The methods described in the following sections are based on an interpretation of the data set as a regular grid of cells, each one defined by eight data samples of the volume located at the cell's vertices. Within cells trilinear interpolation is assumed. For image generation continuous rays are traced through the pixels of the image, allowing arbitrary image sizes as well as oversampling.
For trilinear interpolation within
cells the cell maximum is always located at one of the vertices. Besides
skipping pre-identified empty regions of the volume using distance
volumes, another simple way to increase efficiency is
to perform maximum evaluations only within cells with a cell maximum
greater
than the current ray maximum. This technique avoids the
evaluation of cells reached by rays after processing a (local)
maximum. If, in addition, a good lower-bound estimation of
the ray maximum can be obtained before rendering, also cells
encountered before the maximum can be skipped, if their maximum is
lower than the lower-bound estimation [67].
Although these methods reduce the number of required evaluations significantly, the lower-bound estimation has to be performed for each new viewing direction and much time is spent during rendering on identifying and then skipping cells and empty regions.
To increase time savings during rendering, cells which do not contribute to any MIP should be identified and removed during a preprocessing step.