Equivalence of directions (a programming question)
 

Offhand I'd say that you would probably benefit from using polar coordinates instead of cartesian coordinates, but I haven't used polar coordinates with enough regularity to come up with an algorithm off the top of my head.

There's no way to do this without trig

The best way is via polar coords.

consider a direction as an iterative series of actions (turn plus step) on the following triplex: d,a,h

h is heading, d is distance from origin, a is angle of current position from x axis.

I will write out form of iteration when not on phone. Two directions are equivalent if their final triplexes match in d and a (h doesn't matter). Iteration involves law of sines and law of cosines.

So the non-trig way to do it with pi/4 turns is a special case, the because the results of trig are rational at every step!?

I'm happily married, thank you.. http://www.discussworldissues.com/fo...lies/smile.gif