I know I'm replying to an old post but this answer is just wrong I think.

The original results would give if:
north=90
west=180 or -180
south= -90
east= 0

adding 270 gives:

north=360
west=450 or 90
south=180
east=270

the only result I can think of that would be usefull is:

north=0 or 360
east or west=270
south=180
east or west=90

edit: This gives the right answer if the original answer was "polar":
int nonPolar= 90-((polar+180)%360)
if(nonPolar<0)
{
nonPolar=nonPolar+360;
}

My question: how do you get all those moving parts move over the screen so efficiently? In my (tower defence) game I used the following way way to get the monsters moving:

When I need a new monster, I make an instance of the monster class. That starts a swing-timer. Every time that generates an action event, the integer "steps" goes up by one. The path they need to take is set out pizel by pixel into an arrayList. Because the monster class extends JPanel, it can then paint itself based on those coordinates (arrayList.get(steps)). The JPanel is added to a JLayeredPane and repainted each time the timer generates an action event.

For one monster, this works fine, however at 3 monsters it gets to slow to be practical. Your game consists of 50+ moving parts, how do you do that?