计算几何模板（点类+多边形面积计算最终版+多边形和圆相交面积计算最终版）

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <algorithm>
using namespace std;
typedef long long ll;
const int maxn = 1e3+10;
const double INF = 0x3f3f3f3f;
const double eps = 1e-10;
const double PI = acos(-1.0);
int dcmp(double k) {return k<-eps?-1:k>eps?1:0;}
double sqr(double x) {return x*x;}
double mysqrt(double n) {return sqrt(max(0.0,n));}

struct point{
   double x,y;
   point (double x=0, double y=0):x(x),y(y){}
};

typedef point Vector;

point res[maxn];
double r;
int n;

Vector operator +(Vector A,Vector B) {return Vector(A.x+B.x,A.y+B.y); }
Vector operator -(Vector A,Vector B) {return Vector(A.x-B.x,A.y-B.y); }
Vector operator *(Vector A,double p) {return Vector(A.x*p,A.y*p); }
Vector operator /(Vector A,double p) {return Vector(A.x/p,A.y/p); }
double dot(const point &a, const point &b) {return a.x*b.x+a.y*b.y;}
double cross(const point &a, const point &b) {return a.x*b.y-a.y*b.x;}
double abs(const point &o) {return sqrt(dot(o,o));}

point crosspt(const point &a, const point &b, const point &p, const point &q)
{
    double a1 = cross(b-a,p-a);
    double a2 = cross(b-a,q-a);
    return (p*a2-q*a1)/(a2-a1);
}

void circle_cross_line(point a,point b,point o,double r,point ret[],int &num)
{
    double x0 = o.x,y0 = o.y;
    double x1 = a.x,y1 = a.y;
    double x2 = b.x,y2 = b.y;
    double dx = x2-x1, dy = y2-y1;
    double A = dx*dx+dy*dy;
    double B = 2*dx*(x1-x0)+2*dy*(y1-y0);
    double C = sqr(x1-x0) + sqr(y1-y0) -sqr(r);
    double delta = B*B-4*A*C;
    num = 0;
    if(dcmp(delta)>=0)
    {
        double t1 = (-B-mysqrt(delta))/(2*A);
        double t2 = (-B+mysqrt(delta))/(2*A);
        if(dcmp(t1-1)<=0 && dcmp(t1)>=0)
        {
            ret[num++] = point(x1+t1*dx,y1+t1*dy);
        }
        if(dcmp(t2-1)<=0 && dcmp(t2)>=0)
        {
            ret[num++] = point(x1+t2*dx,y1+t2*dy);
        }
    }
}

double sector_area(const point &a, const point &b)
{
    double theta = atan2(a.y,a.x)-atan2(b.y,b.x);
    while(theta<=0) theta += 2*PI;
    while(theta>2*PI) theta -= 2*PI;
    theta = min(theta,2*PI-theta);
    return r*r*theta/2;
}

double calc(const point &a, const point &b)
{
    point p[2];
    int num=0;
    int ina = dcmp(abs(a)-r)<0;
    int inb = dcmp(abs(b)-r)<0;
    if(ina)
    {
        if(inb)
        {
            return fabs(cross(a,b))/2.0;
        }
        else
        {
            circle_cross_line(a,b,point(0,0),r,p,num);
            return sector_area(b,p[0])+fabs(cross(a,p[0]))/2.0;
        }
    }
    else
    {
        if(inb)
        {
            circle_cross_line(a,b,point(0,0),r,p,num);
            return sector_area(p[0],a)+fabs(cross(p[0],b))/2.0;
        }
        else
        {
            circle_cross_line(a,b,point(0,0),r,p,num);
            if(num==2)
            {
                return sector_area(a,p[0])+sector_area(p[1],b)+fabs(cross(p[0],p[1])) / 2.0;
            }
            else
            {
                return sector_area(a,b);
            }
        }
    }
}

//计算多边形和圆相交的面积，半径为r，圆心为圆点，n边形，n个点顺序存在ret[0~n-1]中，ret[n]=ret[0]
double area()
{
    double ret = 0;
    for(int i=0;i<n;i++)
    {
        int sgn = dcmp(cross(res[i],res[i+1]));
        ret += sgn*calc(res[i],res[i+1]);
//        if(sgn>0) ret += calc(res[i],res[i+1]);
//        else ret -= calc(res[i],res[i+1]);
    }
    return fabs(ret);
}

point p[maxn];
int m;
double P,Q;
double allArea;//多边形面积

//顺时针逆时针均可
double Area()
{
    double ans = 0.0;
    for(int i=0;i<n;i++)
    {
        ans = ans + cross(p[i+1],p[i]);
    }
    return fabs(ans/2);
}


int main()
{
    scanf("%d",&n);
    for(int i=0;i<n;i++)
    {
        double x,y;
        scanf("%lf %lf",&x,&y);
        p[i] = point(x,y);
        a[n-i-1] = point(x,y);
    }
    p[n].x=p[0].x,p[n].y=p[0].y;

    allArea = Area();
    //printf("%.12f
",allArea);

    scanf("%d",&m);
    for(int i=1;i<=m;i++)
    {
        double x,y;
        scanf("%lf %lf %lf %lf",&x,&y,&P,&Q);

        point tmp = point(x,y);
        double goal = (1.-P/Q)*allArea;

        for(int i=0;i<=n;i++)
        {
            res[i] = p[i]-tmp;
        }

        double left = 0,right = 1e5;
        while(right-left>eps)
        {
            double mid = (right+left)*.5;
            r = mid;

            double Area = area();
            if(Area<goal) left = mid;
            else right = mid;
        }
        printf("%.12f
",right);
    }
}