By Guo L.-T.
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Full pre-integration is introduced by R¨ ottger et al.  in the context of the projected-tetrahedra algorithm. Their observation is that barycentric interpolation is the natural interpolation scheme for tetrahedra. 3 Volume Rendering Approaches 31 L sf sb slab Fig. 7. Slab-based representation for pre-integrated texture-based volume rendering. The scalar data values at the entry and the exit point of the viewing ray are denoted by s f and s b , respectively. , no error is introduced by the assumption of a piecewise linear interpolation along light rays.
For example, Weiler and co-workers [458, 460] describe a GPU approach that allows us to render a tetrahedron without an explicit decomposition into triangles. The basic idea is to adopt GPU ray casting (see Sect. 3) for a single tetrahedron, whose implementation primarily relies on fragment programs. Wylie et al.  discuss an alternative approach for a GPU-based projected-tetrahedra algorithm based on vertex processing. Although view-independent scan conversion works well for displaying tetrahedral cells, it still requires spatial sorting (step 1 of the projected-tetrahedra algorithm) when a non-commutative compositing scheme is applied.
15). First, the depth buﬀer is cleared and then ﬁlled with the depth values zfront for the ﬁrst boundary by rendering the front faces of the clip geometry. Afterwards, volume rendering is accomplished with the depth test set to “less” and without modifying the depth buﬀer. 42 2 Visualization of 3D Scalar Fields rendered in second pass eye convex clip object rendered in first pass rectangular volume IMAGE: WEISKOPF, ENGEL, ERTL  c 2003 IEEE Fig. 15. Illustration of depth-based two-pass rendering for a convex clip geometry Single-Pass Rendering for Convex Volume Probing Based on Depth Clipping A volume probing approach for a convex clip object is now considered.
3-restricted connectivity of graphs with given girth by Guo L.-T.