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）

  1 #include <iostream>
  2 #include <stdio.h>
  3 #include <string.h>
  4 #include <stdlib.h>
  5 #include <algorithm>
  6 using namespace std;
  7 typedef long long ll;
  8 const int maxn = 1e3+10;
  9 const double INF = 0x3f3f3f3f;
 10 const double eps = 1e-10;
 11 const double PI = acos(-1.0);
 12 int dcmp(double k) {return k<-eps?-1:k>eps?1:0;}
 13 double sqr(double x) {return x*x;}
 14 double mysqrt(double n) {return sqrt(max(0.0,n));}
 15 
 16 struct point{
 17    double x,y;
 18    point (double x=0, double y=0):x(x),y(y){}
 19 };
 20 
 21 typedef point Vector;
 22 
 23 point res[maxn];
 24 double r;
 25 int n;
 26 
 27 Vector operator +(Vector A,Vector B) {return Vector(A.x+B.x,A.y+B.y); }
 28 Vector operator -(Vector A,Vector B) {return Vector(A.x-B.x,A.y-B.y); }
 29 Vector operator *(Vector A,double p) {return Vector(A.x*p,A.y*p); }
 30 Vector operator /(Vector A,double p) {return Vector(A.x/p,A.y/p); }
 31 double dot(const point &a, const point &b) {return a.x*b.x+a.y*b.y;}
 32 double cross(const point &a, const point &b) {return a.x*b.y-a.y*b.x;}
 33 double abs(const point &o) {return sqrt(dot(o,o));}
 34 
 35 point crosspt(const point &a, const point &b, const point &p, const point &q)
 36 {
 37     double a1 = cross(b-a,p-a);
 38     double a2 = cross(b-a,q-a);
 39     return (p*a2-q*a1)/(a2-a1);
 40 }
 41 
 42 void circle_cross_line(point a,point b,point o,double r,point ret[],int &num)
 43 {
 44     double x0 = o.x,y0 = o.y;
 45     double x1 = a.x,y1 = a.y;
 46     double x2 = b.x,y2 = b.y;
 47     double dx = x2-x1, dy = y2-y1;
 48     double A = dx*dx+dy*dy;
 49     double B = 2*dx*(x1-x0)+2*dy*(y1-y0);
 50     double C = sqr(x1-x0) + sqr(y1-y0) -sqr(r);
 51     double delta = B*B-4*A*C;
 52     num = 0;
 53     if(dcmp(delta)>=0)
 54     {
 55         double t1 = (-B-mysqrt(delta))/(2*A);
 56         double t2 = (-B+mysqrt(delta))/(2*A);
 57         if(dcmp(t1-1)<=0 && dcmp(t1)>=0)
 58         {
 59             ret[num++] = point(x1+t1*dx,y1+t1*dy);
 60         }
 61         if(dcmp(t2-1)<=0 && dcmp(t2)>=0)
 62         {
 63             ret[num++] = point(x1+t2*dx,y1+t2*dy);
 64         }
 65     }
 66 }
 67 
 68 double sector_area(const point &a, const point &b)
 69 {
 70     double theta = atan2(a.y,a.x)-atan2(b.y,b.x);
 71     while(theta<=0) theta += 2*PI;
 72     while(theta>2*PI) theta -= 2*PI;
 73     theta = min(theta,2*PI-theta);
 74     return r*r*theta/2;
 75 }
 76 
 77 double calc(const point &a, const point &b)
 78 {
 79     point p[2];
 80     int num=0;
 81     int ina = dcmp(abs(a)-r)<0;
 82     int inb = dcmp(abs(b)-r)<0;
 83     if(ina)
 84     {
 85         if(inb)
 86         {
 87             return fabs(cross(a,b))/2.0;
 88         }
 89         else
 90         {
 91             circle_cross_line(a,b,point(0,0),r,p,num);
 92             return sector_area(b,p[0])+fabs(cross(a,p[0]))/2.0;
 93         }
 94     }
 95     else
 96     {
 97         if(inb)
 98         {
 99             circle_cross_line(a,b,point(0,0),r,p,num);
100             return sector_area(p[0],a)+fabs(cross(p[0],b))/2.0;
101         }
102         else
103         {
104             circle_cross_line(a,b,point(0,0),r,p,num);
105             if(num==2)
106             {
107                 return sector_area(a,p[0])+sector_area(p[1],b)+fabs(cross(p[0],p[1])) / 2.0;
108             }
109             else
110             {
111                 return sector_area(a,b);
112             }
113         }
114     }
115 }
116 
117 //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]
118 double area()
119 {
120     double ret = 0;
121     for(int i=0;i<n;i++)
122     {
123         int sgn = dcmp(cross(res[i],res[i+1]));
124         ret += sgn*calc(res[i],res[i+1]);
125 //        if(sgn>0) ret += calc(res[i],res[i+1]);
126 //        else ret -= calc(res[i],res[i+1]);
127     }
128     return fabs(ret);
129 }
130 
131 point p[maxn];
132 int m;
133 double P,Q;
134 double allArea;//多边形面积
135 
136 //顺时针逆时针均可
137 double Area()
138 {
139     double ans = 0.0;
140     for(int i=0;i<n;i++)
141     {
142         ans = ans + cross(p[i+1],p[i]);
143     }
144     return fabs(ans/2);
145 }
146 
147 
148 int main()
149 {
150     scanf("%d",&n);
151     for(int i=0;i<n;i++)
152     {
153         double x,y;
154         scanf("%lf %lf",&x,&y);
155         p[i] = point(x,y);
156         a[n-i-1] = point(x,y);
157     }
158     p[n].x=p[0].x,p[n].y=p[0].y;
159 
160     allArea = Area();
161     //printf("%.12f\n",allArea);
162 
163     scanf("%d",&m);
164     for(int i=1;i<=m;i++)
165     {
166         double x,y;
167         scanf("%lf %lf %lf %lf",&x,&y,&P,&Q);
168 
169         point tmp = point(x,y);
170         double goal = (1.-P/Q)*allArea;
171 
172         for(int i=0;i<=n;i++)
173         {
174             res[i] = p[i]-tmp;
175         }
176 
177         double left = 0,right = 1e5;
178         while(right-left>eps)
179         {
180             double mid = (right+left)*.5;
181             r = mid;
182 
183             double Area = area();
184             if(Area<goal) left = mid;
185             else right = mid;
186         }
187         printf("%.12f\n",right);
188     }
189 }