// test_spiral.java  find minimum, plot slope
//                  spiral(x,y) function included below

import java.awt.*;
import java.awt.event.*;

public class test_spiral extends Frame
{
  double xmin, xmax, ymin, ymax, zmin, zmax, atx, aty;
  int width = 620;
  int height = 670;
  double scale = 50.0;
  double xoff = 10.0;
  double yoff = 60.0;
  int n = 41;
  double xg[] = new double[n];
  double yg[] = new double[n];
  double zg[][] = new double[n][n];

  public test_spiral()
  {
    System.out.println("test_spiral.java running");
    setSize(width,height);
    setBackground(Color.white);
    setForeground(Color.black);
    addWindowListener(new WindowAdapter()
    {
      public void windowClosing(WindowEvent e)
      {
        System.exit(0);
      }
    });
    setVisible(true);
    this.addMouseListener (new mousePressHandler());

    xmin = -6.0;
    xmax = 6.0;
    ymin = -6.0;
    ymax = 6.0;
    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;

    xh = (xmax-xmin)/(double)(n-1);
    yh = (ymax-ymin)/(double)(n-1);

    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);
        xg[i] = x;
        yg[j] = y;
	zg[i][j] = z;
        if(z<zmin)
        {
          zmin = z;
          atx = x;
          aty = y;
        }
        if(z>zmax) zmax = z;
      }
    }
  } // end range

  // spiral trough

  double spiral(double x, double y) // return z
  {
    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

  class mousePressHandler extends MouseAdapter
  {
    public void mousePressed (MouseEvent e)
    {
      requestFocus();
      System.out.println("press"); // debug print
      repaint();
      System.exit(0);
    }
  }

  public void paint(Graphics g)
  {
    double ax[] = new double[3];
    double ay[] = new double[3];
    double  x,  y,  xp2,  yp2,  xp3,  yp3,  xp4,  yp4;
    int    ix, iy, ixp2, iyp2, ixp3, iyp3, ixp4, iyp4;
    double z1, z2;

    // draw a boundary
    g.drawRect(10, 45, width-20, height-55);
    g.drawString("test_spiral.java", 20, 60);
    g.drawString("xmin=-6.0,xmax=6.0, ymin=-6.0,ymax=6.0", 130, 60);
    g.drawString("arrow points downward slope", 420, 60);
    for(int i=1; i<n-1; i++)
    {
      for(int j=1; j<n-1; j++)
      {
	x = xg[i];
	y = yg[j];
        z1 = zg[i][j]-zg[i+1][j]; // across
        z2 = zg[i][j]-zg[i][j+1]; // down

        arrow(z1, z2, ax, ay); // [0] point, [1] side, [2] side
        ix = (int)(scale*(x-xmin)+xoff);
        iy = (int)(scale*(y-ymin)+yoff);
        ixp2 = ix+(int)(10.0*ax[0]);
        iyp2 = iy+(int)(10.0*ay[0]);
        ixp3 = ixp2+(int)(5.0*ax[1]);
        iyp3 = iyp2+(int)(5.0*ay[1]);
        ixp4 = ixp2+(int)(5.0*ax[2]);
        iyp4 = iyp2+(int)(5.0*ay[2]);

        g.drawLine(ix, iy, ixp2, iyp2);
        g.drawLine(ixp2, iyp2, ixp3, iyp3);
        g.drawLine(ixp2, iyp2, ixp4, iyp4);
        // if(x<0.0 && y<0.0)
	// {
	//   System.out.println("x="+x+",y="+y+", z1="+z1+", z2="+z2);
	// }
      } // end j
    } // end i
  } // end paint

  void arrow(double ux, double uy, double ax[], double ay[]) // ax, ay returned
  {
    //               \   ax[2],ay[2]
    //     ux,uy  -----  ax[0],ay[0]   normalized range  -1.0 to 1.0
    //               /   ax[1],ay[1]
    double ang = 0.0;
    double fracpi = Math.PI/8.0; // delta angle for arrow
    double frac = 0.75;          // 3/4 radius for arrow
    double r = 0.0;
    ax[0] = 0.0;
    ay[0] = 0.0;
    if((Math.abs(ux)+Math.abs(uy))<0.01) return;
    r = Math.sqrt(ux*ux+uy*uy);
    ax[0] = ux/r;
    ay[0] = uy/r; // in -1.0 to +1.0
    ang = Math.atan2(ay[0],ax[0]);
    ax[1] = -Math.cos(ang+fracpi)*frac;
    ay[1] = -Math.sin(ang+fracpi)*frac;
    ax[2] = -Math.cos(ang-fracpi)*frac;
    ay[2] = -Math.sin(ang-fracpi)*frac;
    return;
  } // end arrow

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