import java.awt.*;

/**
    Program:  Secant
    Purpose:  animation: secant line approaching the tangent
    @author:  Paul Garrett, garrett@math.umn.edu
    @version: Wed, 09 July 1997
*/

public class Secant extends java.applet.Applet implements Runnable {

  Thread timerThread;

  Graphics offScreenGraphics;
  Image offScreenImage;

  final int height = 320;
  final int width = 550;
  final int drawHeight = 310;
  final int drawWidth = 450;
  final int inset = 5;

  final int inc = 4;
  final int range = 110; // want inc * range = 400 or so

  final int xaxInset = 50; // inset of x-axis from bottom of drawing area
  final int yaxInset = 50; // inset of y-axis from left of drawing area

  double x, y, x0, y0;
  int t, t0, t1; // t0 is basepoint, t1 is other point, t is variable

  public void init() {
    offScreenImage = createImage(width,height);
    offScreenGraphics = offScreenImage.getGraphics();
    t0 = 20;
    x0 = tTox(t0);
    y0 = theFunction(tTox(t0));

    t1 = 100;
    x = tTox(t1);
    y = theFunction(tTox(t1));
  }

  public void start() {
    if (timerThread == null) {
      timerThread = new Thread(this);
      timerThread.start();
    }
    repaint();
  }
  public void stop() {
    if (timerThread != null) {
      timerThread.stop();
      try {
	timerThread.join();
      }
      catch (InterruptedException e) { }
      timerThread = null;
    }
  }
  void pause(int time) {
    try { Thread.sleep(time); }
    catch ( InterruptedException e) { }
  }

  public void run() {
    while (true) {
      if (t > t0 + 2) {
	pause(100);
	t--;
	x = tTox(t);
	y = theFunction(tTox(t));
	repaint();
      }
      else {
	pause(500);
	t = t1;
	x = tTox(t);
	y = theFunction(tTox(t));
	repaint();
	pause(500);
      }
    }
  }

  public void update(Graphics g) {
    paint(g);
  }

  /************************************************/

  void drawAxes(Graphics g) { 
    g.setColor(Color.black);
    g.fillRect(inset, drawHeight - xaxInset, drawWidth, 2); // x-axis
    int[] xs = {inset + drawWidth + 2, inset + drawWidth - 10, 
		inset + drawWidth - 6, inset + drawWidth - 10};
    int[] ys = {drawHeight - xaxInset, drawHeight - xaxInset-6, 
		drawHeight - xaxInset, drawHeight - xaxInset+6};
    g.fillPolygon(new Polygon(xs, ys, 4)); // arrowhead on x-axis

    g.fillRect(yaxInset-1, inset, 2, drawHeight); // y-axis
    int[] xs2 = {yaxInset, yaxInset - 6, yaxInset, yaxInset + 6};
    int[] ys2 = {inset - 2, inset + 10, inset + 6, inset + 10};
    g.fillPolygon(new Polygon(xs2, ys2, 4)); // arrowhead on y-axis
  }

  /********************************************************/

  double theFunction(double x) {
    // should roughly map -1 < x < 2 to -1 < y < 2, for example
    return (x*x - 0.5 * x + 1.0)/2.0; //__EDIT__
  } 

  int xToPix (double x) { // rescales -1 < x < 2 to ...
    return (int) ( (x + 1.0) * ((double) drawWidth) / 3.0) + inset;
  }

  int yToPix (double y) { // rescales [-1,2] to ...
    return inset + drawHeight - ((int) ( (y + 1.0) * ((double) drawHeight) / 3.0));
  }
  
  double tTox (int t) { // rescales [0,range] to [-1,2]
    return ((double) (t * inc)) * 3.0 / ((double) drawWidth) - 1.0;
  }

  void drawCurve(Graphics g) { //__EDIT__HERE__
    g.setColor(Color.red);
    for (int i=0; i<= range; i++) {
      g.drawLine(xToPix(tTox(i)), yToPix(theFunction(tTox(i))), 
		 xToPix(tTox(i+1)), yToPix(theFunction(tTox(i+1))));
    }
    g.setColor(Color.green);
    for (int i=0; i<= range; i++) {
      g.drawLine(xToPix(tTox(i)), yToPix(theFunction(tTox(i))) - 1, 
		 xToPix(tTox(i+1)), yToPix(theFunction(tTox(i+1))) - 1);
    }
  }

  void drawSecant(Graphics g) {
    g.setColor(Color.white);
    double left = -1.0;
    double right = 2.0;
    g.drawLine(inset, 
	       yToPix(y0 + (y-y0) * (left - x0)/(x-x0)),
	       inset + drawWidth, 
	       yToPix(y0 + (y-y0) * (right - x0)/(x-x0)));
    g.setColor(Color.red);
    g.fillOval(xToPix(x)-2, yToPix(y), 6, 6);
    g.fillOval(xToPix(x0)-2, yToPix(y0), 6, 6);
  }

  /*****************************************************/

  void drawOffScreen() {
    offScreenGraphics.setColor(Color.gray);
    offScreenGraphics.fillRect(0,0,width,height);
    offScreenGraphics.setColor(Color.black);
    drawAxes(offScreenGraphics);

    drawCurve(offScreenGraphics);
    drawSecant(offScreenGraphics);
  }

  public void paint(Graphics g) {
    drawOffScreen();
    g.drawImage(offScreenImage,0,0,this);
  }

} //__THE__END__