In a previous work, orthogonal polyhedra were proposed as geometric bounds in Constructice Solid Geometry (CSG). CSG primitives were approximated by orthogonal polyhedra, and the orthogonal bound of the object was obtained by applying the corresponding boolean algebra. Also, a specific model for orthogonal polyhedra was presented, the Extreme Vertices Model (EVM). EVM allows simple and robust algorithms for performing the most usual demanding tasks such as closed and regularized boolean operations as presented in the mentioned previous work, and the remaining set membership classification algorithms as will be shown in this paper. In this work we continue with this proposal in three directions. First, we extend the EVM domain in order to represent pseudomanifold orthogonal polyhedra; then we discuss the formal properties of EVM, and finally we present and analyze set membership classification algorithms on EVM.