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As others have shown before, I compared our algorithm with all
transformations to that with just edge collapses. Without the
possibilities of tetrahedral swaps and vertex smoothing it is more
likely that we will get stuck in a local minima with very poor quality
elements. Even if they are successfully removed it may require a
larger value for the boundary error E to reach the target tetrahedral
count. Our algorithm with all transformations is not guaranteed to
remove all of the poorest quality elements. It may be impossible for
a particular mesh and target count. But in practice we have found it
very effective.
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