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Derivatives.java

/*************************************************************************
*                                                                        *
*  This source code file, and compiled classes derived from it, can      *
*  be used and distributed without restriction, including for commercial *
*  use.  (Attribution is not required but is appreciated.)               * 
*                                                                        *
*   David J. Eck                                                         *
*   Department of Mathematics and Computer Science                       *
*   Hobart and William Smith Colleges                                    *
*   Geneva, New York 14456,   USA                                        *
*   Email: eck@hws.edu          WWW: http://math.hws.edu/eck/            *
*                                                                        *
*************************************************************************/


// Draws the graph of a function and its first derivative (and optionally
// its second derivative).  It shows the tangent line to the graph and
// marks the corresponding point on the graph of the derivative.  The
// user controls the position of the tangent line with a slider and/or
// a number-input box.  A formula for the derivative can be displayed 
// at the bototm of the applet.

import java.awt.*;
import java.awt.event.*;
import java.applet.Applet;
import java.util.StringTokenizer;
import edu.hws.jcm.draw.*;
import edu.hws.jcm.data.*;
import edu.hws.jcm.functions.*;
import edu.hws.jcm.awt.*;


public class Derivatives extends GenericGraphApplet {

   private String functionName;  // name of the fuction beging graphed, 'f' by default; used in labels etc
   private Function func;   // The function that is graphed.
   private Function deriv;         // derivative of func
   private Expression derivExpression;  // The Expression that defines the derivative
   private Function deriv2;        // if non-null, second derivative of func
   private Controller subController = new Controller();  // Respond to changes in x-coord input; won't redraw graph

   private VariableInput xInput; // x-coord of point of tangency
   
   private class ExprLbl extends Label implements Computable {
          // A class for displaying the formula for deriv
      String label;
      ExprLbl(String label) {
         this.label = label;
         compute();
      }
      public void compute() {
         setText(label + derivExpression.toString());
      }
   }
   
   protected void setUpParameterDefaults() { // I don't want to use abs(x)^x as the default function, since it's derivative is so funny
      parameterDefaults = new java.util.Hashtable();
      parameterDefaults.put("Function", " tan(" + getParameter("Variable","x") + ")");
   }
   
   protected void setUpMainPanel() {  // add a bunch of extra components at the end
      super.setUpMainPanel();
      
      // now that limitsPanel has been set up, add the two extra coordinate rects to it
      
      if (limitsPanel != null) {
         limitsPanel.addCoords(canvas.getCoordinateRect(1));  
         if (deriv2 != null)
            limitsPanel.addCoords(canvas.getCoordinateRect(2));  
      }
      else {  // CoordinateRects must synchronize with each other
         Tie coordTie = new Tie(canvas.getCoordinateRect(0),canvas.getCoordinateRect(1));
         if (deriv2 != null)
            coordTie.add(canvas.getCoordinateRect(2));
         canvas.getCoordinateRect(0).setSyncWith(coordTie);
         canvas.getCoordinateRect(1).setSyncWith(coordTie);
         if (deriv2 != null)
            canvas.getCoordinateRect(2).setSyncWith(coordTie);
      }
      
      
      // Add controls at the bottom of the panel for setting the value of x.
      // Also add the derivative formula, if it's supposed to be displayed
   
      Value xMin = canvas.getCoordinateRect().getValueObject(CoordinateRect.XMIN);
      Value xMax = canvas.getCoordinateRect().getValueObject(CoordinateRect.XMAX);
      canvas.getCoordinateRect().setOnChange(subController);
      VariableSlider xSlider = new VariableSlider(xMin,xMax);
      xSlider.setOnUserAction(subController);
      xInput.setOnTextChange(subController);
      subController.add(xSlider);
      subController.add(xInput);
      subController.add( new Tie(xSlider,xInput) );
      
      Panel p = new Panel();
      p.setLayout(new BorderLayout(5,5));
      p.add(xInput.withLabel(), BorderLayout.WEST);
      p.add(xSlider, BorderLayout.CENTER);
      
      // If there is no limits panel, make it possible to add a RestoreLimits button to the input panel
      
      if (limitsPanel == null && ! "no".equalsIgnoreCase(getParameter("UseRestoreButton","no"))) {
               // add button to left of slider
           Button res = new Button("Restore Limits");
           p.add(res, BorderLayout.EAST);
           res.setBackground(Color.lightGray);
           res.addActionListener( new ActionListener() {
                   public void actionPerformed(ActionEvent evt) {
                      canvas.getCoordinateRect(0).restore();
                      canvas.getCoordinateRect(1).restore();
                      if (deriv2  != null) 
                         canvas.getCoordinateRect(2).restore();
                   }
              });
      }

      if ("yes".equalsIgnoreCase(getParameter("ShowFormula", "yes"))) { // add derivative formula
         Panel s = new Panel();
         s.setLayout(new GridLayout(2,1,3,3));
         s.add(p);
         ExprLbl lbl = new ExprLbl(" " + functionName + "'(" + xVar.getName() + ") = ");
         mainController.add(lbl);
         s.add(lbl);
         p = s;
      }
      
      if (inputPanel == null) {
            // Add the control panel directly to the main panel
         p.setBackground(getColorParam("PanelBackground",Color.lightGray));
         mainPanel.add(p,BorderLayout.SOUTH);
      }
      else {
            // Add control panel to bottom of input panel.
         inputPanel.add(p,BorderLayout.SOUTH);
      }
      

   } // end setUpMainPanel


   protected void setUpCanvas() {  // Override this to add more stuff to the canvas.
                                   // I don't call super.setUpCanvas(), since
                                   // the canvas in this case is quite a bit different
                                   // from the standard one.

      boolean showSecond = ! "no".equalsIgnoreCase(getParameter("SecondDerivative","no"));

      xInput = new VariableInput(xVar.getName(), getParameter("X","1"));
      
      if (functionInput != null) {
         func = functionInput.getFunction(xVar);
         derivExpression = functionInput.getExpression().derivative(xVar);
      }
      else {
         String def = getParameter("Function");
         Expression exp = parser.parse(def);
         Function f = new SimpleFunction( exp, xVar );
         derivExpression = exp.derivative(xVar);
         func = new WrapperFunction(f);
      }
      Graph1D graph = new Graph1D(func);
      Color color = getColorParam("GraphColor",Color.black);
      graph.setColor(color);
      deriv = func.derivative(1);
      Graph1D derivGraph = new Graph1D(deriv);
      derivGraph.setColor(color);
      Graph1D deriv2Graph = null;
      if (showSecond) {
         deriv2 = deriv.derivative(1);
         deriv2Graph = new Graph1D(deriv2);
         deriv2Graph.setColor(color);
      }

      // Set up 2 or 3 coordinate retcs
      
      if (showSecond) {
         canvas.addNewCoordinateRect(0, 1.0/3.0, 0, 1);
         canvas.addNewCoordinateRect(1.0/3.0, 2.0/3.0, 0, 1);
         canvas.addNewCoordinateRect(2.0/3.0, 1, 0, 1);
      }
      else {
         canvas.addNewCoordinateRect(0, 0.5, 0, 1);
         canvas.addNewCoordinateRect(0.5, 1, 0, 1);
      }

      // do the type of stuff that's usually done in super.setUpCanvas
      
      color = getColorParam("CanvasColor");
      if (color != null)
         canvas.setBackground(color);
      if (! "no".equalsIgnoreCase(getParameter("UsePanner", "no")) ) {
         canvas.add(new Panner(),0);
         canvas.add(new Panner(),1);
         if (showSecond)
            canvas.add(new Panner(),2);
      }
      if ( ! "no".equalsIgnoreCase(getParameter("UseGrid", "no")) ) {
         Grid g = new Grid();
         color = getColorParam("GridColor");
         if (color != null)
            g.setColor(color);
         canvas.add(g,0);
         g = new Grid();
         color = getColorParam("GridColor");
         if (color != null)
            g.setColor(color);
         canvas.add(g,1);
         if (showSecond) {
            g = new Grid();
            color = getColorParam("GridColor");
            if (color != null)
               g.setColor(color);
            canvas.add(g,2);
         }
      }
      canvas.add(makeAxes(),0);
      canvas.add(makeAxes(),1);
      if (showSecond)
         canvas.add(makeAxes(),2);
      if ( ! "no".equalsIgnoreCase(getParameter("UseMouseZoom", "no")) )
         canvas.setHandleMouseZooms(true);
      if ( "yes".equalsIgnoreCase(getParameter("UseOffscreenCanvas", "yes")) )
         canvas.setUseOffscreenCanvas(true);
      mainController.setErrorReporter(canvas);
      mainPanel.add(canvas, BorderLayout.CENTER);
      
      // add graphs, tangent lines etc.
      
      canvas.add(graph,0);
      canvas.add(derivGraph,1);
      if (showSecond)
         canvas.add(deriv2Graph,2);
         
      Color tangentColor = getColorParam("TangentColor", Color.red);
      Color tangentColor2 = getColorParam("TangentColor2", new Color(0, 180, 0));
            
      mainController.remove(canvas);
      mainController.add(graph);
      mainController.add(derivGraph);
      if (showSecond)
         mainController.add(deriv2Graph);
      
      subController = new Controller();
      mainController.add(subController);
      
      TangentLine tan = new TangentLine(xInput, func);
      Crosshair cross = new Crosshair(xInput,deriv);
      tan.setColor(tangentColor);
      cross.setColor(tangentColor);
      canvas.add(tan, 0);
      canvas.add(cross, 1);
      subController.add(tan);
      subController.add(cross);
      
      if (showSecond) {
         tan = new TangentLine(xInput, deriv);
         cross = new Crosshair(xInput, deriv2);
         tan.setColor(tangentColor2);
         cross.setColor(tangentColor2);
         canvas.add(tan, 1);
         canvas.add(cross, 2);
         subController.add(tan);
         subController.add(cross);
      }

      functionName = getParameter("FunctionName", "f");

      String yName = getParameter("YName","y");
      Color textColor = getColorParam("TextColor",Color.black);
      Color bgColor = getColorParam("TextBackground",Color.white);
      DrawString str;
      
      if ("yes".equalsIgnoreCase(getParameter("ShowGraphLabels","yes"))) {
         str = new DrawString(yName + " = " + functionName + "(" + xVar.getName() + ")");
         str.setColor(textColor);
         str.setBackgroundColor(bgColor);
         str.setFrameWidth(1);
         canvas.add(str,0);
         str = new DrawString(yName + " = " + functionName + " ' (" + xVar.getName() + ")");
         str.setColor(textColor);
         str.setBackgroundColor(bgColor);
         str.setFrameWidth(1);
         canvas.add(str,1);
         if (showSecond) {
             str = new DrawString(yName + " = " + functionName + " ' ' (" + xVar.getName() + ")");
             str.setColor(textColor);
             str.setBackgroundColor(bgColor);
             str.setFrameWidth(1);
             canvas.add(str,2);
         }
      }
      if ("yes".equalsIgnoreCase(getParameter("ShowValues","yes"))) {
          str = new DrawString(functionName + "(#) = #", DrawString.BOTTOM_LEFT, new Value[] { xInput, new ValueMath(func,xInput) });
          str.setColor(textColor);
          str.setBackgroundColor(bgColor);
          str.setFrameWidth(1);
          str.setNumSize(7);
          canvas.add(str,0);
          subController.add(str);
          str = new DrawString(functionName + " ' (#) = #", DrawString.BOTTOM_LEFT, new Value[] { xInput, new ValueMath(deriv,xInput) });
          str.setColor(textColor);
          str.setBackgroundColor(bgColor);
          str.setFrameWidth(1);
          str.setNumSize(7);
          canvas.add(str,1);
          subController.add(str);
          if (showSecond) {
             str = new DrawString(functionName + " ' ' (#) = #", DrawString.BOTTOM_LEFT, new Value[] { xInput, new ValueMath(deriv2,xInput) });
             str.setColor(textColor);
             str.setBackgroundColor(bgColor);
             str.setFrameWidth(1);
             str.setNumSize(7);
             canvas.add(str,2);
             subController.add(str);
          }
      }

   } // end setUpCanvas()
   
   
   protected void addCanvasBorder() { // override to add the border to each coordinate rect, and make default width equal to 1
      int borderWidth;
      double[] bw = getNumericParam("BorderWidth");
      if (bw == null || bw.length == 0 || bw[0] > 25)
         borderWidth = 2;
      else
         borderWidth = (int)Math.round(bw[0]);
      if (borderWidth > 0) {
         canvas.add( new DrawBorder( getColorParam("BorderColor", Color.black), borderWidth  ), 0 );
         canvas.add( new DrawBorder( getColorParam("BorderColor", Color.black), borderWidth  ), 1 );
         if (deriv2 != null)
            canvas.add( new DrawBorder( getColorParam("BorderColor", Color.black), borderWidth  ), 2 );
      }
   }



   protected void doLoadExample(String example) {
         // This method is called when the user loads an example from the 
         // example menu (if there is one).  It overrides an empty method
         // in GenericGraphApplet.
         //   For the SecantTangent applet, the example string should contain
         // an expression that defines the function to be graphed.  This can optionally
         // be followed by a semicoloon and a list of four or five numbers.
         // The first four numbers give the x- and y-limits to be used for the
         // example.  If they are not present, then -5,5,-5,5 is used.  The
         // fifth number, if present, gives the x-coord where the tangent line
         // is drawn initially.
   
      int pos = example.indexOf(";");

      double[] limits = { -5,5,-5,5 };  // x- and y-limits to use
      
      if (pos > 0) { // get limits from example text
         String limitsText = example.substring(pos+1);
         example = example.substring(0,pos);
         StringTokenizer toks = new StringTokenizer(limitsText, " ,");
         if (toks.countTokens() >= 4) {
            for (int i = 0; i < 4; i++) {
               try {
                   Double d = new Double(toks.nextToken());
                   limits[i] = d.doubleValue();
               }
               catch (NumberFormatException e) {
               }
            }
            if (toks.countTokens() > 0) { // Get point for tangent line
               try {
                   Double d = new Double(toks.nextToken());
                   xInput.setVal( d.doubleValue() );
               }
               catch (NumberFormatException e) {
               }
            }
         }
      }
      
      // Set up the example data and recompute everything.

      if (functionInput != null) {
            // If there is a function input box, put the example text in it.
         functionInput.setText(example);
      }
      else { 
           // If there is no user input, set the function in the graph directly.
           // Also, in this case, func is a "WrapperFunction".  Set the
           // definition of that WrapperFunction to be the same as f
         try {
            Expression exp = parser.parse(example);
            derivExpression = exp.derivative(xVar);
            Function f = new SimpleFunction( exp, xVar );
            ((WrapperFunction)func).setFunction(f);
         }
         catch (ParseError e) {  
             // There should't be parse error's in the Web-page
             // author's examples!  If there are, the function
             // just won't change.
         }
      }
      CoordinateRect coords = canvas.getCoordinateRect(0);
      coords.setLimits(limits);
      coords.setRestoreBuffer();
      canvas.getCoordinateRect(1).setRestoreBuffer();
      if (deriv2 != null)
         canvas.getCoordinateRect(0).setRestoreBuffer();
      mainController.compute();
      
   } // end doLoadExample()
   


} // end class SimpleGraph

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