uva 12304

题意：要求解答6个关于圆的问题。
1.给出三角形坐标求外接圆
2.给出三角形坐标求内切圆
3.给出一个圆心和半径已知的圆，求过点(x,y)的所有和这个圆相切的直线
4.求所有和已知直线相切的过定点(x,y)的已知半径的圆的圆心
5.给出两个不平行的直线，求所有半径为r的同时和这两个直线相切的圆
6.给定两个相离的圆，求出所有和这两个圆外切的半径为r的圆。

比较恶心的计算几何模板题，直接模板吧。。。。

 #include<cstdio>
 #include<cmath>
 #include<cstring>
 #include<algorithm>
 #include<iostream>
 #include<memory.h>
 #include<cstdlib>
 #include<vector>
 #define clc(a,b) memset(a,b,sizeof(a))
 #define LL long long int
 #define up(i,x,y) for(i=x;i<=y;i++)
 #define w(a) while(a)
 using namespace std;
 const int inf=0x3f3f3f3f;
 const int N = ;
 const int maxn = ;
 const double eps = 1e-;        //调到1e-6以上第4问就可以用delta判断切线,但《训练指南》建议，尽量不要调eps
 const double pi = acos(-);

 char type[maxn];

 int dcmp(double x)
 {
     return fabs(x) < eps ?  : (x >  ?  : -);
 }

 struct Point
 {
     double x;
     double y;

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

     bool operator < (const Point& e) const
     {
         return dcmp(x - e.x) <  || (dcmp(x - e.x) ==  && dcmp(y - e.y) < );
     }

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

     int read()
     {
         return scanf("%lf%lf", &x, &y);
     }
 } p[];

 typedef Point Vector;

 Vector operator + (Point A, Point B)
 {
     return Vector(A.x + B.x, A.y + B.y);
 }

 Vector operator - (Point A, Point B)
 {
     return Vector(A.x - B.x, A.y - B.y);
 }

 Vector operator * (Point A, double p)
 {
     return Vector(A.x * p, A.y * p);
 }

 Vector operator / (Point A, double p)
 {
     return Vector(A.x / p, A.y / p);
 }

 struct Line
 {
     Point p;
     Point v;

     Line() {}
     Line(Point p, Point v):p(p), v(v) {}

     int read()
     {
         return scanf("%lf%lf%lf%lf", &p.x, &p.y, &v.x, &v.y);
     }

     Point point(double t)
     {
         return p + v * t;
     }
 };

 struct Circle
 {
     Point c;
     double r;

     Circle() {}
     Circle(Point c, double r):c(c), r(r) {}

     int read()
     {
         return scanf("%lf%lf%lf", &c.x, &c.y, &r);
     }

     Point point(double a)
     {
         return Point(c.x + r * cos(a), c.y + r * sin(a));
     }
 };

 double Dot(Vector A, Vector B)
 {
     return A.x * B.x + A.y * B.y;
 }

 double Cross(Vector A, Vector B)
 {
     return A.x * B.y - B.x * A.y;
 }

 double Length(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));
 }

 Vector Normal(Vector A)
 {
     double L = Length(A);
     return Vector(-A.y / L, A.x / L);
 }

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

 double angle(Vector v)      //求向量的极角
 {
     return atan2(v.y, v.x);
 }

 Point GetLineIntersection(Line l1, Line l2)         //求两直线的交点（前提：相交）
 {
     Vector u = l1.p - l2.p;
     double t = Cross(l2.v, u) / Cross(l1.v, l2.v);
     return l1.point(t);
 }

 int getLineCircleIntersection(Line l, Circle C, double& t1, double& t2, vector<Point>& sol)         //求直线与圆的交点
 {
     double a = l.v.x;
     double b = l.p.x - C.c.x;
     double c = l.v.y;
     double d = l.p.y - C.c.y;
     double e = a * a + c * c;
     double f =  * (a * b + c * d);
     double g = b * b + d * d - C.r * C.r;
     double delta = f * f -  * e * g;
     double dist = DistanceToLine(C.c, l.p, l.p+l.v);
     if(dcmp(dist - C.r) == )       //相切，此处需特殊判断，不能用delta
     {
         t1 = t2 = -f / ( * e);
         sol.push_back(l.point(t1));
         return ;
     }
     if(dcmp(delta) < ) return ;       //相离
     else        //相交
     {
         t1 = (-f - sqrt(delta)) / ( * e);
         sol.push_back(l.point(t1));
         t2 = (-f + sqrt(delta)) / ( * e);
         sol.push_back(l.point(t2));
         return ;
     }
 }

 int GetCircleCircleIntersection(Circle C1, Circle C2, vector<Point>& sol)       //求圆与圆的交点
 {
     double d = Length(C1.c - C2.c);
     if(dcmp(d) == )
     {
         if(dcmp(C1.r - C2.r) == ) return -;       //两圆重合
         return ;       //同心圆但不重合
     }
     if(dcmp(C1.r + C2.r - d) < ) return ;     //外离
     if(dcmp(fabs(C1.r - C2.r) - d) > ) return ;       //内含
     double a = angle(C2.c - C1.c);
     double da = acos((C1.r * C1.r + d * d - C2.r * C2.r) / ( * C1.r * d));
     Point p1 = C1.point(a + da);
     Point p2 = C1.point(a - da);
     sol.push_back(p1);
     if(p1 == p2) return ;      //外切
     sol.push_back(p2);
     return ;
 }

 Circle CircumscribedCircle(Point p1, Point p2, Point p3)        //求三角形的外心
 {
     double Bx = p2.x - p1.x, By = p2.y - p1.y;
     double Cx = p3.x - p1.x, Cy = p3.y - p1.y;
     double D =  * (Bx * Cy - By * Cx);
     double cx = (Cy * (Bx * Bx + By * By) - By * (Cx * Cx + Cy * Cy)) / D + p1.x;
     double cy = (Bx * (Cx * Cx + Cy * Cy) - Cx * (Bx * Bx + By * By)) / D + p1.y;
     Point p(cx, cy);
     return Circle(p, Length(p1-p));
 }

 Circle InscribedCircle(Point p1, Point p2, Point p3)        //求三角形的内切圆
 {
     double a = Length(p3 - p2);
     double b = Length(p3 - p1);
     double c = Length(p2 - p1);
     Point p = (p1 * a + p2 * b + p3 * c) / (a + b + c);
     return Circle(p, DistanceToLine(p, p2, p3));
 }

 int TangentLineThroughPoint(Point p, Circle C, Vector *v)       //求点到圆的直线
 {
     Vector u = C.c - p;
     double dist = Length(u);
     if(dcmp(dist - C.r) < ) return ;
     else if(dcmp(dist - C.r) < eps)
     {
         v[] = Rotate(u, pi / );
         return ;
     }
     else
     {
         double ang = asin(C.r / dist);
         v[] = Rotate(u, ang);
         v[] = Rotate(u, -ang);
         return ;
     }
 }

 void CircleThroughAPointAndTangentToALineWithRadius(Point p, Point p1, Point p2, double r)
 {
     Vector AB = p2 - p1;
     Vector change1 = Rotate(AB, pi / ) / Length(AB) * r;
     Vector change2 = Rotate(AB, -pi / ) / Length(AB) * r;
     Line l1(p1 + change1, AB);
     Line l2(p1 + change2, AB);
     vector<Point> sol;
     sol.clear();
     double t1, t2;
     int cnt1 = getLineCircleIntersection(l1, Circle(p, r), t1, t2, sol);
     int cnt2 = getLineCircleIntersection(l2, Circle(p, r), t1, t2, sol);
     int cnt = cnt1 + cnt2;
     if(cnt) sort(sol.begin(), sol.end());
     printf("[");
     for(int i = ; i < cnt; i++)
     {
         printf("(%.6f,%.6f)", sol[i].x, sol[i].y);
         if(cnt ==  && !i) printf(",");
     }
     puts("]");
 }

 void CircleTangentToTwoLinesWithRadius(Point A, Point B, Point C, Point D, double r)
 {
     Vector AB = B - A;
     Vector change = Normal(AB) * r;
     Point newA1 = A + change;
     Point newA2 = A - change;
     Vector CD = D - C;
     Vector update = Normal(CD) * r;
     Point newC1 = C + update;
     Point newC2 = C - update;
     Point p[];
     p[] = GetLineIntersection(Line(newA1, AB), Line(newC1, CD));
     p[] = GetLineIntersection(Line(newA1, AB), Line(newC2, CD));
     p[] = GetLineIntersection(Line(newA2, AB), Line(newC1, CD));
     p[] = GetLineIntersection(Line(newA2, AB), Line(newC2, CD));
     sort(p, p + );
     printf("[");
     printf("(%.6f,%.6f)", p[].x, p[].y);
     for(int i = ; i < ; i++)
     {
         printf(",(%.6f,%.6f)", p[i].x, p[i].y);
     }
     puts("]");
 }

 void CircleTangentToTwoDisjointCirclesWithRadius(Circle C1, Circle C2, double r)
 {
     Vector CC = C2.c - C1.c;
     double rdist = Length(CC);
     if(dcmp( * r - rdist + C1.r + C2.r) < ) puts("[]");
     else if(dcmp( * r - rdist + C1.r + C2.r) == )
     {
         double ang = angle(CC);
         Point A = C1.point(ang);
         Point B = C2.point(ang + pi);
         Point ret = (A + B) / ;
         printf("[(%.6f,%.6f)]\n", ret.x, ret.y);
     }
     else
     {
         Circle A = Circle(C1.c, C1.r + r);
         Circle B = Circle(C2.c, C2.r + r);
         vector<Point> sol;
         sol.clear();
         GetCircleCircleIntersection(A, B, sol);
         sort(sol.begin(), sol.end());
         printf("[(%.6f,%.6f),(%.6f,%.6f)]\n", sol[].x, sol[].y, sol[].x, sol[].y);
     }
 }

 int main()
 {
     while(scanf("%s", type) == )
     {
         if(strcmp(type, "CircumscribedCircle") == )
         {
             Point p1, p2, p3;
             p1.read();
             p2.read();
             p3.read();
             Circle ret = CircumscribedCircle(p1, p2, p3);
             printf("(%f,%f,%f)\n", ret.c.x, ret.c.y, ret.r);
         }
         else if(strcmp(type, "InscribedCircle") == )
         {
             Point p1, p2, p3;
             p1.read();
             p2.read();
             p3.read();
             Circle ret = InscribedCircle(p1, p2, p3);
             printf("(%f,%f,%f)\n", ret.c.x, ret.c.y, ret.r);
         }
         else if(strcmp(type, "TangentLineThroughPoint") == )
         {
             Circle C;
             Point p;
             C.read();
             p.read();
             Vector v[];
             int cnt = TangentLineThroughPoint(p, C, v);
             double ret[];
             for(int i = ; i < cnt; i++)
             {
                 ret[i] = angle(v[i]);
                 if(dcmp(ret[i] - pi) == ) ret[i] = ;
                 if(dcmp(ret[i]) < ) ret[i] += pi;
             }
             sort(ret, ret + cnt);
             printf("[");
             for(int i = ; i < cnt; i++)
             {
                 printf("%.6f", ret[i] / pi * );
                 if(cnt ==  && !i) printf(",");
             }
             puts("]");
         }
         else if(strcmp(type, "CircleThroughAPointAndTangentToALineWithRadius") == )
         {
             Point p, p1, p2;
             double r;
             p.read();
             p1.read();
             p2.read();
             scanf("%lf", &r);
             CircleThroughAPointAndTangentToALineWithRadius(p, p1, p2, r);
         }
         else if(strcmp(type, "CircleTangentToTwoLinesWithRadius") == )
         {
             Point A, B, C, D;
             double r;
             A.read();
             B.read();
             C.read();
             D.read();
             scanf("%lf", &r);
             CircleTangentToTwoLinesWithRadius(A, B, C, D, r);
         }
         else
         {
             Circle C1, C2;
             double r;
             C1.read();
             C2.read();
             scanf("%lf", &r);
             CircleTangentToTwoDisjointCirclesWithRadius(C1, C2, r);
         }
     }
     return ;
 }