Here, and are the start and end points of the portion of the ray passing through the bounding volume, respectively. The function describes the density of the medium at a given point in space . Because not all functions have a closed-form solution for their integral, we often resort to numerical methods to evaluate it, i.e. moving along the ray in small steps and adding up the area of rectangular ‘slices’ of density along the way.
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The warden Friedmann sued, Kevin Myers, told me that he found Friedmann to be “an arrogant nuisance” with no interest in perspectives other than his own. But Myers developed a grudging respect for his opponent’s tenacity: “He was very adamant about his beliefs, which I appreciate.”