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

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:

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:

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