// test_faces.java  see test_faces_java.out 
//                  compile    javac -cp . test_faces.java
//                  execute    java  -cp . test_faces

public class test_faces
{
  double a1, a2, a3, a4, a5; // angles 
  double a1c, a2c, a3c, a4c, a5c; // angles recomputed 
  double x1, x2, x3, x4, x5, x6; // orthoganal coordinates 
  double R = 1.0;
  double sumsq, sq2, sq3, sq4, err, maxerr;
  double Pi = 3.141592653589793238462643;
  double twoPi = 2.0*Pi;
  double halfPi = Pi/2.0;
  double fourthPi = Pi/4.0;
  double eighthPi = Pi/8.0;
  int i1, i2, i3, i4, i5;

  public test_faces()
  {
    System.out.println("test_faces.java running, R = 1");
    System.out.println("2D circle  1 angle radius 1 ");
    System.out.println("  x1 = R * cos(a1) ");
    System.out.println("  x2 = R * sin(a1) ");
    System.out.println("  R = sqrt(x1*x1 + x2*x2) ");
    System.out.println("  a1 = acos(x1/R) ");
    System.out.println("  if(x2<0.0) a1 = 2*Pi - a1 ");
    maxerr = 0.0;
    a1 = 0.0;
    for(i1=0; i1<8; i1++)
    {
      x1 = R*Math.cos(a1);
      x2 = R*Math.sin(a1);
      sumsq = x1*x1 + x2*x2;
      a1c = Math.acos(x1/Math.sqrt(sumsq));
      if(x2<0.0) a1c = twoPi - a1c;
      maxerr = Math.max(maxerr,Math.abs(R*R-sumsq));
      System.out.println("a1 ="+a1+", x1="+x1+", x2="+x2);
      System.out.println("a1c="+a1c);
      System.out.println(" ");
      a1 += fourthPi;
    } // end i1
    System.out.println("                              maxerr"+maxerr);
    System.out.println(" ");

    System.out.println("3D sphere  2 angles radius 1 ");
    System.out.println("  x1 = R * cos(a1) ");
    System.out.println("  x2 = R * sin(a1) * cos(a2) ");
    System.out.println("  x3 = R * sin(a1) * sin(a2) ");
    System.out.println("  R = sqrt(x1*x1 + x2*x2 + x3*x3) ");
    System.out.println("  R2 = sqrt(x2*x2 + x3*x3) ");
    System.out.println("  if R2 < 10^-8 then a2 = 0.0 ");
    System.out.println("  else  a2 = acos(x2/R2) ");
    System.out.println("  if(x2<0.0) a2 = 2*Pi - a2 ");
    maxerr = 0.0;
    a1 = 0.0;
    for(i1=0; i1<=4; i1++) // both include poles 
    {
      a2 = 0.0;
      for(i2=0; i2<8; i2++)
      {
        x1 = R*Math.cos(a1);
        x2 = R*Math.sin(a1)*Math.cos(a2);
        x3 = R*Math.sin(a1)*Math.sin(a2);
        sumsq = x1*x1 + x2*x2 + x3*x3;
        sq2 = x2*x2+x3*x3;
        a1c = Math.acos(x1/Math.sqrt(sumsq));
        a2c = Math.acos(x2/Math.sqrt(sq2));
        if(sq2<1.0e-8) a2c = 0.0;
        if(x3<0.0) a2c = twoPi - a2c;
        maxerr = Math.max(maxerr,Math.abs(R*R-sumsq));
        System.out.println("a1 ="+a1+", a2 ="+a2+", x1="+x1+", x2="+x2+", x3="+x3);
        System.out.println("a1c="+a1c+", a2c="+a2c);
        System.out.println(" ");
      a2 += fourthPi;
        if(a1==0.0 || Math.abs(a1-Pi)<0.0001) break; // only one point on pole 
      } // end i2
      a1 += fourthPi;
    } // end i1
    System.out.println("                              maxerr="+maxerr);
    System.out.println(" ");

    System.out.println("4D sphere  3 angels radius 1 ");
    System.out.println("  x1 = R Math.cos(a1) ");
    System.out.println("  x2 = R Math.sin(a1)*Math.cos(a2) ");
    System.out.println("  x3 = R Math.sin(a1)*Math.sin(a2)*Math.cos(a3) ");
    System.out.println("  x4 = R Math.sin(a1)*Math.sin(a2)*Math.sin(a3) ");
    System.out.println("  R = sqrt(x1*x1 + x2*x2 + x3*x3 + x4*x4) ");
    System.out.println("  R2 = sqrt(x2*x2 + x3*x3 + x4*x4) ");
    System.out.println("  if R2 < 10^-8 then a2 = 0.0 ");
    System.out.println("  else  a2 = acos(x2/R2) ");
    System.out.println("  R3 = sqrt(x3*x3 + x4*x4) ");
    System.out.println("  if R3 < 10^-8 then a3 = 0.0 ");
    System.out.println("  else  a3 = acos(x3/R3) ");
    System.out.println("  if(x4<0.0) a3 = 2*Pi - a3 ");

    maxerr = 0.0;
    a1 = 0.0;
    for(i1=0; i1<4; i1++)
    {
      a2 = 0.0;
      for(i2=0; i2<4; i2++)
      {
        a3 = 0.0;
        for(i3=0; i3<8; i3++)
        {
          x1 = R*Math.cos(a1);
          x2 = R*Math.sin(a1)*Math.cos(a2);
          x3 = R*Math.sin(a1)*Math.sin(a2)*Math.cos(a3);
          x4 = R*Math.sin(a1)*Math.sin(a2)*Math.sin(a3);
          sumsq = x1*x1 + x2*x2 + x3*x3 + x4*x4;
          a1c = Math.acos(x1/Math.sqrt(sumsq));
          sq2 = x2*x2+x3*x3+x4*x4;
          a2c = Math.acos(x2/Math.sqrt(sq2));
          if(sq2<1.0e-8) a2c = 0.0;
          sq3 = x3*x3+x4*x4;
          a3c = Math.acos(x3/Math.sqrt(sq3));
          if(sq3<1.0e-8) a3c = 0.0;
          if(x4<0.0) a3c = twoPi - a3c;

          maxerr = Math.max(maxerr,Math.abs(R*R-sumsq));
          System.out.println("a1 ="+a1+", a2 ="+a2+", a3 ="+a3);
	  System.out.println("x1 ="+a1+", x2 ="+x2+", x3 ="+x3+", x4 ="+x4);
          System.out.println("a1c="+a1c+", a2c="+a2c+", a3c="+a3c);
          System.out.println(" ");
          a3 += fourthPi;
          if(a1==0.0 || Math.abs(a1-Pi)<0.0001) break;//only one point on pole 
          if(a2==0.0 || Math.abs(a2-Pi)<0.0001) break;//only one point on pole 
        }  // end i1
        a2 += fourthPi;
        if(a2==0.0 || Math.abs(a2-Pi)<0.0001) break; // only one point on pole 
      } // end i2
      a1 += fourthPi;
    } // end i3
    System.out.println("                              maxerr="+maxerr);
    System.out.println(" ");


    System.out.println("5D sphere  4 angles radius 1 ");
    System.out.println("    x1 = R Math.cos(a1) ");
    System.out.println("    x2 = R Math.sin(a1) Math.cos(a2) ");
    System.out.println("    x3 = R Math.sin(a1) Math.sin(a2) Math.cos(a3) ");
    System.out.println("    x4 = R Math.sin(a1) Math.sin(a2) Math.sin(a3) Math.cos(a4) ");
    System.out.println("    x5 = R Math.sin(a1) Math.sin(a2) Math.sin(a3) Math.sin(a4) ");
    System.out.println("  R = sqrt(x1*x1 + x2*x2 + x3*x3 + x4*x4 + x5*x5) ");
    System.out.println("  R2 = sqrt(x2*x2 + x3*x3 + x4*x4 + x5*x5) ");
    System.out.println("  if R2 < 10^-8 then a2 = 0.0 ");
    System.out.println("  else  a2 = acos(x2/R2) ");
    System.out.println("  R3 = sqrt(x3*x3 + x4*x4 + x5*x5) ");
    System.out.println("  if R3 < 10^-8 then a3 = 0.0 ");
    System.out.println("  else  a3 = acos(x3/R3) ");
    System.out.println("  R4 = sqrt(x4*x4 + x5*x5) ");
    System.out.println("  if R4 < 10^-8 then a4 = 0.0 ");
    System.out.println("  else  a4 = acos(x4/R4) ");
    System.out.println("  if(x5<0.0) a4 = 2*Pi - a3 ");
    maxerr = 0.0;
    a1 = 0.0;
    for(i1=0; i1<=4; i1++)
    {
      a2 = 0.0;
      for(i2=0; i2<=4; i2++)
      {
        a3 = 0.0;
        for(i3=0; i3<=4; i3++) // both include poles 
        {
          a4 = 0.0;
          for(i4=0; i4<8; i4++)
          {
            x1 = R*Math.cos(a1);
            x2 = R*Math.sin(a1)*Math.cos(a2);
            x3 = R*Math.sin(a1)*Math.sin(a2)*Math.cos(a3);
            x4 = R*Math.sin(a1)*Math.sin(a2)*Math.sin(a3)*Math.cos(a4);
            x5 = R*Math.sin(a1)*Math.sin(a2)*Math.sin(a3)*Math.sin(a4);
            sumsq = x1*x1 + x2*x2 + x3*x3 + x4*x4 + x5*x5;
            a1c = Math.acos(x1/Math.sqrt(sumsq));
            sq2 = x2*x2 + x3*x3 + x4*x4 + x5*x5;
            a2c = Math.acos(x2/Math.sqrt(sq2));
            if(sq4<1.0e-8) a2c = 0.0;
            sq3 = x3*x3 + x4*x4 + x5*x5;
            a3c = Math.acos(x3/Math.sqrt(sq3));
            if(sq3<1.0e-8) a3c = 0.0;
            sq4 = x4*x4 + x5*x5;
            a4c = Math.acos(x4/Math.sqrt(sq4));
            if(sq2<1.0e-8) a4c = 0.0;
            if(x5<0.0) a4c = twoPi - a4c;

            maxerr = Math.max(maxerr,Math.abs(R*R-sumsq));
            System.out.println("a1 ="+a1+", a2 ="+a2+", a3 ="+a3+" a4 ="+a4);
	    System.out.println("x1="+x1+", x2="+x2+", x3="+x3+" x4="+x4+" x5="+x5);
            System.out.println("a1c="+a1c+", a2c="+a2c+", a3c="+a3c+", a4c="+a4c);
            System.out.println(" ");
            a4 += fourthPi;
            if(a1==0.0 || Math.abs(a1-Pi)<0.0001) break; // only one point on pole 
            if(a2==0.0 || Math.abs(a2-Pi)<0.0001) break; // only one point on pole 
            if(a3==0.0 || Math.abs(a3-Pi)<0.0001) break; // only one point on pole 
          } // end i1
          a3 += fourthPi;
          if(a1==0.0 || Math.abs(a1-Pi)<0.0001) break; // only one point on pole 
          if(a2==0.0 || Math.abs(a2-Pi)<0.0001) break; // only one point on pole 
        } // end i2
        a2 += fourthPi;
        if(a1==0.0 || Math.abs(a1-Pi)<0.0001) break; // only one point on pole 
      } // end i3
      a1 += fourthPi;
    } // end i3
    System.out.println("                            maxerr="+maxerr);
    System.out.println(" ");

    System.out.println("test_faces.java finished");
  } // end test_faces

  public static void main (String[] args)
  {
    new test_faces();
  }
}  // end test_faces.java