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Slide 26 of 42

... map the histogram volume to an opacity function. There are probably ways of doing that which are completely automatic, but I think that would be rather difficult, if not somewhat presumptious. So, we've chosen to break the mapping from data value to opacity into two steps, one of which is automatic, one of which is controlled by the user. The domain in between is an abstract spatial domain which we can sensibly call "position". Each of the two stages are done by seperate functions which I will describe in the next two slides, but I'm going to name them here for context. The position function p(v) maps from data value to position, and the boundary emphasis function b(x) maps from position to opacity. Then, the semi-automatically generated opacity function alpha(v) is just the composition of these two: b(p(v)).