An algorithm for splitting an orthogonal polyhedron with an orthogonal polyplane

Splitting of an orthogonal polyhedron is an essential operation in many orthogonal polyhedron related problems. This paper proposes an algorithm for splitting an orthogonal polyhedron with an orthogonal polyplane. There are four major steps of this algorithm: 1) sort the vertices of the orthogonal polyhedron in ABC-sorted order; 2) calculate the vertices at the intersection between the orthogonal polyhedron and the polyplane; 3) find the polyplane vertices, and 4) group the updated vertices into two groups of orthogonal polyhedra. Overall, the algorithm performs with O(n log n) time where n is the number of vertices of a given orthogonal polyhedron.