Algorithems/Segment 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;

template <class P>
bool onSegment(P s, P e, P p)
{
	return p.cross(s, e) == 0 && (s - p).dot(e - p) <= 0;
}

template <class P>
vector<P> segInter(P a, P b, P c, P d)
{
	auto oa = c.cross(d, a), ob = c.cross(d, b),
		  oc = a.cross(b, c), od = a.cross(b, d);
	// Checks if intersection is single non=
	// endpoint point.
	if (sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0)
		return {(a * ob - b * oa) / (ob - oa)};
	set<P> s;
	if (onSegment(c, d, a))
		s.insert(a);
	if (onSegment(c, d, b))
		s.insert(b);
	if (onSegment(a, b, c))
		s.insert(c);
	if (onSegment(a, b, d))
		s.insert(d);
	return {all(s)};
}
// Usage: vector<P>inter=segInter(s1,e1,s2,e2);
// if(sz(inter)==1)
// cout<<"segmentsintersect at"<<inter[0]<<endl;