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I tested both of your routines for mean value coordinates (both the slower and more robust one, and the faster, but less robust one) - both seem to fail on a very simple example: a triangle with different colors at the vertices. I compared those to an implementation that I made based on Floater's paper, which seems to work correctly. Also note, that you have a mistake in the implementation of the fast routine - there is no multiplication by 0.5 for the cross product in the slides.