Per-pixel displacement mapping algorithms such as [Policarpo et al. 2005; Tatarchuk 2006] became very popular recently as they can take advantage of the parallel nature of programmable GPU pipelines and render detailed surfaces at highly interactive rates. These approaches exhibit pleasing visual quality and render motion parallax effects, however, most of them suffer from lack of correct silhouettes. We perform ray-surface intersection in a volume given by prisms extruded from the input mesh triangles in the direction of the normal. The displaced surface is embedded in the volume of these prisms, bounded by a top and a bottom triangle and three bilinear patches (slabs). [Hirche et al. 2004] propose to triangulate the slabs and split the prisms into three tetrahedra. A consistent triangulation of adjacent prisms ensures that no gaps between tetrahedra exist and no tetrahedra overlap. Ray marching through tetrahedra is then straightforward as texture gradients (for marching along the ray) can be computed per tetrahedron.