private static Direction approxAngle(double theta){
		if(theta <= Math.PI/8 && theta >= -Math.PI/8){
			return Direction.EAST;
		} else if (theta <= 3*Math.PI/8 && theta >= Math.PI/8){
			return Direction.NORTHEAST;
		} else if (theta <= -Math.PI/8 && theta >= -3*Math.PI/8){
			return Direction.NORTHWEST;
		} else {
			return Direction.NORTH;
		}
	}