It is clearly stated to set up a producer process importing a B-rep, externally defined by some standard polygonal format, e.g. either a wave front or java3D obj file, into an input stream for our geometric pipeline. The boundary representation provided by polygons and normal must be coherently oriented. A filtering of the input file to cope with nonplanar polygons and other geometric inaccuracies may be required for generally archived geometric models implemented primarily in computer graphics. The output stream of coherently-oriented triangles, is then transformed into our twin progressive-BSP (Binary Search Partitioning) trees by the algorithmic steps described below.
A basic procedure of our method is the calculation of the inertia of triangle subsets by contraction of the pre-computed inertia of each triangle, and the Eigen decomposition of the inertia of triangle subsets to bound their shape optimally and recursively.
In case of the d-dimensional case, the shape confinement is obtained implementing 2 extremal tangent hyperplanes for each of the d eigenvectors of the Euler matrix. The intersection of the corresponding 2d hyperspaces creates the best-fitting (hyper)parallelepiped of the boundary subset included in the current cell. In 3Dimension, there is 6=2×3 such planes.
The recursive inertia-based division stops when the current cell only consists of a small number of boundary triangles. A final cell division is executed implementing the planes of the boundary triangles.