Circles on circles rotating in opposite directions: Difference between revisions

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(New page: This is an example of a parametric curve plot. The curve is described by the function :<math> [0,2\pi]\to{\mathbf R}^2, \quad t\mapsto {\cos(t)\choose \sin(t)}+c_1{\cos(f_1t)\choose \sin(f...)
 
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This is an example of a parametric curve plot. The curve is described by the function
This is an example of a parametric curve plot. The curve is described by the function
:<math> [0,2\pi]\to{\mathbf R}^2, \quad t\mapsto {\cos(t)\choose \sin(t)}+c_1{\cos(f_1t)\choose \sin(f_1t)}+c_2{\cos(f_2t)\choose \sin(f_2t)}</math>
:<math> [0,2\pi]\to{\mathbf R}^2, \quad t\mapsto {\cos(t)\choose \sin(t)}+c_1{\cos(f_1t)\choose \sin(f_1t)}+c_2{\sin(f_2t)\choose \cos(f_2t)}</math>
The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.
The sliders to adjust the parameters of this curve are from the jQuery UI package, see [http://jqueryui.com http://jqueryui.com]. This example shows the seamless integration of JSXGraph into the web page.


Line 170: Line 170:
var f2 = 17;
var f2 = 17;
var c = board.createElement('curve', [
var c = board.createElement('curve', [
               function(t) { return Math.cos(t)+ c1*Math.cos(f1*t)+ c2*Math.cos(f2*t);},
               function(t) { return Math.cos(t)+ c1*Math.cos(f1*t)+ c2*Math.sin(f2*t);},
               function(t) { return Math.sin(t)+ c1*Math.sin(f1*t)+ c2*Math.sin(f2*t);},
               function(t) { return Math.sin(t)+ c1*Math.sin(f1*t)+ c2*Math.cos(f2*t);},
               0,2.02*Math.PI],{strokeWidth:2});
               0,2.02*Math.PI],{strokeWidth:2});
</script>
</script>

Revision as of 08:46, 30 June 2009

This is an example of a parametric curve plot. The curve is described by the function

[math]\displaystyle{ [0,2\pi]\to{\mathbf R}^2, \quad t\mapsto {\cos(t)\choose \sin(t)}+c_1{\cos(f_1t)\choose \sin(f_1t)}+c_2{\sin(f_2t)\choose \cos(f_2t)} }[/math]

The sliders to adjust the parameters of this curve are from the jQuery UI package, see http://jqueryui.com. This example shows the seamless integration of JSXGraph into the web page.

Variation:

External references

Epicycloidal curves have been used by the ancient greeks to describe the orbits of the planets, see

The source code of this construction

This is the first experiment with the jQuery UI package. So, the code may not be optimized, yet. The main difficulty is to read the values of the sliders. This is done via four JavaScript variables [math]\displaystyle{ c1, c2, f1, f2 }[/math]. 

<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<link rel="Stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/css/ui-lightness/jquery-ui-1.7.2.custom.css"/>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery.min.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jquery-ui.min.js"></script>
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>

<style type="text/css">
		#slider-frame > div.sliders { padding: 10px !important; };
	</style>
	<script type="text/javascript">
	$(function() {
		$("#sliderc1").slider({
			orientation: "horizontal",range: "min",min: 0,max: 100,value: 60,
			slide: function(event, ui) {
				$("#c1").val(ui.value*0.01);
                                c1 = ui.value*0.01;
                                board.update();
			}
		});
		$("#sliderf1").slider({
			orientation: "horizontal",range: "min",min: 1,max: 100,value: 7,
			slide: function(event, ui) {
				$("#f1").val(ui.value);
                                f1 = ui.value;
                                board.update();
			}
		});
		$("#c1").val($("#sliderc1").slider("value")*0.01);
		$("#f1").val($("#sliderf1").slider("value"));

		$("#sliderc2").slider({
			orientation: "horizontal",range: "min",min: 0,max: 100,value: 0,
			slide: function(event, ui) {
				$("#c2").val(ui.value*0.01);
                                c2 = ui.value*0.01;
                                board.update();
			}
		});
		$("#sliderf2").slider({
			orientation: "horizontal",range: "min",min: 1,max: 100,value: 17,
			slide: function(event, ui) {
				$("#f2").val(ui.value);
                                f2 = ui.value;
                                board.update();
			}
		});
		$("#c2").val($("#sliderc2").slider("value")*0.01);
		$("#f2").val($("#sliderf2").slider("value"));
	});
	</script>

<div class="sliders" style="margin:5px">
  <p>
    <label for="c1">c1:</label>
    <input type="text" id="c1" style="border:0; color:#f6931f; font-weight:bold;" />
    <label for="f1">f1:</label>
    <input type="text" id="f1" style="border:0; color:#f6931f; font-weight:bold;" />
    <label for="c2">c2:</label>
    <input type="text" id="c2" style="border:0; color:#f6931f; font-weight:bold;" />
    <label for="f2">f2:</label>
    <input type="text" id="f2" style="border:0; color:#f6931f; font-weight:bold;" />
  </p>
  <div id="sliderc1" style="width:300px;margin:10px;"></div>
  <div id="sliderf1" style="width:300px;margin:10px;"></div>
  <div id="sliderc2" style="width:300px;margin:10px;"></div>
  <div id="sliderf2" style="width:300px;margin:10px;"></div>
</div>
<div id="jsxgbox" class="jxgbox" style="width:500px; height:500px;"></div>
<script language="JavaScript"> 			
board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-2.5,2.5,2.5,-2.5], keepaspectratio:true});
var c1 = 0.6;
var c2 = 0.0; 
var f1 = 7; 
var f2 = 17;
var c = board.createElement('curve', [
              function(t) { return Math.cos(t)+ c1*Math.cos(f1*t)+ c2*Math.sin(f2*t);},
              function(t) { return Math.sin(t)+ c1*Math.sin(f1*t)+ c2*Math.cos(f2*t);},
              0,2.02*Math.PI],{strokeWidth:2});
</script>
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