In this section, I discuss the process of determining how the cells in a volumetric model project onto a viewing screen. As discussed in Section 1.2, in a graphics hardware pipeline, this process is the geometric processing. Consequently, when implementing volume rendering on graphics hardware, we usually perform cell-ray intersections on the vertex processor.
In the first two sections, I discuss general methods that work on unstructured grids, which are the types of models this dissertation is mostly concerned. For completeness, I discuss also techniques for rendering regular grids. However, I do not expand on regular grid rendering as the problem of cell-ray intersections is simpler than that for unstructured grids and errors in color computations are less noticeable. Moreover, there already has been significantly more research on the rendering of regular grids. This is because there is a large amount of models defined as regular grids, particularly in medical visualization where CT, MRI, and ultrasound scans result in a regular grid of samples. Nevertheless, unstructured grids are an important modeling tool that can provide far more accuracy with many fewer data. For example, Leven and colleagues [58] built a volume renderer that resampled unstructured grids with regular grids. To create enough samples to maintain the accuracy of the unstructured grids, their data could grow by three orders of magnitude.