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  1. import java.io.*;
  2. import java.util.*;
  3. class CLMNTR{
  4.     static class Sphere{
  5.         int x, y, z, r;
  6.         Sphere(int a, int b, int c, int d){
  7.             x = a;
  8.             y = b;
  9.             z = c;
  10.             r = d;
  11.         }
  12.  
  13.         static double getDist(Sphere a, Sphere b){
  14.             return Math.sqrt(Math.pow(a.x-b.x,2)+Math.pow(a.y-b.y,2)+Math.pow(a.z-b.z,2));
  15.         }
  16.     }
  17.  
  18.     public static void main(String args[])throws Exception{
  19.         Scanner sc = new Scanner(System.in);
  20.         int T = sc.nextInt();
  21.         for(; T>0; T--){
  22.             Sphere s = new Sphere(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt());
  23.             Sphere a = new Sphere(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt());
  24.             Sphere b = new Sphere(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt());
  25.  
  26.             if(check(s, a, b))
  27.                 System.out.println("Yes");
  28.             else
  29.                 System.out.println("No");
  30.         }
  31.     }
  32.  
  33.     static boolean check(Sphere s, Sphere a, Sphere b){
  34.         // Scale to 2d with star at (0,0), body A on +ve Y-axis at (0,sa), body B at (bx,by)
  35.         double sa = Sphere.getDist(s, a);
  36.         double sb = Sphere.getDist(s, b);
  37.         double ab = Sphere.getDist(a, b);
  38.         double by = (sa*sa-ab*ab+sb*sb)/(2*sa);
  39.         double bx = Math.sqrt(sb*sb-by*by);
  40.         // If B is under X axis or B is closer to S than A no way there is eclipse
  41.         if(by<0 || sb<sa)
  42.             return false;
  43.         // B always lies in the first quadrant!!
  44.  
  45.         // Exceptional case when star radius = radius of A, tangent is vertical
  46.         if(s.r==a.r)
  47.             if(bx<s.r || b.x-s.r<b.r)
  48.                 return true;
  49.             else
  50.                 return false;
  51.  
  52.         // Find the external tangent y = mx+c
  53.         // Internal tangent c = s.r*s.a/(s.r+a.r)
  54.         double c = s.r*sa/(s.r-a.r);
  55.         double m = Math.sqrt((c*c/s.r/s.r)-1);
  56.         // If A is smaller than star, c is +ve and we need tangent with -ve slope
  57.         if(c>0)
  58.             m = -m;
  59.  
  60.         // If A is smaller than star, this check eliminates false +ves from antumbra cases
  61.         if(c>0 && c<sb-b.r)
  62.             return false;
  63.  
  64.         // Then B surely lies between tangent and Y-axis
  65.         double lx = (by-c)/m;
  66.         if(bx<lx)
  67.             return true;
  68.  
  69.         // If dist from tangent < radius then body intersects tangent
  70.         double d = Math.abs(m*bx-by+c)/Math.sqrt(m*m+1);
  71.         if(d<b.r)
  72.             return true;
  73.         return false;
  74.     }
  75. }
Success #stdin #stdout 0.15s 321280KB
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https://ideone.com/C7jPeB
language:
Java (HotSpot 12)
created:
8 years ago
visibility:
secret

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