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My question is if a 3D box is/can be fully defined by a min, max and center point even if all rotations (around x,y and z axis) in this 3D space are possible?

If so, can you give me a hint on how I could start calculating one of the other cornerpoints of this box? Thanks.

Bless
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Tommekewatdoedenu
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1 Answers1

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Assuming that these three points are co-linear and equidistant, we can in fact rotate the box around the line formed by these points:

enter image description here

So the answer is no.

However, one can still represent the box with the same number of coordinates (9):

  • 3 for the center point
  • 3 for the scaling in each principal direction
  • 3 for the rotation of the box

The rotation can be represented by:

  1. Euler angles: beware of Gimbal lock!
  2. Implicit axis-angle: a vector with magnitude equal to the clockwise (or anti-clockwise) rotation around an axis parallel / anti-parallel to it.
meowgoesthedog
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