计算几何模板

#include<math.h>#define MAXN 1000#define offset 10000#define eps 1e-8#define PI acos(-1.0)//3.14159265358979323846//判断一个数是否为0,是则返回true,否则返回false#define zero(x)(((x)>0?(x):-(x))<eps)//返回一个数的符号，正数返回1，负数返回2，否则返回0#define _sign(x)((x)>eps?1:((x)<-eps?2:0))struct point {    double x,y;};struct line{    point a,b;};//直线通过的两个点，而不是一般式的三个系数//求矢量[p0,p1],[p0,p2]的叉积//p0是顶点//若结果等于0，则这三点共线//若结果大于0，则p0p2在p0p1的逆时针方向//若结果小于0，则p0p2在p0p1的顺时针方向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);}//计算dotproduct(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);}//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));}//判三点共线int dots_inline(point p1,point p2,point p3){    return zero(xmult(p1,p2,p3));}//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;}//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));}//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;}//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;}//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));}//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));}//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);}//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);}//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;}//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);}//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);}//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);}//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);}struct TPoint{    double x,y;    TPoint operator-(TPoint&a)    {        TPoint p1;        p1.x=x-a.x;        p1.y=y-a.y;        return p1;    }};struct TLine{    double a,b,c;};//求p1关于p2的对称点TPoint symmetricalPoint(TPoint p1,TPoint p2){    TPoint p3;    p3.x=2*p2.x-p1.x;    p3.y=2*p2.y-p1.y;    return p3;}//p点关于直线L的对称点TPoint symmetricalPointofLine(TPoint p,TLine L){    TPoint p2;    double d;    d=L.a*L.a+L.b*L.b;    p2.x=(L.b*L.b*p.x-L.a*L.a*p.x-2*L.a*L.b*p.y-2*L.a*L.c)/d;    p2.y=(L.a*L.a*p.y-L.b*L.b*p.y-2*L.a*L.b*p.x-2*L.b*L.c)/d;    return p2;}//求线段所在直线,返回直线方程的三个系数//两点式化为一般式TLine lineFromSegment(TPoint p1,TPoint p2){    TLine tmp;    tmp.a=p2.y-p1.y;    tmp.b=p1.x-p2.x;    tmp.c=p2.x*p1.y-p1.x*p2.y;    return tmp;}//求直线的交点//求直线的交点，注意平行的情况无解，避免RETPoint LineInter(TLine l1,TLine l2){    //求两直线得交点坐标    TPoint tmp;    double a1=l1.a;    double b1=l1.b;    double c1=l1.c;    double a2=l2.a;    double b2=l2.b;    double c2=l2.c;    //注意这里b1=0    if(fabs(b1)<eps){        tmp.x=-c1/a1;        tmp.y=(-c2-a2*tmp.x)/b2;    }    else{        tmp.x=(c1*b2-b1*c2)/(b1*a2-b2*a1);        tmp.y=(-c1-a1*tmp.x)/b1;    }    //cout<<"交点坐标"<<endl;    //cout<<a1*tmp.x+b1*tmp.y+c1<<endl;    //cout<<a2*tmp.x+b2*tmp.y+c2<<endl;    return tmp;}//矢量（点）V以P为顶点逆时针旋转angle(弧度)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;}//矢量（点）V以P为顶点逆时针旋转angle(弧度)point rotate(point v,point p,double angle){    double cs=cos(angle),sn=sin(angle);    v.x-=p.x,v.y-=p.y;    p.x+=v.x*cs-v.y*sn;    p.y+=v.x*sn+v.y*cs;    return p;}