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Why is this important? Well in 3D determining the legality of a
particular edge collapse is expensive. The shape and connectivity of
the proposed elements must be considered. Also when an edge is
collapsed all edges which touch one of the modified elements (dashed
lines in the bottom image), must be re-computed. This diagram is only
2D, and its much worse in 3D. On average 100 edge weights must be
re-computed. Now for a progressive mesh which maintains a priority queue
of all collapse weights, the necessary re-computation and reheaping of
these 100 edges can be very expensive.
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