Change Equation of a Graph: Difference between revisions

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This example shows how you can change the equation of a graph without creating the whole construction again.
This example shows how you can change the equation of a graph without creating the whole construction again. Dependent elements are updated automatically.
<html>
<html><br />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/loadjsxgraphXML.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div style="width:960px">
<div id="jxgbox" class="jxgbox" style="width:600px; height:400px; float:left; "></div>
<p style="float:right">
<input type="text" id="eingabe" value="Math.sin(x)*Math.cos(x)">
<input type="text" id="eingabe" value="Math.sin(x)*Math.cos(x)">
<input type="button" value="set" onClick="doIt()" style='margin:1em'>  
<input type="button" value="set" onClick="doIt()" style='margin:1em'>  
</p>
</html>
</div>
<jsxgraph width="600" height="400" box="jxgbox">
<br clear=all>
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-6, 12, 8, -6], axis: true});
<div id="debug" style="display:none;"></div>
  <script type="text/javascript">
    /* <![CDATA[ */
 
        board = JXG.JSXGraph.initBoard('jxgbox', {originX: 250, originY: 250, unitX: 40, unitY: 20});
// Axes
        b1axisx = board.createElement('axis', [[1,0], [0,0]], {});
        b1axisy = board.createElement('axis', [[0,1], [0,0]], {});
eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
graph = board.createElement('curve', [function(x){ return x; }, function(x){ return f(x); }, "x", -10, 10]);
var graph = board.create('functiongraph', [function(x){ return f(x); }, -10, 10]),
//graph = eval("board.createElement('curve', [function(x){ return x; }, function(x){ return "+document.getElementById("eingabe").value+";}, 'x', -10, 10])");
    p1 = board.create('glider', [0,0,graph], {style:6, name:'P'}),
//graph.curveType = "graph";
    p2 = board.create('point', [function() { return p1.X()+1;}, function() {return p1.Y()+JXG.Math.Numerics.D(graph.Y)(p1.X());}], {style:1, name:''}),
        p1 = board.createElement('glider', [graph], {style:6, name:'P'});
    l1 = board.create('line', [p1,p2],{}),
        g = board.algebra.D(f);
    p3 = board.create('point', [function() { return p2.X();}, function() {return p1.Y();}],{style:1, name:''}),
        p2 = board.createElement('point', [function() { return p1.X()+1;}, function() {return p1.Y()+board.algebra.D(graph.Y)(p1.X());}], {style:1, name:''});
    pol = board.create('polygon', [p1,p2,p3], {}),
        l1 = board.createElement('line', [p1,p2],{});
    t = board.create('text', [function(){return p1.X()+1.1;},function(){return p1.Y()+(p2.Y()-p3.Y())/2;},function(){ return "m="+((p2.Y()-p3.Y()).toFixed(2));}]);
        p3 = board.createElement('point', [function() { return p2.X();}, function() {return p1.Y();}],{style:1, name:''});
        pol = board.createElement('polygon', [p1,p2,p3], {});
        t = board.createElement('text', [function(){return p1.X()+1.1;},function(){return p1.Y()+(p2.Y()-p3.Y())/2;},function(){ return "m="+(board.round(p2.Y()-p3.Y(),2));}]);  
              
              
       
    function doIt(){
        function doIt(){
        eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
        eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
        graph.Y = function(x){ return f(x); };
        graph.yterm = function(x){ return f(x); }; // usually: e.g. "x^2"
        graph.updateCurve();
//graph.yterm = eval("function(x){ return "+document.getElementById("eingabe").value+"; };");
        board.update();
    graph.Y = graph.yterm;
    }  
    graph.updateCurve();
</jsxgraph>
    board.update();
        }  
       
  /* ]]> */
  </script>
</html>




== HowTo Create this Construction ==
== How to Create this Construction ==


=== HTML Part ===
=== HTML Part ===
'''Adding a text input field somewhere on the page together with a button'''
'''Adding a text input field somewhere on the page together with a button'''


<source>
<source lang="xml">
<input type="text" id="eingabe" value="Math.sin(x)*Math.cos(x)">
<input type="text" id="eingabe" value="Math.sin(x)*Math.cos(x)">
<input type="button" value="set" onClick="doIt()">  
<input type="button" value="set" onClick="doIt()">  
Line 60: Line 36:


=== JavaScript Part ===
=== JavaScript Part ===
'''Setting up the board'''
Setting up the board
<source>
<source lang="javascript">
  board = JXG.JSXGraph.initBoard('jxgbox', {originX: 250, originY: 250, unitX: 40, unitY: 20});
board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-6, 12, 8, -6], axis: true});
  // Axes
  b1axisx = board.createElement('axis', [[1,0], [0,0]], {});
  b1axisy = board.createElement('axis', [[0,1], [0,0]], {});
</source>
</source>


'''Create a JavaScript Function f(x) From the Text Field'''
Create a JavaScript Function f(x) From the Text Field
<source>
<source lang="javascript">
  eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
</source>
</source>


'''Use f(x) for defining the Graph'''
Use f(x) for defining the Graph
<source>
<source lang="javascript">
graph = board.createElement('curve', [function(x){ return x; }, function(x){ return f(x); }, "x", -10, 10]);
graph = board.create('functiongraph', [function(x){ return f(x); },-10, 10]);
</source>
</source>


'''Define Further Elements'''
The slope triangle
<source>
<source lang="javascript">
  //glider on the curve
//glider on the curve
  p1 = board.createElement('glider', [graph], {style:6, name:'P'});
p1 = board.create('glider', [0,0,graph], {style:6, name:'P'});
  //define the derivative of f
//define the derivative of f
  g = board.algebra.D(f);
g = JXG.Math.Numerics.D(f);
  //a point on the tangent
//a point on the tangent
  p2 = board.createElement('point', [function() { return p1.X()+1;}, function() {return p1.Y()+board.algebra.D(graph.Y)(p1.X());}], {style:1, name:''});
//                                variable x coordinate          variable y coordinate depending on the derivative of f at point p1.X()
  //the tangent  
p2 = board.create('point', [function() { return p1.X()+1;}, function() {return p1.Y()+JXG.Math.Numerics.D(graph.Y)(p1.X());}], {style:1, name:''});
  l1 = board.createElement('line', [p1,p2],{});  
//the tangent  
  //a third point fpr the slope triangle
l1 = board.create('line', [p1,p2],{});  
  p3 = board.createElement('point', [function() { return p2.X();}, function() {return p1.Y();}],{style:1, name:''});
//a third point fpr the slope triangle
  //the slope triangle
p3 = board.create('point', [function() { return p2.X();}, function() {return p1.Y();}],{style:1, name:''});
  pol = board.createElement('polygon', [p1,p2,p3], {});
//the slope triangle
  //a text for displaying slope's value
pol = board.create('polygon', [p1,p2,p3], {});
  t = board.createElement('text', [function(){return p1.X()+1.1;},function(){return p1.Y()+(p2.Y()-p3.Y())/2;},function(){ return "m="+(board.round(p2.Y()-p3.Y(),2));}]);  
//a text for displaying slope's value
//                              variable x coordinate          variable y coordinate                        variable value
t = board.create('text', [function(){return p1.X()+1.1;},function(){return p1.Y()+(p2.Y()-p3.Y())/2;},function(){ return "m="+(p2.Y()-p3.Y()).toFixed(2);}],{color:ff0000});  
</source>
</source>


'''Define JavaScript Function doIt() for Reacting on User Input'''
Change the plotted function
<source>
<source lang="javascript">
  function doIt(){
function doIt(){
    //redefine function f according to the current text field value
  //redefine function f according to the current text field value
    eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
  eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
    //change the yterm attribute of the graph to the new function  
  //change the Y attribute of the graph to the new function  
    graph.yterm = function(x){ return f(x); }; // usually: e.g. "x^2"
  graph.Y = function(x){ return f(x); };
    graph.Y = graph.yterm;
  //update the graph
    //update the graph
  graph.updateCurve();
    graph.updateCurve();
  //update the whole board
    //update the whole board
  board.update();
    board.update();
}  
  }  
</source>
</source>


== Remarks ==
== Remarks ==
The
The doIt() function is only responsible for updating the graph. All other dependend objects are self-updating, especially the object p2 which depends on the derivative of function f. This is all done by anonymous functions of JavaScript.
 
[[Category:Examples]]
[[Category:Calculus]]

Latest revision as of 08:30, 3 April 2019

This example shows how you can change the equation of a graph without creating the whole construction again. Dependent elements are updated automatically.


How to Create this Construction

HTML Part

Adding a text input field somewhere on the page together with a button

<input type="text" id="eingabe" value="Math.sin(x)*Math.cos(x)">
<input type="button" value="set" onClick="doIt()">

JavaScript Part

Setting up the board

board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-6, 12, 8, -6], axis: true});

Create a JavaScript Function f(x) From the Text Field

eval("function f(x){ return "+document.getElementById("eingabe").value+";}");

Use f(x) for defining the Graph

graph = board.create('functiongraph', [function(x){ return f(x); },-10, 10]);

The slope triangle

//glider on the curve
p1 = board.create('glider', [0,0,graph], {style:6, name:'P'});
//define the derivative of f
g = JXG.Math.Numerics.D(f);
//a point on the tangent
//                                 variable x coordinate           variable y coordinate depending on the derivative of f at point p1.X()
p2 = board.create('point', [function() { return p1.X()+1;}, function() {return p1.Y()+JXG.Math.Numerics.D(graph.Y)(p1.X());}], {style:1, name:''});
//the tangent 
l1 = board.create('line', [p1,p2],{}); 
//a third point fpr the slope triangle
p3 = board.create('point', [function() { return p2.X();}, function() {return p1.Y();}],{style:1, name:''});
//the slope triangle
pol = board.create('polygon', [p1,p2,p3], {});
//a text for displaying slope's value
//                               variable x coordinate          variable y coordinate                        variable value
t = board.create('text', [function(){return p1.X()+1.1;},function(){return p1.Y()+(p2.Y()-p3.Y())/2;},function(){ return "m="+(p2.Y()-p3.Y()).toFixed(2);}],{color:ff0000});

Change the plotted function

function doIt(){
  //redefine function f according to the current text field value
  eval("function f(x){ return "+document.getElementById("eingabe").value+";}");
  //change the Y attribute of the graph to the new function 
  graph.Y = function(x){ return f(x); };
  //update the graph
  graph.updateCurve();
  //update the whole board
  board.update();
}

Remarks

The doIt() function is only responsible for updating the graph. All other dependend objects are self-updating, especially the object p2 which depends on the derivative of function f. This is all done by anonymous functions of JavaScript.