import java.awt.*;

/**
    Program:  Exp
    Purpose:  graph exp with varying-degree Taylor approx
    @author:  Paul Garrett, garrett@math.umn.edu
    @version: Mon 7 July, 16:00 CDT 1997
*/

/* Low-res screen allows 600 wide but only 350 high */

public class Exp extends java.applet.Applet {

  boolean updating; // device ... to keep old curves...

  final int nwx = 5; // nw corner of drawing surface x-coord
  final int nwy = 5; // nw corner of drawing surface x-coord
  final int height = 310; // 'height' of area for drawing
  final int width = 400; // 'width' of area for drawing

  final int vert_scale = 10; // pixels per unit
  final int horiz_scale = 60; // pixels per unit
  final int v_gridsize = 10; // pixels between gridlines?!
  final int h_gridsize = 60; // pixels between gridlines?!
  // 'gridsize' should be divisor of "vert_scale", etc., ... ?

  final int inc = 3; // pixel-size in which to draw the curve
  
  final int rangeOfIndex = (int) width/(2*h_gridsize); // to draw vertical gridlines
  final int rangeOfJndex = (int) height/(2*v_gridsize); // to draw horizontal gridlines
  final int rangeOfInc = (int) width/(2*inc);

  double[] theCoefficients; // of arbitrary degree polynomial
  final int degree = 20; // to know when we're done
  int deg; // this is what we know at any one moment

  final int left = 420; // these are coords for the clickbox
  final int right = 540;
  final int top = 50;
  final int bottom = 80;

  final boolean restrictAccess = true;
  final String theURL = "http://www.math.umn.edu/~garrett/qy/Exp.html";

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

  double theFunction(double input) { // Taylor approx to sine...
    // Note that this calls 'deg' rather than 'degree'
    double output;
    output = theCoefficients[deg] * input;
    for (int i = deg-1; i > 0; i--) {
      output = (output + 1.0) * theCoefficients[i] * input; // good, generally...
    }
    output = output + theCoefficients[0]; // NB this assumes deg>0
    return output;
  }

  int normPara(int para) { // from counter to x-coord
    int thePara;
    thePara = nwx + width/2 + inc * para;
    return thePara;
  }

  int normOut(double output) { // function output to vertical coord
    int theY;
    theY = nwy + height/2 - (int) (output * vert_scale);
    return theY;
  }

  double normIn(int in) { // from counter to function input
    double theX;
    theX = ((double) (in * inc)) / ((double) horiz_scale);
    return theX;
  }

  void initCoefs() { 
    // these are not Taylor coefs, but rather the
    // coefficients convenient for computation...
    // compute lotsa them... maybe 50? but fixed total...
    if (! restrictAccess || this.getDocumentBase().toString().equals(theURL)) {
      theCoefficients = new double[degree+1];
      theCoefficients[0] = 1.0;
      for (int i=1; i<=degree; i++) {
	theCoefficients[i] = 1.0/((double) i);
      }
    }
  }

  public void init() { // stick some coefficients in, tell degree
    deg = 1;
    initCoefs();
    updating = false;
    repaint();
  }

  void drawGrid (Graphics g) {
    for (int i = -rangeOfIndex; i <= rangeOfIndex; i++) { // vertical lines
      g.drawLine(nwx + width/2 + h_gridsize * i, nwy, 
		 nwx + width/2 + h_gridsize * i, nwy + height);
    }
    for (int i = -rangeOfJndex; i <= rangeOfJndex; i++) { // horizontal lines
      g.drawLine(nwx, nwy + height/2 + v_gridsize * i, 
		 nwx + width, nwy + height/2 + v_gridsize * i);
    }
    g.fillRect(nwx + width/2 - 1, nwy, 3, height); // y-axis
    g.fillRect(nwx, nwy + height/2 - 1, width, 3); // x-axis

    // arrow on y-axis
    int[] xs = {nwx + width/2, nwx + width/2 - 6, nwx + width/2, nwx + width/2 + 6};
    int[] ys = {nwy-2, nwy + 10, nwy + 6, nwy + 10};
    g.fillPolygon(new Polygon(xs, ys, 4));
    // arrow on x-axis
    int[] xs2 = {width + nwx + 2, width+ nwx - 10, width + nwx - 6, width + nwx - 10};
    int[] ys2 = {nwy + height/2, nwy + height/2 - 6, nwy + height/2, nwy + height/2 + 6};
    g.fillPolygon(new Polygon(xs2, ys2, 4));

  }

  public void update(Graphics g) {
    paint(g); // no clearing of screen, just over-paint
    // problem if applet is overlaid by some other window...
  }

  public void paint(Graphics g) {

    if (updating == true) {
       tellDegree(g);
       g.setColor(Color.white);
       for (int i = -rangeOfInc ; i < rangeOfInc; i++) {
	 g.drawLine( normPara(i),
		     normOut(theFunction(normIn(i))),
		     normPara(i+1),
		     normOut(theFunction(normIn(i+1))));
       }
       g.setColor(Color.red);
       for (int i = -rangeOfInc ; i < rangeOfInc; i++) {
	 g.drawLine( normPara(i),
		     normOut(Math.exp(normIn(i))),
		     normPara(i+1),
		     normOut(Math.exp(normIn(i+1))));
       }
       g.setColor(Color.black);
       updating = false;
    }
    else {
      g.setColor(Color.gray);
      g.fillRect(0,0,600,350);
      g.setColor(Color.black);
      
      drawClickBox(g);
      tellDegree(g);
      
      drawGrid(g);
      
      g.setColor(Color.white);
      for (int i = -rangeOfInc ; i < rangeOfInc; i++) {
      g.drawLine( normPara(i),
		  normOut(theFunction(normIn(i))),
		  normPara(i+1),
		  normOut(theFunction(normIn(i+1))));
      }
      g.setColor(Color.red);
      for (int i = -rangeOfInc ; i < rangeOfInc; i++) {
	g.drawLine( normPara(i),
		    normOut(Math.exp(normIn(i))),
		    normPara(i+1),
		    normOut(Math.exp(normIn(i+1))));
      }
      g.setColor(Color.black);
      g.drawRect(left,top+100,50,20);
      g.drawString("Reset",left+5,top+100+20-3); // reset clickbox
    }
  }

  void drawClickBox(Graphics g) {
    g.drawRect(left,top,right-left,bottom-top);
    g.drawString("Increase degree",left+5,bottom-3);
  }

  void tellDegree(Graphics g) {
    g.setColor(Color.gray);
    g.fillRect(left,top+40,right-left,bottom-top);
    g.setColor(Color.black);
    //    g.drawRect(left,top+40,right-left,bottom-top);
    g.drawString("Degree "+deg,left+5, bottom+40-3);
  }

  public final boolean mouseDown(Event e, int x, int y) {
    if (x>=left && x<=right && y>=top && y<= bottom &&
	 deg < degree-1) {
      deg++;
      updating = true;
      repaint();
    }
    else if (x>=left && x<=left+50 && y<=top+100+20-3 && y>=top+100) {
      init();
    }
    return true;
  }

} // The End