From AABB to bounding sphere

[shuipi]

Everyone says the method of obtaining a bounding sphere by using the AABB's center as the sphere center and half diagnal length as the radius will not give an optimal bounding sphere.

But I can't think of a case where it's not optimal. It looks pretty optimal to me: the radius can't be any smaller otherwise one of the AABBs' corner vertices will come out.

 

[shuipi]

Ah never mind. I just realized that as long as the enclosed mesh doesn't have vertices coinciding with the AABB's vertices then this method returns bigger than necessary bounding sphere.

 

[Andrew Lauritzen]

Yeah it's an annoyingly difficult problem (even in 2D) if you want a "perfect" solution, but several reasonable heuristics work ok in practice.

 

[sebbbi]

Or you can just use some library to calculate the smallest enclosing circles and spheres for you (assuming you have access to the vertex set of the object). A quick google search gave me this hit at least (GNU General Public License): http://www.inf.ethz.ch/personal/gaertner/miniball.html