UVA12302 Nine-Point Circle

九点圆过 三边中点、三边垂足、三点至垂心线段的中点。
九点圆圆心为外心与垂心中点，半径为外心的一半。

也许是精度问题，求三边中点三角形外心再求距离算半径就WA了。

 1  #include<stdio.h>

 2  #include<string.h>

 3  #include<stdlib.h>

 4  #include<math.h>

 5  struct Point

 6  {

 7      double x, y;

 8      Point(){x = y = 0;}

 9      Point(double a, double b)

10      {x = a, y = b;}

11      Point operator-(const Point &b)const

12      {return Point(x - b.x, y - b.y);}

13      Point operator+(const Point &b)const

14      {return Point(x + b.x, y + b.y);}

15      Point operator-()

16      {return Point(-x, -y);}

17      Point operator*(const double &b)const

18      {return Point(x * b, y * b);}

19      double dot(const Point &b)const

20      {return x * b.x + y * b.y;}

21      double cross(const Point &b, const Point &c)const

22      {return (b.x - x) * (c.y - y) - (c.x - x) * (b.y - y);}

23      double Dis(const Point &b)const

24      {return sqrt((*this - b).dot(*this - b));}

25  };

26  Point CrossPoint(Point a, Point b, Point c, Point d)

27  {

28      double u = a.cross(b, c), v = b.cross(a, d);

29      return Point((c.x * v + d.x * u) / (u + v), (c.y * v + d.y * u) / (u + v));

30  }

31  Point A, B, C, ab, ac, Rcx, Rwx, r;

32  int main()

33  {

34      while(scanf("%lf%lf%lf%lf%lf%lf", &A.x, &A.y, &B.x, &B.y, &C.x, &C.y), 

35         fabs(A.x + 1) > 1e-8)

36      {

37          Rcx = CrossPoint(A, Point(A.x + B.y - C.y, A.y + C.x - B.x), 

38                          B, Point(B.x + C.y - A.y, B.y + A.x - C.x));

39          ab = (A + B) * 0.5, ac = (A + C) * 0.5;

40          Rwx = CrossPoint(ab, Point(ab.x + B.y - A.y, ab.y + A.x - B.x), 

41                          ac, Point(ac.x + C.y - A.y, ac.y + A.x - C.x));

42          r = (Rcx + Rwx) * 0.5;

43          printf("%.6f %.6f %.6f\n", r.x, r.y, Rwx.Dis(A) * 0.5);

44      }

45      return 0;

46  }