线段相交 直线相交 模板

const int maxn  =  100000;
const double eps = 1e-8;
const double pi = acos(-1.0);
#define sgn(x) (fabs(x)<eps?0:(x>0?1:-1))
struct Point {
    double x, y;
    Point(double a=0,double b=0){x=a;y=b;}
    Point operator - (const Point& t) const {
        Point tmp;
        tmp.x = x - t.x;
        tmp.y = y - t.y;
        return tmp;
    }
    bool operator < (const Point &p) const {
        return sgn(x-p.x)<0 || sgn(x-p.x)==0 && sgn(y-p.y)<0; 
    }
    bool operator == (const Point& t) const {
        return sgn(x-t.x)==0 && sgn(y-t.y)==0;
    }
}GP;
struct Line {
    double a, b, c;
};
struct Seg{
    Point s,e;
    Seg(Point a,Point b){s=a;e=b;}
};
inline double Cross(Point a, Point b, Point c) {                    
    return (b.x-a.x)*(c.y-a.y) - (c.x-a.x)*(b.y-a.y); 
};
Line Turn(Point s, Point e) {                                    
    Line ln;
    ln.a =s.y - e.y ;
    ln.b =e.x - s.x;
    ln.c =s.x*e.y - e.x*s.y;
    return ln;
}
bool dotOnSeg(Point p, Point s, Point e) {                
    if ( p == s || p == e )    
        return true;
    return sgn(Cross(s,e,p))==0 && 
        sgn((p.x-s.x)*(p.x-e.x))<=0 && sgn((p.y-s.y)*(p.y-e.y))<=0;//sgn可能等于0，比如线段垂直坐标轴
} 
bool Intersect(Point p1, Point p2, Point p3, Point p4, Point& p) {    // 直线相交
    double a1, b1, c1, a2, b2, c2, d;
    a1 = p1.y - p2.y; b1 = p2.x - p1.x; c1 = p1.x*p2.y - p2.x*p1.y;
    a2 = p3.y - p4.y; b2 = p4.x - p3.x; c2 = p3.x*p4.y - p4.x*p3.y;
    d = a1*b2 - a2*b1;
    if (!sgn(d))    return false;
    p.x = (-c1*b2 + c2*b1) / d;
    p.y = (-a1*c2 + a2*c1) / d;
    return true;
}
bool Line_Inst(Line l1, Line l2, Point &p) {                        // 直线相交 
    double d = l1.a*l2.b - l2.a*l1.b;
    if (!sgn(d))  return false;
    p.x = (-l1.c*l2.b + l2.c*l1.b) / d;
    p.y = (-l1.a*l2.c + l2.a*l1.c) / d;
    return true; 
}
bool Seg_Inst(Seg s1, Seg s2, Point &p) {//判断线段相交，共线时需要特判,先判直线相交，再判点在直线上        
    Line l1=Turn(s1.s,s1.e),l2=Turn(s2.s,s2.e);    
    double d = l1.a*l2.b - l2.a*l1.b;
    if ( sgn(d) ==0 )     return false;
    p.x = (-l1.c*l2.b + l2.c*l1.b) / d;
    p.y = (-l1.a*l2.c + l2.a*l1.c) / d;
    return dotOnSeg(p,s1.s,s1.e) && dotOnSeg(p,s2.s,s2.e);
}
bool check(Seg s1, Seg s2, Point& pp) {//共线，特判
    if ( s1.s==s2.s || s1.s==s2.e ) {    pp = s1.s;    return true;}
    if ( s1.e==s2.s || s1.e==s2.e) {pp = s1.e;return true;}    
    return false;
}