Quote Originally Posted by crayzz View Post
Y = X bisects 2 of the quadrants, Y = -X bisects the other 2.
And then that can in turn be extended with further similar lines to bisect the plane in a new way that narrows your search space from an 8th to a 16th, and so on. It'd probably be easiest to specify where the lines should be using radians, since that system is basically set up to divide circles up nicely, but it could be done with slopes and lines of the form y=mx as well. (All of those would pass through the origin, and you just keep adjusting your m to get the new slopes at the different angles.)

The first few steps of the algorithm would be:

Is the point a solution to x>0? (this answer determines if it's in combined Q1 and Q4, or combined Q2 and Q3)

Is the point a solution to y>0? (this answer determines if it's in combined Q1 and Q2, or combined Q3 and Q4)

At this point, we know which quadrant it's in. Then ask if it's a solution to y>x (if it's determined to be in Q1 or Q3) or y>-x (if it's in Q2 or Q4). You've now narrowed it down to an 8th of the space, or half a quadrant.

Then ask about the similarly appropriate y>mx to bisect your 8th to get a 16th, and so on.