If you care about speed, then there is a linear-time algorithm specifically tuned to intersecting
two convex polygons, described in the book,
<a href="http://cs.smith.edu/~orourke/books/compgeom.html">*Computational Geometry in C*</a>,
with downloadable code.
<hr />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<img src="http://cs.smith.edu/~orourke/MathOverflow/CGinCFig7.15.png" alt="Fig.7.15" />
<hr />
(I took the above snapshot from an illegal scan of the book!)