Bounding box of a moving polygon

gistfile1.txt

https://twitter.com/danielcassidy/status/252792108522545152/photo/1/large

P_A = P at A
P_B = P at B

1. For each edge E in P_A:
2.   Compute a quad containing the edge E and, opposite, its corresponding edge in P_B.
3. Compute the union of all quads.

Leaving the exact algorithm for 3 undefined since I have a geometry library that can do
that bit for me.

This feels suboptimal to me, but I'm not sure why...