Superformula - Revision history

A WASSERMANN at 16:01, 20 February 2013

2013-02-20T16:01:49Z

← Older revision		Revision as of 16:01, 20 February 2013
Line 20:		Line 20:
	var len = b2.create('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});		var len = b2.create('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});
	var c = b2.create('curve', [		var c = b2.create('curve', [
	function(phi){return b2.pow(		function(phi){return JXG.Math.pow(
	b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+		JXG.Math.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+
	b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),		JXG.Math.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),
	-1/n1.Value()); },		-1/n1.Value()); },
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
Line 41:		Line 41:
	var len = b2.create('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});		var len = b2.create('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});
	var c = b2.create('curve', [		var c = b2.create('curve', [
	function(phi){return b2.pow(		function(phi){return JXG.Math.pow(
	b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+		JXG.Math.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+
	b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),		JXG.Math.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),
	-1/n1.Value()); },		-1/n1.Value()); },
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],

Michael at 14:37, 8 June 2011

2011-06-08T14:37:13Z

← Older revision		Revision as of 14:37, 8 June 2011
Line 10:		Line 10:

	<jsxgraph width="550" height="500" box="box2">		<jsxgraph width="550" height="500" box="box2">
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY: 25~~});		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox: [-10, 10, 12, -10]});
	b2.suspendUpdate();		b2.suspendUpdate();
	var a = b2.~~createElement~~('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});		var a = b2.create('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});
	var b = b2.~~createElement~~('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});		var b = b2.create('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});
	var m = b2.~~createElement~~('slider', [[-7,6],[7,6],[0,4,40]],{name:'m'});		var m = b2.create('slider', [[-7,6],[7,6],[0,4,40]],{name:'m'});
	var n1 = b2.~~createElement~~('slider', [[-7,5],[7,5],[0,4,20]],{name:'n_1'});		var n1 = b2.create('slider', [[-7,5],[7,5],[0,4,20]],{name:'n_1'});
	var n2 = b2.~~createElement~~('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});		var n2 = b2.create('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});
	var n3 = b2.~~createElement~~('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});		var n3 = b2.create('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});
	var len = b2.~~createElement~~('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});		var len = b2.create('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});
	var c = b2.~~createElement~~('curve', [		var c = b2.create('curve', [
	function(phi){return b2.pow(		function(phi){return b2.pow(
	b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+		b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+
	b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),		b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),
	-1/n1.Value()); },		-1/n1.Value()); },
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});		{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});
	b2.unsuspendUpdate();		b2.unsuspendUpdate();
	</jsxgraph>		</jsxgraph>

	===The JavaScript code to produce this picture===		===The JavaScript code to produce this picture===
	<source lang="~~xml~~">		<source lang="javascript">
	~~<jsxgraph width="550" height="500" box="box2">~~		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true, boundingbox: [-10, 10, 12, -10]});
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,~~originX~~: ~~250~~, ~~originY: 250~~, ~~unitX: 25~~, ~~unitY: 25~~});		b2.suspendUpdate();
	b2.suspendUpdate();		var a = b2.create('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});
	var a = b2.~~createElement~~('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});		var b = b2.create('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});
	var b = b2.~~createElement~~('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});		var m = b2.create('slider', [[-7,6],[7,6],[0,4,40]],{name:'m'});
	var m = b2.~~createElement~~('slider', [[-7,6],[7,6],[0,4,40]],{name:'m'});		var n1 = b2.create('slider', [[-7,5],[7,5],[0,4,20]],{name:'n_1'});
	var n1 = b2.~~createElement~~('slider', [[-7,5],[7,5],[0,4,20]],{name:'n_1'});		var n2 = b2.create('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});
	var n2 = b2.~~createElement~~('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});		var n3 = b2.create('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});
	var n3 = b2.~~createElement~~('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});		var len = b2.create('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});
	var len = b2.~~createElement~~('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});		var c = b2.create('curve', [
	var c = b2.~~createElement~~('curve', [
	function(phi){return b2.pow(		function(phi){return b2.pow(
	b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+		b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+
	b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),		b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),
	-1/n1.Value()); },		-1/n1.Value()); },
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});		{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});
	b2.unsuspendUpdate();		b2.unsuspendUpdate();
	~~</jsxgraph>~~
	</source>		</source>

A WASSERMANN at 18:09, 22 June 2009

2009-06-22T18:09:33Z

← Older revision		Revision as of 18:09, 22 June 2009
Line 9:		Line 9:
	</math>		</math>

	<jsxgraph width="~~500~~" height="500" box="box2">		<jsxgraph width="550" height="500" box="box2">
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
	b2.suspendUpdate();		b2.suspendUpdate();
Line 31:		Line 31:
	===The JavaScript code to produce this picture===		===The JavaScript code to produce this picture===
	<source lang="xml">		<source lang="xml">
	<jsxgraph width="~~500~~" height="500" box="box2">		<jsxgraph width="550" height="500" box="box2">
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
	b2.suspendUpdate();		b2.suspendUpdate();

A WASSERMANN at 19:50, 18 March 2009

2009-03-18T19:50:21Z

← Older revision		Revision as of 19:50, 18 March 2009
Line 40:		Line 40:
	var n2 = b2.createElement('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});		var n2 = b2.createElement('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});
	var n3 = b2.createElement('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});		var n3 = b2.createElement('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});
	var len = b2.createElement('slider', [[1,2],[7,2],[0,2,2]],{name:'len'});		var len = b2.createElement('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});
	var c = b2.createElement('curve', [		var c = b2.createElement('curve', [
	function(phi){return b2.pow(		function(phi){return b2.pow(

A WASSERMANN at 19:48, 18 March 2009

2009-03-18T19:48:16Z

← Older revision		Revision as of 19:48, 18 March 2009
Line 18:		Line 18:
	var n2 = b2.createElement('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});		var n2 = b2.createElement('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});
	var n3 = b2.createElement('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});		var n3 = b2.createElement('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});
	var len = b2.createElement('slider', [[1,2],[7,2],[0,2,2]],{name:'len'});		var len = b2.createElement('slider', [[1,2],[7,2],[0,2,20]],{name:'len'});
	var c = b2.createElement('curve', [		var c = b2.createElement('curve', [
	function(phi){return b2.pow(		function(phi){return b2.pow(

A WASSERMANN at 19:47, 18 March 2009

2009-03-18T19:47:12Z

← Older revision		Revision as of 19:47, 18 March 2009
Line 11:		Line 11:
	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
			b2.suspendUpdate();
	var a = b2.createElement('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});		var a = b2.createElement('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});
	var b = b2.createElement('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});		var b = b2.createElement('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});
Line 25:		Line 26:
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});		{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});
			b2.unsuspendUpdate();
	</jsxgraph>		</jsxgraph>

	===The JavaScript code to produce this picture===		===The JavaScript code to produce this picture===
	<source lang="xml">		<source lang="xml">
			<jsxgraph width="500" height="500" box="box2">
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
			b2.suspendUpdate();
	var a = b2.createElement('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});		var a = b2.createElement('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});
	var b = b2.createElement('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});		var b = b2.createElement('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});
Line 44:		Line 48:
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});		{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});
			b2.unsuspendUpdate();
			</jsxgraph>
	</source>		</source>

A WASSERMANN at 16:05, 18 March 2009

2009-03-18T16:05:07Z

← Older revision		Revision as of 16:05, 18 March 2009
Line 11:		Line 11:
	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = b2.createElement('slider', [[1,8],[7,8],[0,1,4]],{name:'a'});		var a = b2.createElement('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});
	var b = b2.createElement('slider', [[1,7],[7,7],[0,1,4]],{name:'b'});		var b = b2.createElement('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});
	var m = b2.createElement('slider', [[1,6],[7,6],[0,4,40]],{name:'m'});		var m = b2.createElement('slider', [[-7,6],[7,6],[0,4,40]],{name:'m'});
	var n1 = b2.createElement('slider', [[1,5],[7,5],[0,4,20]],{name:'n_1'});		var n1 = b2.createElement('slider', [[-7,5],[7,5],[0,4,20]],{name:'n_1'});
	var n2 = b2.createElement('slider', [[1,4],[7,4],[0,4,20]],{name:'n_2'});		var n2 = b2.createElement('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});
	var n3 = b2.createElement('slider', [[1,3],[7,3],[0,4,20]],{name:'n_3'});		var n3 = b2.createElement('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});
	var len = b2.createElement('slider', [[1,2],[7,2],[0,2,2]],{name:'len'});		var len = b2.createElement('slider', [[1,2],[7,2],[0,2,2]],{name:'len'});
	var c = b2.createElement('curve', [		var c = b2.createElement('curve', [
Line 30:		Line 30:
	<source lang="xml">		<source lang="xml">
	var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});		var b2 = JXG.JSXGraph.initBoard('box2', {axis:true,originX: 250, originY: 250, unitX: 25, unitY: 25});
	var a = b2.createElement('slider', [[1,8],[7,8],[0,1,4]],{name:'a'});		var a = b2.createElement('slider', [[-7,8],[7,8],[0,1,4]],{name:'a'});
	var b = b2.createElement('slider', [[1,7],[7,7],[0,1,4]],{name:'b'});		var b = b2.createElement('slider', [[-7,7],[7,7],[0,1,4]],{name:'b'});
	var m = b2.createElement('slider', [[1,6],[7,6],[0,4,40]],{name:'m'});		var m = b2.createElement('slider', [[-7,6],[7,6],[0,4,40]],{name:'m'});
	var n1 = b2.createElement('slider', [[1,5],[7,5],[0,4,20]],{name:'n_1'});		var n1 = b2.createElement('slider', [[-7,5],[7,5],[0,4,20]],{name:'n_1'});
	var n2 = b2.createElement('slider', [[1,4],[7,4],[0,4,20]],{name:'n_2'});		var n2 = b2.createElement('slider', [[-7,4],[7,4],[0,4,20]],{name:'n_2'});
	var n3 = b2.createElement('slider', [[1,3],[7,3],[0,4,20]],{name:'n_3'});		var n3 = b2.createElement('slider', [[-7,3],[7,3],[0,4,20]],{name:'n_3'});
	var len = b2.createElement('slider', [[1,2],[7,2],[0,2,2]],{name:'len'});		var len = b2.createElement('slider', [[1,2],[7,2],[0,2,2]],{name:'len'});
	var c = b2.createElement('curve', [		var c = b2.createElement('curve', [

A WASSERMANN at 16:03, 18 March 2009

2009-03-18T16:03:46Z

← Older revision		Revision as of 16:03, 18 March 2009
Line 20:		Line 20:
	var c = b2.createElement('curve', [		var c = b2.createElement('curve', [
	function(phi){return b2.pow(		function(phi){return b2.pow(
	b2.pow(Math.abs(Math.cos~~( Math.floor~~(m.Value())phi0.25/a.Value() )), ~~Math.floor(~~n2.Value()))+		b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+
	b2.pow(Math.abs(Math.sin~~( Math.floor~~(m.Value())phi0.25/b.Value() )), ~~Math.floor(~~n3.Value())),		b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),
	-1/~~Math.floor(~~n1.Value())); },		-1/n1.Value()); },
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.5});		{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});
	</jsxgraph>		</jsxgraph>

Line 39:		Line 39:
	var c = b2.createElement('curve', [		var c = b2.createElement('curve', [
	function(phi){return b2.pow(		function(phi){return b2.pow(
	b2.pow(Math.abs(Math.cos~~( Math.floor~~(m.Value())phi0.25/a.Value() )), ~~Math.floor(~~n2.Value()))+		b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )), n2.Value())+
	b2.pow(Math.abs(Math.sin~~( Math.floor~~(m.Value())phi0.25/b.Value() )), ~~Math.floor(~~n3.Value())),		b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )), n3.Value()),
	-1/~~Math.floor(~~n1.Value())); },		-1/n1.Value()); },
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.5});		{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.3});
	</source>		</source>

A WASSERMANN at 15:58, 18 March 2009

2009-03-18T15:58:42Z

← Older revision		Revision as of 15:58, 18 March 2009
Line 20:		Line 20:
	var c = b2.createElement('curve', [		var c = b2.createElement('curve', [
	function(phi){return b2.pow(		function(phi){return b2.pow(
	b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )),n2.Value())+		b2.pow(Math.abs(Math.cos( Math.floor(m.Value())phi0.25/a.Value() )), Math.floor(n2.Value()))+
	b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )),n3.Value()),		b2.pow(Math.abs(Math.sin( Math.floor(m.Value())phi0.25/b.Value() )), Math.floor(n3.Value())),
	-1/n1.Value()); },		-1/Math.floor(n1.Value())); },
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.5});		{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.5});
Line 39:		Line 39:
	var c = b2.createElement('curve', [		var c = b2.createElement('curve', [
	function(phi){return b2.pow(		function(phi){return b2.pow(
	b2.pow(Math.abs(Math.cos( m.Value()phi0.25/a.Value() )),n2.Value())+		b2.pow(Math.abs(Math.cos( Math.floor(m.Value())phi0.25/a.Value() )), Math.floor(n2.Value()))+
	b2.pow(Math.abs(Math.sin( m.Value()phi0.25/b.Value() )),n3.Value()),		b2.pow(Math.abs(Math.sin( Math.floor(m.Value())phi0.25/b.Value() )), Math.floor(n3.Value())),
	-1/n1.Value()); },		-1/Math.floor(n1.Value())); },
	[0, 0],0, function(){return len.Value()*Math.PI;}],		[0, 0],0, function(){return len.Value()*Math.PI;}],
	{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.5});		{curveType:'polar', strokewidth:1,fillColor:'#765412',fillOpacity:0.5});

A WASSERMANN at 15:57, 18 March 2009

2009-03-18T15:57:18Z

← Older revision		Revision as of 15:57, 18 March 2009
Line 5:		Line 5:
	In polar coordinates, with r the radius and φ the angle, the superformula is:		In polar coordinates, with r the radius and φ the angle, the superformula is:

			: <math>
	r\left(\phi\right) = \left[ \left\| \frac{\cos\left(\frac{m\phi}{4}\right)}{a} \right\| ^{n_{2}} + \left\| \frac{\sin\left(\frac{m\phi}{4}\right)}{b} \right\| ^{n_{3}} \right] ^{-\frac{1}{n_{1}}}		r\left(\phi\right) = \left[ \left\| \frac{\cos\left(\frac{m\phi}{4}\right)}{a} \right\| ^{n_{2}} + \left\| \frac{\sin\left(\frac{m\phi}{4}\right)}{b} \right\| ^{n_{3}} \right] ^{-\frac{1}{n_{1}}}
			</math>

	<jsxgraph width="500" height="500" box="box2">		<jsxgraph width="500" height="500" box="box2">