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To control the selection of transformations a variable representing the
allowable boundary error is increased after each iteration. The initial
value for E is the ideal edge length. The intuition here is that if we
could represent our model with equal-volume, near-equilateral elements
the average edge length would be E. Edges smaller than this length will
probably need to be collapsed.
After each iteration E is updated by an amount proportional to the count reduction remaining. In the limit as delta E approaches zero, and only one collapse is allowed per iteration, this algorithm (restricted to edge collapses) is in fact equivalent to a progressive mesh. | ||