Gym 100942A Three seamarks

题目链接: http://codeforces.com/problemset/gymProblem/100942/A

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我们可以把给定的角看成圆周角 从而算出圆心角

然后每条边以及一个角可以确定两个可能的圆

如果$M1\ M2$确定出来的两个圆与$M2\ M3$确定出来的两个圆圆心不同的话

再判断这两个圆的交点即为答案 另外每次两个交点中一定有一个点是$M2$

如果圆心相同就是四点共圆了

此题卡精度比较严重 不要随意地使用三角函数库函数 尤其是$atan2$这类的

 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 using namespace std;
 const double eps = 1e-, inf = 1e8, pi = acos(-1.0);
 const double eps2 = 1e-;
 struct point
 {
     double x, y;
     point(){}
     point(double _x,double _y)
     {
         x = _x;
         y = _y;
     }
     point operator - (const point &p) const
     {
         return point(x - p.x, y - p.y);
     }
     point operator + (const point &p) const
     {
         return point(x + p.x, y + p.y);
     }
     double operator * (const point &p) const
     {
         return x * p.y - y * p.x;
     }
     double operator / (const point &p) const
     {
         return x * p.x + y * p.y;
     }
 }a[];
 struct circle
 {
     double x, y, r;
 }c[];
 int t, cnt;
 double ang1, ang2;
 bool flag;
 double getdist2(const point &aa)
 {
     return (aa.x * aa.x + aa.y * aa.y);
 }
 double mycos(double B, double C, double A)
 {
     return (B * B + C * C - A * A) / (B * C * );
 }
 double mycos2(const point &aa, const point &bb, const point &cc)
 {
     double C2 = getdist2(aa - bb), A2 = getdist2(bb - cc), B2 = getdist2(cc - aa);
     return (B2 + C2 - A2) / (sqrt(B2 * C2) * );
 }
 point rotate(const point &p, double cost, double sint)
 {
     double x = p.x, y = p.y;
     return point(x * cost - y * sint, x * sint + y * cost);
 }
 void getcircle(const point &aa, const point &bb, double ang)
 {
     ang = (ang < pi * 0.5 ? ang: pi - ang);
     point mid;
     mid.x = (aa.x + bb.x) * 0.5;
     mid.y = (aa.y + bb.y) * 0.5;
     if(ang + eps < pi * 0.5)
     {
         double tan1 = tan(ang);
         c[cnt].x = mid.x + (aa.y - mid.y) / tan1;
         c[cnt].y = mid.y - (aa.x - mid.x) / tan1;
         c[cnt].r = sqrt(getdist2(mid - point(c[cnt].x, c[cnt].y)) +
         getdist2(mid - aa));
         ++cnt;
         c[cnt].x = mid.x - (aa.y - mid.y) / tan1;
         c[cnt].y = mid.y + (aa.x - mid.x) / tan1;
         c[cnt].r = c[cnt - ].r;
         ++cnt;
     }
     else
     {
         c[cnt].x = mid.x;
         c[cnt].y = mid.y;
         c[cnt].r = sqrt(getdist2(mid - aa));
         ++cnt;
         c[cnt] = c[cnt - ];
         ++cnt;
     }
 }
 bool checkpoint(const point &re)
 {
     for(int i = ; i < ; ++i)
         if(getdist2(a[i] -re) < eps)
             return ;
     double tmp = acos(mycos2(re, a[], a[])) - ang1 - pi;
     while(tmp < -eps2)
         tmp += pi;
     if(abs(tmp) > eps2)
         return ;
     tmp = acos(mycos2(re, a[], a[])) - ang2 - pi;
     while(tmp < -eps2)
         tmp += pi;
     return abs(tmp) < eps2;
 }
 void getpoint2(const circle &c1)
 {
     double dab = sqrt(getdist2(point(a[].x - a[].x, a[].y - a[].y)));
     double ang = acos(dab / (c1.r * ));
     ang -= ang1;
     double len = c1.r *  * cos(ang);
     double cang1 = cos(ang1);
     double l2 = len * cang1;
     point d, re;
     d.x = a[].x + (a[].x - a[].x) * l2 / dab;
     d.y = a[].y + (a[].y - a[].y) * l2 / dab;
     double l3 = len * sqrt( - cang1 * cang1);
     re.x = d.x + (a[].y - a[].y) * l3 / dab;
     re.y = d.y - (a[].x - a[].x) * l3 / dab;
     if(checkpoint(re))
     {
         printf("%.8f %.8f\n", re.x, re.y);
         flag = ;
         return;
     }
     re.x = d.x - (a[].y - a[].y) * l3 / dab;
     re.y = d.y + (a[].x - a[].x) * l3 / dab;
     if(checkpoint(re))
     {
         printf("%.8f %.8f\n", re.x, re.y);
         flag = ;
         return;
     }
 }
 void getpoint(circle c1, circle c2)
 {
     double dab = sqrt(getdist2(point(c1.x, c1.y) - point(c2.x, c2.y)));
     if(dab < eps)
     {
         getpoint2(c1);
         return;
     }
     if(c1.r > c2.r)
         swap(c1, c2);
     double cost = mycos(c1.r, dab, c2.r);
     double sint = sqrt( - cost * cost);
     point re = rotate(point(c2.x, c2.y) - point(c1.x, c1.y), cost, sint);
     re.x = c1.x + re.x * (c1.r / dab);
     re.y = c1.y + re.y * (c1.r / dab);
     if(getdist2(a[] - re) < eps)
     {
         re = rotate(point(c2.x, c2.y) - point(c1.x, c1.y), cost, -sint);
         re.x = c1.x + re.x * (c1.r / dab);
         re.y = c1.y + re.y * (c1.r / dab);
     }
     if(!checkpoint(re))
         return;
     flag = ;
     printf("%.8f %.8f\n", re.x, re.y);
 }
 int main()
 {
     scanf("%d", &t);
     while(t--)
     {
         for(int i = ; i < ; ++i)
             scanf("%lf%lf", &a[i].x, &a[i].y);
         scanf("%lf%lf", &ang1, &ang2);
         ang1 = ang1 * pi / ;
         ang2 = ang2 * pi / ;
         cnt = ;
         getcircle(a[], a[], ang1);
         getcircle(a[], a[], ang2);
         flag = ;
             getpoint(c[], c[]);
         if(!flag)
             getpoint(c[], c[]);
         if(!flag)
             getpoint(c[], c[]);
         if(!flag)
             getpoint(c[], c[]);
     }
     return ;
 }