Just recently I have been working on some code which required line generalization for Flash from drawings / poly line data. I have posted up sample code and a demonstration SWF to show the results of these tests. I found that the Douglas Peuker algorithm was the simplest to implement the results are pretty good. The only down point is code only usually runs in O(n log m) time where m the number of points is small. I would like to try and speed this up by a technique using the Melkman convex hull algorithm based on a paper written by Hershberger & Snoeyink they split the lower and higher bounds to increase performance on the simplification process.
Download the source code here