[vtkusers] Is the Oriented Bounded Box unique?

[Rasmus Reinhold Paulsen]

Hi Anwar

The OBB tree is explained in detail in a paper found at UNC:

http://www.cs.unc.edu/~geom/OBB/OBBT.html

(under the paper section).

The first level of the OBB tree is computed in the following way:
-Calculate the eigenvecs of the point cloud.
-Use these eigenvectors as a new coordinate system
-Project all points on the axis of this coordinate system and find the min
and max values of these projections.
-Use these min and max values to generate a box following the axis of the
new coordinate system.
-Voila! That is the first level of the OBB tree.
-I believe that this box is as unique as the eigenvectors of the point
cloud...

Later this box is split in half and the points in each of these halves are
processed recursively.

Please correct me if I am horribly wrong!

Regards
Rasmus

On Tue, 7 May 2002, Anwar Upal wrote:

> I know that OBB computes the eigenvectors and eigenvalues of 3D data but I 
> do not know exactly what that implies...  For example, for a set of 3D 
> points, does the OBB compute a unique bounding box (is it compute a minimum 
> volume or a minimum dimension box)?  Or is there many possibilities and it 
> picks one out of many?  How does it keep track of the orientation?