude of 1 degree).

Among all these rotational combinations, each one of those "n" planes can be found several times to be almost (depending on our rotational precision) parallel to the xz, yz and xy planes.

My question: either using quaternions or Euler angles or other methodologies, how can I minimize the rotation checks, without lowering the rotational precision (criterion 1) and making sure at the same time that among the combinations, each plane surface within the group will be at least once, parallel to any of the 3 axes planes (e.g. if it is only parallel to yz Axes plane it is enough and we do not care about the other 2 axes) (criterion 2).

I thought of checking 90*90*90 degrees combinations but 1) I am not sure whether this will cover my criteria above and 2) maybe there is something more clever.

Gouz
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1 Answers1

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From what I understand, you want to do a number of rotations in sequence, by the the of which each plane will have been (almost) parallel to any of the (xy, xz, yz) planes?

Just rotate around the x-axis then rotate around the y-axis then the z-axis. so 360*3 rotations.

sam46
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  • The criterion 2 is not covered by this though (i.e. each plane surface within the group will be at least once, parallel to any of the 3 axes planes). – Gouz Dec 25 '17 at 18:29