Euler's spiral (Clothoid) - Revision history

A WASSERMANN at 15:04, 20 February 2013

2013-02-20T15:04:14Z

← Older revision		Revision as of 15:04, 20 February 2013
Line 17:		Line 17:
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
	var p = b.create('glider',[1,2,c],{name:''});		var p = b.create('glider',[1,3,c],{name:''});
	var t = b.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</jsxgraph>		</jsxgraph>
Line 24:		Line 24:

	<source lang="javascript">		<source lang="javascript">
	var b2 = JXG.JSXGraph.initBoard('~~box2~~', {boundingbox: [-10, 10, 10, -10]});		var b = JXG.JSXGraph.initBoard('box', {boundingbox: [-10, 10, 10, -10],axis:true});
	var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});		var k1 = b.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});		var len = b.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
	var c = b2.create('curve',		var c = b.create('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()JXG.Math.Numerics.I([0,t],function(u){return Math.sin(uu*0.5);}); },
	function(t){ return k1.Value()b2.I([0,t],function(u){return Math.cos(uu*0.5);}); },		function(t){ return k1.Value()JXG.Math.Numerics.I([0,t],function(u){return Math.cos(uu*0.5);}); },
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
	var p = b2.create('glider',[c],{name:''});		var p = b.create('glider',[1,3,c],{name:''});
	var t = b2.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</source>		</source>

A WASSERMANN at 15:03, 20 February 2013

2013-02-20T15:03:38Z

← Older revision		Revision as of 15:03, 20 February 2013
Line 17:		Line 17:
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
	var p = b.create('glider',[c],{name:''});		var p = b.create('glider',[1,2,c],{name:''});
	var t = b.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</jsxgraph>		</jsxgraph>

A WASSERMANN at 15:02, 20 February 2013

2013-02-20T15:02:44Z

← Older revision		Revision as of 15:02, 20 February 2013
Line 9:		Line 9:

	<jsxgraph width="500" height="500" box="box">		<jsxgraph width="500" height="500" box="box">
	var b2 = JXG.JSXGraph.initBoard('box', {boundingbox: [-10, 10, 10, -10],axis:true});		var b = JXG.JSXGraph.initBoard('box', {boundingbox: [-10, 10, 10, -10],axis:true});
	var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});		var k1 = b.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});		var len = b.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
	var c = b2.create('curve',		var c = b.create('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()JXG.Math.Numerics.I([0,t],function(u){return Math.sin(uu*0.5);}); },
	function(t){ return k1.Value()b2.I([0,t],function(u){return Math.cos(uu*0.5);}); },		function(t){ return k1.Value()JXG.Math.Numerics.I([0,t],function(u){return Math.cos(uu*0.5);}); },
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
	var p = b2.create('glider',[c],{name:''});		var p = b.create('glider',[c],{name:''});
	var t = b2.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</jsxgraph>		</jsxgraph>

A WASSERMANN at 15:01, 20 February 2013

2013-02-20T15:01:16Z

← Older revision		Revision as of 15:01, 20 February 2013
Line 8:		Line 8:
	:<math> y = k\cdot\int_0^t \cos(\frac{u^2}{2}) du\; </math>		:<math> y = k\cdot\int_0^t \cos(\frac{u^2}{2}) du\; </math>

	<jsxgraph width="500" height="500" box="~~box2~~">		<jsxgraph width="500" height="500" box="box">
	var b2 = JXG.JSXGraph.initBoard('~~box2~~', {boundingbox: [-10, 10, 10, -10]});		var b2 = JXG.JSXGraph.initBoard('box', {boundingbox: [-10, 10, 10, -10],axis:true});
	var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});		var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});		var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});

Michael at 14:07, 7 June 2011

2011-06-07T14:07:22Z

← Older revision		Revision as of 14:07, 7 June 2011
Line 24:		Line 24:

	<source lang="javascript">		<source lang="javascript">
	var b2 = JXG.JSXGraph.initBoard('box2', {boundingbox: [-10, 10, 10, -10]});		var b2 = JXG.JSXGraph.initBoard('box2', {boundingbox: [-10, 10, 10, -10]});
	var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});		var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});		var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
	var c = b2.create('curve',		var c = b2.create('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },
	function(t){ return k1.Value()b2.I([0,t],function(u){return Math.cos(uu*0.5);}); },		function(t){ return k1.Value()b2.I([0,t],function(u){return Math.cos(uu*0.5);}); },
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
	var p = b2.create('glider',[c],{name:''});		var p = b2.create('glider',[c],{name:''});
	var t = b2.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b2.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</source>		</source>

Michael at 14:07, 7 June 2011

2011-06-07T14:07:09Z

← Older revision		Revision as of 14:07, 7 June 2011
Line 9:		Line 9:

	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	var b2 = JXG.JSXGraph.initBoard('box2', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY: 25~~});		var b2 = JXG.JSXGraph.initBoard('box2', {boundingbox: [-10, 10, 10, -10]});
	var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});		var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});		var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
Line 23:		Line 23:
	===The JavaScript code to produce this picture===		===The JavaScript code to produce this picture===

	<source lang="~~xml">~~		<source lang="javascript">
	~~<jsxgraph width="500" height="500" box="box2~~">		var b2 = JXG.JSXGraph.initBoard('box2', {boundingbox: [-10, 10, 10, -10]});
	var b2 = JXG.JSXGraph.initBoard('box2', {~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY: 25~~});
	var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});		var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});		var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
Line 35:		Line 34:
	var p = b2.create('glider',[c],{name:''});		var p = b2.create('glider',[c],{name:''});
	var t = b2.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b2.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	~~</jsxgraph>~~
	</source>		</source>

A WASSERMANN at 20:54, 29 September 2010

2010-09-29T20:54:10Z

← Older revision		Revision as of 20:54, 29 September 2010
Line 9:		Line 9:

	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});		var b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var k1 = b2.~~createElement~~('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});		var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.~~createElement~~('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});		var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
	var c = b2.~~createElement~~('curve',		var c = b2.create('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },
	function(t){ return k1.Value()b2.I([0,t],function(u){return Math.cos(uu*0.5);}); },		function(t){ return k1.Value()b2.I([0,t],function(u){return Math.cos(uu*0.5);}); },
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
	var p = b2.~~createElement~~('glider',[c],{name:''});		var p = b2.create('glider',[c],{name:''});
	var t = b2.~~createElement~~('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b2.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</jsxgraph>		</jsxgraph>

Line 25:		Line 25:
	<source lang="xml">		<source lang="xml">
	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});		var b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var k1 = b2.~~createElement~~('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});		var k1 = b2.create('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.~~createElement~~('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});		var len = b2.create('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
	var c = b2.~~createElement~~('curve',		var c = b2.create('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },
	function(t){ return k1.Value()b2.I([0,t],function(u){return Math.cos(uu*0.5);}); },		function(t){ return k1.Value()b2.I([0,t],function(u){return Math.cos(uu*0.5);}); },
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
	var p = b2.~~createElement~~('glider',[c],{name:''});		var p = b2.create('glider',[c],{name:''});
	var t = b2.~~createElement~~('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b2.create('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</jsxgraph>		</jsxgraph>
	</source>		</source>

A WASSERMANN at 14:08, 23 March 2009

2009-03-23T14:08:34Z

A WASSERMANN at 14:07, 23 March 2009

2009-03-23T14:07:51Z

A WASSERMANN at 08:40, 18 March 2009

2009-03-18T08:40:42Z

← Older revision		Revision as of 08:40, 18 March 2009
Line 17:		Line 17:
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
	var p = b2.createElement('glider',[c]);		var p = b2.createElement('glider',[c],{name:''});
	var t = b2.createElement('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});		var t = b2.createElement('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</jsxgraph>		</jsxgraph>
Line 33:		Line 33:
	function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],		function(){return -len.Value()Math.PI;}, function(){return len.Value()Math.PI;}],
	{strokewidth:1});		{strokewidth:1});
			var p = b2.createElement('glider',[c],{name:''});
			var t = b2.createElement('tangent',[p],{dash:3,strokeWidth:1,strokeColor:'red'});
	</jsxgraph>		</jsxgraph>
	</source>		</source>

← Older revision		Revision as of 14:08, 23 March 2009
Line 10:		Line 10:
	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});		b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]],{name:k});		var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]],{name:len});		var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
	var c = b2.createElement('curve',		var c = b2.createElement('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },
Line 26:		Line 26:
	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});		b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]],{name:k});		var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]],{name:'k'});
	var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]],{name:len});		var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]],{name:'len'});
	var c = b2.createElement('curve',		var c = b2.createElement('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },

← Older revision		Revision as of 14:07, 23 March 2009
Line 10:		Line 10:
	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});		b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]]);		var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]],{name:k});
	var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]]);		var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]],{name:len});
	var c = b2.createElement('curve',		var c = b2.createElement('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },
Line 26:		Line 26:
	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});		b2 = JXG.JSXGraph.initBoard('box2', {originX: 250, originY: 250, unitX: 25, unitY: 25});
	var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]]);		var k1 = b2.createElement('slider', [[1,8],[5,8],[0,2,8]],{name:k});
	var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]]);		var len = b2.createElement('slider', [[1,7],[5,7],[1,2,3.2]],{name:len});
	var c = b2.createElement('curve',		var c = b2.createElement('curve',
	[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },		[function(t){ return k1.Value()b2.I([0,t],function(u){return Math.sin(uu*0.5);}); },