Self overlapping polygon

[crunchyfx]

Thank you for making this! Really helpful.
I'm using this with box2Dweb and I can get in situations where a polygon is self overlapping.

The decomp doesn't work with those. (Correct me if I'm wrong)
Do you know of a good solution for those cases?

To clarify, cases like these:
http://schteppe.github.io/poly-decomp.js/#path=577,609/625,593/631,645/604,602/581,557
http://schteppe.github.io/poly-decomp.js/#path=709,486/759,466/809,453/859,454/877,501/882,552/892,604/841,590/789,581/807,533/860,526/910,523/885,478/837,493/787,500/739,517
http://schteppe.github.io/poly-decomp.js/#path=883,326/935,325/990,323/1043,329/1046,379/1022,423/987,465/951,500/914,459/896,412/939,385/954,433/905,445/855,439/815,407

Thanks,
Jakob