// test_spiral.java find min and max for various ranges 
//                  spiral(x,y) function included below

public class test_spiral
{
  double xmin, xmax, ymin, ymax, zmin, zmax, atx, aty;

  public test_spiral()
  {
    System.out.println("test_spiral.java running");

    xmin = -1.0;
    xmax = 1.0;
    ymin = -1.0;
    ymax = 1.0;
    range();
    System.out.println("xmin="+xmin+", xmax="+xmax+
                       ", ymin="+ymin+", ymax="+ymax);
    System.out.println("zmin="+zmin+", zmax="+zmax+
                       ",\n atx="+atx+",  aty="+aty);

    xmin = -2.0;
    xmax = 2.0;
    ymin = -2.0;
    ymax = 2.0;
    range();
    System.out.println("xmin="+xmin+", xmax="+xmax+
                       ", ymin="+ymin+", ymax="+ymax);
    System.out.println("zmin="+zmin+", zmax="+zmax+
                       ",\n atx="+atx+",  aty="+aty);

    xmin = -0.01;
    xmax = -1.0;
    ymin = 0.01;
    ymax = 1.0;
    range();
    System.out.println("xmin="+xmin+", xmax="+xmax+
                       ", ymin="+ymin+", ymax="+ymax);
    System.out.println("zmin="+zmin+", zmax="+zmax+
                       ",\n atx="+atx+",  aty="+aty);

    xmin = 0.01;
    xmax = 1.0;
    ymin = 0.01;
    ymax = 1.0;
    range();
    System.out.println("xmin="+xmin+", xmax="+xmax+
                       ", ymin="+ymin+", ymax="+ymax);
    System.out.println("zmin="+zmin+", zmax="+zmax+
                       ",\n atx="+atx+",  aty="+aty);

    xmin = -0.01;
    xmax = -1.0;
    ymin = -0.01;
    ymax = -1.0;
    range();
    System.out.println("xmin="+xmin+", xmax="+xmax+
                       ", ymin="+ymin+", ymax="+ymax);
    System.out.println("zmin="+zmin+", zmax="+zmax+
                       ",\n atx="+atx+",  aty="+aty);
  } // end constructor test_spiral

  void range()
  {
    double x, y, z, xh, yh;
    int n=101;

    xh = (xmax-xmin)/(double)n;
    yh = (ymax-ymin)/(double)n;

    z = spiral(xmin,ymin);
    zmin = z;
    zmax = z;
    atx = xmin;
    aty = ymin;

    for(int i=0; i<=n; i++)
    {
      x = xmin+(double)i*xh;
      for(int j=0; j<=n;  j++)
      {
        y = ymin+(double)j*yh;
        z = spiral(x,y);
        if(z<zmin)
        {
          zmin = z;
          atx = x;
          aty = y;
        }
        if(z>zmax) zmax = z;
      }
    }
  } // end range

    // spiral trough

  double spiral(double x, double y)
  {
    double halfpi = 1.57079;
    double r, theta, tz;

    r = Math.sqrt(x*x+y*y);
    if(r < 0.001) theta = 0.0;
    else          theta = Math.atan2(y,x);
    tz = theta/halfpi;
    if(tz < 0.0) tz = tz + 4.0;
    return 0.75*r + Math.sin((r+tz)*halfpi);
  } // end of spiral

  public static void main (String[] args)
  {
    new test_spiral();
  }
} // end class test_spiral