line circle intersection.m

- (StellarPosition) getOribitOf:(StellarObject*)target;
{
	//find intersection of line (position.x, position.y)..(target.x, target.y)
	//with circle around (target.x, target.y) with radius 'orbitRadius'
	
	//current angle to target
	double angleRadians = [self angleTo:[target position]];

	//get point with angle on circle with R=orbitRadius, center (target.x, target.y)
	double pointX = [target position].x + orbitRadius * cos(angleRadians);
	double pointY = [target position].y - orbitRadius * sin(angleRadians);
	StellarPosition intersection = { pointX, pointY };
	return intersection;
}

- (double) angleTo:(StellarPosition)pos
{
	double a = pos.x - position.x;
	double b = pos.y - position.y;
	//the cot(angle) = a/b -> angle = acot(a/b) = Pi - atan(b/a)
	return Pi - atan(b / a);
}