/**
  * Ninho Circle ratios Calculation Program.
  * @author Robert J Morton <robmorton@clara.net>
  * @version 14 April 208 */

/* Program to find the ratios p:q:r of the radii of the 3 sizes of circle of the Ninho

   1) Let r = 1 in order to simplify the trigonometry.
   2) Set p and q to the impirically-found values
   3) Reduce p by 5% and q by 10%
   4) Set the increment i=.0001
   5) Compute R1 from p
   6) Compute R2 from q
   7) if(R2 < R1) {q += i; goto 5}
   8) if(a > p+q) {p += i; q -= i; goto 5}
   9) x = p + q - a;
  10) if(x > i/2) p -= i/2; q -= i/2;
  11) p = 2.5; q = q/p; r = 1/p;                   */

import java.io.*;

class lardocecu{
   public static void main(String args[]) throws Exception {
      double                 //the impirically-found values of the radii of the 3 circles
         p = 2.5,            //radius of small circle
         q = 3.7,            //radius of medium circle
         r = 4.449593469,    //radius of large circle
         beta = 0,           //angle used in the SAS case of the Cosine Rule
         i = .000001/r,      //incrementer = a thousandth of a millimetre (rescaled to r = 1)
         j = i/2,            //half the increment
         R1 = 0.02,          //radius of the entire ninho calculated using the small circle
         R2 = 0.01;          //radius of the entire ninho calculated using the medium circle

      p /= r;                //p rescaled to r = 1  0.561849081
      p *= 0.90;             //reduce p by 10%      0.505664173
      q /= r;                //q rescaled to r = 1  0.831536639
      q *= 0.70;             //reduce q by 30%      0.582075648
      r = 1;                 //make the large circle unit radius

      double a = p + q + r;  //dummy starting value to allow entry to outer while-loop

      boolean flag = false;            //remains false if calculation does not converge 
                                       //after 10,000 iterations
      for(int m = 0; m < 10000; m++) { //safety loop to avoid possible infinite iteration
         int n = 0, o = 0;             //loop iteration counters

         while(((p+q) < a) || Double.isNaN(beta)) {
            double h = Math.sqrt(1 + p + p) + 1.701301617;
            R1 = Math.sqrt(h * h + p * p) + p;  //solve right-hand blue right-angle triangle
            R2 = 0.01;       //seed value for R2
            n++;             //iteration counter for the outer while-loop
            while(R2 < R1) { //while medium circle has not reached to touch containing circle
               h = q + 1;              //solve the left-hand right-angle triangle
               R2 = Math.sqrt(h * h - 1) + q + 1.37638192;
               q += i;                 //increment radius of medium circle
               o++;                    //iteration counter for the inner while-loop
            }
            beta = 2.199114857 - Math.acos(1 / (1 + q)) - Math.asin(p / (p + 1));
            if(Double.isNaN(beta)) break;   //break out of loop if beta cannot be resolved
            double P = p + 1, Q = q + 1;    //the 2 sides of the red triangle
            a = Math.sqrt(P * P + Q * Q - 2 * P * Q * Math.cos(beta));  //cosine rule
            q -= i; p += i;     //negate the final loop increment of q and increment p
         }
         p -= i;                //negate the final loop increment of p

         if((p + q - a) > j) {  //if the overshoot is more than half the amount of the increment
            p -= j; q -= j;     //take half the increment off each of p and q
         }


//       Re-scale the circles so that the smallest measures 3 metres
         double x = 3 / p; p = 3; r *= x; q *= x; R1 *= x; R2 *= x; 

         System.out.println(           //display the results on the command line
              "#declare sr = " + p + ";" 
            + "\n#declare mr = " + q  + ";"
            + "\n#declare lr = " + r  + ";"
            + "\n#declare R1 = " + R1  + ";"
            + "\n#declare R2 = " + R2  + ";"
            + "\nbeta = " + beta 
            + "\na = " + a 
            + "\nm = " + m 
            + "\nn = " + n 
            + "\no = " + o
         );
         flag = true; break;           //exit the safety loop because converged successfully

      } // end of safety for-loop

      if(!flag) System.out.println("Didn't converge.");
   }
}