Algorithems/Circle Intersection.cpp at main · alkaosar-ck/Algorithems · GitHub

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template <class T>
int sgn(T x)
{
	return (x > 0) - (x < 0);
}
template <class T>
struct Point
{
	typedef Point P;
	T x, y;
	explicit Point(T x = 0, T y = 0) : x(x), y(y) {}
	bool operator<(P p) const { return tie(x, y) < tie(p.x, p.y); }
	bool operator==(P p) const { return tie(x, y) == tie(p.x, p.y); }
	P operator+(P p) const { return P(x + p.x, y + p.y); }
	P operator-(P p) const { return P(x - p.x, y - p.y); }
	P operator*(T d) const { return P(x * d, y * d); }
	P operator/(T d) const { return P(x / d, y / d); }
	T dot(P p) const { return x * p.x + y * p.y; }
	T cross(P p) const { return x * p.y - y * p.x; }
	T cross(P a, P b) const { return (a - *this).cross(b - *this); }
	T dist2() const { return x * x + y * y; }
	double dist() const { return sqrt((double)dist2()); }
	double angle() const { return atan2(y, x); }
	P unit() const { return *this / dist(); }
	P perp() const { return P(-y, x); }
	P normal() const { return perp().unit(); }
	P rotate(double a) const { return P(x * cos(a) - y * sin(a), x * sin(a) + y * cos(a)); }
	friend ostream &operator<<(ostream &os, P p) { return os << "(" << p.x << "," << p.y << ")"; }
};
typedef Point<double> P;
bool circleInter(P a, P b, double r1, double r2, pair<P, P> *out)
{
	if (a == b)
	{
		assert(r1 != r2);
		return false;
	}
	P vec = b - a;
	double d2 = vec.dist2(), sum = r1 + r2, dif = r1 - r2,
			 p = (d2 + r1 * r1 - r2 * r2) / (d2 * 2), h2 = r1 * r1 - p * p * d2;
	if (sum * sum < d2 || dif * dif > d2)
		return false;
	P mid = a + vec * p, per = vec.perp() * sqrt(fmax(0, h2) / d2);
	*out = {mid + per, mid - per};
	return true;
}