/*
 * h1a.java - revised 18 Apr 05 - width 401, height 201
 * the cycloid, the path that minimizes the transit time between points
 *   in a uniform gravitational field
 * the particle is released from rest and is to reach a point 5 m below and
 *   25.6 m to the right of the release point
 * the trial path has 2^n linear segments where n increases from 0 to 8
 * @author jackord@kw.igs.net
 */

import java.applet.Applet;
import java.awt.*;
import java.awt.event.ActionListener;
import java.awt.event.ActionEvent;

public class h1a extends Applet
                   implements ActionListener { 
  int kk=0; double gr=9.8; int dn;                        
  double [] y=new double[257];
  String b1s="Vary Path"; Button b1=new Button(b1s);
  Image aim, bim;                                      // Graphics buffers...
  Graphics agr, bgr;                                   // ...for cycloid

  public void init() {
    add(b1); b1.addActionListener(this);
    setBackground(new Color(211, 211, 211));
  }

  public void paint(Graphics g) {
    double a, b, c, fa, fb, fc, r, t, aa;
    int x1, y1, x2, y2, rr, del;
    bim=createImage(401, 201);                         // Initial screen
    bgr=bim.getGraphics();
    bgr.setColor(Color.black); bgr.drawRect(0, 0, 400, 200);
    bgr.setColor(Color.red);
    bgr.fillArc(15, 35, 11, 11, 0, 360);
    bgr.drawArc(15, 35, 10, 10, 0, 360);
    bgr.fillArc(271, 85, 11, 11, 0, 360);
    bgr.drawArc(271, 85, 10, 10, 0, 360);
    bgr.setColor(Color.blue);
    dn=256; y[0]=0; y[256]=5; 
    bgr.drawString("T(0) = "+(int)(10000*dt(0))/10000., 300, 35);
    a=Math.PI; fa=(1-Math.cos(a))/(a-Math.sin(a))-50./256;
    b=2*a; fb=(1-Math.cos(b))/(b-Math.sin(b))-50./256;
    while ((b-a)>.00001) {                             // Bisection algorithm
      c=(b+a)/2; fc=(1-Math.cos(c))/(c-Math.sin(c))-50./256;
      if (fc*fa>0) {
        a=c; fa=fc;
      }
      else {
        b=c; fb=fc;
      }
    }
    if (kk==0) {                                       // Show initial screen
      g.drawImage(bim, 0, 0, null);
      g.setColor(Color.blue); g.drawLine(20, 40, 276, 90);
    }
    else {
      aim=createImage(401, 201);                       // Generate cycloid
      agr=aim.getGraphics();
      c=(a+b)/2; r=y[256]/(1-Math.cos(c)); t=c*Math.sqrt(r/gr);
      bgr.setColor(Color.magenta); agr.setColor(Color.black);
      x1=20; y1=40; rr=(int)(10*r);
      del=10; long tt=System.currentTimeMillis();      // Initialize timing
      for (int i=1; i<=200; i=i+1) {
        aa=i*c/200;
        x2=20+(int)(10*r*(aa-Math.sin(aa))); y2=40+(int)(10*r*(1-Math.cos(aa)));
        bgr.drawLine(x1, y1, x2, y2);
        x1=20+(int)(10*r*aa); 
        agr.drawImage(bim, 0, 0, null);
        agr.drawLine(x2, y2, x1, 40+rr);
        agr.drawArc(x1-rr, 40, 2*rr, 2*rr, 0, 360);
        agr.setColor(Color.red); agr.fillArc(x2-5, y2-5, 10, 10, 0, 360);
        agr.setColor(Color.blue); agr.drawLine(20, 40, 276, 90);
        agr.setColor(Color.black);
        g.drawImage(aim, 0, 0, null); x1=x2; y1=y2;
        tt=tt+del;
        while (System.currentTimeMillis()<tt) { }      // Timing loop
      }
      bgr.drawString("T(A) = "+(int)(10000*t)/10000., 300, 20);
      bgr.setColor(Color.blue);
      g.drawImage(bim, 0, 0, null);
      g.setColor(Color.blue); g.drawLine(20, 40, 276, 90);
      del=1000;                                        // Reset timing
      for (int j=1; j<=8; j=j+1) {                     // Vary path
        dn=dn/2;                                       // 2^j line segments
        for (int ii=1; ii<=16; ii=ii+1) {              // Iteration loop
          for (int i=dn; i<=256-dn; i=i+2*dn) {        // Midpoints of...
            yv(i);                                     // ...previous segments
          }
          if (j>1) {
            for (int i=2*dn; i<=256-2*dn; i=i+2*dn) {  // Boundaries of...
              yv(i);                                   // ...previous segments
            }
          }
        }
        t=0; y1=40;
        tt=tt+del;
        while (System.currentTimeMillis()<tt) { }      // Timing loop
        g.drawImage(bim, 0, 0, null);
        for (int i=dn; i<=256; i=i+dn ) {              // Path and travel time
          y2=40+(int)(10*y[i]); g.drawLine(20+i-dn, y1, 20+i, y2); y1=y2;
          t=t+dt(i-dn);
        }
        g.drawString("T("+j+") = "+(int)(10000*t)/10000., 300, 35+15*j);
        bgr.drawString("T("+j+") = "+(int)(10000*t)/10000., 300, 35+15*j);
      }
      kk=0;
    }
  }

  public void yv(int i) {                              // Vary mid-point y...
    double t, t1; double dd=1;                         // ...to minimize t
    y[i]=(y[i-dn]+y[i+dn])/2;
    t1=dt(i-dn)+dt(i);
    while (Math.abs(dd)>.01) {                         // Step back and forth...
      y[i]=y[i]+dd;                                    // ...across minimum
      t=dt(i-dn)+dt(i);
      if (t>t1) {
        dd=-dd/2;
      }
      t1=t;
    }
    y[i]=y[i]+2*dd;
  }

  double dt(int j) {                                   // Time to traverse...
    double u, v, dx, dy, ds;                           // ...single segment
    if (j==0) {
      u=0;
    }
    else {
      u=Math.sqrt(2*gr*y[j]);
    }
    v=Math.sqrt(2*gr*y[j+dn]);
    dx=dn/10.; dy=y[j+dn]-y[j]; ds=Math.sqrt(dx*dx+dy*dy);
    return 2*ds/(u+v);
  }

  public void actionPerformed(ActionEvent e) {         // Button
    String tst;
    tst=e.getActionCommand();
    if (b1s.equals(tst)) { kk=1; }
    repaint();
  }
}