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Oct 5th, 2014
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  1. #include <iostream>
  2. #include <fstream>
  3. #include <cmath>
  4. #include <algorithm>
  5. #include <vector>
  6. #include <set>
  7. #include <map>
  8. #include <stack>
  9. #include <queue>
  10. #include <cstdlib>
  11. #include <cstdio>
  12. #include <string>
  13. #include <cstring>
  14. #include <cassert>
  15. #include <utility>
  16. #include <iomanip>
  17. #define sqr(x) ((x)*(x))
  18.  
  19. using namespace std;
  20.  
  21. const double eps = 1e-9;
  22.  
  23. double xc, yc, zc, r;
  24. double xa, ya, za;
  25. double xb, yb, zb;
  26. double a, b, c;
  27. double cosA, cosB, cosC;// angles
  28. double sinA;
  29. double mysqrt(double x) {
  30.     if (x < 0.0 + eps) x = 0.0;
  31.     return sqrt(x);
  32. }
  33. double myacos(double x) {
  34.     if (x < -1.0 + eps)
  35.         x = -1.0;
  36.     else if (x + eps > 1.0)
  37.         x = 1.0;
  38.     return acos(x);
  39. }
  40.  
  41. int main() {
  42.     assert(freopen("input.txt","r",stdin));
  43.     assert(freopen("output.txt","w",stdout));
  44.     scanf("%lf%lf%lf%lf", &xc, &yc, &zc, &r);
  45.     scanf("%lf%lf%lf", &xa, &ya, &za);
  46.     scanf("%lf%lf%lf", &xb, &yb, &zb);
  47.     b = sqrt( sqr(xa-xc)+sqr(ya-yc) + sqr(za-zc));
  48.     c = sqrt( sqr(xa-xb) + sqr(ya-yb) + sqr(za -zb) );
  49.     a = sqrt( sqr(xc-xb) + sqr(yc-yb) + sqr(zc -zb) );
  50.     double beta = asin(r/b);
  51.     cosA = (b*b + c*c - a*a) / (2*b*c);
  52.     if ( b + c <= a + eps || c + a <= b + eps ) {
  53.         printf("%.12lf\n", 0);
  54.         return 0;
  55.     }
  56.    
  57.  
  58.     double lo = 0, hi = c, x;
  59.     double CO, cosTh, p, cosPhi, q, f;
  60.     int step = 1000;
  61.     while ( step -- ) {
  62.         x = (hi + lo ) / 2;
  63.         CO = mysqrt(x*x + b*b - 2*x*b*cosA);
  64.         cosTh = (b*b + CO*CO - x*x) / (2 * b * CO);
  65.         p = mysqrt(b*b + r*r - 2*b*r*cosTh);
  66.         cosPhi = (CO*CO + a*a - sqr(c - x)) / (2*CO*a);
  67.         q = mysqrt( r*r + a*a - 2*r*a*cosPhi);
  68.         f = p * ( c - x ) / (q*x);
  69.         if (f < 1.0)
  70.             hi = x;
  71.         else
  72.             lo = x;
  73.     }
  74.     double alpha = myacos( (p*p + b*b - r*r) / (2 * p * b) );
  75.     double diff = fabs(p * (c-x) - q*x);
  76.     //printf("diff = %.15lf\n", diff);
  77.  
  78.     //assert( fabs(p * (c-x) - q*x) < 1e-9);
  79.     printf("%.12lf\n", alpha/beta);
  80.                            
  81.     return 0;                          
  82. }
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