Abstract: This paper presents a treatment of first-order discontinuities (DI) that arise in discontinuity meshes. An algorithm is described that, given a planar DI discontinuity surface in a polyhedral scene, computes the corresponding discontinuity curves on the faces of the scene. A method is described to efficiently update the backprojection across a DI discontinuity curve. An alternative update method is presented which is novel and numerically robust.