题意：三个人，在给定正方形内，求第一个人拿到珠宝的概率。珠宝随机出现在正方形内。
思路：中垂线+半平面相交。
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<string>
#include<cmath>
#include<vector>
using namespace std;
const int maxn=1e5+;
const double eps=1e-;
const double pi=acos(-); double dcmp(double x)
{
if(fabs(x) < eps) return ;
else return x < ? - : ;
} struct Point
{
double x, y;
Point(double x=, double y=):x(x),y(y) { }
}; typedef Point Vector; Vector operator + (const Point& A, const Point& B)
{
return Vector(A.x+B.x, A.y+B.y);
} Vector operator - (const Point& A, const Point& B)
{
return Vector(A.x-B.x, A.y-B.y);
} Vector operator * (const Point& A, double v)
{
return Vector(A.x*v, A.y*v);
} Vector operator / (const Point& A, double v)
{
return Vector(A.x/v, A.y/v);
} double Cross(const Vector& A, const Vector& B)
{
return A.x*B.y - A.y*B.x;
} double Dot(const Vector& A, const Vector& B)
{
return A.x*B.x + A.y*B.y;
} double Length(const Vector& A)
{
return sqrt(Dot(A,A));
} Vector Rotate(Vector A,double rad)
{
return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
} bool operator < (const Point& p1, const Point& p2)
{
return p1.x < p2.x || (p1.x == p2.x && p1.y < p2.y);
} bool operator == (const Point& p1, const Point& p2)
{
return p1.x == p2.x && p1.y == p2.y;
} Vector Normal(Vector A)
{
double L=Length(A);
return Vector(-A.y/L,A.x/L);
}
struct Line
{
Point P;
Vector v;
double ang;
Line() {}
Line(Point P, Vector v):P(P),v(v)
{
ang = atan2(v.y, v.x);
}
bool operator < (const Line& L) const
{
return ang < L.ang;
}
}; bool OnLeft(const Line& L, const Point& p)
{
return Cross(L.v, p-L.P) > ;
} Point GetLineIntersection(const Line& a, const Line& b)
{
Vector u = a.P-b.P;
double t = Cross(b.v, u) / Cross(a.v, b.v);
return a.P+a.v*t;
} const double INF = 1e8; Point ansPoly[maxn];
int HalfplaneIntersection(vector<Line> L) //L为切割平面的直线集合，求半平面交，返回点的个数，点存在anspoly数组中
{
int n = L.size();
sort(L.begin(), L.end()); // 按极角排序
int first, last; // 双端队列的第一个元素和最后一个元素的下标
vector<Point> p(n); // p[i]为q[i]和q[i+1]的交点
vector<Line> q(n); //
q[first=last=] = L[]; //
for(int i = ; i < n; i++)
{
while(first < last && !OnLeft(L[i], p[last-])) last--;
while(first < last && !OnLeft(L[i], p[first])) first++;
q[++last] = L[i];
if(fabs(Cross(q[last].v, q[last-].v)) < eps) //
{
last--;
if(OnLeft(q[last], L[i].P)) q[last] = L[i];
}
if(first < last) p[last-] = GetLineIntersection(q[last-], q[last]);
}
while(first < last && !OnLeft(q[first], p[last-])) last--; //
if(last - first <= ) return ; //
p[last] = GetLineIntersection(q[last], q[first]); //
// 从deque复制到输出中
int index=;
for(int i = first; i <= last; i++) ansPoly[index++]=p[i];
return index;
} double PolygonArea(int n,Point *p)
{
double area=;
for(int i=; i<n-; i++)
area+=Cross(p[i]-p[],p[i+]-p[]);
return area/;
} Point p[];
int main()
{
// freopen("in.txt","r",stdin);
while(cin>>p[].x>>p[].y>>p[].x>>p[].y>>p[].x>>p[].y)
{
if(p[].x==p[].x&&p[].y==p[].y&&p[].x==)break;
// Point zd1,zd2;
vector<Line> vec;
vec.push_back(Line(Point(,),Point(,)));
vec.push_back(Line(Point(,),Point(,)));
vec.push_back(Line(Point(,),Point(-,)));
vec.push_back(Line(Point(,),Point(,-)));
Vector v=(p[]-p[]);
vec.push_back(Line((p[]+p[])*0.5,Normal(v)));
v=(p[]-p[]);
vec.push_back(Line((p[]+p[])*0.5,Normal(v)));
int m=HalfplaneIntersection(vec);
double ans=PolygonArea(m,ansPoly);
printf("%.3f\n",ans/(1.0**));
}
return ;
}