UVa12304（计算几何中圆的基本操作）

断断续续写了250多行的模拟，其间被其他事情打扰，总共花了一天才AC吧~

这道题目再次让我明白，有些事情看起来很难，实际上并没有我们想象中的那么难。当然了我主要指的不是这个题的难度……

也是初学计算几何，然后居然胆大妄为地不用刘汝佳的思路去实现这些个功能，其中有三个功能是我用自己的思路实现的吧（瞎暴力），最后果然也是自己写的出锅了。

当一个贼长的模拟题交上去一发WA时，我是欲哭无泪的……这让我怎么debug……只好不断安慰自己要用计算几何题去练习耐心。

只是没想到在不断的固执与冷静的试探之下，不到一个晚上就成功了，当然了，对拍拍出来的呗……

我的主要错误在于在我自己的实现思路里，旋转向量时应该顺时针还是逆时针是取决于输入的，而我粗暴地“一视同仁”了。还好后来发现不难改，加个正负1去control就好了~

自己的辣鸡代码贴一贴留着自己看，难得写这么长：

 #include <bits/stdc++.h>
 using namespace std;

 struct Point
 {
     double x, y;
     Point(double a = , double b = ):x(a), y(b){ }
 };
 typedef Point Vector;

 const double PI = acos(-1.0);
 int dcmp(double x)
 {
     if (fabs(x) < 1e-)    return ;
     else    return x <  ? - : ;
 }
 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 p) { return Vector(A.x * p, A.y * p); }
 Vector operator / (const Point &A, double p) { return Vector(A.x / p, A.y / p); }
 bool operator < (const Point &A, const Point &B) { return dcmp(A.x - B.x) <  || (dcmp(A.x - B.x) ==  && dcmp(A.y - B.y) < ); }
 bool operator == (const Point &A, const Point &B) { return dcmp(A.x - B.x) ==  && dcmp(A.y - B.y) == ; }

 double Cross(Vector A, Vector B) { return A.x * B.y - A.y * B.x; }
 double Dot(Vector A, Vector B) { return A.x * B.x + A.y * B.y; }
 double Length(Vector A) { return sqrt(Dot(A, A)); }
 double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
 Vector Normal(Vector A) { double L = Length(A); return Vector(-A.y / L, A.x / L); }
 Vector Rotate(Vector A, double rad) { return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); }

 Point Get_Line_Intersect(Point P, Vector v, Point Q, Vector w)
 {
     Point u = P - Q;
     double t = Cross(w, u) / Cross(v, w);
     return P + v*t;
 }

 double Distance_to_Line(Point P, Point A, Point B)
 {
     Vector v1 = P - A, v2 = B - A;
     return fabs(Cross(v1, v2) / Length(v2));
 }

 struct Circle
 {
     Point c;
     double r;
     // Circle(Point a = (0, 0), double x = 0):c(a), r(x){}
     Point point(double seta) { return Point(c.x + cos(seta)*r, c.y + sin(seta)*r); }
 };

 struct Line
 {
     Point p;
     Vector v;
     Line(Point p, Vector v):p(p), v(v) { }

     Point point(double t) { return p + v*t; }
     Line move(double d) { return Line(p + Normal(v)*d, v); }
 };

 double formattedAngle(Vector A)
 {
     double a = atan2(A.y, A.x) / PI * ;
     if (dcmp(a) < )    a += ;
     if (dcmp(a - ) >= )    a -= ;
     return a;
 }

 int getTangents(Point P, Circle C, vector<double> &v)
 {
     Vector u = C.c - P;
     double d = Length(u);

     if (dcmp(d - C.r) < )    return ;
     else if (dcmp(d - C.r) == )
     {
         v.push_back(formattedAngle(Rotate(u, PI/)));
         return ;
     }
     else
     {
         double a = asin(C.r / d);
         v.push_back(formattedAngle(Rotate(u, a)));
         v.push_back(formattedAngle(Rotate(u, -a)));
         return ;
     }
 }

 void get_Line_Circle_Intersection(Line L, Circle C, vector<Point> &ans)
 {
     double t1, t2;
     double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y;
     double e = a*a + c*c, f = *(a*b + c*d), g = b*b + d*d - C.r*C.r;
     double delta = f*f - *e*g;

     if (dcmp(delta) < )    return;
     else if (dcmp(delta) == )
     {
         t1 = t2 = -f//e;
         ans.push_back(L.point(t1));
     }
     else
     {
         t1 = (-f + sqrt(delta)) /  / e;
         t2 = (-f - sqrt(delta)) /  / e;
         ans.push_back(L.point(t1)), ans.push_back(L.point(t2));
     }
 }

 inline double angle(Vector A) { return atan2(A.y, A.x); }

 int get_Circle_Circle_Intersection(Circle C1, Circle C2, vector<Point> &v)
 {
     double d = Length(C1.c - C2.c);
     if (dcmp(d) == )
     {
         if (dcmp(C1.r - C2.r) == )    return -;
         return ;
     }
     if (dcmp(C1.r + C2.r - d) < )    return ;
     if (dcmp(fabs(C1.r - C2.r) - d) > )    return ;

     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), p2 = C1.point(a + da);

     v.push_back(p1);
     if (p1 == p2)    return ;
     v.push_back(p2);
     return ;
 }

 void CircumscribedCircle()
 {
     Point P[];
     for (int i = ; i < ; i++)    scanf("%lf%lf", &P[i].x, &P[i].y);

     Point c = Get_Line_Intersect((P[] + P[])/, Rotate(P[] - P[], PI/), (P[] + P[])/, Rotate(P[] - P[], -PI/));

     printf("(%.6lf,%.6lf,%.6lf)\n", c.x, c.y, Length(c - P[]));
 }

 void InscribedCircle()
 {
     Point P[];
     for (int i = ; i < ; i++)    scanf("%lf%lf", &P[i].x, &P[i].y);

     Vector v1 = Rotate(P[] - P[], (Cross(P[] - P[], P[] - P[]) >  ? - : ) * Angle(P[]-P[], P[]-P[]) / );
     Vector v2 = Rotate(P[] - P[], (Cross(P[] - P[], P[] - P[]) >  ? - : ) * Angle(P[]-P[], P[]-P[]) / );
     Point c = Get_Line_Intersect(P[], v1, P[], v2);

     printf("(%.6lf,%.6lf,%.6lf)\n", c.x, c.y, Distance_to_Line(c, P[], P[]));
 }

 void TangentLineThroughPoint()
 {
     Circle C;
     Point P;
     vector<double> v;
     scanf("%lf%lf%lf", &C.c.x, &C.c.y, &C.r);
     scanf("%lf%lf", &P.x, &P.y);

     printf("[");
     if (getTangents(P, C, v))    sort(v.begin(), v.end()), printf("%.6lf", v[]);
     if (v.size() == )    printf(",%.6lf", v[]);
     printf("]\n");
 }

 void CircleThroughAPointAndTangentToALineWithRadius()
 {
     Circle P;
     Point A, B;
     scanf("%lf%lf%lf%lf%lf%lf%lf", &P.c.x, &P.c.y, &A.x, &A.y, &B.x, &B.y, &P.r);

     Line original(A, B - A);
     vector<Point> v;
     get_Line_Circle_Intersection(original.move(P.r), P, v);
     get_Line_Circle_Intersection(original.move(-P.r), P, v);
     sort(v.begin(), v.end());

     printf("[");
     if (v.size())    printf("(%.6lf,%.6lf)", v[].x, v[].y);
     for (int i = ; i < v.size(); i++)    printf(",(%.6lf,%.6lf)", v[i].x, v[i].y);
     printf("]\n");
 }

 inline Point e_to_go(Vector A, double len) { return A / Length(A) * len; }

 void CircleTangentToTwoLinesWithRadius()
 {
     Point A, B, C ,D;
     double r;
     scanf("%lf%lf %lf%lf %lf%lf %lf%lf %lf", &A.x, &A.y, &B.x, &B.y, &C.x, &C.y, &D.x, &D.y, &r);

     vector<Point> v;
     int control = Cross(B - A, D - C) <  ? - : ;

     Point P = Get_Line_Intersect(A, B-A, C, D-C);
     double seta = Angle(B - A, D - C)/;
     Vector v1 = Rotate(B - A, control*seta);
     Vector v2 = Rotate(B - A, -control*(PI/ - seta));

     v.push_back(P + e_to_go(v1, r/sin(seta)));
     v.push_back(P - e_to_go(v1, r/sin(seta)));
     v.push_back(P + e_to_go(v2, r/cos(seta)));
     v.push_back(P - e_to_go(v2, r/cos(seta)));
     sort(v.begin(), v.end());

     for (int i = ; i < v.size(); i++)
         printf("%c(%.6lf,%.6lf)", ",["[i == ], v[i].x, v[i].y);
     printf("]\n");
 }

 void CircleTangentToTwoDisjointCirclesWithRadius()
 {
     Circle C1, C2;
     double r;
     scanf("%lf%lf%lf %lf%lf%lf %lf", &C1.c.x, &C1.c.y, &C1.r, &C2.c.x, &C2.c.y, &C2.r, &r);
     C1.r += r, C2.r += r;
     vector<Point> v;
     get_Circle_Circle_Intersection(C1, C2, v);
     sort(v.begin(), v.end());

     if (!v.size())    printf("[");
     for (int i = ; i < v.size(); i++)
         printf("%c(%.6lf,%.6lf)", ",["[i == ], v[i].x, v[i].y);
     printf("]\n");
 }

 int main()
 {
     string s;
     while (cin >> s)
     {
         if (s.length() < )    InscribedCircle();
         else
         {
             switch(s[])
             {
                 case 'e':
                     CircumscribedCircle(); break;
                 case 'P':
                     TangentLineThroughPoint(); break;
                 case 't':
                     CircleThroughAPointAndTangentToALineWithRadius(); break;
                 case 'L':
                     CircleTangentToTwoLinesWithRadius(); break;
                 case 'D':
                     CircleTangentToTwoDisjointCirclesWithRadius(); break;
                 default : break;
             }
         }
     }
     return ;
 }