[Algorithms] Best Fit Oriented Bounding Box

[John R. <jra...@in...>]

Ok, I realize this may be a dumb question but I suppose that is the point.
I want to do something that I believe should be really simple to do.  In
fact I have an enormous amount of reference material that implies the
solution is simple.  However, I have yet to find a solution that is
presented in a form that, to me, makes common sense.

 

I am curious, can anyone on this list direct me to a routine that does the
following:

 

void computeOBB(unsigned int vcount,const float *points,float *sides,float
*matrix);

 

This hypothetical, and eminently useful, routine would accept an array of 3d
data points and return and oriented bounding box represented as
'width,depth,height' (stored in 'sides') and a 4x4 rotation and translation
matrix where the translation is the center of the box.

 

I have found all manner of samples that compute some magical mathematical
entity called an 'eigen vector' but when I try to use the matrix  it
produces it is not valid.

 

Maybe I'm just dumb.  In fact, I know I'm dumb.  It just surprises me that
something so basic, so common, isn't just laying around in a Gem somewhere.
In fact, it probably is and I haven't found it yet.  Or, maybe the problem
is more difficult than I think and there are any number of possible 'best
fit' oriented bounding boxes possible for an arbitrary point cloud.  Maybe
this is, in fact, a really difficult optimization problem.

 

I would appreciate a code snippet and, if you can't provide one, I will just
write my own the slow, painful, dumb way.  I just hate writing code that I
figured I should find somewhere on the net as easily as a quaternion or
matrix implementation.

 

Thanks,

 

John