This report describes an algorithm that computes the configuration space of a polyhedron with planar motion relative to a fixed polyhedral obstacle. The algorithm decomposes the configuration space along the orientation axis into intervals of cross-sections with the same structure. It computes the angles where the structure changes. In each interval between two changes, it computes the (fixed) free-space structure from a representative cross-section then lifts the contact curves to construct an adjacency graph of contact patches.