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Baraff pivoting lcp

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This  is about the paper "Fast contact force computation for non-penetrating rigid bodies".  Has anybody made sense of this?  I have questions.  Do I completely neglect the unprocessed a's that are neither mc nor c?  If the sign for an unprocessed "a" changes, should I stop and pivot and put that index in either nc or c?  I know that the unprocessed "f's" remain zero, but what if the sign of an unprocessed  "a" changes?    Do I actually perform a pivot operation on a matrix? Or is that done by moving between a "c" and an "mc"?

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