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polarization.html
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polarization.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>Polarization</title>
<script type="text/javascript" charset="utf-8" src="js/vendor/mathbox.js"></script>
<script type="text/javascript" charset="utf-8" src="js/vendor/jwerty.js"></script>
<script type="text/javascript" charset="utf-8" src="js/mathbox.mod.js"></script>
<script type="text/javascript" charset="utf-8" src="js/controls.js"></script>
<script type="text/javascript" charset="utf-8">
$( function() {
ThreeBox.preload([
"js/vendor/MathBox.glsl.html",
], function() {
// mathBox boilerplate
var mathbox = window.mathbox = mathBox( document.getElementById( "mathbox" ), {
cameraControls: true,
cursor: true,
controlClass: ThreeBox.OrbitControls,
elementResize: true,
fullscreen: true,
screenshot: false,
stats: false,
scale: 1,
// don't use perspective
camera: new THREE.OrthographicCamera( -1.1, 1.1, .8, -.8, 0.005, 10000 ),
} ).start();
// set up director
var script = window.mathboxScript;
var director = window.director = new MathBox.Director( mathbox, script );
// slow down the animation
director.stage().speed( 1/3 );
window.mathboxSetup( mathbox );
} );
// EXTRA CONTROLS
jwerty.key( "R", function() {
toggleResultant();
} );
handleRange( "#phase-difference", function( value ) { return value / 4; }, setPhaseDifference );
} );
</script>
<script type="text/javascript" charset="utf-8">
// toggle the resultant wave, if any
var resultantIsVisible = true;
function toggleResultant() {
// show or hide the resultant wave
mathbox
.animate( "#resultant-curve, #resultant-vector, #resultant-surface", {
opacity: ( resultantIsVisible ? 0 : 1 )
}, duration );
resultantIsVisible = !resultantIsVisible;
}
function setPhaseDifference( difference, animate ) {
mathbox[ animate ? "animate" : "set" ]( "#phase-difference", {
value: difference
}, duration );
}
window.mathboxSetup = function (mathbox) {
mathbox
.viewport( {
type: "cartesian",
range: [ [ 0, 2.2 ], [ -1.2, 1.8 ], [ -1.5, 1.5 ] ],
scale: [ 1, .3, -.3 ],
} )
// frontal view
.camera( {
orbit: 3.5,
phi: τ/4,
theta: 0,
} )
// phase difference between the vertical and horizontal component
.value( {
id: "phase-difference",
key: "phaseDifference"
} )
// horizontal component in resultant wave
.value( {
id: "horizontal-component",
key: "horizontalComponent"
} )
// multiplier for the resultant vectors
.value( {
id: "vector-length",
key: "vectorLength"
} )
// propagating the waves
.value( {
id: "wave-propagation",
callback: function() {
var t = director.clock( 0 ), s = 0;
if ( t > 1 ) {
t = director.clock( 0, true );
}
if ( propagation.isStarting ) {
if ( t === 0 ) {
propagation.running = true;
propagation.isStarting = false;
}
else {
window.wavePropagation = t * t / 2;
return
}
}
if ( propagation.isStopping ) {
if ( t === 0 ) {
propagation.running = false;
propagation.isStopping = false;
}
else {
window.wavePropagation = 1 - ( 1 - t ) * ( 1 - t ) / 2;
}
return;
}
if ( propagation.running ) {
if ( propagation.shouldStop && ( t === 0 ) ) {
propagation.isStopping = true;
propagation.shouldStop = false;
}
// during start-up, half a wave has been moved
window.wavePropagation = t + .5;
return
}
}
} )
// x-y plane
.surface( {
id: "vertical-plane-surface",
n: [ 2, 2 ],
color: colors.white,
data: [
[ [ 0, -1.2 ], [ 0, 1.2 ] ],
[ [ 2, -1.2 ], [ 2, 1.2 ] ],
],
shaded: false,
opacity: .001,
live: false,
zIndex: .01,
} ).curve( {
id: "vertical-plane-curve",
color: colors.gray,
lineWidth: 1,
n: 5,
data: [
[ 0, -1.2, -0.005 ], [ 0, 1.2, -0.005 ], [ 2, 1.2, -0.005 ], [ 2, -1.2, -0.005 ], [ 0, -1.2, -0.005 ]
],
live: false,
zIndex: .01,
opacity: .001
} )
// x-z plane
.surface( {
id: "horizontal-plane-surface",
n: [ 2, 2 ],
color: colors.white,
data: [
[ [ 0, 0, -1.2 ], [ 0, 0, 1.2 ] ],
[ [ 2, 0, -1.2 ], [ 2, 0, 1.2 ] ],
],
shaded: false,
opacity: .8,
live: false,
zIndex: .01,
opacity: .001
} )
.curve( {
id: "horizontal-plane-curve",
color: colors.gray,
lineWidth: 1,
n: 5,
data: [
[ 0, 0.005, -1.2 ], [ 0, 0.005, 1.2 ], [ 2, 0.005, 1.2 ], [ 2, 0.005, -1.2 ], [ 0, 0.005, -1.2 ]
],
live: false,
zIndex: .01,
opacity: .001
} )
// vertical axis
.axis( {
id: "vertical-axis",
axis: 1,
labels: false,
ticks: 0,
color: colors.black,
size: .04,
lineWidth: 2,
live: false
} )
// horizontal axis
.axis( {
id: "horizontal-axis",
axis: 2,
labels: false,
ticks: 0,
color: colors.black,
size: .04,
lineWidth: 2,
live: false,
opacity: .001
} )
// propagation axis
.axis( {
id: "propagation-axis",
axis: 0,
labels: false,
ticks: 0,
color: colors.black,
size: .04,
lineWidth: 2,
live: false
} )
.curve( {
id: "propagation-axis-overlay",
n: 2,
data: [ [ 0, 0.01, -0.01 ], [ 2, 0.01, -0.01 ] ],
lineWidth: 2,
color: colors.black,
live: false,
opacity: .001
} )
// resultant wave
.curve( {
id: "resultant-curve",
domain: [ 0, 0 ],
n: 192,
expression: function ( x, i ) {
var θy = ( x - window.wavePropagation ) * 2 * π;
var θz = ( x - window.wavePropagation - window.phaseDifference ) * 2 * π;
return [ x, Math.sin( θy ), Math.sin( θz ) * window.horizontalComponent - 0.005 ];
},
line: true,
lineWidth: 5,
color: colors.black,
zIndex: .01
} )
.surface( {
id: "resultant-surface",
n: [ 512, 2 ],
domain: [ [ 0, 0 ], [ 0, 1 ] ],
expression: function ( x, y ) {
var θy = ( x - window.wavePropagation ) * 2 * π;
var θz = ( x - window.wavePropagation - window.phaseDifference ) * 2 * π;
// multiply by y to get an actual surface by putting one endpoint on the axis
return [ x, Math.sin( θy ) * y, Math.sin( θz ) * y * window.horizontalComponent - 0.005 ];
},
shaded: false,
opacity: 1,
color: colors.gray,
zIndex: .01
} )
.vector( {
id: "resultant-vector",
n: 32,
expression: function( i, end ) {
var x = i / 32 * 2;
// modify the vector length slightly per vector
var vectorLength_ = Math.max( 0, Math.min( window.vectorLength - i/32, 1 ) );
var θy = ( x - window.wavePropagation ) * 2 * π;
var θz = ( x - window.wavePropagation - window.phaseDifference ) * 2 * π;
return [ x, Math.sin( θy ) * end * vectorLength_, Math.sin( θz ) * end * window.horizontalComponent - 0.005 ]
},
color: colors.black,
lineWidth: 1,
size: .02,
zIndex: .04
} )
// polarization plane
.surface( {
id: "polarization-plane-surface",
n: [ 2, 2 ],
color: colors.white,
data: [
[ [ 2.001, -1.2, -1.2 ], [ 2.001, -1.2, 1.2 ] ],
[ [ 2.001, 1.2, -1.2 ], [ 2.001, 1.2, 1.2 ] ],
],
shaded: false,
opacity: .001,
live: false,
zIndex: 0.04
} )
.curve( {
id: "polarization-plane-curve",
color: colors.gray,
lineWidth: 1,
n: 5,
data: [
[ 2.002, -1.2, -1.2 ], [ 2.002, -1.2, 1.2 ], [ 2.002, 1.2, 1.2 ], [ 2.002, 1.2, -1.2 ], [ 2.002, -1.2, -1.2 ]
],
live: false,
zIndex: 0.05,
opacity: .001
} )
// polarization
.curve( {
id: "polarization-curve",
domain: [ 0, τ ],
n: 192,
expression: function ( θ, i ) {
return [ 2, Math.sin( θ ), Math.sin( θ - window.phaseDifference * 2 * π ) * window.horizontalComponent ];
},
line: true,
lineWidth: 1,
color: colors.red,
zIndex: 0.2,
opacity: .001
} )
.vector( {
id: "polarization-vector",
n: 1,
expression: function( i, end ) {
var x = i / 32 * 2;
var θy = ( x - window.wavePropagation ) * 2 * π;
var θz = ( x - window.wavePropagation - window.phaseDifference ) * 2 * π;
return [ 2, Math.sin( θy ) * end, Math.sin( θz ) * end * window.horizontalComponent ]
},
color: colors.red,
size: .03,
zIndex: 0.3,
lineWidth: 4,
opacity: .001
} )
}
/**
* Script
*/
window.mathboxScript = [
// draw the resultant wave
[
[ "animate", "#resultant-curve", {
domain: [ 0, 2 ]
}, duration ],
[ "animate", "#resultant-surface", {
domain: [ [ 0, 2 ], [ 0, 1 ] ]
}, duration ]
],
[
// add the vector field
[ "animate", "#vector-length", {
value: 2
}, duration ]
],
[
// change to a 3D view
[ "animate", "camera", {
orbit: 1.5,
phi: π / 4,
theta: π / 8
}, duration ],
[ "animate", "#horizontal-axis", {
opacity: 1
}, duration ],
[ "animate", "#horizontal-plane-surface, #vertical-plane-surface", {
opacity: .8
}, duration ],
[ "animate", "#horizontal-plane-curve, #vertical-plane-curve, #propagation-axis-overlay", {
opacity: 1
}, duration ]
],
[
// add the vertical wave
[ "add", "curve", {
id: "vertical-curve",
domain: [ 0, 2 ],
n: 96,
expression: function ( x, i ) {
var θy = ( x - window.wavePropagation ) * 2 * π;
return [ x, Math.sin( θy ), 0 ];
},
line: true,
lineWidth: 2,
color: colors.black,
zIndex: .02
} ],
[ "add", "vector", {
id: "vertical-vector",
n: 32,
expression: function( i, end ) {
var x = i / 32 * 2;
var θy = ( x - window.wavePropagation ) * 2 * π;
return [ x, Math.sin( θy ) * end, 0 ]
},
color: colors.black,
lineWidth: 1,
size: .02,
zIndex: .02
} ],
// add the horizontal wave
[ "add", "curve", {
domain: [ 0, 2 ],
id: "horizontal-curve",
n: 96,
expression: function ( x, i ) {
var θz = ( x - window.wavePropagation - window.phaseDifference ) * 2 * π;
return [ x, 0, Math.sin( θz ) * window.horizontalComponent ];
},
line: true,
lineWidth: 2,
color: colors.black,
zIndex: .02
} ],
[ "add", "vector", {
id: "horizontal-vector",
n: 32,
expression: function( i, end ) {
var x = i / 32 * 2;
var θz = ( x - window.wavePropagation - window.phaseDifference ) * 2 * π;
return [ x, 0, Math.sin( θz ) * end * window.horizontalComponent ]
},
color: colors.black,
lineWidth: 1,
size: .02,
zIndex: .02
} ],
// change the linear polarization from 90deg to 45 deg
[ "animate", "#horizontal-component", {
value: 1
}, duration ]
],
[
// color the components
[ "animate", "#horizontal-vector, #horizontal-curve", {
color: colors.green
}, duration ],
[ "animate", "#vertical-vector, #vertical-curve", {
color: colors.blue
}, duration ]
],
[
// show the polarization
[ "animate", "#polarization-plane-curve, #polarization-vector, #polarization-curve", {
opacity: 1
}, duration ],
[ "animate", "#polarization-plane-surface", {
opacity: .8
}, duration ],
]
];
</script>
<link href="css/base.css" rel="stylesheet" type="text/css" media="screen">
</head>
<body>
<div id="mathbox"></div>
<div id="controls">
<label for="phase-difference">phase difference:
<input type=range min="0" max="4" value="0" step=".001" id="phase-difference" list="phase-difference-list" data-min="0" data-max="2π"/>
<datalist id="phase-difference-list">
<option>0</option>
<option>1</option>
<option>2</option>
<option>3</option>
<option>4</option>
</datalist>
</label>
</div>
</body>
</html>