Slide 41 of 42

The idea here was to motivate the use of a two-dimensional opacity function. A one-dimensional opacity function works on a certain assumption about the relationship betweent the data value and the bouandaries: every data value can be unambiguously associated with exactly one boundary. For some dataset this is true, but there are others for which it isn't. The lower of the two synthetic datasets has two boundaries associated with the indicated data value, so there is no way to make a one-dimensional opacity function which selectively renders the different boundaries.