POJ 1419 Intersection (判线段与矩形相交）

题意：判断线段是否与矩形相交（非规范相交）。需要注意的是，当线段在矩形内部时也算作相交。

#include<cmath>#include<cstdio>#include<cstdlib>#include<algorithm>using std::swap;#define eps 1e-8#define zero(x) (((x)>0?(x):-(x))<eps)struct Point{double x,y;};struct Line{Point a,b;};//计算cross product (P1-P0)x(P2-P0)double xmult(Point p1,Point p2,Point p0){return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);}double xmult(double x1,double y1,double x2,double y2,double x0,double y0){return (x1-x0)*(y2-y0)-(x2-x0)*(y1-y0);}//计算dot product (P1-P0).(P2-P0)double dmult(Point p1,Point p2,Point p0){return (p1.x-p0.x)*(p2.x-p0.x)+(p1.y-p0.y)*(p2.y-p0.y);}double dmult(double x1,double y1,double x2,double y2,double x0,double y0){return (x1-x0)*(x2-x0)+(y1-y0)*(y2-y0);}//两点距离double distance(Point p1,Point p2){return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));}double distance(double x1,double y1,double x2,double y2){return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));}//判三点共线int dots_inline(Point p1,Point p2,Point p3){return zero(xmult(p1,p2,p3));}int dots_inline(double x1,double y1,double x2,double y2,double x3,double y3){return zero(xmult(x1,y1,x2,y2,x3,y3));}//判点是否在线段上,包括端点int dot_online_in(Point p,Line l){return zero(xmult(p,l.a,l.b))&&(l.a.x-p.x)*(l.b.x-p.x)<eps&&(l.a.y-p.y)*(l.b.y-p.y)<eps;}int dot_online_in(Point p,Point l1,Point l2){return zero(xmult(p,l1,l2))&&(l1.x-p.x)*(l2.x-p.x)<eps&&(l1.y-p.y)*(l2.y-p.y)<eps;}int dot_online_in(double x,double y,double x1,double y1,double x2,double y2){return zero(xmult(x,y,x1,y1,x2,y2))&&(x1-x)*(x2-x)<eps&&(y1-y)*(y2-y)<eps;}//判点是否在线段上,不包括端点int dot_online_ex(Point p,Line l){return dot_online_in(p,l)&&(!zero(p.x-l.a.x)||!zero(p.y-l.a.y))&&(!zero(p.x-l.b.x)||!zero(p.y-l.b.y));}int dot_online_ex(Point p,Point l1,Point l2){return dot_online_in(p,l1,l2)&&(!zero(p.x-l1.x)||!zero(p.y-l1.y))&&(!zero(p.x-l2.x)||!zero(p.y-l2.y));}int dot_online_ex(double x,double y,double x1,double y1,double x2,double y2){return dot_online_in(x,y,x1,y1,x2,y2)&&(!zero(x-x1)||!zero(y-y1))&&(!zero(x-x2)||!zero(y-y2));}//判两点在线段同侧,点在线段上返回0int same_side(Point p1,Point p2,Line l){return xmult(l.a,p1,l.b)*xmult(l.a,p2,l.b)>eps;}int same_side(Point p1,Point p2,Point l1,Point l2){return xmult(l1,p1,l2)*xmult(l1,p2,l2)>eps;}//判两点在线段异侧,点在线段上返回0int opposite_side(Point p1,Point p2,Line l){return xmult(l.a,p1,l.b)*xmult(l.a,p2,l.b)<-eps;}int opposite_side(Point p1,Point p2,Point l1,Point l2){return xmult(l1,p1,l2)*xmult(l1,p2,l2)<-eps;}//判两直线平行int parallel(Line u,Line v){return zero((u.a.x-u.b.x)*(v.a.y-v.b.y)-(v.a.x-v.b.x)*(u.a.y-u.b.y));}int parallel(Point u1,Point u2, Point v1,Point v2){return zero((u1.x-u2.x)*(v1.y-v2.y)-(v1.x-v2.x)*(u1.y-u2.y));}//判两直线垂直int perpendicular(Line u,Line v){return zero((u.a.x-u.b.x)*(v.a.x-v.b.x)+(u.a.y-u.b.y)*(v.a.y-v.b.y));}int perpendicular(Point u1,Point u2,Point v1,Point v2){return zero((u1.x-u2.x)*(v1.x-v2.x)+(u1.y-u2.y)*(v1.y-v2.y));}//判两线段相交,包括端点和部分重合int intersect_in(Line u,Line v){if (!dots_inline(u.a,u.b,v.a)||!dots_inline(u.a,u.b,v.b))return !same_side(u.a,u.b,v)&&!same_side(v.a,v.b,u);return dot_online_in(u.a,v)||dot_online_in(u.b,v)||dot_online_in(v.a,u)||dot_online_in(v.b,u);}int intersect_in(Point u1,Point u2,Point v1,Point v2){if (!dots_inline(u1,u2,v1)||!dots_inline(u1,u2,v2))return !same_side(u1,u2,v1,v2)&&!same_side(v1,v2,u1,u2);return dot_online_in(u1,v1,v2)||dot_online_in(u2,v1,v2)||dot_online_in(v1,u1,u2)||dot_online_in(v2,u1,u2);}//判两线段相交,不包括端点和部分重合int intersect_ex(Line u,Line v){return opposite_side(u.a,u.b,v)&&opposite_side(v.a,v.b,u);}int intersect_ex(Point u1,Point u2,Point v1,Point v2){return opposite_side(u1,u2,v1,v2)&&opposite_side(v1,v2,u1,u2);}//计算两直线交点,注意事先判断直线是否平行!//线段交点请另外判线段相交(同时还是要判断是否平行!)Point intersection(Line u,Line v){Point ret=u.a;double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))/((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));ret.x+=(u.b.x-u.a.x)*t;ret.y+=(u.b.y-u.a.y)*t;return ret;}Point intersection(Point u1,Point u2,Point v1,Point v2){Point ret=u1;double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))/((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));ret.x+=(u2.x-u1.x)*t;ret.y+=(u2.y-u1.y)*t;return ret;}//点到直线上的最近点Point ptoline(Point p,Line l){Point t=p;t.x+=l.a.y-l.b.y,t.y+=l.b.x-l.a.x;return intersection(p,t,l.a,l.b);}Point ptoline(Point p,Point l1,Point l2){Point t=p;t.x+=l1.y-l2.y,t.y+=l2.x-l1.x;return intersection(p,t,l1,l2);}//点到直线距离double disptoline(Point p,Line l){return fabs(xmult(p,l.a,l.b))/distance(l.a,l.b);}double disptoline(Point p,Point l1,Point l2){return fabs(xmult(p,l1,l2))/distance(l1,l2);}double disptoline(double x,double y,double x1,double y1,double x2,double y2){return fabs(xmult(x,y,x1,y1,x2,y2))/distance(x1,y1,x2,y2);}//点到线段上的最近点Point ptoseg(Point p,Line l){Point t=p;t.x+=l.a.y-l.b.y,t.y+=l.b.x-l.a.x;if (xmult(l.a,t,p)*xmult(l.b,t,p)>eps)return distance(p,l.a)<distance(p,l.b)?l.a:l.b;return intersection(p,t,l.a,l.b);}Point ptoseg(Point p,Point l1,Point l2){Point t=p;t.x+=l1.y-l2.y,t.y+=l2.x-l1.x;if (xmult(l1,t,p)*xmult(l2,t,p)>eps)return distance(p,l1)<distance(p,l2)?l1:l2;return intersection(p,t,l1,l2);}//点到线段距离double disptoseg(Point p,Line l){Point t=p;t.x+=l.a.y-l.b.y,t.y+=l.b.x-l.a.x;if (xmult(l.a,t,p)*xmult(l.b,t,p)>eps)return distance(p,l.a)<distance(p,l.b)?distance(p,l.a):distance(p,l.b);return fabs(xmult(p,l.a,l.b))/distance(l.a,l.b);}double disptoseg(Point p,Point l1,Point l2){Point t=p;t.x+=l1.y-l2.y,t.y+=l2.x-l1.x;if (xmult(l1,t,p)*xmult(l2,t,p)>eps)return distance(p,l1)<distance(p,l2)?distance(p,l1):distance(p,l2);return fabs(xmult(p,l1,l2))/distance(l1,l2);}//矢量V以P为顶点逆时针旋转angle并放大scale倍Point rotate(Point v,Point p,double angle,double scale){Point ret=p;v.x-=p.x,v.y-=p.y;p.x=scale*cos(angle);p.y=scale*sin(angle);ret.x+=v.x*p.x-v.y*p.y;ret.y+=v.x*p.y+v.y*p.x;return ret;}int main(){    int t, i;    //freopen("a.txt","r",stdin);    double x1, y1, x2, y2;    Line l0, l[5];    scanf("%d",&t);    while ( t-- )    {        scanf("%lf%lf%lf%lf",&l0.a.x, &l0.a.y, &l0.b.x, &l0.b.y);        scanf("%lf%lf%lf%lf",&x1, &y1, &x2, &y2);        if ( x1 > x2 ) swap (x1, x2);        if ( y1 > y2 ) swap (y1, y2);        l[1].a.x = x1; l[1].a.y = y1; l[1].b.x = x2; l[1].b.y = y1;        l[2].a.x = x2; l[2].a.y = y1; l[2].b.x = x2; l[2].b.y = y2;        l[3].a.x = x2; l[3].a.y = y2; l[3].b.x = x1; l[3].b.y = y2;        l[4].a.x = x1; l[4].a.y = y2; l[4].b.x = x1; l[4].b.y = y1;        bool flag = false;        for ( i = 1; i <= 4; i++ )            if ( intersect_in (l[i],l0) ) flag = true;        if ( flag == false )        {            for ( i = 1; i <= 4; i++ )                if ( xmult(l[i].b, l0.a, l[i].a) < -eps || xmult(l[i].b, l0.b, l[i].a) < -eps )                    break;            if ( i > 4 ) flag = true;        }        if ( flag ) printf("T\n");        else printf("F\n");    }    return 0;}