Segments

struct Point{
    double x, y;

    Point(double a = 0, double b = 0){
        x = a;
        y = b;
    }

    Point(const Point &v){
        x = v.x;
        y = v.y;
    }

    friend istream &operator >> (istream &stream, Point &v){
        stream >> v.x >> v.y;
        return stream;
    }

    friend Point operator - (const Point &u, const Point &v){
        return Point(u.x - v.x, u.y - v.y);
    }

    friend double Cross(const Point &u, const Point &v){
        return u.x*v.y - u.y*v.x;
    }

    friend bool operator == (const Point &u, const Point &v){
        return abs(u.x-v.x) <= ESP && abs(u.y-v.y) <= ESP;
    }

    friend bool operator != (const Point &u, const Point &v){
        return abs(u.x-v.x) > ESP || abs(u.y-v.y) > ESP;
    }

    friend bool operator < (const Point &u, const Point &v){
        return u != v && mp(u.x, u.y) < mp(v.x, v.y);
    }

    friend ostream &operator << (ostream &stream, const Point &v){
        stream << "(" << v.x << ", " << v.y << ")";
        return stream;
    }
};

struct Line{
    Point x, y;

    Line(Point u = Point(0, 0), Point v = Point(0, 0)){
        x = u;
        y = v;
    }

    friend bool Intersect(const Line &u, const Line &v){
        return Cross(u.x-u.y, v.x-u.y) * Cross(u.x-u.y, v.y-u.y) <= 0
        && Cross(v.x-v.y, u.x-v.y) * Cross(v.x-v.y, u.y-v.y) <= 0;
    }

    friend Point GiaoDiem(const Line &u, const Line &v){
        Point nu = u.x - u.y;
        Point nv = v.x - v.y;
        //cout << nu.x << ' ' << nu.y << endl;
        //cout << nv.x << ' ' << nv.y << endl;
        double a1 = nu.y, b1 = -nu.x, c1 = u.x.x*nu.y - u.x.y*nu.x;
        //cout << a1 << ' ' << b1 << ' ' << c1 << endl;
        double a2 = nv.y, b2 = -nv.x, c2 = v.x.x*nv.y - v.x.y*nv.x;
        //cout << a2 << ' ' << b2 << ' ' << c2 << endl;
        if (a1 == 0){
            swap(a1, a2);
            swap(b1, b2);
            swap(c1, c2);
        }
        //a1*x+b1*y=c1
        //a2*x+b2*y=c2
        double y = (c2-(a2*c1)/a1)/(b2-a2*b1/a1);
        double x = (c1-b1*y)/a1;
        return Point(x, y);
    }

};