计算几何模板一（点、线段、直线）

计算几何模板一（点、线段、直线）

#include<iostream>#include<cstdio>#include<cmath>#include<algorithm>using namespace std;#define Sgn(x) (((x)<0)?(-1):(1))#define eps 1e-8#define INF 1e10#define Pi (acos(-1.0))double Deg2Rad(double deg) {return (deg*Pi/180.0);}double Rad2Deg(double rad) {return (rad*180.0/Pi);}double Sin(double deg) {return sin(Deg2Rad(deg));}double Cos(double deg) {return cos(Deg2Rad(deg));}double ArcSin(double val) {return Rad2Deg(asin(val));}double ArcCos(double val) {return Rad2Deg(acos(val));}//点struct POINT{    double x,y;    POINT():x(0),y(0){}    POINT(double _x,double _y):x(_x),y(_y){};};//两个点的距离double Distance(const POINT &a,const POINT &b){    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}//线段struct SEG{    POINT a;//起点    POINT b;//终点    SEG(){};    SEG(POINT _a,POINT _b):a(_a),b(_b){};};//直线（两点式）struct LINE{    POINT a,b;    LINE(){};    LINE(POINT _a,POINT _b):a(_a),b(_b){};};//直线（一般式）struct LINE2{    double A,B,C;    LINE2(){};    LINE2(double _A,double _B,double _C):A(_A),B(_B),C(_C){};};//两点式化一般式LINE2 Line2line(const LINE &L){    LINE2 L2;    L2.A=L.b.y-L.a.y;    L2.B=L.a.x-L.b.x;    L2.C=L.b.x*L.a.y-L.a.x*L.b.y;    return L2;}//返回直线Ax+By+C=0的系数void Coefficient(const LINE &L,double &A,double &B,double &C){    A=L.b.y-L.a.y;    B=L.a.x-L.b.x;    C=L.b.x*L.a.y-L.a.x*L.b.y;}void Coefficient(const POINT &p,const double a,double &A,double &B,double &C){    A=Cos(a);    B=Sin(a);    C=-(p.y*B+p.x*A);}//直线相交的交点POINT Intersection(const LINE &A,const LINE &B){    double A1,B1,C1;    double A2,B2,C2;    Coefficient(A,A1,B1,C1);    Coefficient(B,A2,B2,C2);    POINT I(0,0);    I.x=-(B2*C1-B1*C2)/(A1*B2-A2*B1);    I.y= (A2*C1-A1*C2)/(A1*B2-A2*B1);    return I;}//点到直线的距离double Ptol(const POINT p,const LINE2 L){    return fabs(L.A*p.x+L.B*p.y+L.C)/sqrt(L.A*L.A+L.B*L.B);}//两线段叉乘double Cross2(const SEG &p,const SEG &q){    return (p.b.x-p.a.x)*(q.b.y-q.a.y)-(q.b.x-q.a.x)*(p.b.y-p.a.y);}//有公共端点o叉乘，并判拐，若正p0->p1->p2拐向左double Cross(const POINT &a,const POINT &b,const POINT &o){    return (a.x-o.x)*(b.y-o.y)-(b.x-o.x)*(a.y-o.y);}//判等（值，点，直线）bool IsEqual(double a,double b){    return (abs(a-b)<eps);}bool IsEqual(const POINT &a,const POINT &b){    return (IsEqual(a.x,b.x)&&IsEqual(a.y,b.y));}bool IsEqual(const LINE &A,const LINE &B){    double A1,B1,C1;    double A2,B2,C2;    Coefficient(A,A1,B1,C1);    Coefficient(B,A2,B2,C2);    return IsEqual(A1*B2,A2*B1)&&           IsEqual(A1*C2,A2*C1)&&           IsEqual(B1*C2,B2*C1);}//判断点是否在线段上bool IsOnSeg(const SEG &seg,const POINT &p){    return (IsEqual(p,seg.a)||IsEqual(p,seg.b))||           (((p.x-seg.a.x)*(p.x-seg.b.x)<0||             (p.y-seg.a.y)*(p.y-seg.b.y)<0)&&             (IsEqual(Cross(seg.b,p,seg.a),0)));}//判断两条线段是否相交，端点重合算相交bool IsIntersect(const SEG &u,const SEG &v){    return (Cross(v.a,u.b,u.a)*Cross(u.b,v.b,u.a)>=0)&&           (Cross(u.a,v.b,v.a)*Cross(v.b,u.b,v.a)>=0)&&           (max(u.a.x,u.b.x)>=min(v.a.x,v.b.x))&&           (max(v.a.x,v.b.x)>=min(u.a.x,u.b.x))&&           (max(u.a.y,u.b.y)>=min(v.a.y,v.b.y))&&           (max(v.a.y,v.b.y)>=min(u.a.y,u.b.y));}//判断线段P和直线Q是否相交，端点重合算相交bool IsOnLine(const SEG &p,const LINE &q){    SEG p1,p2,q0;    p1.a=q.a;p1.b=p.a;    p2.a=q.a;p2.b=p.b;    q0.a=q.a;q0.b=q.b;    return (Cross2(p1,q0)*Cross2(q0,p2)>=0);}//判断两条线段是否平行bool IsParallel(const LINE &A,const LINE &B){    double A1,B1,C1;    double A2,B2,C2;    Coefficient(A,A1,B1,C1);    Coefficient(B,A2,B2,C2);    //共线不算平行    /*return (A1*B2==A2*B1)&&    ((A1*C2!=A2*C1)||(B1*C2!=B2*C1));*/    //共线算平行    return (A1*B2==A2*B1);}//判断两条直线是否相交bool IsIntersect(const LINE &A,const LINE &B){    return !IsParallel(A,B);}