51nod 1298 圆与三角形 (计算几何)

http://www.51nod.com/onlineJudge/questionCode.html#!problemId=1298

求出圆心到三条线段的最短距离,然后判断是否有顶点在圆外,就把全部情况举出来。

 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 using namespace std;
 const double PI = acos(-1.0);
 double torad(double deg) { return deg/ * PI; }

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

 typedef Point Vector;

 Vector operator + (const Vector& A, const Vector& 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 Vector& A, double p) { return Vector(A.x*p, A.y*p); }
 Vector operator / (const Vector& A, double p) { return Vector(A.x/p, A.y/p); }

 bool operator < (const Point& a, const Point& b)    //结构体运算符的重载
 {
   return a.x < b.x || (a.x == b.x && a.y < b.y);
 }

 const double eps = 1e-;
 int dcmp(double x) { if(fabs(x) < eps) return ; else return x <  ? - : ; }

 bool operator == (const Point& a, const Point &b)
 {
   return dcmp(a.x-b.x) ==  && dcmp(a.y-b.y) == ;
 }

 //基本运算：
 double dist(const Vector& A, const Vector& B) {return sqrt(pow(A.x-B.x,)+pow(A.y-B.y,));}
 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)); }
 double Angle(const Vector& A, const Vector& B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
 double Cross(const Vector& A, const Vector& B) { return A.x*B.y - A.y*B.x; }
 double Area2(Point A, Point B, Point C) {return Cross(B-A, C-A);}

 //向量旋转 rad是弧度
 Vector Rotate(const Vector& A, double rad)
 {
   return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
 }
 //点和直线：
 //两直线的交点
 Point GetLineIntersection(const Point& P, const Point& v, const Point& Q, const Point& w)
 {
   Vector u = P-Q;
   double t = Cross(w, u) / Cross(v, w);
   return P+v*t;
 }

 //点到直线的距离
 double DistanceToLine(const Point& P, const Point& A, const Point& B)
 {
   Vector v1=B-A, v2=P-A;
   return fabs(Cross(v1,v2)) / Length(v1);
 }

 //点到线段的距离
 double DistanceToSegment(const Point& P, const Point& A, const Point& B)
 {
   if(A == B) return Length(P-A);
   Vector v1 = B - A, v2 = P - A, v3 = P - B;
   if(dcmp(Dot(v1, v2)) < ) return Length(v2);
   else if(dcmp(Dot(v1, v3)) > ) return Length(v3);
   else return fabs(Cross(v1, v2)) / Length(v1);
 }

 //点在直线上的投影
 Point GetLineProjection(const Point &P, const Point &A,const Point &B)
 {
     Vector v = B - A;
     return A+v*(Dot(v, P-A) / Dot(v, v));
 }

 //线段相交判定
 bool SegmentProperIntersection(const Point& a1, const Point& a2, const Point& b1, const Point& b2)
 {
   double c1 = Cross(a2-a1,b1-a1), c2 = Cross(a2-a1,b2-a1),
   c3 = Cross(b2-b1,a1-b1), c4=Cross(b2-b1,a2-b1);
   return dcmp(c1)*dcmp(c2)< && dcmp(c3)*dcmp(c4)<;
 }

 //判断点在线段上(两个端点除外)
 bool OnSegment(const Point& p, const Point& a1, const Point& a2)
 {
   return dcmp(Cross(a1-p, a2-p)) ==  && dcmp(Dot(a1-p, a2-p)) < ;
 }

 int main()
 {
     freopen("a.txt","r",stdin);
     int t;
     Vector s,p[];
     double r,x;
     scanf("%d",&t);
     while(t--)
     {
         scanf("%lf%lf%lf",&s.x,&s.y,&r);
         for(int i=;i<;i++)
             scanf("%lf%lf",&p[i].x,&p[i].y);
         int ans=;
         x=DistanceToSegment(s,p[],p[]);
         if(x<=r) ans++;
         x=DistanceToSegment(s,p[],p[]);
         if(x<=r) ans++;
         x=DistanceToSegment(s,p[],p[]);
         if(x<=r) ans++;
         bool flag=;
         for(int i=;i<;i++)
         {
             if(dist(s,p[i])>r)
             {
                 flag=;break;
             }
         }
      //   printf("%d %d\n",ans,flag);
         if(ans>=&&flag) puts("Yes");
         else puts("No");
     }
     return ;
 }