计算几何模板——点类以及线段类

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<vector>
#include<algorithm>
#include <iostream>
#include <string>
#include <set>
#include <map>
using namespace std;
const int MAXN = 500+10;
const int INF=1e9+7;
const double eps=1e-8;
const double pi=acos(-1.0);
//计算几何误差修正
//输入为一个double类型的数，返回-1表示负数，1表示正数，0表示x为0
int cmp(double x){
    if(fabs(x)<eps)
        return 0;
    if(x>0) return 1;
    return -1;
}

//计算几何点类
inline double sqr(double x){
    return x*x;
}

struct point{
    double x,y;
    double xx;
    point(){}
    point(double a,double b):x(a),y(b){}
    void input(){
        scanf("%lf%lf",&x,&y);
    }
    //加法
    friend point operator + (const point &a,const point &b){
        return point(a.x+b.x,a.y+b.y);
    }
    //减法
    friend point operator - (const point &a,const point &b){
        return point(a.x-b.x,a.y-b.y);
    }
    //判断相等
    friend bool operator == (const point &a,const point &b){
        return cmp(a.x-b.x)==0&&cmp(a.y-b.y)==0;
    }
    //倍增
    friend point operator * (const point &a,const double &b){
        return point(a.x*b,a.y*b);
    }
    //倍增
    friend point operator * (const double &b,const point &a){
        return point(a.x*b,a.y*b);
    }
    //除法
    friend point operator / (const point &a,const double b){
        return point(a.x/b,a.y/b);
    }
    //模长
    double norm(){
        return sqrt(sqrt(x)+sqr(y));
    }
};

//叉积，a×b>0代表a在b的顺时针方向，<0代表a在b的逆时针方向，等于0代表a和b向量共线，但不确定方向是否相同
double det(const point &a,const point &b){
    return a.x*b.y-a.y*b.x;
}
//点积
double dot(const point &a,const point &b){
    return a.x*b.x+a.y*b.y;
}
//距离
double dist(const point &a,const point &b){
    return (a-b).norm();
}
//op向量绕原点逆时针旋转A（弧度）
point rotate_point(const point &p,double A){
    double tx=p.x,ty=p.y;
    return point(tx*cos(A)-ty*sin(A),tx*sin(A)+ty*cos(A));
}

//计算几何线段类
struct line{
    point a,b;
    line(){}
    line(point x,point y):a(x),b(y){}
    void input(){
        a.input();
        b.input();
    }
};

//用两个点a,b生成的一个线段或者直线
line point_make_line(point a,point b){
    return line(a,b);
}

//求点p到线段st的距离
double dis_point_segment(point p,point s,point t){
    if(cmp(dot(p-s,t-s))<0) return (p-s).norm();
    if(cmp(dot(p-s,s-t))<0) return (p-t).norm();
    return fabs(det(s-p,t-p)/dist(s,t));
}
//求点p到线段st的垂足，保存在cp中
void PointProjLine(point p,point s,point t,point &cp){
    double r=dot((t-s),(p-s))/dot(t-s,t-s);
    cp=s+(t-s)*r;
}

//判断p点是否在线段st上
bool PointOnSegment(point p,point s,point t){
    return cmp(det(p-s,t-s))==0&&cmp(dot(p-s,p-t))<=0;
}

//判断a和b是否平行
bool parallel(line a,line b){
    return !cmp(det(a.a-a.b,b.a-b.b));
}

//判断a和b是否共线
bool contribution(line a,line b){
    if(!parallel(a, b))
        return false;
    if(!cmp(det(a.b-a.a,b.a-a.b)))
        return true;
    return false;
}

//判断a和b是否相交，若相交则返回true且交点保存在res中
bool line_make_point(line a,line b,point &res){
    if(parallel(a, b))
        return false;
    double s1=det(a.a-b.a,b.b-b.a);
    double s2=det(a.b-b.a,b.b-b.a);
    res=(s1*a.b-s2*a.a)/(s1-s2);
    return true;
}
//判断线段是否相交
bool segment_make_point(line a,line b,point &res){
    if(!line_make_point(a,b,res))
        return false;
    if(PointOnSegment(res, a.a, a.b)&&PointOnSegment(res, b.a, b.b))
        return true;
    return false;
}
//判断线段和直线是否相交,a是直线，b是线段
bool line_across_segment(line a,line b){
    if(cmp(det(a.b-a.a,b.a-a.a)*det(a.b-a.a,b.b-a.a))==1){
        return false;
    }
    return true;
}

//将直线a沿法向量方向平移距离len得到的直线
line move_d(line a,const double &len){
    point d=a.b-a.a;
    d=d/d.norm();
    d=rotate_point(d, pi/2);
    return line(a.a+d*len,a.b+d*len);
}