Trochoid - Revision history

A WASSERMANN at 16:12, 20 February 2013

2013-02-20T16:12:23Z

← Older revision		Revision as of 16:12, 20 February 2013
Line 31:		Line 31:
	board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});		board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
	board.suspendUpdate();		board.suspendUpdate();
			var D = JXG.Math.Numerics.D;
	var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});		var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
	var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});		var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
Line 38:		Line 39:

	var dualCurve = function(x,y,board) {		var dualCurve = function(x,y,board) {
	var X = function(phi) { return ~~board.~~D(y)(phi)/(y(phi)~~board.~~D(x)(phi)-x(phi)~~board.~~D(y)(phi)); }		var X = function(phi) { return D(y)(phi)/(y(phi)D(x)(phi)-x(phi)D(y)(phi)); }
	var Y = function(phi) { return ~~board.~~D(x)(phi)/(x(phi)~~board.~~D(y)(phi)-y(phi)~~board.~~D(x)(phi)); }		var Y = function(phi) { return D(x)(phi)/(x(phi)D(y)(phi)-y(phi)D(x)(phi)); }
	return [X,Y];		return [X,Y];
	}		}

A WASSERMANN at 16:11, 20 February 2013

2013-02-20T16:11:58Z

← Older revision		Revision as of 16:11, 20 February 2013
Line 7:		Line 7:
	board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});		board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
	board.suspendUpdate();		board.suspendUpdate();
			var D = JXG.Math.Numerics.D;
	var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});		var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
	var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});		var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
Line 14:		Line 15:

	var dualCurve = function(x,y,board) {		var dualCurve = function(x,y,board) {
	var X = function(phi) { return ~~board.~~D(y)(phi)/(y(phi)~~board.~~D(x)(phi)-x(phi)~~board.~~D(y)(phi)); }		var X = function(phi) { return D(y)(phi)/(y(phi)D(x)(phi)-x(phi)D(y)(phi)); }
	var Y = function(phi) { return ~~board.~~D(x)(phi)/(x(phi)~~board.~~D(y)(phi)-y(phi)~~board.~~D(x)(phi)); }		var Y = function(phi) { return D(x)(phi)/(x(phi)D(y)(phi)-y(phi)D(x)(phi)); }
	return [X,Y];		return [X,Y];
	}		}

Michael at 07:37, 9 June 2011

2011-06-09T07:37:54Z

← Older revision		Revision as of 07:37, 9 June 2011
Line 4:		Line 4:
	:<math>y = a-b\cos(\phi)</math>		:<math>y = a-b\cos(\phi)</math>

	<~~html>~~		<jsxgraph box="jsxgbox" width="550" height="500">
	~~<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/~~jsxgraph~~.css" />~~		board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
	~~<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>~~		board.suspendUpdate();
	~~<div id~~="jsxgbox" ~~class~~="~~jxgbox~~" ~~style="width:550px;~~ height~~:500px;"></div>~~		var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
	~~<script language~~="~~JavaScript~~">		var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
	board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});		var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }
	board.suspendUpdate();		var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
	var a = board.~~createElement~~('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});		var c1 = board.create('curve', [x,y,-Math.PI4,Math.PI4],{strokeWidth:3});
	var b = board.~~createElement~~('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
	var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }
	var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
	var c1 = board.~~createElement~~('curve', [x,y,-Math.PI4,Math.PI4],{strokeWidth:3});

	var dualCurve = function(x,y,board) {		var dualCurve = function(x,y,board) {
	var X = function(phi) { return board.D(y)(phi)/(y(phi)board.D(x)(phi)-x(phi)board.D(y)(phi)); }		var X = function(phi) { return board.D(y)(phi)/(y(phi)board.D(x)(phi)-x(phi)board.D(y)(phi)); }
	var Y = function(phi) { return board.D(x)(phi)/(x(phi)board.D(y)(phi)-y(phi)board.D(x)(phi)); }		var Y = function(phi) { return board.D(x)(phi)/(x(phi)board.D(y)(phi)-y(phi)board.D(x)(phi)); }
	return [X,Y];		return [X,Y];
	}		}
	var dual = dualCurve(x,y,board);		var dual = dualCurve(x,y,board);
	var c2 = board.~~createElement~~('curve', [dual[0],dual[1],-Math.PI1,Math.PI1],{strokeWidth:3, strokeColor:'red'});		var c2 = board.create('curve', [dual[0],dual[1],-Math.PI1,Math.PI1],{strokeWidth:3, strokeColor:'red'});
	board.unsuspendUpdate();		board.unsuspendUpdate();
	</~~script~~>		</jsxgraph>
	~~</html>~~
	===References===		===References===
	* [http://en.wikipedia.org/wiki/Trochoid http://en.wikipedia.org/wiki/Trochoid]		* [http://en.wikipedia.org/wiki/Trochoid http://en.wikipedia.org/wiki/Trochoid]
	* [http://en.wikipedia.org/wiki/Dual_curve http://en.wikipedia.org/wiki/Dual_curve]		* [http://en.wikipedia.org/wiki/Dual_curve http://en.wikipedia.org/wiki/Dual_curve]
	===The underlying JavaScript code===		===The underlying JavaScript code===
	<source lang="~~xml">~~		<source lang="javascript">
	~~<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />~~		board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
	~~<script type="text/~~javascript~~" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>~~		board.suspendUpdate();
	~~<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>~~		var a = board.create('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
	~~<script language="JavaScript~~">		var b = board.create('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
	board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});		var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }
	board.suspendUpdate();		var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
	var a = board.~~createElement~~('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});		var c1 = board.create('curve', [x,y,-Math.PI4,Math.PI4],{strokeWidth:3});
	var b = board.~~createElement~~('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
	var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }
	var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
	var c1 = board.~~createElement~~('curve', [x,y,-Math.PI4,Math.PI4],{strokeWidth:3});

	var dualCurve = function(x,y,board) {		var dualCurve = function(x,y,board) {
	var X = function(phi) { return board.D(y)(phi)/(y(phi)board.D(x)(phi)-x(phi)board.D(y)(phi)); }		var X = function(phi) { return board.D(y)(phi)/(y(phi)board.D(x)(phi)-x(phi)board.D(y)(phi)); }
	var Y = function(phi) { return board.D(x)(phi)/(x(phi)board.D(y)(phi)-y(phi)board.D(x)(phi)); }		var Y = function(phi) { return board.D(x)(phi)/(x(phi)board.D(y)(phi)-y(phi)board.D(x)(phi)); }
	return [X,Y];		return [X,Y];
	}		}
	var dual = dualCurve(x,y,board);		var dual = dualCurve(x,y,board);
	var c2 = board.~~createElement~~('curve', [dual[0],dual[1],-Math.PI1,Math.PI1],{strokeWidth:3, strokeColor:'red'});		var c2 = board.create('curve', [dual[0],dual[1],-Math.PI1,Math.PI1],{strokeWidth:3, strokeColor:'red'});
	board.unsuspendUpdate();		board.unsuspendUpdate();
	~~</script>~~
	</source>		</source>
	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Curves]]		[[Category:Curves]]

A WASSERMANN at 14:33, 29 October 2009

2009-10-29T14:33:31Z

← Older revision		Revision as of 14:33, 29 October 2009
Line 6:		Line 6:
	<html>		<html>
	<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/jsxgraph.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/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>		<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>
Line 32:		Line 31:
	* [http://en.wikipedia.org/wiki/Dual_curve http://en.wikipedia.org/wiki/Dual_curve]		* [http://en.wikipedia.org/wiki/Dual_curve http://en.wikipedia.org/wiki/Dual_curve]
	===The underlying JavaScript code===		===The underlying JavaScript code===
	~~This is an example where [http://jquery.com jQuery] is used.~~
	<source lang="xml">		<source lang="xml">
	<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/jsxgraph.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/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>		<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>

A WASSERMANN at 20:35, 21 September 2009

2009-09-21T20:35:45Z

← Older revision		Revision as of 20:35, 21 September 2009
Line 39:		Line 39:
	<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>		<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY~~: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
	board.suspendUpdate();		board.suspendUpdate();
	~~board.createElement('axis', [[0,0],[1,0]]);~~
	~~board.createElement('axis', [[0,0],[0,1]]);~~
	var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});		var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
	var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});		var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});

A WASSERMANN at 20:34, 21 September 2009

2009-09-21T20:34:33Z

← Older revision		Revision as of 20:34, 21 September 2009
Line 10:		Line 10:
	<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>		<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY~~: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {boundingbox:[-10,10,10,-10], axis:true});
	board.suspendUpdate();		board.suspendUpdate();
	~~board.createElement('axis', [[0,0],[1,0]]);~~
	~~board.createElement('axis', [[0,0],[0,1]]);~~
	var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});		var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
	var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});		var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});

A WASSERMANN at 21:09, 7 April 2009

2009-04-07T21:09:13Z

← Older revision		Revision as of 21:09, 7 April 2009
Line 8:		Line 8:
	<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.min.js"></script>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<div id="jsxgbox" class="jxgbox" style="width:~~500px~~; height:500px;"></div>		<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});
Line 39:		Line 39:
	<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.min.js"></script>
	<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>		<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
	<div id="jsxgbox" class="jxgbox" style="width:~~500px~~; height:500px;"></div>		<div id="jsxgbox" class="jxgbox" style="width:550px; height:500px;"></div>
	<script language="JavaScript">		<script language="JavaScript">
	board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});		board = JXG.JSXGraph.initBoard('jsxgbox', {originX: 250, originY: 250, unitX: 25, unitY: 25});

A WASSERMANN at 21:08, 7 April 2009

2009-04-07T21:08:43Z

A WASSERMANN at 12:15, 10 March 2009

2009-03-10T12:15:14Z

← Older revision		Revision as of 12:15, 10 March 2009
Line 18:		Line 18:
	var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }		var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }
	var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }		var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
	var c1 = board.createElement('curve', [x,y~~,'phi'~~,-Math.PI4,Math.PI4],{strokeWidth:3});		var c1 = board.createElement('curve', [x,y,-Math.PI4,Math.PI4],{strokeWidth:3});

	var dualCurve = function(x,y,board) {		var dualCurve = function(x,y,board) {
Line 26:		Line 26:
	}		}
	var dual = dualCurve(x,y,board);		var dual = dualCurve(x,y,board);
	var c2 = board.createElement('curve', [dual[0],dual[1]~~,'phi'~~,-Math.PI1,Math.PI1],{strokeWidth:3, strokeColor:'red'});		var c2 = board.createElement('curve', [dual[0],dual[1],-Math.PI1,Math.PI1],{strokeWidth:3, strokeColor:'red'});
	board.unsuspendUpdate();		board.unsuspendUpdate();
	</script>		</script>
Line 49:		Line 49:
	var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }		var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }
	var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }		var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
	var c1 = board.createElement('curve', [x,y~~,'phi'~~,-Math.PI4,Math.PI4],{strokeWidth:3});		var c1 = board.createElement('curve', [x,y,-Math.PI4,Math.PI4],{strokeWidth:3});

	var dualCurve = function(x,y,board) {		var dualCurve = function(x,y,board) {
Line 57:		Line 57:
	}		}
	var dual = dualCurve(x,y,board);		var dual = dualCurve(x,y,board);
	var c2 = board.createElement('curve', [dual[0],dual[1]~~,'phi'~~,-Math.PI1,Math.PI1],{strokeWidth:3, strokeColor:'red'});		var c2 = board.createElement('curve', [dual[0],dual[1],-Math.PI1,Math.PI1],{strokeWidth:3, strokeColor:'red'});
	board.unsuspendUpdate();		board.unsuspendUpdate();
	</script>		</script>

A WASSERMANN at 12:04, 10 February 2009

2009-02-10T12:04:00Z

← Older revision		Revision as of 12:04, 10 February 2009
Line 62:		Line 62:
	</source>		</source>
	[[Category:Examples]]		[[Category:Examples]]
			[[Category:Curves]]

← Older revision		Revision as of 21:08, 7 April 2009
Line 14:		Line 14:
	board.createElement('axis', [[0,0],[1,0]]);		board.createElement('axis', [[0,0],[1,0]]);
	board.createElement('axis', [[0,0],[0,1]]);		board.createElement('axis', [[0,0],[0,1]]);
	var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6});		var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
	var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6});		var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
	var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }		var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }
	var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }		var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }
Line 45:		Line 45:
	board.createElement('axis', [[0,0],[1,0]]);		board.createElement('axis', [[0,0],[1,0]]);
	board.createElement('axis', [[0,0],[0,1]]);		board.createElement('axis', [[0,0],[0,1]]);
	var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6});		var a = board.createElement('slider', [[1,-1],[8,-1],[-5,1,5]], {style:6,name:'a'});
	var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6});		var b = board.createElement('slider', [[1,-2],[8,-2],[-5,1,5]], {style:6,name:'b'});
	var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }		var x = function(phi) { return a.Value()phi-b.Value()Math.sin(phi); }
	var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }		var y = function(phi) { return a.Value()-b.Value()*Math.cos(phi); }