624 Chapter 13 Containment Methods
hidden subexpressions that can be factored out, as was shown in [Ebe03], and leads
to even faster computation but requires that the mesh faces be triangles. Using basic
mathematics, an extension was made by [Kal] to handle polygon faces, but I will
not discuss this algorithm here.
1
The implementation of the algorithm in [Ebe03]
is found in the files named
Wm4PolyhedralMassProperties. Mirtich’s implementation
of the algorithm in [Mir96] is available online. It is simple enough to set up an
experiment to compare the execution times.
Minimum-Volume Box
Naturally, a good candidate for the best-fitting bounding box of a set of points is the
OBB of minimum volume of all those OBBs that contain the points. The construc-
tion