I am creating a polygon animation from lotus shapes. The lotus shapes are crossing each other in circles, so sometimes the resulting polygon is overlapping itself. This causes the overlapped areas to not get painted at all.
Look at this screenshot of the polygon to see what I mean:

http://www.astralvisuals.com/polyLotus.jpg

Here you can see that there are small black areas, where the lotus shapes intersect. It should be blue instead here. What can I do to get these overlapping areas painted?

It says on the fillPolygon description:
"The area inside the polygon is defined using an even-odd fill rule". Is it this rule that causes the overlapping areas to not get painted?