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3dpointsbounding

3D bounding box fully defined by min, max and center point?

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.

Solution

  • 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.