From Ohm

# Tetrahedra Decomposition

Problem: $2^8$ cases to take into account.
Goal: Simplification of cut geometry by reduction of unit volume to tetrahedra.
Solution: Every hexahedron (unit cube or brick with 6 faces and 8 corner points) can be decomposed into 5 tetrahedra with 4 faces and 4 corner points.

Decomposition of the volume with corner points $P_0..P_7$ into a central tetrahedron (blue)

• $P_0, P_3, P_5, P_6$

and 4 neighbouring tetrahedra (gray)

• $P_0, P_5, P_3, P_1$
• $P_3, P_6, P_0, P_2$
• $P_0, P_6, P_5, P_4$
• $P_3, P_5, P_6, P_7$