Creating an appropriate mesh is one of demanding tasks of many global illumination algorithms. Discontinuity meshing proved to diminish artifacts caused by other meshing strategies. Since naive discontinuity meshing would produce a great amount of geometric computations, accelerating techniques are usually involved. In this paper, we present results obtained with help of k-discrete orientation polytopes (k-DOPs) and oriented bounding boxes (OBBs) and compare them to previously used accelerating schemes like voxels, BSP-trees and octrees.