├── .gitignore
├── README.md
├── common.js
├── style
    └── style.css
├── lib
    ├── jquery
    │   ├── jquery.slider-1.3.css
    │   ├── jquery.slider-1.3.js
    │   └── jquery-1.8.2.min.js
    ├── kalmanjs
    │   └── LinearKalmanFilter.js
    ├── plotjs
    │   └── PlotJS.js
    └── sylvester
    │   └── sylvester.js
├── 1D.html
└── 2D.html


/.gitignore:
--------------------------------------------------------------------------------
1 | 
2 | /.idea


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/README.md:
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1 | KalmanJS
2 | ========
3 | 
4 | JavaScript implementation and interactive playground for Kalman filters.


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/common.js:
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 1 | function createControl(name, value, min, max, step) {
 2 | 	$('#controls').append(
 3 | 		'<p><label for="' + name + '">' + name + ': <input type="text" id="' + name + '" value="' + value + '" data-min="' + min + '" data-max="' + max + '" data-step="' + step + '"></label></p>'
 4 | 	);
 5 | 
 6 | 	$('#' + name)
 7 | 		.slider({
 8 | 			showValue: true,
 9 | 			showRange: true,
10 | 			onChange: function(value, el) {
11 | 				options[name] = parseFloat(value);
12 | 				run();
13 | 			}
14 | 		});
15 | };


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/style/style.css:
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 1 | BODY, HTML {
 2 | 	width: 100%;
 3 | 	height: 100%;
 4 | 	margin: 0;
 5 | 	padding: 0;
 6 | }
 7 | .plot-main {
 8 | 	width: 50%;
 9 | 	height: 690px;
10 | 	float: left;
11 | }
12 | .plot-sub {
13 | 	width: 25%;
14 | 	height: 230px;
15 | 	float: left;
16 | }
17 | #controls {
18 | 	clear: both;
19 | }
20 | #controls P {
21 | 	width: 22%;
22 | 	float: left;
23 | 	margin-left: 40px;
24 | }
25 | #github {
26 | 	position: absolute;
27 | 	left: 1px;
28 | 	top: 1px;
29 | }
30 | #github A {
31 | 	display: block;
32 | 	float: left;
33 | 	line-height: 24px;
34 | 	padding: 0 10px;
35 | 	color: #FFF;
36 | 	background-color: rgba(0, 0, 0, 0.5);
37 | 	margin: 0 1px 0 0;
38 | }


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/lib/jquery/jquery.slider-1.3.css:
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 1 | .slider-wrap {
 2 | 	position: relative;
 3 | 	box-sizing: border-box;
 4 | 	width: 100%;
 5 | 	height: 4px;
 6 | 	margin: 4px 0;
 7 | 	background-color: #CCC;
 8 | 	border-radius: 2px;
 9 | }
10 | .slider-wrap.with-value,
11 | .slider-wrap.with-range {
12 | 	margin: 4px 0 24px;
13 | }
14 | .slider-connector-left {
15 | 	position: absolute;
16 | 	width: 0;
17 | 	height: 4px;
18 | 	left: 0;
19 | 	top: 0;
20 | 	background-color: #AAA;
21 | 	border-radius: 2px 0 0 2px;
22 | }
23 | .slider-handle-left,
24 | .slider-handle-right {
25 | 	position: absolute;
26 | 	width: 6px;
27 | 	height: 12px;
28 | 	left: 0;
29 | 	top: -4px;
30 | 	margin-left: -4px;
31 | 	background-color: #666;
32 | 	border-left: 1px solid #CCC;
33 | 	border-right: 1px solid #CCC;
34 | 	border-radius: 2px;
35 | 	box-shadow: 0 0 5px #666;
36 | }
37 | .slider-handle-left:hover,
38 | .slider-handle-right:hover {
39 | 	box-shadow: 0 0 10px #666;
40 | }
41 | .slider-value {
42 | 	position: absolute;
43 | 	width: 60px;
44 | 	text-align: center;
45 | 	left: 50%;
46 | 	margin-left: -20px;
47 | 	top: 8px;
48 | 	font-size: 12px;
49 | 	color: #666;
50 | }
51 | .slider-range-min,
52 | .slider-range-max {
53 | 	position: absolute;
54 | 	top: 8px;
55 | 	font-size: 12px;
56 | 	color: #666;
57 | }
58 | .slider-range-min {
59 | 	left: 0;
60 | }
61 | .slider-range-max {
62 | 	right: 0;
63 | }
64 | .slider-unselectable {
65 | 	-moz-user-select: none;
66 | 	-khtml-user-select: none;
67 | 	-webkit-user-select: none;
68 | 	user-select: none;
69 | }


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/lib/kalmanjs/LinearKalmanFilter.js:
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 1 | function LinearKalmanFilter(
 2 | 	stateTransitionMatrix,		// A
 3 | 	controlMatrix,				// B
 4 | 	observationMatrix,			// H
 5 | 	initialStateEstimate,		// X
 6 | 	initialCovarianceEstimate,	// P
 7 | 	processErrorEstimate,		// Q
 8 | 	measurementErrorEstimate	// R
 9 | ) {
10 | 	this.stateTransitionMatrix = stateTransitionMatrix;
11 | 	this.controlMatrix = controlMatrix;
12 | 	this.observationMatrix = observationMatrix;
13 | 	this.stateEstimate = initialStateEstimate;
14 | 	this.covarianceEstimate = initialCovarianceEstimate;
15 | 	this.processErrorEstimate = processErrorEstimate;
16 | 	this.measurementErrorEstimate = measurementErrorEstimate;
17 | 
18 | 	this.predictedStateEstimate = null;
19 | 	this.predictedProbabilityEstimate = null;
20 | 	this.innovation = null;
21 | 	this.innovationCovariance = null;
22 | 	this.kalmanGain = null;
23 | }
24 | 
25 | LinearKalmanFilter.prototype.getStateEstimate = function() {
26 | 	return this.stateEstimate;
27 | };
28 | 
29 | LinearKalmanFilter.prototype.predict = function(controlVector) {
30 | 	this.predictedStateEstimate = this.stateTransitionMatrix
31 | 			.multiply(this.stateEstimate)
32 | 			.add(this.controlMatrix.multiply(controlVector));
33 | 
34 | 	this.predictedProbabilityEstimate = this.stateTransitionMatrix
35 | 		.multiply(this.covarianceEstimate)
36 | 		.multiply(this.stateTransitionMatrix.transpose())
37 | 		.add(this.processErrorEstimate);
38 | };
39 | 
40 | LinearKalmanFilter.prototype.observe = function(measurementVector) {
41 | 	if (measurementVector !== null) {
42 | 		this.innovation = measurementVector
43 | 				.subtract(this.observationMatrix.multiply(this.predictedStateEstimate));
44 | 
45 | 		this.innovationCovariance = this.observationMatrix
46 | 			.multiply(this.predictedProbabilityEstimate)
47 | 			.multiply(this.observationMatrix.transpose())
48 | 			.add(this.measurementErrorEstimate);
49 | 	} else {
50 | 		this.innovation = Matrix.Zero(this.stateEstimate.dimensions().rows, this.stateEstimate.dimensions().cols);
51 | 
52 | 		if (this.innovationCovariance === null) {
53 | 			this.innovationCovariance = Matrix.I(this.stateEstimate.dimensions().rows);
54 | 		}
55 | 	}
56 | };
57 | 
58 | LinearKalmanFilter.prototype.update = function() {
59 | 	this.kalmanGain = this.predictedProbabilityEstimate
60 | 		.multiply(this.observationMatrix.transpose())
61 | 		.multiply(this.innovationCovariance.inverse());
62 | 
63 | 	this.stateEstimate = this.predictedStateEstimate
64 | 			.add(this.kalmanGain.multiply(this.innovation));
65 | 
66 | 	this.covarianceEstimate = Matrix.I(this.covarianceEstimate.dimensions().rows)
67 | 			.subtract(this.kalmanGain.multiply(this.observationMatrix))
68 | 			.multiply(this.predictedProbabilityEstimate);
69 | };
70 | 
71 | LinearKalmanFilter.prototype.inspect = function() {
72 | 	for (var key in this) {
73 | 		if (this[key] === null || typeof(this[key]) !== 'object' || typeof(this[key].inspect) !== 'function') {
74 | 			continue;
75 | 		}
76 | 
77 | 		console.log(key, '\n' + this[key].inspect());
78 | 	}
79 | };
80 | 
81 | Math.randomGaussian = function(deviation, mean) {
82 | 	deviation = typeof(deviation) !== 'undefined' ? deviation : 0.5;
83 | 	mean = typeof(mean) !== 'undefined' ? mean : 0;
84 | 
85 | 	return ((Math.random() * 2 - 1) + (Math.random() * 2 - 1) + (Math.random() * 2 - 1)) * deviation + mean;
86 | };


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/1D.html:
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  1 | <!DOCTYPE html>
  2 | <html>
  3 | <head>
  4 |     <title>KalmanJS :: Singe Variable Linear Kalman Filter</title>
  5 |     <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
  6 | 	<script src="lib/jquery/jquery-1.8.2.min.js"></script>
  7 | 	<script src="lib/jquery/jquery.slider-1.3.js"></script>
  8 | 	<link rel="stylesheet" href="lib/jquery/jquery.slider-1.3.css" type="text/css">
  9 |     <script src="common.js"></script>
 10 |     <script src="lib/plotjs/PlotJS.js"></script>
 11 |     <script src="lib/sylvester/sylvester.js"></script>
 12 |     <script src="lib/kalmanjs/LinearKalmanFilter.js"></script>
 13 | 	<link rel="stylesheet" href="style/style.css">
 14 | </head>
 15 | <body>
 16 |     <canvas id="data-plot" class="plot-main"></canvas>
 17 |     <canvas id="predicted-state-plot" class="plot-sub"></canvas>
 18 |     <canvas id="predicted-probability-plot" class="plot-sub"></canvas>
 19 |     <canvas id="covariance-plot" class="plot-sub"></canvas>
 20 |     <canvas id="gain-plot" class="plot-sub"></canvas>
 21 |     <canvas id="innovation-plot" class="plot-sub"></canvas>
 22 |     <canvas id="innovation-covariance-plot" class="plot-sub"></canvas>
 23 | 
 24 |     <div id="controls"></div>
 25 | 
 26 | 	<script>
 27 | 
 28 | 	var options = {
 29 | 		offset: 0.0,
 30 | 		stateTransition: 1.0,
 31 | 		observation: 1.0,
 32 | 		initialState: 1.0,
 33 | 		initialCovariance: 1.0,
 34 | 		processError: 0.001,
 35 | 		measurementError: 0.001,
 36 | 		noise: 0.25,
 37 | 		iterations: 1000,
 38 | 		observationCutoff: 1000
 39 | 	};
 40 | 
 41 | 	function run() {
 42 | 		// Single-variable linear Kalman Filter
 43 | 		Process = function(offset, noise) {
 44 | 			this.offset = offset;
 45 | 			this.noise = noise;
 46 | 		};
 47 | 
 48 | 		Process.prototype.getRealValue = function(i) {
 49 | 			return this.offset;
 50 | 		};
 51 | 
 52 | 		Process.prototype.getMeasuredValue = function(i) {
 53 | 			return Math.randomGaussian(this.noise, this.getRealValue(i));
 54 | 		};
 55 | 
 56 | 		var stateTransitionMatrix       = $M([[options.stateTransition]]),      // A
 57 | 			controlMatrix               = $M([[0]]),                            // B
 58 | 			observationMatrix           = $M([[options.observation]]),          // H
 59 | 			initialStateEstimate        = $M([[options.initialState]]),         // X
 60 | 			initialCovarianceEstimate   = $M([[options.initialCovariance]]),    // P
 61 | 			processErrorEstimate        = $M([[options.processError]]),         // Q
 62 | 			measurementErrorEstimate    = $M([[options.measurementError]]),     // R
 63 | 			controlVector               = $M([[0]]),                            // C
 64 | 			measurementVector,
 65 | 			filter = new LinearKalmanFilter(
 66 | 				stateTransitionMatrix,
 67 | 				controlMatrix,
 68 | 				observationMatrix,
 69 | 				initialStateEstimate,
 70 | 				initialCovarianceEstimate,
 71 | 				processErrorEstimate,
 72 | 				measurementErrorEstimate
 73 | 			),
 74 | 			process = new Process(options.offset, options.noise),
 75 | 			dataPlot = new PlotJS(),
 76 | 			predictedStatePlot = new PlotJS(),
 77 | 			predictedProbabilityPlot = new PlotJS(),
 78 | 			covariancePlot = new PlotJS(),
 79 | 			gainPlot = new PlotJS(),
 80 | 			innovationPlot = new PlotJS(),
 81 | 			innovationCovariancePlot = new PlotJS(),
 82 | 			realValues = [],
 83 | 			measuredValues = [],
 84 | 			filteredValues = [],
 85 | 			predictedStateValues = [],
 86 | 			predictionProbabilityValues = [],
 87 | 			covarianceValues = [],
 88 | 			gainValues = [],
 89 | 			innovationValues = [],
 90 | 			innovationCovarianceValues = [],
 91 | 			realValue,
 92 | 			measuredValue,
 93 | 			filteredValue,
 94 | 			predictedState,
 95 | 			predictedProbability,
 96 | 			covariance,
 97 | 			gain,
 98 | 			innovation,
 99 | 			innovationCovariance,
100 | 			i;
101 | 
102 | 		for (i = 0; i < options.iterations; i++) {
103 | 			measuredValue = process.getMeasuredValue(i);
104 | 
105 | 			measurementVector = $M([[measuredValue]]);
106 | 
107 | 			filter.predict(controlVector);
108 | 			filter.observe(i < options.observationCutoff ? measurementVector : null);
109 | 			filter.update();
110 | 
111 | 			realValue = process.getRealValue(i);
112 | 			filteredValue = filter.getStateEstimate().e(1, 1);
113 | 
114 | 			predictedState = filter.predictedStateEstimate.e(1, 1);
115 | 			predictedProbability = filter.predictedProbabilityEstimate.e(1, 1);
116 | 			covariance = filter.covarianceEstimate.e(1, 1);
117 | 			gain = filter.kalmanGain.e(1, 1);
118 | 			innovation = filter.innovation.e(1, 1);
119 | 			innovationCovariance = filter.innovationCovariance.e(1, 1);
120 | 
121 | 			realValues.push(realValue);
122 | 			measuredValues.push(measuredValue);
123 | 			filteredValues.push(filteredValue);
124 | 
125 | 			predictedStateValues.push(predictedState);
126 | 			predictionProbabilityValues.push(predictedProbability);
127 | 			covarianceValues.push(covariance);
128 | 			gainValues.push(gain);
129 | 			innovationValues.push(innovation);
130 | 			innovationCovarianceValues.push(innovationCovariance);
131 | 
132 | 			//console.log(filter);
133 | 		}
134 | 
135 | 		dataPlot
136 | 			.addData(realValues, 'Real values')
137 | 			.addData(measuredValues, 'Measured values')
138 | 			.addData(filteredValues, 'Filtered values')
139 | 			.setTitle('Linear Kalman Filter')
140 | 			.draw('data-plot', {
141 | 				showPoints: false,
142 | 				drawLegend: true,
143 | 				valueDecimals: 1,
144 | 				paddingTop: 60,
145 | 				rangeMin: 0,
146 | 				rangeMax: 10
147 | 			});
148 | 
149 | 		predictedStatePlot
150 | 			.addData(predictedStateValues)
151 | 			.setTitle('State estimate')
152 | 			.draw('predicted-state-plot', {
153 | 			showPoints: false,
154 | 				valueDecimals: 1,
155 | 				paddingTop: 60,
156 | 				rangeMin: 0,
157 | 				rangeMax: 10
158 | 			});
159 | 
160 | 		predictedProbabilityPlot
161 | 			.addData(predictionProbabilityValues)
162 | 			.setTitle('Probability estimate')
163 | 			.draw('predicted-probability-plot', {
164 | 			showPoints: false,
165 | 				valueDecimals: 1,
166 | 				paddingTop: 60,
167 | 				rangeMin: -1,
168 | 				rangeMax: 1
169 | 			});
170 | 
171 | 		covariancePlot
172 | 			.addData(covarianceValues)
173 | 			.setTitle('Covariance estimate')
174 | 			.draw('covariance-plot', {
175 | 			showPoints: false,
176 | 				valueDecimals: 1,
177 | 				paddingTop: 60,
178 | 				rangeMin: 0,
179 | 				rangeMax: 1
180 | 			});
181 | 
182 | 		gainPlot
183 | 			.addData(gainValues)
184 | 			.setTitle('Kalman gain')
185 | 			.draw('gain-plot', {
186 | 			showPoints: false,
187 | 				valueDecimals: 1,
188 | 				paddingTop: 60,
189 | 				rangeMin: 0,
190 | 				rangeMax: 1
191 | 			});
192 | 
193 | 		innovationPlot
194 | 			.addData(innovationValues)
195 | 			.setTitle('Innovation')
196 | 			.draw('innovation-plot', {
197 | 			showPoints: false,
198 | 				valueDecimals: 1,
199 | 				paddingTop: 60,
200 | 				rangeMin: -5,
201 | 				rangeMax: 5
202 | 			});
203 | 
204 | 		innovationCovariancePlot
205 | 			.addData(innovationCovarianceValues)
206 | 			.setTitle('Innovation covariance')
207 | 			.draw('innovation-covariance-plot', {
208 | 			showPoints: false,
209 | 				valueDecimals: 1,
210 | 				paddingTop: 60,
211 | 				rangeMin: -1,
212 | 				rangeMax: 1
213 | 			});
214 | 
215 | 		window.filter = filter;
216 | 	};
217 | 
218 | 	var controls = [
219 | 		// control              value       min         max         step
220 | 		['offset',			    5,			0,			10,			0.1],
221 | 		//['stateTransition',		1,			0,			2,			0.1],
222 | 		//['observation',			1,			0,			2,			0.1],
223 | 		['initialState',	    0,			-5,			5,			0.1],
224 | 		['initialCovariance',	50,			0,		    100,	    1],
225 | 		['processError',		0.0,		0.0,		0.1,		0.0001],
226 | 		['measurementError',    0.25,		0.01,		2,			0.01],
227 | 		['noise',			    2.0,		0,			4,			0.1],
228 | 		['iterations',			1000,		10,			2000,		10],
229 | 		['observationCutoff',	1000,		10,			2000,		10]
230 | 	];
231 | 
232 | 	for (var i = 0; i < controls.length; i++) {
233 | 		createControl.apply(this, controls[i]);
234 | 	}
235 | 
236 | 	run();
237 | 
238 | 	</script>
239 |     <div id="github"><a href="https://github.com/kallaspriit/KalmanJS" target="_blank">Github Project</a><a href="https://github.com/kallaspriit/KalmanJS/zipball/master">Download Latest</a></div>
240 | </body>
241 | </html>
242 | 


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/2D.html:
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  1 | <!DOCTYPE html>
  2 | <html>
  3 | <head>
  4 |     <title>KalmanJS :: 2D Linear Kalman Filter</title>
  5 |     <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
  6 | 	<script src="lib/jquery/jquery-1.8.2.min.js"></script>
  7 | 	<script src="lib/jquery/jquery.slider-1.3.js"></script>
  8 | 	<link rel="stylesheet" href="lib/jquery/jquery.slider-1.3.css" type="text/css">
  9 | 	<script src="common.js"></script>
 10 | 	<script src="lib/plotjs/PlotJS.js"></script>
 11 | 	<script src="lib/sylvester/sylvester.js"></script>
 12 | 	<script src="lib/kalmanjs/LinearKalmanFilter.js"></script>
 13 | 	<link rel="stylesheet" href="style/style.css">
 14 | </head>
 15 | <body>
 16 |     <canvas id="data-plot" class="plot-main"></canvas>
 17 |     <canvas id="predicted-state-plot" class="plot-sub"></canvas>
 18 |     <canvas id="predicted-probability-plot" class="plot-sub"></canvas>
 19 |     <canvas id="covariance-plot" class="plot-sub"></canvas>
 20 |     <canvas id="gain-plot" class="plot-sub"></canvas>
 21 |     <canvas id="innovation-plot" class="plot-sub"></canvas>
 22 |     <canvas id="innovation-covariance-plot" class="plot-sub"></canvas>
 23 | 
 24 |     <div id="controls"></div>
 25 | 
 26 | 	<script>
 27 | 
 28 | 	// Multi-variable cannonball
 29 | 	Cannon = function(gravity, angle, muzzleVelocity, noise) {
 30 | 		this.angle = angle;
 31 | 		this.muzzleVelocity = muzzleVelocity;
 32 | 		this.gravity = [0, gravity];
 33 | 		this.velocity = [this.muzzleVelocity * Math.cos(this.angle * Math.PI / 180.0), this.muzzleVelocity * Math.sin(angle * Math.PI / 180.0)];
 34 | 		this.pos = [0, 0];
 35 | 		this.noise = noise;
 36 | 		
 37 | 		this.getX = function() {
 38 | 			return this.pos[0];
 39 | 		};
 40 | 		
 41 | 		this.getY = function() {
 42 | 			return this.pos[1];
 43 | 		};
 44 | 		
 45 | 		this.getMeasurementX = function() {
 46 | 			return Math.randomGaussian(this.noise, this.getX());
 47 | 		};
 48 | 		
 49 | 		this.getMeasurementY = function() {
 50 | 			return Math.randomGaussian(this.noise, this.getY());
 51 | 		};
 52 | 	
 53 | 		this.getVelocityX = function() {
 54 | 			return this.velocity[0];
 55 | 		};
 56 | 		
 57 | 		this.getVelocityY = function() {
 58 | 			return this.velocity[1];
 59 | 		};
 60 | 		
 61 | 		this.hasLanded = function() {
 62 | 			return this.pos[1] < 0.0;
 63 | 		};
 64 | 	
 65 | 		this.step = function(dt) {
 66 | 			var stepGravity = [
 67 | 					this.gravity[0] * dt,
 68 | 					this.gravity[1] * dt
 69 | 				];
 70 | 		
 71 | 			this.velocity = [
 72 | 				this.velocity[0] + stepGravity[0],
 73 | 				this.velocity[1] + stepGravity[1]
 74 | 			];
 75 | 		
 76 | 			var stepVelocity = [
 77 | 				this.velocity[0] * dt,
 78 | 				this.velocity[1] * dt
 79 | 			];
 80 | 		
 81 | 			this.pos = [
 82 | 				this.pos[0] + stepVelocity[0],
 83 | 				this.pos[1] + stepVelocity[1]
 84 | 			];
 85 | 		};
 86 | 	};
 87 | 
 88 | 	var options = {
 89 | 		muzzleVelocity: 100.0,
 90 | 		angle: 45.0,
 91 | 		gravity: -9.81,
 92 | 		initialCovariance: 0.0,
 93 | 		processError: 0.0,
 94 | 		measurementError: 0.2,
 95 | 		noise: 30.0,
 96 | 		dt: 0.1,
 97 | 		observationCutoff: 1000
 98 | 	};
 99 | 
100 | 	function run() {
101 | 		var cannon = new Cannon(options.gravity, options.angle, options.muzzleVelocity, options.noise),
102 | 			startPosX = 0.0,
103 | 			startPosY = 0.0,
104 | 			startVelocityX = options.muzzleVelocity * Math.cos(options.angle * Math.PI / 180),
105 | 			startVelocityY = options.muzzleVelocity * Math.sin(options.angle * Math.PI / 180);
106 | 
107 | 		// This is the state transition vector, which represents part of the kinematics.
108 | 		// 1, ts, 0,  0  =>  x(n+1) = x(n) + vx(n)
109 | 		// 0,  1, 0,  0  => vx(n+1) =        vx(n)
110 | 		// 0,  0, 1, ts  =>  y(n+1) =              y(n) + vy(n)
111 | 		// 0,  0, 0,  1  => vy(n+1) =                     vy(n)
112 | 		// Remember, acceleration gets added to these at the control vector.
113 | 		var stateTransitionMatrix = $M([
114 | 			[1, options.dt, 0, 0],
115 | 			[0, 1, 0, 0],
116 | 			[0, 0, 1, options.dt],
117 | 			[0, 0, 0, 1]
118 | 		]);
119 | 
120 | 		// The control vector, which adds acceleration to the kinematic equations.
121 | 		// 0          =>  x(n+1) =  x(n+1)
122 | 		// 0          => vx(n+1) = vx(n+1)
123 | 		// -9.81*ts^2 =>  y(n+1) =  y(n+1) + 0.5*-9.81*ts^2
124 | 		// -9.81*ts   => vy(n+1) = vy(n+1) + -9.81*ts
125 | 		var controlMatrix = $M([
126 | 				[0, 0, 0, 0],
127 | 				[0, 0, 0, 0],
128 | 				[0, 0, 1, 0],
129 | 				[0, 0, 0, 1]
130 | 			]),
131 | 			controlVector = $M([
132 | 				[0],
133 | 				[0],
134 | 				[0.5 * options.gravity * options.dt * options.dt],
135 | 				[options.gravity * options.dt]
136 | 			]);
137 | 
138 | 		// After state transition and control, here are the equations:
139 | 		//  x(n+1) = x(n) + vx(n)
140 | 		// vx(n+1) = vx(n)
141 | 		//  y(n+1) = y(n) + vy(n) - 0.5*9.81*ts^2
142 | 		// vy(n+1) = vy(n) + -9.81*ts
143 | 		// Which, if you recall, are the equations of motion for a parabola.  Perfect.
144 | 
145 | 		// Observation matrix is the identity matrix, since we can get direct
146 | 		// measurements of all values in our example.
147 | 		var observationMatrix = $M([
148 | 			[1, 0, 0, 0],
149 | 			[0, 1, 0, 0],
150 | 			[0, 0, 1, 0],
151 | 			[0, 0, 0, 1]
152 | 		]);
153 | 
154 | 		// This is our guess of the initial state.  I intentionally set the Y value
155 | 		// wrong to illustrate how fast the Kalman filter will pick up on that.
156 | 		var initialStateEstimate = $M([
157 | 				[startPosX],
158 | 				[startVelocityX],
159 | 				[startPosY],
160 | 				[startVelocityY]
161 | 			]),
162 | 			initialCovarianceEstimate = $M([
163 | 				[options.initialCovariance, 0, 0, 0],
164 | 				[0, options.initialCovariance, 0, 0],
165 | 				[0, 0, options.initialCovariance, 0],
166 | 				[0, 0, 0, options.initialCovariance]
167 | 			]),
168 | 			processErrorEstimate = $M([
169 | 				[options.processError, 0, 0, 0],
170 | 				[0, options.processError, 0, 0],
171 | 				[0, 0, options.processError, 0],
172 | 				[0, 0, 0, options.processError]
173 | 			]),
174 | 			measurementErrorEstimate = $M([
175 | 				[options.measurementError, 0, 0, 0],
176 | 				[0, options.measurementError, 0, 0],
177 | 				[0, 0, options.measurementError, 0],
178 | 				[0, 0, 0, options.measurementError]
179 | 			]);
180 | 
181 | 		var filter = new LinearKalmanFilter(
182 | 				stateTransitionMatrix,
183 | 				controlMatrix,
184 | 				observationMatrix,
185 | 				initialStateEstimate,
186 | 				initialCovarianceEstimate,
187 | 				processErrorEstimate,
188 | 				measurementErrorEstimate
189 | 			),
190 | 			dataPlot = new PlotJS(),
191 | 			predictedStatePlot = new PlotJS(),
192 | 			predictedProbabilityPlot = new PlotJS(),
193 | 			covariancePlot = new PlotJS(),
194 | 			gainPlot = new PlotJS(),
195 | 			innovationPlot = new PlotJS(),
196 | 			innovationCovariancePlot = new PlotJS(),
197 | 			realPos = {},
198 | 			measuredPos = {},
199 | 			filterPos = {},
200 | 			predictedPosX = [], predictedPosY = [], predictedVelX = [], predictedVelY = [],
201 | 			probabilityPosX = [], probabilityPosY = [], probabilityVelX = [], probabilityVelY = [],
202 | 			covariancePosX = [], covariancePosY = [], covarianceVelX = [], covarianceVelY = [],
203 | 			gainPosX = [], gainPosY = [], gainVelX = [], gainVelY = [],
204 | 			innovationPosX = [], innovationPosY = [], innovationVelX = [], innovationVelY = [],
205 | 			innovationCovariancePosX = [], innovationCovariancePosY = [], innovationCovarianceVelX = [], innovationCovarianceVelY = [],
206 | 			realX, realY,
207 | 			measurementX, measurementY,
208 | 			velocityX, velocityY,
209 | 			measurementVector,
210 | 			filterState, filterX, filterY,
211 | 			gain,
212 | 			innovation,
213 | 			innovationCovariance,
214 | 			step = 0;
215 | 
216 | 		while (!cannon.hasLanded()) {
217 | 			cannon.step(options.dt);
218 | 
219 | 			realX = cannon.getX();
220 | 			realY = cannon.getY();
221 | 			measurementX = cannon.getMeasurementX();
222 | 			measurementY = cannon.getMeasurementY();
223 | 			velocityX = cannon.getVelocityX();
224 | 			velocityY = cannon.getVelocityY();
225 | 
226 | 			measurementVector = $M([
227 | 				[measurementX],
228 | 				[velocityX],
229 | 				[measurementY],
230 | 				[velocityY]
231 | 			]);
232 | 
233 | 			filter.predict(controlVector);
234 | 			filter.observe(realX < options.observationCutoff ? measurementVector : null);
235 | 			filter.update();
236 | 
237 | 			filterState = filter.getStateEstimate();
238 | 			/*q = {
239 | 				x: covariance.a11
240 | 			}*/
241 | 
242 | 			filterX = filterState.e(1, 1);
243 | 			filterY = filterState.e(3, 1);
244 | 
245 | 			realPos[realX] = realY;
246 | 			measuredPos[measurementX] = measurementY;
247 | 			filterPos[filterX] = filterY;
248 | 
249 | 			predictedPosY.push(filter.predictedStateEstimate.e(3, 1));
250 | 			predictedPosX.push(filter.predictedStateEstimate.e(1, 1));
251 | 			predictedVelY.push(filter.predictedStateEstimate.e(4, 1));
252 | 			predictedVelX.push(filter.predictedStateEstimate.e(2, 1));
253 | 
254 | 			probabilityPosY.push(filter.predictedProbabilityEstimate.e(3, 1));
255 | 			probabilityPosX.push(filter.predictedProbabilityEstimate.e(1, 1));
256 | 			probabilityVelY.push(filter.predictedProbabilityEstimate.e(4, 1));
257 | 			probabilityVelX.push(filter.predictedProbabilityEstimate.e(2, 1));
258 | 
259 | 			covariancePosY.push(filter.covarianceEstimate.e(3, 1));
260 | 			covariancePosX.push(filter.covarianceEstimate.e(1, 1));
261 | 			covarianceVelY.push(filter.covarianceEstimate.e(4, 1));
262 | 			covarianceVelX.push(filter.covarianceEstimate.e(2, 1));
263 | 
264 | 			gainPosY.push(filter.kalmanGain.e(3, 1));
265 | 			gainPosX.push(filter.kalmanGain.e(1, 1));
266 | 			gainVelY.push(filter.kalmanGain.e(4, 1));
267 | 			gainVelX.push(filter.kalmanGain.e(2, 1));
268 | 
269 | 			innovationPosY.push(filter.innovation.e(3, 1));
270 | 			innovationPosX.push(filter.innovation.e(1, 1));
271 | 			innovationVelY.push(filter.innovation.e(4, 1));
272 | 			innovationVelX.push(filter.innovation.e(2, 1));
273 | 
274 | 			innovationCovariancePosY.push(filter.innovationCovariance.e(3, 1));
275 | 			innovationCovariancePosX.push(filter.innovationCovariance.e(1, 1));
276 | 			innovationCovarianceVelY.push(filter.innovationCovariance.e(4, 1));
277 | 			innovationCovarianceVelX.push(filter.innovationCovariance.e(2, 1));
278 | 
279 | 			step++;
280 | 
281 | 			//console.log('#' + step, filter);
282 | 		}
283 | 
284 | 		dataPlot
285 | 			.addData(realPos, 'Real position')
286 | 			.addData(measuredPos, 'Measured position')
287 | 			.addData(filterPos, 'Filter position')
288 | 			.setTitle('Multi-Variable Kalman Filter - Cannonball Flight')
289 | 			.draw('data-plot', {
290 | 				showPoints: false,
291 | 				drawLegend: true,
292 | 				paddingTop: 60,
293 | 				rangeMin: 0,
294 | 				rangeMax: 100
295 | 			});
296 | 
297 | 		predictedStatePlot
298 | 			.addData(predictedPosX, 'Px')
299 | 			.addData(predictedPosY, 'Py')
300 | 			.addData(predictedVelX, 'Vx')
301 | 			.addData(predictedVelY, 'Vy')
302 | 			.setTitle('State estimate')
303 | 			.draw('predicted-state-plot', {
304 | 				showPoints: false,
305 | 				drawLegend: true,
306 | 				valueDecimals: 1,
307 | 				paddingTop: 60,
308 | 				rangeMin: 0,
309 | 				rangeMax: 250
310 | 			});
311 | 
312 | 		predictedProbabilityPlot
313 | 			.addData(probabilityPosX, 'Px')
314 | 			.addData(probabilityPosY, 'Py')
315 | 			.addData(probabilityVelX, 'Vx')
316 | 			.addData(probabilityVelY, 'Vy')
317 | 			.setTitle('Probability estimate')
318 | 			.draw('predicted-probability-plot', {
319 | 				showPoints: false,
320 | 				drawLegend: true,
321 | 				valueDecimals: 1,
322 | 				paddingTop: 60,
323 | 				rangeMin: 0,
324 | 				rangeMax: 5
325 | 			});
326 | 
327 | 		covariancePlot
328 | 			.addData(covariancePosX, 'Px')
329 | 			.addData(covariancePosY, 'Py')
330 | 			.addData(covarianceVelX, 'Vx')
331 | 			.addData(covarianceVelY, 'Vy')
332 | 			.setTitle('Covariance estimate')
333 | 			.draw('covariance-plot', {
334 | 				showPoints: false,
335 | 				drawLegend: true,
336 | 				valueDecimals: 1,
337 | 				paddingTop: 60,
338 | 				rangeMin: 0,
339 | 				rangeMax: 5
340 | 			});
341 | 
342 | 		gainPlot
343 | 			.addData(gainPosX, 'Px')
344 | 			.addData(gainPosY, 'Py')
345 | 			.addData(gainVelX, 'Vx')
346 | 			.addData(gainVelY, 'Vy')
347 | 			.setTitle('Kalman gain')
348 | 			.draw('gain-plot', {
349 | 				showPoints: false,
350 | 				drawLegend: true,
351 | 				valueDecimals: 1,
352 | 				paddingTop: 60,
353 | 				rangeMin: 0,
354 | 				rangeMax: 0.5
355 | 			});
356 | 
357 | 		innovationPlot
358 | 			.addData(innovationPosX, 'Px')
359 | 			.addData(innovationPosY, 'Py')
360 | 			.addData(innovationVelX, 'Vx')
361 | 			.addData(innovationVelY, 'Vy')
362 | 			.setTitle('Innovation')
363 | 			.draw('innovation-plot', {
364 | 				showPoints: false,
365 | 				drawLegend: true,
366 | 				valueDecimals: 1,
367 | 				paddingTop: 60,
368 | 				rangeMin: -30,
369 | 				rangeMax: 30
370 | 			});
371 | 
372 | 		innovationCovariancePlot
373 | 			.addData(innovationCovariancePosX, 'Px')
374 | 			.addData(innovationCovariancePosY, 'Py')
375 | 			.addData(innovationCovarianceVelX, 'Vx')
376 | 			.addData(innovationCovarianceVelY, 'Vy')
377 | 			.setTitle('Innovation covariance')
378 | 			.draw('innovation-covariance-plot', {
379 | 				showPoints: false,
380 | 				drawLegend: true,
381 | 				valueDecimals: 1,
382 | 				paddingTop: 60,
383 | 				rangeMin: -1,
384 | 				rangeMax: 1
385 | 			});
386 | 	}
387 | 
388 | 	var controls = [
389 | 		// control              value       min         max         step
390 | 		['muzzleVelocity',      50.0,       0,          100,        1],
391 | 		['angle',               60.0,       1,          90,         1],
392 | 		['gravity',             -9.81,      -20,        0,          0.1],
393 | 		['initialCovariance',   50.0,       0,          100,        1],
394 | 		['processError',        0.0,        0,          1,          0.001],
395 | 		['measurementError',    50,         0,          100,        0.1],
396 | 		['noise',               10.0,       0,          50,         1],
397 | 		['dt',                  0.02,       0.01,       0.2,        0.01],
398 | 		['observationCutoff',   250,        10,         500,       10]
399 | 	];
400 | 
401 | 	for (var i = 0; i < controls.length; i++) {
402 | 		createControl.apply(this, controls[i]);
403 | 	}
404 | 
405 | 	run();
406 | 	
407 | 	</script>
408 |     <div id="github"><a href="https://github.com/kallaspriit/KalmanJS" target="_blank">Github Project</a><a href="https://github.com/kallaspriit/KalmanJS/zipball/master">Download Latest</a></div>
409 | </body>
410 | </html>
411 | 


--------------------------------------------------------------------------------
/lib/plotjs/PlotJS.js:
--------------------------------------------------------------------------------
  1 | /**
  2 |  * PlotJS is a very simple and minimalistic library to plot simple data as
  3 |  * line-graphs.
  4 |  */
  5 | var PlotJS = function() {
  6 | 	var id,
  7 | 		data = [],
  8 | 		title = null,
  9 | 		colors = ['#F00', '#0F0', '#00F', '#FF0', '#0FF', '#F0F'],
 10 | 		canvas,
 11 | 		c,
 12 | 		width,
 13 | 		height,
 14 | 		plotWidth,
 15 | 		plotHeight,
 16 | 		lastFunctionRangeStart = null,
 17 | 		lastFunctionRangeEnd = null,
 18 | 		lastFunctionRangeStep = null;
 19 | 
 20 | 	function getItemCount() {
 21 | 		var max = 0,
 22 | 			i;
 23 | 
 24 | 		for (i = 0; i < data.length; i++) {
 25 | 			if (data[i].values.length > max) {
 26 | 				max = data[i].values.length;
 27 | 			}
 28 | 		}
 29 | 
 30 | 		return max;
 31 | 	}
 32 | 
 33 | 	function getExtVal(src, cmp) {
 34 | 		var min = null,
 35 | 			i;
 36 | 
 37 |         for (i = 0; i < src.length; i++) {
 38 |             if (
 39 |                 !isNaN(src[i])
 40 |                 && (min === null || cmp(src[i], min))
 41 |             ) {
 42 |                 min = src[i];
 43 |             }
 44 |         }
 45 | 
 46 | 		return min;
 47 | 	}
 48 | 
 49 | 	function getMinVal() {
 50 |         var min = null,
 51 |             value,
 52 |             i;
 53 | 
 54 |         for (i = 0; i < data.length; i++) {
 55 |             value = getExtVal(data[i].values, function(a, b) { return a < b; });
 56 | 
 57 |             if (min === null || value < min) {
 58 |                 min = value;
 59 |             }
 60 |         }
 61 | 
 62 | 		return min;
 63 | 	}
 64 | 
 65 | 	function getMaxVal() {
 66 |         var max = null,
 67 |             value,
 68 |             i;
 69 | 
 70 |         for (i = 0; i < data.length; i++) {
 71 |             value = getExtVal(data[i].values, function(a, b) { return a > b; });
 72 | 
 73 |             if (max === null || value > max) {
 74 |                 max = value;
 75 |             }
 76 |         }
 77 | 
 78 |         return max;
 79 | 	}
 80 | 
 81 | 	function getMinSeries() {
 82 | 		var min = null,
 83 | 			value,
 84 | 			i;
 85 | 
 86 | 		for (i = 0; i < data.length; i++) {
 87 | 			value = getExtVal(data[i].series, function(a, b) { return a < b; });
 88 | 
 89 | 			if (min === null || value < min) {
 90 | 				min = value;
 91 | 			}
 92 | 		}
 93 | 
 94 | 		if (min !== null) {
 95 |             return min;
 96 | 		} else {
 97 | 			return 0;
 98 | 		}
 99 | 	}
100 | 
101 | 	function getMaxSeries() {
102 | 		var max = null,
103 | 			value,
104 | 			i;
105 | 
106 | 		for (i = 0; i < data.length; i++) {
107 | 			value = getExtVal(data[i].series, function(a, b) { return a > b; });
108 | 
109 | 			if (max === null || value > max) {
110 | 				max = value;
111 | 			}
112 | 		}
113 | 
114 |         if (max !== null) {
115 |             return max;
116 |         } else {
117 | 	        if (data.length > 0) {
118 | 				return data[0].values.length;
119 | 	        } else {
120 | 		        return 1;
121 | 	        }
122 |         }
123 | 	}
124 | 
125 | 	function getRange(minVal, maxVal) {
126 | 		var rangeMin = minVal;
127 | 
128 | 		if (maxVal > 10 && rangeMin > 0 && rangeMin < 2) {
129 | 			rangeMin = 0;
130 | 		}
131 | 
132 | 		return {
133 | 			min: rangeMin,
134 | 			max: maxVal
135 | 		};
136 | 	}
137 | 
138 | 	function round(number, decimals) {
139 | 		if (typeof(number) !== 'number') {
140 | 			return number;
141 | 		}
142 | 
143 | 		return number.toFixed(decimals);
144 | 	}
145 | 
146 | 	function map(x, inMin, inMax, outMin, outMax) {
147 | 		return (x - inMin) * (outMax - outMin) / (inMax - inMin) + outMin;
148 | 	}
149 | 
150 | 	var PlotJS = function() {
151 | 
152 | 	};
153 | 
154 | 	PlotJS.prototype.setSeries = function(items) {
155 | 		for (var i = 0; i < data.length; i++) {
156 | 			data[i].series = items;
157 | 		}
158 | 
159 | 		return this;
160 | 	};
161 | 
162 | 	PlotJS.prototype.isNumericSeries = function() {
163 | 		return data.length === 0 || (data[0].series.length > 0 && typeof(data[0].series[0]) === 'number');
164 | 	};
165 | 
166 | 	PlotJS.prototype.addData = function(items, name, color) {
167 | 		if (typeof(items) !== 'object' || items === null) {
168 | 			return this;
169 | 		}
170 | 
171 | 		var series = [],
172 | 			values = [],
173 | 			key,
174 | 			i;
175 | 
176 | 		if (typeof(items.length) === 'undefined') {
177 | 			for (key in items) {
178 | 				if (typeof(key) === 'string' && parseFloat(key) == key) {
179 | 					key = parseFloat(key);
180 | 				}
181 | 
182 | 				series.push(key);
183 | 				values.push(items[key]);
184 | 			}
185 | 		} else {
186 | 			values = items;
187 | 
188 | 			for (i = 0; i < items.length; i++) {
189 | 				series.push(i + 1);
190 | 			}
191 | 		}
192 | 
193 | 		data.push({
194 | 			series: series,
195 | 			values: values,
196 | 			name: name || 'Series ' + (data.length + 1),
197 | 			color: color || colors[data.length % colors.length]
198 | 		});
199 | 
200 | 		return this;
201 | 	};
202 | 
203 | 	PlotJS.prototype.setData = function(items, name, color) {
204 | 		this.clearData().addData(items, name, color);
205 | 
206 | 		return this;
207 | 	};
208 | 
209 | 	PlotJS.prototype.addFunction = function(
210 | 		fn,
211 | 		rangeStart,
212 | 		rangeEnd,
213 | 		step,
214 | 		name,
215 | 		color
216 | 	) {
217 | 		rangeStart = typeof(rangeStart) === 'number' ? rangeStart : lastFunctionRangeStart || 0;
218 | 		rangeEnd = typeof(rangeEnd) === 'number' ? rangeEnd : lastFunctionRangeEnd || 100;
219 | 		step = typeof(step) === 'number' ? step : lastFunctionRangeStep || 0.1;
220 | 
221 | 		var items = {},
222 | 			x;
223 | 
224 | 		for (x = rangeStart; x < rangeEnd; x += step) {
225 | 			items[x] = fn(x);
226 | 		}
227 | 
228 | 		lastFunctionRangeStart = rangeStart;
229 | 		lastFunctionRangeEnd = rangeEnd;
230 | 		lastFunctionRangeStep = step;
231 | 
232 | 		return this.addData(items, name, color);
233 | 	};
234 | 
235 | 	PlotJS.prototype.clearData = function() {
236 | 		data = [];
237 | 
238 | 		return this;
239 | 	};
240 | 
241 | 	PlotJS.prototype.getData = function() {
242 | 		return data;
243 | 	};
244 | 
245 | 	PlotJS.prototype.getCanvas = function() {
246 | 		return canvas;
247 | 	};
248 | 
249 | 	PlotJS.prototype.getContext = function() {
250 | 		return c;
251 | 	};
252 | 
253 | 	PlotJS.prototype.setTitle = function(newTitle) {
254 | 		title = newTitle;
255 | 
256 | 		return this;
257 | 	};
258 | 
259 | 	PlotJS.prototype.getTitle = function() {
260 | 		return title;
261 | 	};
262 | 
263 | 	PlotJS.prototype.draw = function(canvasId, options) {
264 | 		var baseOptions = {
265 | 				paddingLeft: 40,
266 | 				paddingBottom: 40,
267 | 				paddingRight: 10,
268 | 				paddingTop: 10,
269 | 				textPaddingX: 4,
270 | 				textPaddingY: 4,
271 | 				xMinStep: 40,
272 | 				seriesDecimals: 0,
273 | 				valueDecimals: 0,
274 | 				titleTop: 20,
275 | 				legendLineWidth: 20,
276 | 				legendLineHeight: 20,
277 | 				legendTop: 60,
278 | 				rangeMin: null,
279 | 				rangeMax: null,
280 | 				axisStyle: '#333',
281 | 				axisWidth: 1,
282 | 				axisFont: '12px Arial',
283 | 				titleFont: '20px Arial',
284 | 				legendFont: '16px Arial',
285 | 				titleStyle: '#333',
286 | 				bgStyle: 'rgba(255, 255, 255, 255)',
287 | 				plotStyle: '#FFF',
288 | 				axisTextStyle: '#333',
289 | 				zeroLineStyle: '#EEE',
290 | 				stepWidth: 4,
291 | 				stepHeight: 4,
292 | 				ySteps: 5,
293 |                 seriesSteps: 10,
294 | 				drawZeroLine: true,
295 | 				drawLegend: false,
296 | 				showPoints: true,
297 | 				animate: false,
298 | 				animationDuration: 1000
299 | 			},
300 | 			optionKey;
301 | 
302 | 		if (options === null || typeof(options) !== 'object') {
303 | 			options = {};
304 | 		}
305 | 
306 | 		for (optionKey in baseOptions) {
307 | 			if (typeof(options[optionKey]) === 'undefined') {
308 | 				options[optionKey] = baseOptions[optionKey];
309 | 			}
310 | 		}
311 | 
312 | 		id = canvasId || 'plot';
313 | 		canvas = document.getElementById(id);
314 | 
315 | 		if (canvas === null) {
316 | 			throw new Error('Canvas element #' + id + ' not found');
317 | 		}
318 | 
319 | 		c = canvas.getContext('2d');
320 | 		width = canvas.width = canvas.offsetWidth;
321 | 		height = canvas.height = canvas.offsetHeight;
322 | 		plotWidth = width - options.paddingLeft - options.paddingRight;
323 | 		plotHeight = height - options.paddingTop - options.paddingBottom;
324 | 
325 | 		var itemCount = getItemCount(),
326 | 			displayLimit = itemCount;
327 | 
328 | 		if (options.animate) {
329 | 			if (arguments.length > 2) {
330 | 				displayLimit = arguments[2];
331 | 			} else {
332 | 				displayLimit = 1;
333 | 			}
334 | 		}
335 | 
336 | 		// transform so that plot zero is the image origin and y is flipped
337 | 		c.setTransform(
338 | 			1,
339 | 			0,
340 | 			0,
341 | 			-1,
342 | 			options.paddingLeft + 0.5,
343 | 			height - options.paddingBottom + 0.5
344 | 		);
345 | 
346 | 		// draw entire background
347 | 		c.fillStyle = options.bgStyle;
348 | 		c.fillRect(-options.paddingLeft, -options.paddingBottom, width, height);
349 | 
350 | 		// draw plot background
351 | 		c.fillStyle = options.plotStyle;
352 | 		c.fillRect(0, 0, plotWidth, plotHeight);
353 | 
354 | 		// draw ticks
355 | 		var xPos,
356 | 			yVal,
357 | 			yPos,
358 | 			lastDrawnX = null,
359 | 			minVal = getMinVal(),
360 | 			maxVal = getMaxVal(),
361 |             minSeries = getMinSeries(),
362 |             maxSeries = getMaxSeries(),
363 | 			valueRange = getRange(minVal, maxVal),
364 | 			seriesRange = {
365 | 				min: minSeries,
366 | 				max: maxSeries,
367 | 				diff: maxSeries - minSeries
368 | 			};
369 | 
370 | 		if (options.rangeMin !== null) {
371 | 			valueRange.min = options.rangeMin;
372 | 		}
373 | 
374 | 		if (options.rangeMax !== null) {
375 | 			valueRange.max = options.rangeMax;
376 | 		}
377 |         var valDiff = valueRange.max - valueRange.min,
378 |             xStep = plotWidth / (itemCount - 1),
379 |             yStep = valDiff / options.ySteps,
380 |             itemToX = function(item) {
381 |                 return item * xStep;
382 |             },
383 |             seriesToX = function(value) {
384 |                 return map(
385 |                     value,
386 |                     seriesRange.min,
387 |                     seriesRange.max,
388 |                     0,
389 |                     plotWidth
390 |                 );
391 |             },
392 |             valToY = function(value) {
393 |                 return map(
394 |                     value,
395 |                     valueRange.min,
396 |                     valueRange.max,
397 |                     0,
398 |                     plotHeight
399 |                 );
400 |             },
401 |             drawText = function(text, x, y, align, baseline, font) {
402 |                 c.save();
403 |                 c.textAlign = align || 'left';
404 |                 c.textBaseline = baseline || 'middle';
405 |                 c.font = font || '13px Arial';
406 |                 c.setTransform(
407 |                     1,
408 |                     0,
409 |                     0,
410 |                     1,
411 |                     options.paddingLeft + 0.5,
412 |                     height - options.paddingBottom + 0.5
413 |                 );
414 |                 c.fillStyle = options.axisTextStyle;
415 |                 c.fillText(text, x, -y);
416 |                 c.restore();
417 |             };
418 | 
419 | 
420 | 		// draw zero line if requested
421 |         if (options.drawZeroLine) {
422 |             var zeroLineY = valToY(0),
423 |                 zeroLineX = seriesToX(0);
424 | 
425 |             if (zeroLineY > 0) {
426 |                 c.strokeStyle = options.zeroLineStyle;
427 |                 c.beginPath();
428 |                 c.moveTo(0, zeroLineY);
429 |                 c.lineTo(plotWidth, zeroLineY);
430 |                 c.closePath();
431 |                 c.stroke();
432 |             }
433 | 
434 |             if (zeroLineX > 0) {
435 |                 c.strokeStyle = options.zeroLineStyle;
436 |                 c.beginPath();
437 |                 c.moveTo(zeroLineX, 0);
438 |                 c.lineTo(zeroLineX, plotHeight);
439 |                 c.closePath();
440 |                 c.stroke();
441 |             }
442 |         }
443 | 
444 | 		// horizontal ticks and labels
445 | 		c.strokeStyle = options.axisStyle;
446 | 		c.lineWidth = options.axisWidth;
447 | 
448 |         if (this.isNumericSeries()) {
449 |             var seriesStep = seriesRange.diff / options.seriesSteps,
450 | 	            seriesVal,
451 |                 seriesAlign,
452 |                 seriesCounter = 0;
453 | 
454 |             for (i = seriesRange.min; i <= seriesRange.max + 0.0001; i += seriesStep) {
455 |                 xPos = seriesToX(i);
456 | 
457 |                 /*if (
458 |                     (lastDrawnX !== null && xPos - lastDrawnX < options.xMinStep)
459 |                     && xVal !== itemCount - 1
460 |                 ) {
461 |                     continue;
462 |                 }*/
463 | 
464 |                 c.beginPath();
465 |                 c.moveTo(xPos, 0);
466 |                 c.lineTo(xPos, options.stepHeight);
467 |                 c.closePath();
468 |                 c.stroke();
469 | 
470 |                 seriesVal = round(i, options.seriesDecimals);
471 | 
472 |                 if (seriesCounter == 0) {
473 |                     seriesAlign = 'left';
474 |                 } else if (seriesCounter == options.seriesSteps) {
475 |                     seriesAlign = 'right';
476 |                 } else {
477 |                     seriesAlign = 'center';
478 |                 }
479 | 
480 |                 drawText(
481 | 	                seriesVal,
482 |                     xPos,
483 |                     -options.textPaddingY,
484 |                     seriesAlign,
485 |                     'top',
486 |                     options.axisFont
487 |                 );
488 | 
489 |                 lastDrawnX = xPos;
490 |                 seriesCounter++;
491 |             }
492 |         } else {
493 | 	        var xVal,
494 | 		        text,
495 | 		        fillMap = {};
496 | 
497 | 	        for (i = 0; i < data.length; i++) {
498 | 	            for (xVal = 0; xVal < itemCount; xVal++) {
499 | 	                xPos = itemToX(xVal);
500 | 
501 | 	                if (
502 | 	                    (lastDrawnX !== null && xPos - lastDrawnX < options.xMinStep)
503 | 	                        && xVal !== itemCount - 1
504 | 	                        //&& Math.floor(series[xVal]) !== series[xVal]
505 | 	                    ) {
506 | 	                    continue;
507 | 	                }
508 | 
509 | 		            text = typeof(data[i].series[xVal]) !== 'undefined'
510 | 			            ? round(data[i].series[xVal], options.seriesDecimals)
511 | 			            : round(xVal, options.seriesDecimals);
512 | 
513 | 		            if (typeof(fillMap[xPos]) !== 'undefined') {
514 | 			            continue;
515 | 		            }
516 | 
517 | 	                c.beginPath();
518 | 	                c.moveTo(xPos, 0);
519 | 	                c.lineTo(xPos, options.stepHeight);
520 | 	                c.closePath();
521 | 	                c.stroke();
522 | 
523 | 	                drawText(
524 | 	                    text,
525 | 	                    xPos,
526 | 	                    -options.textPaddingY,
527 | 	                    'center',
528 | 	                    'top',
529 | 	                    options.axisFont
530 | 	                );
531 | 
532 | 	                lastDrawnX = xPos;
533 | 
534 | 		            fillMap[xPos] = text;
535 | 	            }
536 | 	        }
537 |         }
538 | 
539 | 		// vertical ticks and labels
540 | 		for (yVal = valueRange.min; yVal <= valueRange.max; yVal += yStep) {
541 | 			yPos = valToY(yVal);
542 | 
543 | 			c.beginPath();
544 | 			c.moveTo(0, yPos);
545 | 			c.lineTo(options.stepWidth, yPos);
546 | 			c.closePath();
547 | 			c.stroke();
548 | 
549 | 			drawText(
550 | 				round(yVal, options.valueDecimals),
551 | 				-options.textPaddingX,
552 | 				yPos,
553 | 				'right',
554 | 				'middle',
555 | 				options.axisFont
556 | 			);
557 | 		}
558 | 
559 | 		// draw axis lines
560 | 		c.strokeStyle = options.axisStyle;
561 | 		c.lineWidth = options.axisWidth;
562 | 
563 | 		c.beginPath();
564 | 		c.moveTo(0, 0);
565 | 		c.lineTo(plotWidth, 0);
566 | 		c.closePath();
567 | 		c.stroke();
568 | 
569 | 		c.beginPath();
570 | 		c.moveTo(0, 0);
571 | 		c.lineTo(0, plotHeight);
572 | 		c.closePath();
573 | 		c.stroke();
574 | 
575 | 		// draw data
576 | 		var xValue,
577 |             yValue,
578 | 			i,
579 | 			j,
580 | 			lastNaN = false,
581 |             lastItem = null;
582 | 
583 | 		for (i = 0; i < data.length; i++) {
584 | 			if (data[i].values.length === 0) {
585 | 				continue;
586 | 			}
587 | 
588 | 			c.strokeStyle = data[i].color;
589 | 			c.fillStyle = data[i].color;
590 | 			c.beginPath();
591 | 
592 | 			for (j = 0; j < Math.min(data[i].values.length, displayLimit); j++) {
593 |                 xValue = data[i].series[j];
594 | 				yValue = data[i].values[j];
595 | 
596 | 				if (isNaN(yValue)) {
597 | 					lastNaN = true;
598 | 
599 | 					continue;
600 | 				}
601 | 
602 |                 if (data[i].series.length == 0 || !this.isNumericSeries()) {
603 |                     xPos = itemToX(j);
604 |                 } else {
605 |                     xPos = seriesToX(xValue);
606 |                 }
607 | 
608 | 				yPos = valToY(yValue);
609 | 
610 | 				if (lastNaN) {
611 | 					c.moveTo(xPos, yPos);
612 | 				} else {
613 | 					c.lineTo(xPos, yPos);
614 | 				}
615 | 
616 | 				if (options.showPoints) {
617 | 					c.fillRect(xPos - 1, yPos - 1, 3, 3);
618 | 				}
619 | 
620 | 				lastNaN = false;
621 |                 lastItem = yValue;
622 | 			}
623 | 
624 | 			c.stroke();
625 | 		}
626 | 
627 | 		// draw legent if requested
628 | 		if (options.drawLegend) {
629 | 			for (i = 0; i < data.length; i++) {
630 | 				if (data[i].values.length === 0) {
631 | 					continue;
632 | 				}
633 | 
634 | 				xPos = plotWidth - plotWidth / 4;
635 | 				yPos = plotHeight - options.legendTop + options.legendLineHeight * i;
636 | 
637 | 				c.strokeStyle = data[i].color;
638 | 				c.beginPath();
639 | 				c.moveTo(xPos, yPos);
640 | 				c.lineTo(xPos + options.legendLineWidth, yPos);
641 | 				c.stroke();
642 | 
643 | 				drawText(
644 | 					data[i].name,
645 | 					xPos + options.legendLineWidth * 1.25,
646 | 					yPos,
647 | 					'left',
648 | 					'middle',
649 | 					options.legendFont
650 | 				);
651 | 			}
652 | 		}
653 | 
654 | 		// draw title if available
655 | 		if (title !== null) {
656 | 			drawText(
657 | 				title,
658 | 				plotWidth / 2,
659 | 				height - options.paddingBottom - options.titleTop,
660 | 				'center',
661 | 				'top',
662 | 				options.titleFont
663 | 			);
664 | 		}
665 | 
666 | 		if (options.animate && displayLimit < itemCount) {
667 | 			var self = this;
668 | 
669 | 			window.setTimeout(function() {
670 | 				self.draw(canvasId, options, displayLimit + 1);
671 | 			}, options.animationDuration / itemCount);
672 | 		}
673 | 
674 | 		return this;
675 | 	};
676 | 
677 | 	return new PlotJS;
678 | };


--------------------------------------------------------------------------------
/lib/jquery/jquery.slider-1.3.js:
--------------------------------------------------------------------------------
  1 | (function($){
  2 | 	var instances = 0;
  3 | 
  4 | 	function Slider(input, options) {
  5 | 		this.defaults = {
  6 | 			classPrefix: '',
  7 | 			width: '100%',
  8 | 			showValue: false,
  9 | 			showRange: false,
 10 | 			onStart: null,
 11 | 			onChange: null,
 12 | 			onEnd: null,
 13 | 			minChangeInterval: 0,
 14 | 			decimals: 1
 15 | 		};
 16 | 
 17 | 		var step = $(input).data('step') || 1;
 18 | 
 19 | 		this.defaults['decimals'] = step < 1 ? ((1 / step) + '').length - 1 : 0;
 20 | 
 21 | 		this.options = $.extend({}, this.defaults, options);
 22 | 		this.input = $(input);
 23 | 		this.dragging = 0;
 24 | 		this.ranged = false;
 25 | 		this.startValue = 0;
 26 | 		this.startValueLeft = null;
 27 | 		this.startValueRight = null;
 28 | 		this.wrapId = null;
 29 | 		this.handleLeftId = null;
 30 | 		this.handleRightId = null;
 31 | 		this.connectorId = null;
 32 | 		this.valueId = null;
 33 | 		this.rangeMinId = null;
 34 | 		this.rangeMaxId = null;
 35 | 		this.wrap = null;
 36 | 		this.handleLeft = null;
 37 | 		this.handleRight = null;
 38 | 		this.connector = null;
 39 | 		this.value = null;
 40 | 		this.rangeMin = null;
 41 | 		this.rangeMax = null;
 42 | 		this.lastChangeTime = null;
 43 | 		this.activeHandle = 0;
 44 | 
 45 | 		this.setupDom = function() {
 46 | 			instances++;
 47 | 
 48 | 			// check for range slider
 49 | 			this.startValue = this.input.val();
 50 | 
 51 | 			if (this.startValue.indexOf(' ') != -1) {
 52 | 				var startValues = this.startValue.split(' ');
 53 | 
 54 | 				this.startValueLeft = parseInt(startValues[0]);
 55 | 				this.startValueRight = startValues[1];
 56 | 
 57 | 				this.startValue = this.startValueLeft;
 58 | 				this.ranged = true;
 59 | 			}
 60 | 
 61 | 			// create the main wrap
 62 | 			var baseId = this.input.attr('id');
 63 | 
 64 | 			if (baseId == null) {
 65 | 				baseId = instances;
 66 | 			}
 67 | 
 68 | 			this.wrapId = 'slider-wrap-' + baseId;
 69 | 
 70 | 			this.input.after($('<div/>', {
 71 | 				'id': this.wrapId,
 72 | 				'class': this.options.classPrefix + 'slider-wrap'
 73 | 			}));
 74 | 
 75 | 			this.wrap = $('#' + this.wrapId);
 76 | 			this.wrap.css({
 77 | 				width: this.options.width
 78 | 			});
 79 | 
 80 | 			// add connector
 81 | 			this.connectorId = 'slider-connector-left-' + baseId;
 82 | 
 83 | 			this.wrap.append($('<div/>', {
 84 | 				'id': this.connectorId,
 85 | 				'class': this.options.classPrefix + 'slider-connector-left'
 86 | 			}));
 87 | 
 88 | 			this.connector = $('#' + this.connectorId);
 89 | 
 90 | 			// add left handle
 91 | 			this.handleLeftId = 'slider-handle-left-' + baseId;
 92 | 
 93 | 			this.wrap.append($('<div/>', {
 94 | 				'id': this.handleLeftId,
 95 | 				'class': this.options.classPrefix + 'slider-handle-left'
 96 | 			}));
 97 | 
 98 | 			this.handleLeft = $('#' + this.handleLeftId);
 99 | 
100 | 			if (this.ranged) {
101 | 				this.handleRightId = 'slider-handle-right-' + baseId;
102 | 
103 | 				this.wrap.append($('<div/>', {
104 | 					'id': this.handleRightId,
105 | 					'class': this.options.classPrefix + 'slider-handle-right'
106 | 				}));
107 | 
108 | 				this.handleRight = $('#' + this.handleRightId);
109 | 			}
110 | 
111 | 			// add labels
112 | 			if (this.options.showValue) {
113 | 				this.valueId = 'slider-value-' + baseId;
114 | 
115 | 				this.wrap.append($('<div/>', {
116 | 					'id': this.valueId,
117 | 					'class': this.options.classPrefix + 'slider-value'
118 | 				}));
119 | 
120 | 				this.wrap.addClass('with-value');
121 | 
122 | 				this.value = $('#' + this.valueId);
123 | 
124 | 				if (!this.ranged) {
125 | 					this.value.html(this.round(this.startValue, this.options.decimals));
126 | 				} else {
127 | 					this.value.html(
128 | 						this.round(this.startValueLeft, this.options.decimals) + ' - ' +
129 | 						this.round(this.startValueRight, this.options.decimals)
130 | 					);
131 | 				}
132 | 			}
133 | 
134 | 			if (this.options.showRange) {
135 | 				var minValue = this.input.data('min') || 0,
136 | 					maxValue = this.input.data('max') || 100;
137 | 
138 | 				this.rangeMinId = 'slider-range-min-' + baseId;
139 | 				this.rangeMaxId = 'slider-range-max-' + baseId;
140 | 
141 | 				this.wrap.append($('<div/>', {
142 | 					'id': this.rangeMinId,
143 | 					'class': this.options.classPrefix + 'slider-range-min'
144 | 				}));
145 | 
146 | 				this.wrap.append($('<div/>', {
147 | 					'id': this.rangeMaxId,
148 | 					'class': this.options.classPrefix + 'slider-range-max'
149 | 				}));
150 | 
151 | 				this.wrap.addClass('with-range');
152 | 
153 | 				this.rangeMin = $('#' + this.rangeMinId);
154 | 				this.rangeMax = $('#' + this.rangeMaxId);
155 | 
156 | 				this.rangeMin.html(minValue);
157 | 				this.rangeMax.html(maxValue);
158 | 			}
159 | 
160 | 			// set default value
161 | 			this.setValue(this.input.val());
162 | 
163 | 			this.input.hide();
164 | 		};
165 | 
166 | 		this.setupEvents = function() {
167 | 			var self = this;
168 | 
169 | 			this.handleLeft.mousedown(function(e) {
170 | 				self.onDragStart(e);
171 | 				self.onDragStartLeft(e);
172 | 
173 | 				$(document).unbind('mousemove').mousemove(function(e) {
174 | 					self.onDragProgress(e);
175 | 				});
176 | 
177 | 				$(document).one('mouseup', function(e) {
178 | 					$(document).unbind('mousemove');
179 | 
180 | 					self.onDragEnd(e);
181 | 				});
182 | 
183 | 				$(document).one('mousedown', function() {
184 | 					self.activeHandle = 0;
185 | 				});
186 | 
187 | 				for (var i = 0; i < window._jQsliders.length; i++) {
188 | 					window._jQsliders[i].activeHandle = 0;
189 | 				}
190 | 
191 | 				self.activeHandle = 1;
192 | 
193 | 				e.preventDefault();
194 | 
195 | 				return false;
196 | 			});
197 | 
198 | 			if (this.ranged) {
199 | 				this.handleRight.mousedown(function(e) {
200 | 					self.onDragStart(e);
201 | 					self.onDragStartRight(e);
202 | 
203 | 					$(document).unbind('mousemove').mousemove(function(e) {
204 | 						self.onDragProgress(e);
205 | 					});
206 | 
207 | 					$(document).one('mouseup', function(e) {
208 | 						$(document).unbind('mousemove');
209 | 
210 | 						self.onDragEnd(e);
211 | 					});
212 | 
213 | 					$(document).one('mousedown', function() {
214 | 						self.activeHandle = 0;
215 | 					});
216 | 
217 | 					for (var i = 0; i < window._jQsliders.length; i++) {
218 | 						window._jQsliders[i].activeHandle = 0;
219 | 					}
220 | 
221 | 					self.activeHandle = 2;
222 | 
223 | 					e.preventDefault();
224 | 
225 | 					return false;
226 | 				});
227 | 			}
228 | 
229 | 			$(document).keydown(function(e) {
230 | 				self.onKeyDown(e);
231 | 			});
232 | 
233 | 			this.wrap.click(function(e) {
234 | 				self.jumpTo(e.clientX);
235 | 			});
236 | 		};
237 | 
238 | 		this.onDragStart = function() {
239 | 			this.disableTextSelect();
240 | 		};
241 | 
242 | 		this.onDragStartLeft = function() {
243 | 			this.dragging = 1;
244 | 
245 | 			if (typeof(this.options.onStart) == 'function') {
246 | 				this.options.onStart('left', this.input[0]);
247 | 			}
248 | 
249 | 			if (typeof(this.options.onStartLeft) == 'function') {
250 | 				this.options.onStartLeft(this.input[0]);
251 | 			}
252 | 		};
253 | 
254 | 		this.onDragStartRight = function() {
255 | 			this.dragging = 2;
256 | 
257 | 			if (typeof(this.options.onStart) == 'function') {
258 | 				this.options.onStart('right', this.input[0]);
259 | 			}
260 | 
261 | 			if (typeof(this.options.onStartRight) == 'function') {
262 | 				this.options.onStartRight(this.input[0]);
263 | 			}
264 | 		};
265 | 
266 | 		this.onDragProgress = function(e) {
267 | 			if (this.dragging == 0) {
268 | 				return;
269 | 			}
270 | 
271 | 			var wrapLeft = this.wrap.offset().left,
272 | 				wrapWidth = parseInt(this.wrap.width()),
273 | 				pos = Math.min(Math.max(e.clientX - wrapLeft, 0), wrapWidth);
274 | 
275 | 			if (this.ranged) {
276 | 				var leftPos = this.handleLeft.position().left,
277 | 					rightPos = this.handleRight.position().left;
278 | 
279 | 				if (this.dragging == 1 && pos > rightPos) {
280 | 					pos = rightPos;
281 | 				} else if (this.dragging == 2 && pos < leftPos) {
282 | 					pos = leftPos;
283 | 				}
284 | 			}
285 | 
286 | 			var minValue = this.input.data('min') || 0,
287 | 				maxValue = this.input.data('max') || 100,
288 | 				step = this.input.data('step') || 1,
289 | 				range = maxValue - minValue,
290 | 				normalizedValue = pos / wrapWidth,
291 | 				value = Math.round(
292 | 					(range * normalizedValue + minValue) / step
293 | 				) * step,
294 | 				currentTime,
295 | 				sinceLast;
296 | 
297 | 			normalizedValue = (value - minValue) / range;
298 | 			pos = wrapWidth * normalizedValue;
299 | 
300 | 			if (!this.ranged) {
301 | 				this.handleLeft.css({
302 | 					left: pos
303 | 				});
304 | 
305 | 				this.connector.css({
306 | 					width: pos
307 | 				});
308 | 
309 | 				this.input.attr('value', value);
310 | 
311 | 				if (this.options.showValue) {
312 | 					this.value.html(this.round(value, this.options.decimals));
313 | 				}
314 | 
315 | 				if (typeof(this.options.onChange) == 'function') {
316 | 					if (this.options.minChangeInterval == 0) {
317 | 						this.options.onChange(value, this.input[0]);
318 | 					} else {
319 | 						currentTime = this.getMillitime();
320 | 						sinceLast = currentTime - this.lastChangeTime;
321 | 
322 | 						if (
323 | 							this.options.minChangeInterval == null
324 | 							|| sinceLast >= this.options.minChangeInterval
325 | 						) {
326 | 							this.options.onChange(value, this.input[0]);
327 | 							this.lastChangeTime = currentTime;
328 | 						}
329 | 					}
330 | 				}
331 | 			} else {
332 | 				var handle = this.dragging == 1
333 | 						? this.handleLeft
334 | 						: this.handleRight,
335 | 					currentValues = this.input.val().split(' '),
336 | 					valueLeft = parseInt(currentValues[0]),
337 | 					valueRight = parseInt(currentValues[1]);
338 | 
339 | 				handle.css({
340 | 					left: pos
341 | 				});
342 | 
343 | 				var posLeft = this.handleLeft.position().left,
344 | 					posRight = this.handleRight.position().left;
345 | 
346 | 				this.connector.css({
347 | 					left: posLeft,
348 | 					width: posRight - posLeft
349 | 				});
350 | 
351 | 				if (this.dragging == 1) {
352 | 					valueLeft = value;
353 | 				} else {
354 | 					valueRight = value;
355 | 				}
356 | 
357 | 				this.input.attr('value', valueLeft + ' ' + valueRight);
358 | 
359 | 				if (this.options.showValue) {
360 | 					this.value.html(
361 | 						this.round(valueLeft, this.options.decimals) + ' - ' +
362 | 						this.round(valueRight, this.options.decimals)
363 | 					);
364 | 				}
365 | 
366 | 				if (typeof(this.options.onChange) == 'function') {
367 | 					this.options.onChange(
368 | 						valueLeft,
369 | 						valueRight,
370 | 						this.input[0]
371 | 					);
372 | 				}
373 | 
374 | 				if (typeof(this.options.onChange) == 'function') {
375 | 					if (this.options.minChangeInterval == 0) {
376 | 						this.options.onChange(
377 | 							valueLeft,
378 | 							valueRight,
379 | 							this.input[0]
380 | 						);
381 | 					} else {
382 | 						currentTime = this.getMillitime();
383 | 						sinceLast = currentTime - this.lastChangeTime;
384 | 
385 | 						if (
386 | 							this.options.minChangeInterval == null
387 | 							|| sinceLast >= this.options.minChangeInterval
388 | 						) {
389 | 							this.options.onChange(
390 | 								valueLeft,
391 | 								valueRight,
392 | 								this.input[0]
393 | 							);
394 | 							this.lastChangeTime = currentTime;
395 | 						}
396 | 					}
397 | 				}
398 | 			}
399 | 
400 | 			this.input.trigger('change');
401 | 		};
402 | 
403 | 		this.onDragEnd = function() {
404 | 			if (this.dragging == 0) {
405 | 				return;
406 | 			}
407 | 
408 | 			if (typeof(this.options.onEnd) == 'function') {
409 | 				this.options.onEnd(
410 | 					this.input.val(),
411 | 					this.dragging == 1 ? 'left' : 'right',
412 | 					this.input[0]
413 | 				);
414 | 			}
415 | 
416 | 			this.dragging = 0;
417 | 
418 | 			this.enableTextSelect();
419 | 		};
420 | 
421 | 		this.onKeyDown = function(e) {
422 | 			if (
423 | 				this.activeHandle == 0
424 | 				|| (e.keyCode != 37 && e.keyCode != 39)
425 | 			) {
426 | 				return;
427 | 			}
428 | 
429 | 			var rawValue = this.input.val(),
430 | 				leftValue,
431 | 				rightValue,
432 | 				changeValue;
433 | 
434 | 			if (this.ranged) {
435 | 				leftValue = parseInt(rawValue.split(' ')[0]);
436 | 				rightValue = parseInt(rawValue.split(' ')[1]);
437 | 
438 | 				if (this.activeHandle == 1) {
439 | 					changeValue = leftValue;
440 | 				} else {
441 | 					changeValue = rightValue;
442 | 				}
443 | 			} else {
444 | 				leftValue = parseInt(rawValue);
445 | 				changeValue = leftValue;
446 | 			}
447 | 
448 | 			var	minValue = parseInt(this.input.data('min')) || 0,
449 | 				maxValue = parseInt(this.input.data('max')) || 100,
450 | 				step = parseInt(this.input.data('step')) || 1;
451 | 
452 | 			if (e.shiftKey) {
453 | 				step *= 10;
454 | 			}
455 | 
456 | 			if (e.keyCode == 37) {
457 | 				changeValue = Math.max(changeValue - step, minValue);
458 | 			} else {
459 | 				changeValue = Math.min(changeValue + step, maxValue);
460 | 			}
461 | 
462 | 			if (this.ranged) {
463 | 				if (this.activeHandle == 1) {
464 | 					if (changeValue > rightValue) {
465 | 						changeValue = rightValue;
466 | 					}
467 | 
468 | 					this.setValue(changeValue + ' ' + rightValue);
469 | 				} else {
470 | 					if (changeValue < leftValue) {
471 | 						changeValue = leftValue;
472 | 					}
473 | 
474 | 					this.setValue(leftValue + ' ' + changeValue);
475 | 				}
476 | 			} else {
477 | 				this.setValue(changeValue);
478 | 			}
479 | 		};
480 | 
481 | 		this.jumpTo = function(clientX) {
482 | 			if (this.dragging != 0) {
483 | 				return;
484 | 			}
485 | 
486 | 			var wrapLeft = this.wrap.offset().left,
487 | 				wrapWidth = parseInt(this.wrap.width()),
488 | 				pos = Math.min(Math.max(clientX - wrapLeft, 0), wrapWidth),
489 | 				event = {
490 | 					clientX: clientX
491 | 				};
492 | 
493 | 			for (var i = 0; i < window._jQsliders.length; i++) {
494 | 				window._jQsliders[i].activeHandle = 0;
495 | 			}
496 | 
497 | 			this.dragging = !this.ranged || pos < wrapWidth / 2 ? 1 : 2;
498 | 			this.activeHandle = this.dragging;
499 | 			this.onDragProgress(event);
500 | 			this.dragging = 0;
501 | 		};
502 | 
503 | 		this.setValue = function(value) {
504 | 			this.startValue = value;
505 | 
506 | 			if (typeof(value) == 'string' && value.indexOf(' ') != -1) {
507 | 				var startValues = value.split(' ');
508 | 
509 | 				this.startValueLeft = parseInt(startValues[0]);
510 | 				this.startValueRight = startValues[1];
511 | 
512 | 				this.startValue = this.startValueLeft;
513 | 				this.ranged = true;
514 | 			}
515 | 
516 | 			var minValue = this.input.data('min') || 0,
517 | 				maxValue = this.input.data('max') || 100,
518 | 				step = this.input.data('step') || 1,
519 | 				range = maxValue - minValue,
520 | 				wrapWidth = parseInt(this.wrap.width());
521 | 
522 | 			if (this.ranged) {
523 | 				if (this.startValueLeft < minValue) {
524 | 					this.startValueLeft = minValue;
525 | 				}
526 | 
527 | 				if (this.startValueRight < minValue) {
528 | 					this.startValueRight = minValue;
529 | 				}
530 | 
531 | 				if (this.startValueLeft > maxValue) {
532 | 					this.startValueLeft = maxValue;
533 | 				}
534 | 
535 | 				if (this.startValueRight > maxValue) {
536 | 					this.startValueRight = maxValue;
537 | 				}
538 | 
539 | 				var valueLeft = Math.round(this.startValueLeft / step) * step,
540 | 					normalizedValueLeft = (valueLeft - minValue) / range,
541 | 					posLeft = wrapWidth * normalizedValueLeft,
542 | 					valueRight = Math.round(this.startValueRight / step) * step,
543 | 					normalizedValueRight = (valueRight - minValue) / range,
544 | 					posRight = wrapWidth * normalizedValueRight;
545 | 
546 | 				this.handleLeft.css({
547 | 					left: posLeft
548 | 				});
549 | 
550 | 				this.handleRight.css({
551 | 					left: posRight
552 | 				});
553 | 
554 | 				this.connector.css({
555 | 					left: posLeft,
556 | 					width: posRight - posLeft
557 | 				});
558 | 
559 | 				this.input.attr('value', valueLeft + ' ' + valueRight);
560 | 
561 | 				if (this.options.showValue) {
562 | 					this.value.html(
563 | 						this.round(valueLeft, this.options.decimals) + ' - ' +
564 | 						this.round(valueRight, this.options.decimals)
565 | 					);
566 | 				}
567 | 
568 | 				if (typeof(this.options.onChange) == 'function') {
569 | 					this.options.onChange(
570 | 						valueLeft,
571 | 						valueRight,
572 | 						this.input[0]
573 | 					);
574 | 				}
575 | 			} else {
576 | 				if (this.startValue < minValue) {
577 | 					this.startValue = minValue;
578 | 				} else if (this.startValue > maxValue) {
579 | 					this.startValue = maxValue;
580 | 				}
581 | 
582 | 				var singleValue = Math.round(this.startValue / step) * step,
583 | 					normalizedValue = (singleValue - minValue) / range,
584 | 					pos = wrapWidth * normalizedValue;
585 | 
586 | 				this.handleLeft.css({
587 | 					left: pos
588 | 				});
589 | 
590 | 				this.connector.css({
591 | 					width: pos
592 | 				});
593 | 
594 | 				this.input.attr('value', value);
595 | 
596 | 				if (this.options.showValue) {
597 | 					this.value.html(this.round(singleValue, this.options.decimals));
598 | 				}
599 | 
600 | 				if (typeof(this.options.onChange) == 'function') {
601 | 					this.options.onChange(
602 | 						singleValue,
603 | 						this.input[0]
604 | 					);
605 | 				}
606 | 			}
607 | 
608 | 			this.input.trigger('change');
609 | 		};
610 | 
611 | 		this.disableTextSelect = function() {
612 | 			$('*')
613 | 				.attr('unselectable', 'on')
614 | 				.css('user-select', 'none')
615 | 				.on('selectstart', false)
616 | 				.addClass('slider-unselectable');
617 | 		};
618 | 
619 | 		this.enableTextSelect = function() {
620 | 			$('*')
621 | 				.removeAttr('unselectable')
622 | 				.css('user-select', '')
623 | 				.unbind('selectstart')
624 | 				.removeClass('slider-unselectable');
625 | 		};
626 | 
627 | 		this.getMillitime = function() {
628 | 			return (new Date()).getTime();
629 | 		};
630 | 
631 | 		this.round = function(number, decimals) {
632 | 			if (typeof(number) !== 'number') {
633 | 				return number;
634 | 			}
635 | 
636 | 			return number.toFixed(decimals);
637 | 		};
638 | 	}
639 | 
640 | 	Slider.prototype = {
641 | 		init: function() {
642 | 			if (typeof(window._jQsliders) == 'undefined') {
643 | 				window._jQsliders = [];
644 | 			}
645 | 
646 | 			window._jQsliders.push(this);
647 | 
648 | 			this.setupDom();
649 | 			this.setupEvents();
650 | 		},
651 | 
652 | 		range: function(min, max, step) {
653 | 			this.input.data('min', min);
654 | 			this.input.data('max', max);
655 | 
656 | 			if (typeof(step) == 'number') {
657 | 				this.input.data('step', step);
658 | 			}
659 | 
660 | 			if (this.options.showRange) {
661 | 				this.rangeMin.html(min);
662 | 				this.rangeMax.html(max);
663 | 			}
664 | 
665 | 			this.setValue(this.input.val());
666 | 		},
667 | 
668 | 		min: function(min) {
669 | 			this.range(min, this.input.data('max'));
670 | 		},
671 | 
672 | 		max: function(max) {
673 | 			this.range(this.input.data('min'), max);
674 | 		},
675 | 
676 | 		val: function(value, right) {
677 | 			if (typeof(right) != 'undefined') {
678 | 				value = parseInt(value) + ' ' + parseInt(right);
679 | 			} else if (parseInt(value) == value) {
680 | 				value = parseInt(value);
681 | 			}
682 | 
683 | 			this.setValue(value);
684 | 		},
685 | 
686 | 		change: function(callback) {
687 | 			this.options.onChange = callback;
688 | 		},
689 | 
690 | 		start: function(callback) {
691 | 			this.options.onStart = callback;
692 | 		},
693 | 
694 | 		end: function(callback) {
695 | 			this.options.onEnd = callback;
696 | 		}
697 | 	};
698 | 
699 | 	$.fn.slider = function(options) {
700 | 		var args = Array.prototype.slice.call(arguments);
701 | 
702 | 		if(this.length) {
703 | 			this.each(function() {
704 | 				var slider = $(this).data('slider');
705 | 
706 | 				if (slider == null) {
707 | 					slider = new Slider(this, options);
708 | 
709 | 					slider.init();
710 | 
711 | 					$(this).data('slider', slider);
712 | 				} else {
713 | 					if (args.length == 0) {
714 | 						return;
715 | 					}
716 | 
717 | 					var method = args[0];
718 | 
719 | 					if (typeof(slider[method]) == 'function') {
720 | 						slider[method].apply(slider, args.slice(1));
721 | 					}
722 | 				}
723 | 			});
724 | 		}
725 | 
726 | 		return this;
727 | 	};
728 | })(jQuery);


--------------------------------------------------------------------------------
/lib/sylvester/sylvester.js:
--------------------------------------------------------------------------------
   1 | var Sylvester = {
   2 |   precision: 1e-6
   3 | };
   4 | 
   5 | Sylvester.Vector = function() {};
   6 | 
   7 | Sylvester.Vector.create = function(elements) {
   8 |   var V = new Sylvester.Vector();
   9 |   return V.setElements(elements);
  10 | };
  11 | var $V = Sylvester.Vector.create;
  12 | 
  13 | Sylvester.Vector.Random = function(n) {
  14 |   var elements = [];
  15 |   while (n--) { elements.push(Math.random()); }
  16 |   return Sylvester.Vector.create(elements);
  17 | };
  18 | 
  19 | Sylvester.Vector.Zero = function(n) {
  20 |   var elements = [];
  21 |   while (n--) { elements.push(0); }
  22 |   return Sylvester.Vector.create(elements);
  23 | };
  24 | 
  25 | Sylvester.Vector.prototype = {
  26 |   e: function(i) {
  27 |     return (i < 1 || i > this.elements.length) ? null : this.elements[i-1];
  28 |   },
  29 | 
  30 |   dimensions: function() {
  31 |     return this.elements.length;
  32 |   },
  33 | 
  34 |   modulus: function() {
  35 |     return Math.sqrt(this.dot(this));
  36 |   },
  37 | 
  38 |   eql: function(vector) {
  39 |     var n = this.elements.length;
  40 |     var V = vector.elements || vector;
  41 |     if (n !== V.length) { return false; }
  42 |     while (n--) {
  43 |       if (Math.abs(this.elements[n] - V[n]) > Sylvester.precision) { return false; }
  44 |     }
  45 |     return true;
  46 |   },
  47 | 
  48 |   dup: function() {
  49 |     return Sylvester.Vector.create(this.elements);
  50 |   },
  51 | 
  52 |   map: function(fn, context) {
  53 |     var elements = [];
  54 |     this.each(function(x, i) {
  55 |       elements.push(fn.call(context, x, i));
  56 |     });
  57 |     return Sylvester.Vector.create(elements);
  58 |   },
  59 | 
  60 |   forEach: function(fn, context) {
  61 |     var n = this.elements.length;
  62 |     for (var i = 0; i < n; i++) {
  63 |       fn.call(context, this.elements[i], i+1);
  64 |     }
  65 |   },
  66 | 
  67 |   toUnitVector: function() {
  68 |     var r = this.modulus();
  69 |     if (r === 0) { return this.dup(); }
  70 |     return this.map(function(x) { return x/r; });
  71 |   },
  72 | 
  73 |   angleFrom: function(vector) {
  74 |     var V = vector.elements || vector;
  75 |     var n = this.elements.length, k = n, i;
  76 |     if (n !== V.length) { return null; }
  77 |     var dot = 0, mod1 = 0, mod2 = 0;
  78 |     // Work things out in parallel to save time
  79 |     this.each(function(x, i) {
  80 |       dot += x * V[i-1];
  81 |       mod1 += x * x;
  82 |       mod2 += V[i-1] * V[i-1];
  83 |     });
  84 |     mod1 = Math.sqrt(mod1); mod2 = Math.sqrt(mod2);
  85 |     if (mod1*mod2 === 0) { return null; }
  86 |     var theta = dot / (mod1*mod2);
  87 |     if (theta < -1) { theta = -1; }
  88 |     if (theta > 1) { theta = 1; }
  89 |     return Math.acos(theta);
  90 |   },
  91 | 
  92 |   isParallelTo: function(vector) {
  93 |     var angle = this.angleFrom(vector);
  94 |     return (angle === null) ? null : (angle <= Sylvester.precision);
  95 |   },
  96 | 
  97 |   isAntiparallelTo: function(vector) {
  98 |     var angle = this.angleFrom(vector);
  99 |     return (angle === null) ? null : (Math.abs(angle - Math.PI) <= Sylvester.precision);
 100 |   },
 101 | 
 102 |   isPerpendicularTo: function(vector) {
 103 |     var dot = this.dot(vector);
 104 |     return (dot === null) ? null : (Math.abs(dot) <= Sylvester.precision);
 105 |   },
 106 | 
 107 |   add: function(vector) {
 108 |     var V = vector.elements || vector;
 109 |     if (this.elements.length !== V.length) { return null; }
 110 |     return this.map(function(x, i) { return x + V[i-1]; });
 111 |   },
 112 | 
 113 |   subtract: function(vector) {
 114 |     var V = vector.elements || vector;
 115 |     if (this.elements.length !== V.length) { return null; }
 116 |     return this.map(function(x, i) { return x - V[i-1]; });
 117 |   },
 118 | 
 119 |   multiply: function(k) {
 120 |     return this.map(function(x) { return x*k; });
 121 |   },
 122 | 
 123 |   dot: function(vector) {
 124 |     var V = vector.elements || vector;
 125 |     var i, product = 0, n = this.elements.length;
 126 |     if (n !== V.length) { return null; }
 127 |     while (n--) { product += this.elements[n] * V[n]; }
 128 |     return product;
 129 |   },
 130 | 
 131 |   cross: function(vector) {
 132 |     var B = vector.elements || vector;
 133 |     if (this.elements.length !== 3 || B.length !== 3) { return null; }
 134 |     var A = this.elements;
 135 |     return Sylvester.Vector.create([
 136 |       (A[1] * B[2]) - (A[2] * B[1]),
 137 |       (A[2] * B[0]) - (A[0] * B[2]),
 138 |       (A[0] * B[1]) - (A[1] * B[0])
 139 |     ]);
 140 |   },
 141 | 
 142 |   max: function() {
 143 |     var m = 0, i = this.elements.length;
 144 |     while (i--) {
 145 |       if (Math.abs(this.elements[i]) > Math.abs(m)) { m = this.elements[i]; }
 146 |     }
 147 |     return m;
 148 |   },
 149 | 
 150 |   indexOf: function(x) {
 151 |     var index = null, n = this.elements.length;
 152 |     for (var i = 0; i < n; i++) {
 153 |       if (index === null && this.elements[i] === x) {
 154 |         index = i + 1;
 155 |       }
 156 |     }
 157 |     return index;
 158 |   },
 159 | 
 160 |   toDiagonalMatrix: function() {
 161 |     return Sylvester.Matrix.Diagonal(this.elements);
 162 |   },
 163 | 
 164 |   round: function() {
 165 |     return this.map(function(x) { return Math.round(x); });
 166 |   },
 167 | 
 168 |   snapTo: function(x) {
 169 |     return this.map(function(y) {
 170 |       return (Math.abs(y - x) <= Sylvester.precision) ? x : y;
 171 |     });
 172 |   },
 173 | 
 174 |   distanceFrom: function(obj) {
 175 |     if (obj.anchor || (obj.start && obj.end)) { return obj.distanceFrom(this); }
 176 |     var V = obj.elements || obj;
 177 |     if (V.length !== this.elements.length) { return null; }
 178 |     var sum = 0, part;
 179 |     this.each(function(x, i) {
 180 |       part = x - V[i-1];
 181 |       sum += part * part;
 182 |     });
 183 |     return Math.sqrt(sum);
 184 |   },
 185 | 
 186 |   liesOn: function(line) {
 187 |     return line.contains(this);
 188 |   },
 189 | 
 190 |   liesIn: function(plane) {
 191 |     return plane.contains(this);
 192 |   },
 193 | 
 194 |   rotate: function(t, obj) {
 195 |     var V, R = null, x, y, z;
 196 |     if (t.determinant) { R = t.elements; }
 197 |     switch (this.elements.length) {
 198 |       case 2:
 199 |         V = obj.elements || obj;
 200 |         if (V.length !== 2) { return null; }
 201 |         if (!R) { R = Sylvester.Matrix.Rotation(t).elements; }
 202 |         x = this.elements[0] - V[0];
 203 |         y = this.elements[1] - V[1];
 204 |         return Sylvester.Vector.create([
 205 |           V[0] + R[0][0] * x + R[0][1] * y,
 206 |           V[1] + R[1][0] * x + R[1][1] * y
 207 |         ]);
 208 |         break;
 209 |       case 3:
 210 |         if (!obj.direction) { return null; }
 211 |         var C = obj.pointClosestTo(this).elements;
 212 |         if (!R) { R = Sylvester.Matrix.Rotation(t, obj.direction).elements; }
 213 |         x = this.elements[0] - C[0];
 214 |         y = this.elements[1] - C[1];
 215 |         z = this.elements[2] - C[2];
 216 |         return Sylvester.Vector.create([
 217 |           C[0] + R[0][0] * x + R[0][1] * y + R[0][2] * z,
 218 |           C[1] + R[1][0] * x + R[1][1] * y + R[1][2] * z,
 219 |           C[2] + R[2][0] * x + R[2][1] * y + R[2][2] * z
 220 |         ]);
 221 |         break;
 222 |       default:
 223 |         return null;
 224 |     }
 225 |   },
 226 | 
 227 |   reflectionIn: function(obj) {
 228 |     if (obj.anchor) {
 229 |       // obj is a plane or line
 230 |       var P = this.elements.slice();
 231 |       var C = obj.pointClosestTo(P).elements;
 232 |       return Sylvester.Vector.create([C[0] + (C[0] - P[0]), C[1] + (C[1] - P[1]), C[2] + (C[2] - (P[2] || 0))]);
 233 |     } else {
 234 |       // obj is a point
 235 |       var Q = obj.elements || obj;
 236 |       if (this.elements.length !== Q.length) { return null; }
 237 |       return this.map(function(x, i) { return Q[i-1] + (Q[i-1] - x); });
 238 |     }
 239 |   },
 240 | 
 241 |   to3D: function() {
 242 |     var V = this.dup();
 243 |     switch (V.elements.length) {
 244 |       case 3: break;
 245 |       case 2: V.elements.push(0); break;
 246 |       default: return null;
 247 |     }
 248 |     return V;
 249 |   },
 250 | 
 251 |   inspect: function() {
 252 |     return '[' + this.elements.join(', ') + ']';
 253 |   },
 254 | 
 255 |   setElements: function(els) {
 256 |     this.elements = (els.elements || els).slice();
 257 |     return this;
 258 |   }
 259 | };
 260 | 
 261 | Sylvester.Vector.prototype.x = Sylvester.Vector.prototype.multiply;
 262 | Sylvester.Vector.prototype.each = Sylvester.Vector.prototype.forEach;
 263 | 
 264 | Sylvester.Vector.i = Sylvester.Vector.create([1,0,0]);
 265 | Sylvester.Vector.j = Sylvester.Vector.create([0,1,0]);
 266 | Sylvester.Vector.k = Sylvester.Vector.create([0,0,1]);
 267 | 
 268 | Sylvester.Matrix = function() {};
 269 | 
 270 | Sylvester.Matrix.create = function(elements) {
 271 |   var M = new Sylvester.Matrix();
 272 |   return M.setElements(elements);
 273 | };
 274 | var $M = Sylvester.Matrix.create;
 275 | 
 276 | Sylvester.Matrix.I = function(n) {
 277 |   var els = [], i = n, j;
 278 |   while (i--) { j = n;
 279 |     els[i] = [];
 280 |     while (j--) {
 281 |       els[i][j] = (i === j) ? 1 : 0;
 282 |     }
 283 |   }
 284 |   return Sylvester.Matrix.create(els);
 285 | };
 286 | 
 287 | Sylvester.Matrix.Diagonal = function(elements) {
 288 |   var i = elements.length;
 289 |   var M = Sylvester.Matrix.I(i);
 290 |   while (i--) {
 291 |     M.elements[i][i] = elements[i];
 292 |   }
 293 |   return M;
 294 | };
 295 | 
 296 | Sylvester.Matrix.Rotation = function(theta, a) {
 297 |   if (!a) {
 298 |     return Sylvester.Matrix.create([
 299 |       [Math.cos(theta),  -Math.sin(theta)],
 300 |       [Math.sin(theta),   Math.cos(theta)]
 301 |     ]);
 302 |   }
 303 |   var axis = a.dup();
 304 |   if (axis.elements.length !== 3) { return null; }
 305 |   var mod = axis.modulus();
 306 |   var x = axis.elements[0]/mod, y = axis.elements[1]/mod, z = axis.elements[2]/mod;
 307 |   var s = Math.sin(theta), c = Math.cos(theta), t = 1 - c;
 308 |   // Formula derived here: http://www.gamedev.net/reference/articles/article1199.asp
 309 |   // That proof rotates the co-ordinate system so theta becomes -theta and sin
 310 |   // becomes -sin here.
 311 |   return Sylvester.Matrix.create([
 312 |     [ t*x*x + c, t*x*y - s*z, t*x*z + s*y ],
 313 |     [ t*x*y + s*z, t*y*y + c, t*y*z - s*x ],
 314 |     [ t*x*z - s*y, t*y*z + s*x, t*z*z + c ]
 315 |   ]);
 316 | };
 317 | 
 318 | Sylvester.Matrix.RotationX = function(t) {
 319 |   var c = Math.cos(t), s = Math.sin(t);
 320 |   return Sylvester.Matrix.create([
 321 |     [  1,  0,  0 ],
 322 |     [  0,  c, -s ],
 323 |     [  0,  s,  c ]
 324 |   ]);
 325 | };
 326 | Sylvester.Matrix.RotationY = function(t) {
 327 |   var c = Math.cos(t), s = Math.sin(t);
 328 |   return Sylvester.Matrix.create([
 329 |     [  c,  0,  s ],
 330 |     [  0,  1,  0 ],
 331 |     [ -s,  0,  c ]
 332 |   ]);
 333 | };
 334 | Sylvester.Matrix.RotationZ = function(t) {
 335 |   var c = Math.cos(t), s = Math.sin(t);
 336 |   return Sylvester.Matrix.create([
 337 |     [  c, -s,  0 ],
 338 |     [  s,  c,  0 ],
 339 |     [  0,  0,  1 ]
 340 |   ]);
 341 | };
 342 | 
 343 | Sylvester.Matrix.Random = function(n, m) {
 344 |   return Sylvester.Matrix.Zero(n, m).map(
 345 |     function() { return Math.random(); }
 346 |   );
 347 | };
 348 | 
 349 | Sylvester.Matrix.Zero = function(n, m) {
 350 |   var els = [], i = n, j;
 351 |   while (i--) { j = m;
 352 |     els[i] = [];
 353 |     while (j--) {
 354 |       els[i][j] = 0;
 355 |     }
 356 |   }
 357 |   return Sylvester.Matrix.create(els);
 358 | };
 359 | 
 360 | Sylvester.Matrix.prototype = {
 361 |   e: function(i,j) {
 362 |     if (i < 1 || i > this.elements.length || j < 1 || j > this.elements[0].length) { return null; }
 363 |     return this.elements[i-1][j-1];
 364 |   },
 365 | 
 366 |   row: function(i) {
 367 |     if (i > this.elements.length) { return null; }
 368 |     return Sylvester.Vector.create(this.elements[i-1]);
 369 |   },
 370 | 
 371 |   col: function(j) {
 372 |     if (this.elements.length === 0) { return null; }
 373 |     if (j > this.elements[0].length) { return null; }
 374 |     var col = [], n = this.elements.length;
 375 |     for (var i = 0; i < n; i++) { col.push(this.elements[i][j-1]); }
 376 |     return Sylvester.Vector.create(col);
 377 |   },
 378 | 
 379 |   dimensions: function() {
 380 |     var cols = (this.elements.length === 0) ? 0 : this.elements[0].length;
 381 |     return {rows: this.elements.length, cols: cols};
 382 |   },
 383 | 
 384 |   rows: function() {
 385 |     return this.elements.length;
 386 |   },
 387 | 
 388 |   cols: function() {
 389 |     if (this.elements.length === 0) { return 0; }
 390 |     return this.elements[0].length;
 391 |   },
 392 | 
 393 |   eql: function(matrix) {
 394 |     var M = matrix.elements || matrix;
 395 |     if (!M[0] || typeof(M[0][0]) === 'undefined') { M = Sylvester.Matrix.create(M).elements; }
 396 |     if (this.elements.length === 0 || M.length === 0) {
 397 |       return this.elements.length === M.length;
 398 |     }
 399 |     if (this.elements.length !== M.length) { return false; }
 400 |     if (this.elements[0].length !== M[0].length) { return false; }
 401 |     var i = this.elements.length, nj = this.elements[0].length, j;
 402 |     while (i--) { j = nj;
 403 |       while (j--) {
 404 |         if (Math.abs(this.elements[i][j] - M[i][j]) > Sylvester.precision) { return false; }
 405 |       }
 406 |     }
 407 |     return true;
 408 |   },
 409 | 
 410 |   dup: function() {
 411 |     return Sylvester.Matrix.create(this.elements);
 412 |   },
 413 | 
 414 |   map: function(fn, context) {
 415 |     if (this.elements.length === 0) { return Sylvester.Matrix.create([]); }
 416 |     var els = [], i = this.elements.length, nj = this.elements[0].length, j;
 417 |     while (i--) { j = nj;
 418 |       els[i] = [];
 419 |       while (j--) {
 420 |         els[i][j] = fn.call(context, this.elements[i][j], i + 1, j + 1);
 421 |       }
 422 |     }
 423 |     return Sylvester.Matrix.create(els);
 424 |   },
 425 | 
 426 |   isSameSizeAs: function(matrix) {
 427 |     var M = matrix.elements || matrix;
 428 |     if (typeof(M[0][0]) === 'undefined') { M = Sylvester.Matrix.create(M).elements; }
 429 |     if (this.elements.length === 0) { return M.length === 0; }
 430 |     return (this.elements.length === M.length &&
 431 |         this.elements[0].length === M[0].length);
 432 |   },
 433 | 
 434 |   add: function(matrix) {
 435 |     if (this.elements.length === 0) return this.map(function(x) { return x });
 436 |     var M = matrix.elements || matrix;
 437 |     if (typeof(M[0][0]) === 'undefined') { M = Sylvester.Matrix.create(M).elements; }
 438 |     if (!this.isSameSizeAs(M)) { return null; }
 439 |     return this.map(function(x, i, j) { return x + M[i-1][j-1]; });
 440 |   },
 441 | 
 442 |   subtract: function(matrix) {
 443 |     if (this.elements.length === 0) return this.map(function(x) { return x });
 444 |     var M = matrix.elements || matrix;
 445 |     if (typeof(M[0][0]) === 'undefined') { M = Sylvester.Matrix.create(M).elements; }
 446 |     if (!this.isSameSizeAs(M)) { return null; }
 447 |     return this.map(function(x, i, j) { return x - M[i-1][j-1]; });
 448 |   },
 449 | 
 450 |   canMultiplyFromLeft: function(matrix) {
 451 |     if (this.elements.length === 0) { return false; }
 452 |     var M = matrix.elements || matrix;
 453 |     if (typeof(M[0][0]) === 'undefined') { M = Sylvester.Matrix.create(M).elements; }
 454 |     // this.columns should equal matrix.rows
 455 |     return (this.elements[0].length === M.length);
 456 |   },
 457 | 
 458 |   multiply: function(matrix) {
 459 |     if (this.elements.length === 0) { return null; }
 460 |     if (!matrix.elements) {
 461 |       return this.map(function(x) { return x * matrix; });
 462 |     }
 463 |     var returnVector = matrix.modulus ? true : false;
 464 |     var M = matrix.elements || matrix;
 465 |     if (typeof(M[0][0]) === 'undefined') { M = Sylvester.Matrix.create(M).elements; }
 466 |     if (!this.canMultiplyFromLeft(M)) { return null; }
 467 |     var i = this.elements.length, nj = M[0].length, j;
 468 |     var cols = this.elements[0].length, c, elements = [], sum;
 469 |     while (i--) { j = nj;
 470 |       elements[i] = [];
 471 |       while (j--) { c = cols;
 472 |         sum = 0;
 473 |         while (c--) {
 474 |           sum += this.elements[i][c] * M[c][j];
 475 |         }
 476 |         elements[i][j] = sum;
 477 |       }
 478 |     }
 479 |     var M = Sylvester.Matrix.create(elements);
 480 |     return returnVector ? M.col(1) : M;
 481 |   },
 482 | 
 483 |   minor: function(a, b, c, d) {
 484 |     if (this.elements.length === 0) { return null; }
 485 |     var elements = [], ni = c, i, nj, j;
 486 |     var rows = this.elements.length, cols = this.elements[0].length;
 487 |     while (ni--) { i = c - ni - 1;
 488 |       elements[i] = [];
 489 |       nj = d;
 490 |       while (nj--) { j = d - nj - 1;
 491 |         elements[i][j] = this.elements[(a+i-1)%rows][(b+j-1)%cols];
 492 |       }
 493 |     }
 494 |     return Sylvester.Matrix.create(elements);
 495 |   },
 496 | 
 497 |   transpose: function() {
 498 |     if (this.elements.length === 0) return Sylvester.Matrix.create([]);
 499 |     var rows = this.elements.length, i, cols = this.elements[0].length, j;
 500 |     var elements = [], i = cols;
 501 |     while (i--) { j = rows;
 502 |       elements[i] = [];
 503 |       while (j--) {
 504 |         elements[i][j] = this.elements[j][i];
 505 |       }
 506 |     }
 507 |     return Sylvester.Matrix.create(elements);
 508 |   },
 509 | 
 510 |   isSquare: function() {
 511 |     var cols = (this.elements.length === 0) ? 0 : this.elements[0].length;
 512 |     return (this.elements.length === cols);
 513 |   },
 514 | 
 515 |   max: function() {
 516 |     if (this.elements.length === 0) { return null; }
 517 |     var m = 0, i = this.elements.length, nj = this.elements[0].length, j;
 518 |     while (i--) { j = nj;
 519 |       while (j--) {
 520 |         if (Math.abs(this.elements[i][j]) > Math.abs(m)) { m = this.elements[i][j]; }
 521 |       }
 522 |     }
 523 |     return m;
 524 |   },
 525 | 
 526 |   indexOf: function(x) {
 527 |     if (this.elements.length === 0) { return null; }
 528 |     var index = null, ni = this.elements.length, i, nj = this.elements[0].length, j;
 529 |     for (i = 0; i < ni; i++) {
 530 |       for (j = 0; j < nj; j++) {
 531 |         if (this.elements[i][j] === x) { return {i: i+1, j: j+1}; }
 532 |       }
 533 |     }
 534 |     return null;
 535 |   },
 536 | 
 537 |   diagonal: function() {
 538 |     if (!this.isSquare) { return null; }
 539 |     var els = [], n = this.elements.length;
 540 |     for (var i = 0; i < n; i++) {
 541 |       els.push(this.elements[i][i]);
 542 |     }
 543 |     return Sylvester.Vector.create(els);
 544 |   },
 545 | 
 546 |   toRightTriangular: function() {
 547 |     if (this.elements.length === 0) return Sylvester.Matrix.create([]);
 548 |     var M = this.dup(), els;
 549 |     var n = this.elements.length, i, j, np = this.elements[0].length, p;
 550 |     for (i = 0; i < n; i++) {
 551 |       if (M.elements[i][i] === 0) {
 552 |         for (j = i + 1; j < n; j++) {
 553 |           if (M.elements[j][i] !== 0) {
 554 |             els = [];
 555 |             for (p = 0; p < np; p++) { els.push(M.elements[i][p] + M.elements[j][p]); }
 556 |             M.elements[i] = els;
 557 |             break;
 558 |           }
 559 |         }
 560 |       }
 561 |       if (M.elements[i][i] !== 0) {
 562 |         for (j = i + 1; j < n; j++) {
 563 |           var multiplier = M.elements[j][i] / M.elements[i][i];
 564 |           els = [];
 565 |           for (p = 0; p < np; p++) {
 566 |             // Elements with column numbers up to an including the number of the
 567 |             // row that we're subtracting can safely be set straight to zero,
 568 |             // since that's the point of this routine and it avoids having to
 569 |             // loop over and correct rounding errors later
 570 |             els.push(p <= i ? 0 : M.elements[j][p] - M.elements[i][p] * multiplier);
 571 |           }
 572 |           M.elements[j] = els;
 573 |         }
 574 |       }
 575 |     }
 576 |     return M;
 577 |   },
 578 | 
 579 |   determinant: function() {
 580 |     if (this.elements.length === 0) { return 1; }
 581 |     if (!this.isSquare()) { return null; }
 582 |     var M = this.toRightTriangular();
 583 |     var det = M.elements[0][0], n = M.elements.length;
 584 |     for (var i = 1; i < n; i++) {
 585 |       det = det * M.elements[i][i];
 586 |     }
 587 |     return det;
 588 |   },
 589 | 
 590 |   isSingular: function() {
 591 |     return (this.isSquare() && this.determinant() === 0);
 592 |   },
 593 | 
 594 |   trace: function() {
 595 |     if (this.elements.length === 0) { return 0; }
 596 |     if (!this.isSquare()) { return null; }
 597 |     var tr = this.elements[0][0], n = this.elements.length;
 598 |     for (var i = 1; i < n; i++) {
 599 |       tr += this.elements[i][i];
 600 |     }
 601 |     return tr;
 602 |   },
 603 | 
 604 |   rank: function() {
 605 |     if (this.elements.length === 0) { return 0; }
 606 |     var M = this.toRightTriangular(), rank = 0;
 607 |     var i = this.elements.length, nj = this.elements[0].length, j;
 608 |     while (i--) { j = nj;
 609 |       while (j--) {
 610 |         if (Math.abs(M.elements[i][j]) > Sylvester.precision) { rank++; break; }
 611 |       }
 612 |     }
 613 |     return rank;
 614 |   },
 615 | 
 616 |   augment: function(matrix) {
 617 |     if (this.elements.length === 0) { return this.dup(); }
 618 |     var M = matrix.elements || matrix;
 619 |     if (typeof(M[0][0]) === 'undefined') { M = Sylvester.Matrix.create(M).elements; }
 620 |     var T = this.dup(), cols = T.elements[0].length;
 621 |     var i = T.elements.length, nj = M[0].length, j;
 622 |     if (i !== M.length) { return null; }
 623 |     while (i--) { j = nj;
 624 |       while (j--) {
 625 |         T.elements[i][cols + j] = M[i][j];
 626 |       }
 627 |     }
 628 |     return T;
 629 |   },
 630 | 
 631 |   inverse: function() {
 632 |     if (this.elements.length === 0) { return null; }
 633 |     if (!this.isSquare() || this.isSingular()) { return null; }
 634 |     var n = this.elements.length, i= n, j;
 635 |     var M = this.augment(Sylvester.Matrix.I(n)).toRightTriangular();
 636 |     var np = M.elements[0].length, p, els, divisor;
 637 |     var inverse_elements = [], new_element;
 638 |     // Sylvester.Matrix is non-singular so there will be no zeros on the
 639 |     // diagonal. Cycle through rows from last to first.
 640 |     while (i--) {
 641 |       // First, normalise diagonal elements to 1
 642 |       els = [];
 643 |       inverse_elements[i] = [];
 644 |       divisor = M.elements[i][i];
 645 |       for (p = 0; p < np; p++) {
 646 |         new_element = M.elements[i][p] / divisor;
 647 |         els.push(new_element);
 648 |         // Shuffle off the current row of the right hand side into the results
 649 |         // array as it will not be modified by later runs through this loop
 650 |         if (p >= n) { inverse_elements[i].push(new_element); }
 651 |       }
 652 |       M.elements[i] = els;
 653 |       // Then, subtract this row from those above it to give the identity matrix
 654 |       // on the left hand side
 655 |       j = i;
 656 |       while (j--) {
 657 |         els = [];
 658 |         for (p = 0; p < np; p++) {
 659 |           els.push(M.elements[j][p] - M.elements[i][p] * M.elements[j][i]);
 660 |         }
 661 |         M.elements[j] = els;
 662 |       }
 663 |     }
 664 |     return Sylvester.Matrix.create(inverse_elements);
 665 |   },
 666 | 
 667 |   round: function() {
 668 |     return this.map(function(x) { return Math.round(x); });
 669 |   },
 670 | 
 671 |   snapTo: function(x) {
 672 |     return this.map(function(p) {
 673 |       return (Math.abs(p - x) <= Sylvester.precision) ? x : p;
 674 |     });
 675 |   },
 676 | 
 677 |   inspect: function() {
 678 |     var matrix_rows = [];
 679 |     var n = this.elements.length;
 680 |     if (n === 0) return '[]';
 681 |     for (var i = 0; i < n; i++) {
 682 |       matrix_rows.push(Sylvester.Vector.create(this.elements[i]).inspect());
 683 |     }
 684 |     return matrix_rows.join('\n');
 685 |   },
 686 | 
 687 |   setElements: function(els) {
 688 |     var i, j, elements = els.elements || els;
 689 |     if (elements[0] && typeof(elements[0][0]) !== 'undefined') {
 690 |       i = elements.length;
 691 |       this.elements = [];
 692 |       while (i--) { j = elements[i].length;
 693 |         this.elements[i] = [];
 694 |         while (j--) {
 695 |           this.elements[i][j] = elements[i][j];
 696 |         }
 697 |       }
 698 |       return this;
 699 |     }
 700 |     var n = elements.length;
 701 |     this.elements = [];
 702 |     for (i = 0; i < n; i++) {
 703 |       this.elements.push([elements[i]]);
 704 |     }
 705 |     return this;
 706 |   }
 707 | };
 708 | 
 709 | Sylvester.Matrix.prototype.toUpperTriangular = Sylvester.Matrix.prototype.toRightTriangular;
 710 | Sylvester.Matrix.prototype.det = Sylvester.Matrix.prototype.determinant;
 711 | Sylvester.Matrix.prototype.tr = Sylvester.Matrix.prototype.trace;
 712 | Sylvester.Matrix.prototype.rk = Sylvester.Matrix.prototype.rank;
 713 | Sylvester.Matrix.prototype.inv = Sylvester.Matrix.prototype.inverse;
 714 | Sylvester.Matrix.prototype.x = Sylvester.Matrix.prototype.multiply;
 715 | 
 716 | Sylvester.Line = function() {};
 717 | 
 718 | Sylvester.Line.prototype = {
 719 |   eql: function(line) {
 720 |     return (this.isParallelTo(line) && this.contains(line.anchor));
 721 |   },
 722 | 
 723 |   dup: function() {
 724 |     return Sylvester.Line.create(this.anchor, this.direction);
 725 |   },
 726 | 
 727 |   translate: function(vector) {
 728 |     var V = vector.elements || vector;
 729 |     return Sylvester.Line.create([
 730 |       this.anchor.elements[0] + V[0],
 731 |       this.anchor.elements[1] + V[1],
 732 |       this.anchor.elements[2] + (V[2] || 0)
 733 |     ], this.direction);
 734 |   },
 735 | 
 736 |   isParallelTo: function(obj) {
 737 |     if (obj.normal || (obj.start && obj.end)) { return obj.isParallelTo(this); }
 738 |     var theta = this.direction.angleFrom(obj.direction);
 739 |     return (Math.abs(theta) <= Sylvester.precision || Math.abs(theta - Math.PI) <= Sylvester.precision);
 740 |   },
 741 | 
 742 |   distanceFrom: function(obj) {
 743 |     if (obj.normal || (obj.start && obj.end)) { return obj.distanceFrom(this); }
 744 |     if (obj.direction) {
 745 |       // obj is a line
 746 |       if (this.isParallelTo(obj)) { return this.distanceFrom(obj.anchor); }
 747 |       var N = this.direction.cross(obj.direction).toUnitVector().elements;
 748 |       var A = this.anchor.elements, B = obj.anchor.elements;
 749 |       return Math.abs((A[0] - B[0]) * N[0] + (A[1] - B[1]) * N[1] + (A[2] - B[2]) * N[2]);
 750 |     } else {
 751 |       // obj is a point
 752 |       var P = obj.elements || obj;
 753 |       var A = this.anchor.elements, D = this.direction.elements;
 754 |       var PA1 = P[0] - A[0], PA2 = P[1] - A[1], PA3 = (P[2] || 0) - A[2];
 755 |       var modPA = Math.sqrt(PA1*PA1 + PA2*PA2 + PA3*PA3);
 756 |       if (modPA === 0) return 0;
 757 |       // Assumes direction vector is normalized
 758 |       var cosTheta = (PA1 * D[0] + PA2 * D[1] + PA3 * D[2]) / modPA;
 759 |       var sin2 = 1 - cosTheta*cosTheta;
 760 |       return Math.abs(modPA * Math.sqrt(sin2 < 0 ? 0 : sin2));
 761 |     }
 762 |   },
 763 | 
 764 |   contains: function(obj) {
 765 |     if (obj.start && obj.end) { return this.contains(obj.start) && this.contains(obj.end); }
 766 |     var dist = this.distanceFrom(obj);
 767 |     return (dist !== null && dist <= Sylvester.precision);
 768 |   },
 769 | 
 770 |   positionOf: function(point) {
 771 |     if (!this.contains(point)) { return null; }
 772 |     var P = point.elements || point;
 773 |     var A = this.anchor.elements, D = this.direction.elements;
 774 |     return (P[0] - A[0]) * D[0] + (P[1] - A[1]) * D[1] + ((P[2] || 0) - A[2]) * D[2];
 775 |   },
 776 | 
 777 |   liesIn: function(plane) {
 778 |     return plane.contains(this);
 779 |   },
 780 | 
 781 |   intersects: function(obj) {
 782 |     if (obj.normal) { return obj.intersects(this); }
 783 |     return (!this.isParallelTo(obj) && this.distanceFrom(obj) <= Sylvester.precision);
 784 |   },
 785 | 
 786 |   intersectionWith: function(obj) {
 787 |     if (obj.normal || (obj.start && obj.end)) { return obj.intersectionWith(this); }
 788 |     if (!this.intersects(obj)) { return null; }
 789 |     var P = this.anchor.elements, X = this.direction.elements,
 790 |         Q = obj.anchor.elements, Y = obj.direction.elements;
 791 |     var X1 = X[0], X2 = X[1], X3 = X[2], Y1 = Y[0], Y2 = Y[1], Y3 = Y[2];
 792 |     var PsubQ1 = P[0] - Q[0], PsubQ2 = P[1] - Q[1], PsubQ3 = P[2] - Q[2];
 793 |     var XdotQsubP = - X1*PsubQ1 - X2*PsubQ2 - X3*PsubQ3;
 794 |     var YdotPsubQ = Y1*PsubQ1 + Y2*PsubQ2 + Y3*PsubQ3;
 795 |     var XdotX = X1*X1 + X2*X2 + X3*X3;
 796 |     var YdotY = Y1*Y1 + Y2*Y2 + Y3*Y3;
 797 |     var XdotY = X1*Y1 + X2*Y2 + X3*Y3;
 798 |     var k = (XdotQsubP * YdotY / XdotX + XdotY * YdotPsubQ) / (YdotY - XdotY * XdotY);
 799 |     return Sylvester.Vector.create([P[0] + k*X1, P[1] + k*X2, P[2] + k*X3]);
 800 |   },
 801 | 
 802 |   pointClosestTo: function(obj) {
 803 |     if (obj.start && obj.end) {
 804 |       // obj is a line segment
 805 |       var P = obj.pointClosestTo(this);
 806 |       return (P === null) ? null : this.pointClosestTo(P);
 807 |     } else if (obj.direction) {
 808 |       // obj is a line
 809 |       if (this.intersects(obj)) { return this.intersectionWith(obj); }
 810 |       if (this.isParallelTo(obj)) { return null; }
 811 |       var D = this.direction.elements, E = obj.direction.elements;
 812 |       var D1 = D[0], D2 = D[1], D3 = D[2], E1 = E[0], E2 = E[1], E3 = E[2];
 813 |       // Create plane containing obj and the shared normal and intersect this
 814 |       // with it Thank you:
 815 |       // http://www.cgafaq.info/wiki/Sylvester.Line-line_distance
 816 |       var x = (D3 * E1 - D1 * E3), y = (D1 * E2 - D2 * E1), z = (D2 * E3 - D3 * E2);
 817 |       var N = [x * E3 - y * E2, y * E1 - z * E3, z * E2 - x * E1];
 818 |       var P = Sylvester.Plane.create(obj.anchor, N);
 819 |       return P.intersectionWith(this);
 820 |     } else {
 821 |       // obj is a point
 822 |       var P = obj.elements || obj;
 823 |       if (this.contains(P)) { return Sylvester.Vector.create(P); }
 824 |       var A = this.anchor.elements, D = this.direction.elements;
 825 |       var D1 = D[0], D2 = D[1], D3 = D[2], A1 = A[0], A2 = A[1], A3 = A[2];
 826 |       var x = D1 * (P[1]-A2) - D2 * (P[0]-A1), y = D2 * ((P[2] || 0) - A3) - D3 * (P[1]-A2),
 827 |           z = D3 * (P[0]-A1) - D1 * ((P[2] || 0) - A3);
 828 |       var V = Sylvester.Vector.create([D2 * x - D3 * z, D3 * y - D1 * x, D1 * z - D2 * y]);
 829 |       var k = this.distanceFrom(P) / V.modulus();
 830 |       return Sylvester.Vector.create([
 831 |         P[0] + V.elements[0] * k,
 832 |         P[1] + V.elements[1] * k,
 833 |         (P[2] || 0) + V.elements[2] * k
 834 |       ]);
 835 |     }
 836 |   },
 837 | 
 838 |   // Returns a copy of the line rotated by t radians about the given line. Works
 839 |   // by finding the argument's closest point to this line's anchor point (call
 840 |   // this C) and rotating the anchor about C. Also rotates the line's direction
 841 |   // about the argument's. Be careful with this - the rotation axis' direction
 842 |   // affects the outcome!
 843 |   rotate: function(t, line) {
 844 |     // If we're working in 2D
 845 |     if (typeof(line.direction) === 'undefined') { line = Sylvester.Line.create(line.to3D(), Sylvester.Vector.k); }
 846 |     var R = Sylvester.Matrix.Rotation(t, line.direction).elements;
 847 |     var C = line.pointClosestTo(this.anchor).elements;
 848 |     var A = this.anchor.elements, D = this.direction.elements;
 849 |     var C1 = C[0], C2 = C[1], C3 = C[2], A1 = A[0], A2 = A[1], A3 = A[2];
 850 |     var x = A1 - C1, y = A2 - C2, z = A3 - C3;
 851 |     return Sylvester.Line.create([
 852 |       C1 + R[0][0] * x + R[0][1] * y + R[0][2] * z,
 853 |       C2 + R[1][0] * x + R[1][1] * y + R[1][2] * z,
 854 |       C3 + R[2][0] * x + R[2][1] * y + R[2][2] * z
 855 |     ], [
 856 |       R[0][0] * D[0] + R[0][1] * D[1] + R[0][2] * D[2],
 857 |       R[1][0] * D[0] + R[1][1] * D[1] + R[1][2] * D[2],
 858 |       R[2][0] * D[0] + R[2][1] * D[1] + R[2][2] * D[2]
 859 |     ]);
 860 |   },
 861 | 
 862 |   reverse: function() {
 863 |     return Sylvester.Line.create(this.anchor, this.direction.x(-1));
 864 |   },
 865 | 
 866 |   reflectionIn: function(obj) {
 867 |     if (obj.normal) {
 868 |       // obj is a plane
 869 |       var A = this.anchor.elements, D = this.direction.elements;
 870 |       var A1 = A[0], A2 = A[1], A3 = A[2], D1 = D[0], D2 = D[1], D3 = D[2];
 871 |       var newA = this.anchor.reflectionIn(obj).elements;
 872 |       // Add the line's direction vector to its anchor, then mirror that in the plane
 873 |       var AD1 = A1 + D1, AD2 = A2 + D2, AD3 = A3 + D3;
 874 |       var Q = obj.pointClosestTo([AD1, AD2, AD3]).elements;
 875 |       var newD = [Q[0] + (Q[0] - AD1) - newA[0], Q[1] + (Q[1] - AD2) - newA[1], Q[2] + (Q[2] - AD3) - newA[2]];
 876 |       return Sylvester.Line.create(newA, newD);
 877 |     } else if (obj.direction) {
 878 |       // obj is a line - reflection obtained by rotating PI radians about obj
 879 |       return this.rotate(Math.PI, obj);
 880 |     } else {
 881 |       // obj is a point - just reflect the line's anchor in it
 882 |       var P = obj.elements || obj;
 883 |       return Sylvester.Line.create(this.anchor.reflectionIn([P[0], P[1], (P[2] || 0)]), this.direction);
 884 |     }
 885 |   },
 886 | 
 887 |   setVectors: function(anchor, direction) {
 888 |     // Need to do this so that line's properties are not references to the
 889 |     // arguments passed in
 890 |     anchor = Sylvester.Vector.create(anchor);
 891 |     direction = Sylvester.Vector.create(direction);
 892 |     if (anchor.elements.length === 2) {anchor.elements.push(0); }
 893 |     if (direction.elements.length === 2) { direction.elements.push(0); }
 894 |     if (anchor.elements.length > 3 || direction.elements.length > 3) { return null; }
 895 |     var mod = direction.modulus();
 896 |     if (mod === 0) { return null; }
 897 |     this.anchor = anchor;
 898 |     this.direction = Sylvester.Vector.create([
 899 |       direction.elements[0] / mod,
 900 |       direction.elements[1] / mod,
 901 |       direction.elements[2] / mod
 902 |     ]);
 903 |     return this;
 904 |   }
 905 | };
 906 | 
 907 | Sylvester.Line.create = function(anchor, direction) {
 908 |   var L = new Sylvester.Line();
 909 |   return L.setVectors(anchor, direction);
 910 | };
 911 | var $L = Sylvester.Line.create;
 912 | 
 913 | Sylvester.Line.X = Sylvester.Line.create(Sylvester.Vector.Zero(3), Sylvester.Vector.i);
 914 | Sylvester.Line.Y = Sylvester.Line.create(Sylvester.Vector.Zero(3), Sylvester.Vector.j);
 915 | Sylvester.Line.Z = Sylvester.Line.create(Sylvester.Vector.Zero(3), Sylvester.Vector.k);
 916 | 
 917 | Sylvester.Line.Segment = function() {};
 918 | 
 919 | Sylvester.Line.Segment.prototype = {
 920 |   eql: function(segment) {
 921 |     return (this.start.eql(segment.start) && this.end.eql(segment.end)) ||
 922 |         (this.start.eql(segment.end) && this.end.eql(segment.start));
 923 |   },
 924 | 
 925 |   dup: function() {
 926 |     return Sylvester.Line.Segment.create(this.start, this.end);
 927 |   },
 928 | 
 929 |   length: function() {
 930 |     var A = this.start.elements, B = this.end.elements;
 931 |     var C1 = B[0] - A[0], C2 = B[1] - A[1], C3 = B[2] - A[2];
 932 |     return Math.sqrt(C1*C1 + C2*C2 + C3*C3);
 933 |   },
 934 | 
 935 |   toVector: function() {
 936 |     var A = this.start.elements, B = this.end.elements;
 937 |     return Sylvester.Vector.create([B[0] - A[0], B[1] - A[1], B[2] - A[2]]);
 938 |   },
 939 | 
 940 |   midpoint: function() {
 941 |     var A = this.start.elements, B = this.end.elements;
 942 |     return Sylvester.Vector.create([(B[0] + A[0])/2, (B[1] + A[1])/2, (B[2] + A[2])/2]);
 943 |   },
 944 | 
 945 |   bisectingPlane: function() {
 946 |     return Sylvester.Plane.create(this.midpoint(), this.toVector());
 947 |   },
 948 | 
 949 |   translate: function(vector) {
 950 |     var V = vector.elements || vector;
 951 |     var S = this.start.elements, E = this.end.elements;
 952 |     return Sylvester.Line.Segment.create(
 953 |       [S[0] + V[0], S[1] + V[1], S[2] + (V[2] || 0)],
 954 |       [E[0] + V[0], E[1] + V[1], E[2] + (V[2] || 0)]
 955 |     );
 956 |   },
 957 | 
 958 |   isParallelTo: function(obj) {
 959 |     return this.line.isParallelTo(obj);
 960 |   },
 961 | 
 962 |   distanceFrom: function(obj) {
 963 |     var P = this.pointClosestTo(obj);
 964 |     return (P === null) ? null : P.distanceFrom(obj);
 965 |   },
 966 | 
 967 |   contains: function(obj) {
 968 |     if (obj.start && obj.end) { return this.contains(obj.start) && this.contains(obj.end); }
 969 |     var P = (obj.elements || obj).slice();
 970 |     if (P.length === 2) { P.push(0); }
 971 |     if (this.start.eql(P)) { return true; }
 972 |     var S = this.start.elements;
 973 |     var V = Sylvester.Vector.create([S[0] - P[0], S[1] - P[1], S[2] - (P[2] || 0)]);
 974 |     var vect = this.toVector();
 975 |     return V.isAntiparallelTo(vect) && V.modulus() <= vect.modulus();
 976 |   },
 977 | 
 978 |   intersects: function(obj) {
 979 |     return (this.intersectionWith(obj) !== null);
 980 |   },
 981 | 
 982 |   intersectionWith: function(obj) {
 983 |     if (!this.line.intersects(obj)) { return null; }
 984 |     var P = this.line.intersectionWith(obj);
 985 |     return (this.contains(P) ? P : null);
 986 |   },
 987 | 
 988 |   pointClosestTo: function(obj) {
 989 |     if (obj.normal) {
 990 |       // obj is a plane
 991 |       var V = this.line.intersectionWith(obj);
 992 |       if (V === null) { return null; }
 993 |       return this.pointClosestTo(V);
 994 |     } else {
 995 |       // obj is a line (segment) or point
 996 |       var P = this.line.pointClosestTo(obj);
 997 |       if (P === null) { return null; }
 998 |       if (this.contains(P)) { return P; }
 999 |       return (this.line.positionOf(P) < 0 ? this.start : this.end).dup();
1000 |     }
1001 |   },
1002 | 
1003 |   setPoints: function(startPoint, endPoint) {
1004 |     startPoint = Sylvester.Vector.create(startPoint).to3D();
1005 |     endPoint = Sylvester.Vector.create(endPoint).to3D();
1006 |     if (startPoint === null || endPoint === null) { return null; }
1007 |     this.line = Sylvester.Line.create(startPoint, endPoint.subtract(startPoint));
1008 |     this.start = startPoint;
1009 |     this.end = endPoint;
1010 |     return this;
1011 |   }
1012 | };
1013 | 
1014 | Sylvester.Line.Segment.create = function(v1, v2) {
1015 |   var S = new Sylvester.Line.Segment();
1016 |   return S.setPoints(v1, v2);
1017 | };
1018 | 
1019 | Sylvester.Plane = function() {};
1020 | 
1021 | Sylvester.Plane.prototype = {
1022 |   eql: function(plane) {
1023 |     return (this.contains(plane.anchor) && this.isParallelTo(plane));
1024 |   },
1025 | 
1026 |   dup: function() {
1027 |     return Sylvester.Plane.create(this.anchor, this.normal);
1028 |   },
1029 | 
1030 |   translate: function(vector) {
1031 |     var V = vector.elements || vector;
1032 |     return Sylvester.Plane.create([
1033 |       this.anchor.elements[0] + V[0],
1034 |       this.anchor.elements[1] + V[1],
1035 |       this.anchor.elements[2] + (V[2] || 0)
1036 |     ], this.normal);
1037 |   },
1038 | 
1039 |   isParallelTo: function(obj) {
1040 |     var theta;
1041 |     if (obj.normal) {
1042 |       // obj is a plane
1043 |       theta = this.normal.angleFrom(obj.normal);
1044 |       return (Math.abs(theta) <= Sylvester.precision || Math.abs(Math.PI - theta) <= Sylvester.precision);
1045 |     } else if (obj.direction) {
1046 |       // obj is a line
1047 |       return this.normal.isPerpendicularTo(obj.direction);
1048 |     }
1049 |     return null;
1050 |   },
1051 | 
1052 |   isPerpendicularTo: function(plane) {
1053 |     var theta = this.normal.angleFrom(plane.normal);
1054 |     return (Math.abs(Math.PI/2 - theta) <= Sylvester.precision);
1055 |   },
1056 | 
1057 |   distanceFrom: function(obj) {
1058 |     if (this.intersects(obj) || this.contains(obj)) { return 0; }
1059 |     if (obj.anchor) {
1060 |       // obj is a plane or line
1061 |       var A = this.anchor.elements, B = obj.anchor.elements, N = this.normal.elements;
1062 |       return Math.abs((A[0] - B[0]) * N[0] + (A[1] - B[1]) * N[1] + (A[2] - B[2]) * N[2]);
1063 |     } else {
1064 |       // obj is a point
1065 |       var P = obj.elements || obj;
1066 |       var A = this.anchor.elements, N = this.normal.elements;
1067 |       return Math.abs((A[0] - P[0]) * N[0] + (A[1] - P[1]) * N[1] + (A[2] - (P[2] || 0)) * N[2]);
1068 |     }
1069 |   },
1070 | 
1071 |   contains: function(obj) {
1072 |     if (obj.normal) { return null; }
1073 |     if (obj.direction) {
1074 |       return (this.contains(obj.anchor) && this.contains(obj.anchor.add(obj.direction)));
1075 |     } else {
1076 |       var P = obj.elements || obj;
1077 |       var A = this.anchor.elements, N = this.normal.elements;
1078 |       var diff = Math.abs(N[0]*(A[0] - P[0]) + N[1]*(A[1] - P[1]) + N[2]*(A[2] - (P[2] || 0)));
1079 |       return (diff <= Sylvester.precision);
1080 |     }
1081 |   },
1082 | 
1083 |   intersects: function(obj) {
1084 |     if (typeof(obj.direction) === 'undefined' && typeof(obj.normal) === 'undefined') { return null; }
1085 |     return !this.isParallelTo(obj);
1086 |   },
1087 | 
1088 |   intersectionWith: function(obj) {
1089 |     if (!this.intersects(obj)) { return null; }
1090 |     if (obj.direction) {
1091 |       // obj is a line
1092 |       var A = obj.anchor.elements, D = obj.direction.elements,
1093 |           P = this.anchor.elements, N = this.normal.elements;
1094 |       var multiplier = (N[0]*(P[0]-A[0]) + N[1]*(P[1]-A[1]) + N[2]*(P[2]-A[2])) / (N[0]*D[0] + N[1]*D[1] + N[2]*D[2]);
1095 |       return Sylvester.Vector.create([A[0] + D[0]*multiplier, A[1] + D[1]*multiplier, A[2] + D[2]*multiplier]);
1096 |     } else if (obj.normal) {
1097 |       // obj is a plane
1098 |       var direction = this.normal.cross(obj.normal).toUnitVector();
1099 |       // To find an anchor point, we find one co-ordinate that has a value of
1100 |       // zero somewhere on the intersection, and remember which one we picked
1101 |       var N = this.normal.elements, A = this.anchor.elements,
1102 |           O = obj.normal.elements, B = obj.anchor.elements;
1103 |       var solver = Sylvester.Matrix.Zero(2,2), i = 0;
1104 |       while (solver.isSingular()) {
1105 |         i++;
1106 |         solver = Sylvester.Matrix.create([
1107 |           [ N[i%3], N[(i+1)%3] ],
1108 |           [ O[i%3], O[(i+1)%3]  ]
1109 |         ]);
1110 |       }
1111 |       // Then we solve the simultaneous equations in the remaining dimensions
1112 |       var inverse = solver.inverse().elements;
1113 |       var x = N[0]*A[0] + N[1]*A[1] + N[2]*A[2];
1114 |       var y = O[0]*B[0] + O[1]*B[1] + O[2]*B[2];
1115 |       var intersection = [
1116 |         inverse[0][0] * x + inverse[0][1] * y,
1117 |         inverse[1][0] * x + inverse[1][1] * y
1118 |       ];
1119 |       var anchor = [];
1120 |       for (var j = 1; j <= 3; j++) {
1121 |         // This formula picks the right element from intersection by cycling
1122 |         // depending on which element we set to zero above
1123 |         anchor.push((i === j) ? 0 : intersection[(j + (5 - i)%3)%3]);
1124 |       }
1125 |       return Sylvester.Line.create(anchor, direction);
1126 |     }
1127 |   },
1128 | 
1129 |   pointClosestTo: function(point) {
1130 |     var P = point.elements || point;
1131 |     var A = this.anchor.elements, N = this.normal.elements;
1132 |     var dot = (A[0] - P[0]) * N[0] + (A[1] - P[1]) * N[1] + (A[2] - (P[2] || 0)) * N[2];
1133 |     return Sylvester.Vector.create([P[0] + N[0] * dot, P[1] + N[1] * dot, (P[2] || 0) + N[2] * dot]);
1134 |   },
1135 | 
1136 |   rotate: function(t, line) {
1137 |     var R = t.determinant ? t.elements : Sylvester.Matrix.Rotation(t, line.direction).elements;
1138 |     var C = line.pointClosestTo(this.anchor).elements;
1139 |     var A = this.anchor.elements, N = this.normal.elements;
1140 |     var C1 = C[0], C2 = C[1], C3 = C[2], A1 = A[0], A2 = A[1], A3 = A[2];
1141 |     var x = A1 - C1, y = A2 - C2, z = A3 - C3;
1142 |     return Sylvester.Plane.create([
1143 |       C1 + R[0][0] * x + R[0][1] * y + R[0][2] * z,
1144 |       C2 + R[1][0] * x + R[1][1] * y + R[1][2] * z,
1145 |       C3 + R[2][0] * x + R[2][1] * y + R[2][2] * z
1146 |     ], [
1147 |       R[0][0] * N[0] + R[0][1] * N[1] + R[0][2] * N[2],
1148 |       R[1][0] * N[0] + R[1][1] * N[1] + R[1][2] * N[2],
1149 |       R[2][0] * N[0] + R[2][1] * N[1] + R[2][2] * N[2]
1150 |     ]);
1151 |   },
1152 | 
1153 |   reflectionIn: function(obj) {
1154 |     if (obj.normal) {
1155 |       // obj is a plane
1156 |       var A = this.anchor.elements, N = this.normal.elements;
1157 |       var A1 = A[0], A2 = A[1], A3 = A[2], N1 = N[0], N2 = N[1], N3 = N[2];
1158 |       var newA = this.anchor.reflectionIn(obj).elements;
1159 |       // Add the plane's normal to its anchor, then mirror that in the other plane
1160 |       var AN1 = A1 + N1, AN2 = A2 + N2, AN3 = A3 + N3;
1161 |       var Q = obj.pointClosestTo([AN1, AN2, AN3]).elements;
1162 |       var newN = [Q[0] + (Q[0] - AN1) - newA[0], Q[1] + (Q[1] - AN2) - newA[1], Q[2] + (Q[2] - AN3) - newA[2]];
1163 |       return Sylvester.Plane.create(newA, newN);
1164 |     } else if (obj.direction) {
1165 |       // obj is a line
1166 |       return this.rotate(Math.PI, obj);
1167 |     } else {
1168 |       // obj is a point
1169 |       var P = obj.elements || obj;
1170 |       return Sylvester.Plane.create(this.anchor.reflectionIn([P[0], P[1], (P[2] || 0)]), this.normal);
1171 |     }
1172 |   },
1173 | 
1174 |   setVectors: function(anchor, v1, v2) {
1175 |     anchor = Sylvester.Vector.create(anchor);
1176 |     anchor = anchor.to3D(); if (anchor === null) { return null; }
1177 |     v1 = Sylvester.Vector.create(v1);
1178 |     v1 = v1.to3D(); if (v1 === null) { return null; }
1179 |     if (typeof(v2) === 'undefined') {
1180 |       v2 = null;
1181 |     } else {
1182 |       v2 = Sylvester.Vector.create(v2);
1183 |       v2 = v2.to3D(); if (v2 === null) { return null; }
1184 |     }
1185 |     var A1 = anchor.elements[0], A2 = anchor.elements[1], A3 = anchor.elements[2];
1186 |     var v11 = v1.elements[0], v12 = v1.elements[1], v13 = v1.elements[2];
1187 |     var normal, mod;
1188 |     if (v2 !== null) {
1189 |       var v21 = v2.elements[0], v22 = v2.elements[1], v23 = v2.elements[2];
1190 |       normal = Sylvester.Vector.create([
1191 |         (v12 - A2) * (v23 - A3) - (v13 - A3) * (v22 - A2),
1192 |         (v13 - A3) * (v21 - A1) - (v11 - A1) * (v23 - A3),
1193 |         (v11 - A1) * (v22 - A2) - (v12 - A2) * (v21 - A1)
1194 |       ]);
1195 |       mod = normal.modulus();
1196 |       if (mod === 0) { return null; }
1197 |       normal = Sylvester.Vector.create([normal.elements[0] / mod, normal.elements[1] / mod, normal.elements[2] / mod]);
1198 |     } else {
1199 |       mod = Math.sqrt(v11*v11 + v12*v12 + v13*v13);
1200 |       if (mod === 0) { return null; }
1201 |       normal = Sylvester.Vector.create([v1.elements[0] / mod, v1.elements[1] / mod, v1.elements[2] / mod]);
1202 |     }
1203 |     this.anchor = anchor;
1204 |     this.normal = normal;
1205 |     return this;
1206 |   }
1207 | };
1208 | 
1209 | Sylvester.Plane.create = function(anchor, v1, v2) {
1210 |   var P = new Sylvester.Plane();
1211 |   return P.setVectors(anchor, v1, v2);
1212 | };
1213 | var $P = Sylvester.Plane.create;
1214 | 
1215 | Sylvester.Plane.XY = Sylvester.Plane.create(Sylvester.Vector.Zero(3), Sylvester.Vector.k);
1216 | Sylvester.Plane.YZ = Sylvester.Plane.create(Sylvester.Vector.Zero(3), Sylvester.Vector.i);
1217 | Sylvester.Plane.ZX = Sylvester.Plane.create(Sylvester.Vector.Zero(3), Sylvester.Vector.j);
1218 | Sylvester.Plane.YX = Sylvester.Plane.XY; Sylvester.Plane.ZY = Sylvester.Plane.YZ; Sylvester.Plane.XZ = Sylvester.Plane.ZX;
1219 | 
1220 | Sylvester.Plane.fromPoints = function(points) {
1221 |   var np = points.length, list = [], i, P, n, N, A, B, C, D, theta, prevN, totalN = Sylvester.Vector.Zero(3);
1222 |   for (i = 0; i < np; i++) {
1223 |     P = Sylvester.Vector.create(points[i]).to3D();
1224 |     if (P === null) { return null; }
1225 |     list.push(P);
1226 |     n = list.length;
1227 |     if (n > 2) {
1228 |       // Compute plane normal for the latest three points
1229 |       A = list[n-1].elements; B = list[n-2].elements; C = list[n-3].elements;
1230 |       N = Sylvester.Vector.create([
1231 |         (A[1] - B[1]) * (C[2] - B[2]) - (A[2] - B[2]) * (C[1] - B[1]),
1232 |         (A[2] - B[2]) * (C[0] - B[0]) - (A[0] - B[0]) * (C[2] - B[2]),
1233 |         (A[0] - B[0]) * (C[1] - B[1]) - (A[1] - B[1]) * (C[0] - B[0])
1234 |       ]).toUnitVector();
1235 |       if (n > 3) {
1236 |         // If the latest normal is not (anti)parallel to the previous one, we've
1237 |         // strayed off the plane. This might be a slightly long-winded way of
1238 |         // doing things, but we need the sum of all the normals to find which
1239 |         // way the plane normal should point so that the points form an
1240 |         // anticlockwise list.
1241 |         theta = N.angleFrom(prevN);
1242 |         if (theta !== null) {
1243 |           if (!(Math.abs(theta) <= Sylvester.precision || Math.abs(theta - Math.PI) <= Sylvester.precision)) { return null; }
1244 |         }
1245 |       }
1246 |       totalN = totalN.add(N);
1247 |       prevN = N;
1248 |     }
1249 |   }
1250 |   // We need to add in the normals at the start and end points, which the above
1251 |   // misses out
1252 |   A = list[1].elements; B = list[0].elements; C = list[n-1].elements; D = list[n-2].elements;
1253 |   totalN = totalN.add(Sylvester.Vector.create([
1254 |     (A[1] - B[1]) * (C[2] - B[2]) - (A[2] - B[2]) * (C[1] - B[1]),
1255 |     (A[2] - B[2]) * (C[0] - B[0]) - (A[0] - B[0]) * (C[2] - B[2]),
1256 |     (A[0] - B[0]) * (C[1] - B[1]) - (A[1] - B[1]) * (C[0] - B[0])
1257 |   ]).toUnitVector()).add(Sylvester.Vector.create([
1258 |     (B[1] - C[1]) * (D[2] - C[2]) - (B[2] - C[2]) * (D[1] - C[1]),
1259 |     (B[2] - C[2]) * (D[0] - C[0]) - (B[0] - C[0]) * (D[2] - C[2]),
1260 |     (B[0] - C[0]) * (D[1] - C[1]) - (B[1] - C[1]) * (D[0] - C[0])
1261 |   ]).toUnitVector());
1262 |   return Sylvester.Plane.create(list[0], totalN);
1263 | };
1264 | 
1265 | Sylvester.Polygon = function() {};
1266 | 
1267 | Sylvester.Polygon.prototype = {
1268 |   v: function(i) {
1269 |     return this.vertices.at(i - 1).data;
1270 |   },
1271 | 
1272 |   nodeFor: function(vertex) {
1273 |     return this.vertices.withData(vertex);
1274 |   },
1275 | 
1276 |   dup: function() {
1277 |     return Sylvester.Polygon.create(this.vertices, this.plane);
1278 |   },
1279 | 
1280 |   translate: function(vector) {
1281 |     var P = vector.elements || vector;
1282 |     this.vertices.each(function(node) {
1283 |       var E = node.data.elements;
1284 |       node.data.setElements([E[0] + P[0], E[1] + P[1], E[2] + (P[2] || 0)]);
1285 |     });
1286 |     this.plane = this.plane.translate(vector);
1287 |     this.updateTrianglePlanes(function(plane) { return plane.translate(vector); });
1288 |     return this;
1289 |   },
1290 | 
1291 |   rotate: function(t, line) {
1292 |     var R = Sylvester.Matrix.Rotation(t, line.direction);
1293 |     this.vertices.each(function(node) {
1294 |       node.data.setElements(node.data.rotate(R, line).elements);
1295 |     });
1296 |     this.plane = this.plane.rotate(R, line);
1297 |     this.updateTrianglePlanes(function(plane) { return plane.rotate(R, line); });
1298 |     return this;
1299 |   },
1300 | 
1301 |   scale: function(k, point) {
1302 |     var P = point.elements || point;
1303 |     this.vertices.each(function(node) {
1304 |       var E = node.data.elements;
1305 |       node.data.setElements([
1306 |         P[0] + k * (E[0] - P[0]),
1307 |         P[1] + k * (E[1] - P[1]),
1308 |         (P[2] || 0) + k * (E[2] - (P[2] || 0))
1309 |       ]);
1310 |     });
1311 |     var anchor = this.vertices.first.data;
1312 |     this.plane.anchor.setElements(anchor);
1313 |     this.updateTrianglePlanes(function(plane) { return Sylvester.Plane.create(anchor, plane.normal); });
1314 |     return this;
1315 |   },
1316 | 
1317 |   // Updates the plane properties of all the cached triangles belonging to the
1318 |   // polygon according to the given function. For example, suppose you just
1319 |   // rotated the polygon, you should call:
1320 |   //
1321 |   //   poly.updateTrianglePlanes(function(plane) { return plane.rotate(t, line); });
1322 |   //
1323 |   // This method is called automatically by Sylvester.Polygon.translate,
1324 |   // Sylvester.Polygon.rotate and Sylvester.Polygon.scale transformation methods.
1325 |   updateTrianglePlanes: function(fn) {
1326 |     var i;
1327 |     if (this.cached.triangles !== null) {
1328 |       i = this.cached.triangles.length;
1329 |       while (i--) {
1330 |         this.cached.triangles[i].plane = fn(this.cached.triangles[i].plane);
1331 |       }
1332 |     }
1333 |     if (this.cached.surfaceIntegralElements !== null) {
1334 |       i = this.cached.surfaceIntegralElements.length;
1335 |       while (i--) {
1336 |         this.cached.surfaceIntegralElements[i].plane = fn(this.cached.surfaceIntegralElements[i].plane);
1337 |       }
1338 |     }
1339 |   },
1340 | 
1341 |   isTriangle: function() {
1342 |     return this.vertices.length === 3;
1343 |   },
1344 | 
1345 |   // Returns a collection of triangles used for calculating area and center of
1346 |   // mass. Some of the triangles will not lie inside the polygon - this
1347 |   // collection is essentially a series of itervals in a surface integral, so
1348 |   // some are 'negative'. If you want the polygon broken into constituent
1349 |   // triangles, use toTriangles(). This method is used because it's much faster
1350 |   // than toTriangles().
1351 |   // 
1352 |   // The triangles generated share vertices with the original polygon, so they
1353 |   // transform with the polygon. They are cached after first calculation and
1354 |   // should remain in sync with changes to the parent polygon.
1355 |   trianglesForSurfaceIntegral: function() {
1356 |     if (this.cached.surfaceIntegralElements !== null) { return this.cached.surfaceIntegralElements; }
1357 |     var triangles = [];
1358 |     var firstVertex = this.vertices.first.data;
1359 |     var plane = this.plane;
1360 |     this.vertices.each(function(node, i) {
1361 |       if (i < 2) { return; }
1362 |       var points = [firstVertex, node.prev.data, node.data];
1363 |       // If the vertices lie on a straigh line, give the polygon's own plane. If
1364 |       // the element has no area, it doesn't matter which way its normal faces.
1365 |       triangles.push(Sylvester.Polygon.create(points, Sylvester.Plane.fromPoints(points) || plane));
1366 |     });
1367 |     return this.setCache('surfaceIntegralElements', triangles);
1368 |   },
1369 | 
1370 |   area: function() {
1371 |     if (this.isTriangle()) {
1372 |       // Area is half the modulus of the cross product of two sides
1373 |       var A = this.vertices.first, B = A.next, C = B.next;
1374 |       A = A.data.elements; B = B.data.elements; C = C.data.elements;
1375 |       return 0.5 * Sylvester.Vector.create([
1376 |         (A[1] - B[1]) * (C[2] - B[2]) - (A[2] - B[2]) * (C[1] - B[1]),
1377 |         (A[2] - B[2]) * (C[0] - B[0]) - (A[0] - B[0]) * (C[2] - B[2]),
1378 |         (A[0] - B[0]) * (C[1] - B[1]) - (A[1] - B[1]) * (C[0] - B[0])
1379 |       ]).modulus();
1380 |     } else {
1381 |       var trigs = this.trianglesForSurfaceIntegral(), area = 0;
1382 |       var i = trigs.length;
1383 |       while (i--) {
1384 |         area += trigs[i].area() * trigs[i].plane.normal.dot(this.plane.normal);
1385 |       }
1386 |       return area;
1387 |     }
1388 |   },
1389 | 
1390 |   centroid: function() {
1391 |     if (this.isTriangle()) {
1392 |       var A = this.v(1).elements, B = this.v(2).elements, C = this.v(3).elements;
1393 |       return Sylvester.Vector.create([(A[0] + B[0] + C[0])/3, (A[1] + B[1] + C[1])/3, (A[2] + B[2] + C[2])/3]);
1394 |     } else {
1395 |       var A, M = 0, V = Sylvester.Vector.Zero(3), P, C, trigs = this.trianglesForSurfaceIntegral();
1396 |       var i = trigs.length;
1397 |       while (i--) {
1398 |         A = trigs[i].area() * trigs[i].plane.normal.dot(this.plane.normal);
1399 |         M += A;
1400 |         P = V.elements;
1401 |         C = trigs[i].centroid().elements;
1402 |         V.setElements([P[0] + C[0] * A, P[1] + C[1] * A, P[2] + C[2] * A]);
1403 |       }
1404 |       return V.x(1/M);
1405 |     }
1406 |   },
1407 | 
1408 |   projectionOn: function(plane) {
1409 |     var points = [];
1410 |     this.vertices.each(function(node) { points.push(plane.pointClosestTo(node.data)); });
1411 |     return Sylvester.Polygon.create(points);
1412 |   },
1413 | 
1414 |   removeVertex: function(vertex) {
1415 |     if (this.isTriangle()) { return; }
1416 |     var node = this.nodeFor(vertex);
1417 |     if (node === null) { return null; }
1418 |     this.clearCache();
1419 |     // Previous and next entries in the main vertex list
1420 |     var prev = node.prev, next = node.next;
1421 |     var prevWasConvex = prev.data.isConvex(this);
1422 |     var nextWasConvex = next.data.isConvex(this);
1423 |     if (node.data.isConvex(this)) {
1424 |       this.convexVertices.remove(this.convexVertices.withData(node.data));
1425 |     } else {
1426 |       this.reflexVertices.remove(this.reflexVertices.withData(node.data));
1427 |     }
1428 |     this.vertices.remove(node);
1429 |     // Deal with previous vertex's change of class
1430 |     if (prevWasConvex !== prev.data.isConvex(this)) {
1431 |       if (prevWasConvex) {
1432 |         this.convexVertices.remove(this.convexVertices.withData(prev.data));
1433 |         this.reflexVertices.append(new Sylvester.LinkedList.Node(prev.data));
1434 |       } else {
1435 |         this.reflexVertices.remove(this.reflexVertices.withData(prev.data));
1436 |         this.convexVertices.append(new Sylvester.LinkedList.Node(prev.data));
1437 |       }
1438 |     }
1439 |     // Deal with next vertex's change of class
1440 |     if (nextWasConvex !== next.data.isConvex(this)) {
1441 |       if (nextWasConvex) {
1442 |         this.convexVertices.remove(this.convexVertices.withData(next.data));
1443 |         this.reflexVertices.append(new Sylvester.LinkedList.Node(next.data));
1444 |       } else {
1445 |         this.reflexVertices.remove(this.reflexVertices.withData(next.data));
1446 |         this.convexVertices.append(new Sylvester.LinkedList.Node(next.data));
1447 |       }
1448 |     }
1449 |     return this;
1450 |   },
1451 | 
1452 |   contains: function(point) {
1453 |     return this.containsByWindingNumber(point);
1454 |   },
1455 | 
1456 |   containsByWindingNumber: function(point) {
1457 |     var P = point.elements || point;
1458 |     if (!this.plane.contains(P)) { return false; }
1459 |     if (this.hasEdgeContaining(P)) { return false; }
1460 |     var V, W, A, B, theta = 0, dt, loops = 0, self = this;
1461 |     this.vertices.each(function(node) {
1462 |       V = node.data.elements;
1463 |       W = node.next.data.elements;
1464 |       A = Sylvester.Vector.create([V[0] - P[0], V[1] - P[1], V[2] - (P[2] || 0)]);
1465 |       B = Sylvester.Vector.create([W[0] - P[0], W[1] - P[1], W[2] - (P[2] || 0)]);
1466 |       dt = A.angleFrom(B);
1467 |       if (dt === null || dt === 0) { return; }
1468 |       theta += (A.cross(B).isParallelTo(self.plane.normal) ? 1 : -1) * dt;
1469 |       if (theta >= 2 * Math.PI - Sylvester.precision) { loops++; theta -= 2 * Math.PI; }
1470 |       if (theta <= -2 * Math.PI + Sylvester.precision) { loops--; theta += 2 * Math.PI; }
1471 |     });
1472 |     return loops !== 0;
1473 |   },
1474 | 
1475 |   hasEdgeContaining: function(point) {
1476 |     var P = (point.elements || point);
1477 |     var success = false;
1478 |     this.vertices.each(function(node) {
1479 |       if (Sylvester.Line.Segment.create(node.data, node.next.data).contains(P)) { success = true; }
1480 |     });
1481 |     return success;
1482 |   },
1483 | 
1484 |   toTriangles: function() {
1485 |     if (this.cached.triangles !== null) { return this.cached.triangles; }
1486 |     return this.setCache('triangles', this.triangulateByEarClipping());
1487 |   },
1488 | 
1489 |   // Implementation of ear clipping algorithm
1490 |   // Found in 'Triangulation by ear clipping', by David Eberly
1491 |   // at http://www.geometrictools.com
1492 |   // This will not deal with overlapping sections - contruct your polygons
1493 |   // sensibly
1494 |   triangulateByEarClipping: function() {
1495 |     var poly = this.dup(), triangles = [], success, convexNode, mainNode, trig;
1496 |     while (!poly.isTriangle()) {
1497 |       success = false;
1498 |       while (!success) {
1499 |         success = true;
1500 |         // Ear tips must be convex vertices - let's pick one at random
1501 |         convexNode = poly.convexVertices.randomNode();
1502 |         mainNode = poly.vertices.withData(convexNode.data);
1503 |         // For convex vertices, this order will always be anticlockwise
1504 |         trig = Sylvester.Polygon.create([mainNode.data, mainNode.next.data, mainNode.prev.data], this.plane);
1505 |         // Now test whether any reflex vertices lie within the ear
1506 |         poly.reflexVertices.each(function(node) {
1507 |           // Don't test points belonging to this triangle. node won't be equal
1508 |           // to convexNode as node is reflex and vertex is convex.
1509 |           if (node.data !== mainNode.prev.data && node.data !== mainNode.next.data) {
1510 |             if (trig.contains(node.data) || trig.hasEdgeContaining(node.data)) { success = false; }
1511 |           }
1512 |         });
1513 |       }
1514 |       triangles.push(trig);
1515 |       poly.removeVertex(mainNode.data);
1516 |     }
1517 |     // Need to do this to renumber the remaining vertices
1518 |     triangles.push(Sylvester.Polygon.create(poly.vertices, this.plane));
1519 |     return triangles;
1520 |   },
1521 | 
1522 |   setVertices: function(points, plane) {
1523 |     var pointSet = points.toArray ? points.toArray() : points;
1524 |     this.plane = (plane && plane.normal) ? plane.dup() : Sylvester.Plane.fromPoints(pointSet);
1525 |     if (this.plane === null) { return null; }
1526 |     this.vertices = new Sylvester.LinkedList.Circular();
1527 |     // Construct linked list of vertices. If each point is already a polygon
1528 |     // vertex, we reference it rather than creating a new vertex.
1529 |     var i = pointSet.length, newVertex;
1530 |     while (i--) {
1531 |       newVertex = pointSet[i].isConvex ? pointSet[i] : new Sylvester.Polygon.Vertex(pointSet[i]);
1532 |       this.vertices.prepend(new Sylvester.LinkedList.Node(newVertex));
1533 |     }
1534 |     this.clearCache();
1535 |     this.populateVertexTypeLists();
1536 |     return this;
1537 |   },
1538 | 
1539 |   populateVertexTypeLists: function() {
1540 |     this.convexVertices = new Sylvester.LinkedList.Circular();
1541 |     this.reflexVertices = new Sylvester.LinkedList.Circular();
1542 |     var self = this;
1543 |     this.vertices.each(function(node) {
1544 |       // Split vertices into convex / reflex groups. The
1545 |       // Sylvester.LinkedList.Node class wraps each vertex so it can belong to
1546 |       // many linked lists.
1547 |       self[node.data.type(self) + 'Vertices'].append(new Sylvester.LinkedList.Node(node.data));
1548 |     });
1549 |   },
1550 | 
1551 |   copyVertices: function() {
1552 |     this.clearCache();
1553 |     this.vertices.each(function(node) {
1554 |       node.data = new Sylvester.Polygon.Vertex(node.data);
1555 |     });
1556 |     this.populateVertexTypeLists();
1557 |   },
1558 | 
1559 |   clearCache: function() {
1560 |     this.cached = {
1561 |       triangles: null,
1562 |       surfaceIntegralElements: null
1563 |     };
1564 |   },
1565 | 
1566 |   setCache: function(key, value) {
1567 |     this.cached[key] = value;
1568 |     return value;
1569 |   },
1570 | 
1571 |   inspect: function() {
1572 |     var points = [];
1573 |     this.vertices.each(function(node) { points.push(node.data.inspect()); });
1574 |     return points.join(' -> ');
1575 |   }
1576 | };
1577 | 
1578 | Sylvester.Polygon.create = function(points, plane) {
1579 |   var P = new Sylvester.Polygon();
1580 |   return P.setVertices(points, plane);
1581 | };
1582 | 
1583 | Sylvester.Polygon.Vertex = function(point) {
1584 |   this.setElements(point);
1585 |   if (this.elements.length === 2) { this.elements.push(0); }
1586 |   if (this.elements.length !== 3) { return null; }
1587 | };
1588 | Sylvester.Polygon.Vertex.prototype = new Sylvester.Vector;
1589 | 
1590 | // Returns true iff the vertex's internal angle is 0 <= x < 180
1591 | // in the context of the given polygon object. Returns null if the
1592 | // vertex does not exist in the polygon.
1593 | Sylvester.Polygon.Vertex.prototype.isConvex = function(polygon) {
1594 |   var node = polygon.nodeFor(this);
1595 |   if (node === null) { return null; }
1596 |   var prev = node.prev.data, next = node.next.data;
1597 |   var A = next.subtract(this);
1598 |   var B = prev.subtract(this);
1599 |   var theta = A.angleFrom(B);
1600 |   if (theta <= Sylvester.precision) { return true; }
1601 |   if (Math.abs(theta - Math.PI) <= Sylvester.precision) { return false; }
1602 |   return (A.cross(B).dot(polygon.plane.normal) > 0);
1603 | };
1604 | // Returns true iff the vertex's internal angle is 180 <= x < 360
1605 | Sylvester.Polygon.Vertex.prototype.isReflex = function(polygon) {
1606 |   var result = this.isConvex(polygon);
1607 |   return (result === null) ? null : !result;
1608 | };
1609 | Sylvester.Polygon.Vertex.prototype.type = function(polygon) {
1610 |   var result = this.isConvex(polygon);
1611 |   return (result === null) ? null : (result ? 'convex' : 'reflex');
1612 | };
1613 | 
1614 | // Method for converting a set of arrays/vectors/whatever to a set of Sylvester.Polygon.Vertex objects
1615 | Sylvester.Polygon.Vertex.convert = function(points) {
1616 |   var pointSet = points.toArray ? points.toArray() : points;
1617 |   var list = [], n = pointSet.length;
1618 |   for (var i = 0; i < n; i++) {
1619 |     list.push(new Sylvester.Polygon.Vertex(pointSet[i]));
1620 |   }
1621 |   return list;
1622 | };
1623 | 
1624 | Sylvester.LinkedList = function() {};
1625 | 
1626 | Sylvester.LinkedList.prototype = {
1627 |   length: 0,
1628 |   first: null,
1629 |   last: null,
1630 | 
1631 |   forEach: function(fn, context) {
1632 |     var node = this.first, n = this.length;
1633 |     for (var i = 0; i < n; i++) {
1634 |       fn.call(context, node, i);
1635 |       node = node.next;
1636 |     }
1637 |   },
1638 | 
1639 |   at: function(i) {
1640 |     if (!(i >= 0 && i < this.length)) { return null; }
1641 |     var node = this.first;
1642 |     while (i--) { node = node.next; }
1643 |     return node;
1644 |   },
1645 | 
1646 |   randomNode: function() {
1647 |     var n = Math.floor(Math.random() * this.length);
1648 |     return this.at(n);
1649 |   },
1650 | 
1651 |   toArray: function() {
1652 |     var arr = [], node = this.first, n = this.length;
1653 |     while (n--) {
1654 |       arr.push(node.data || node);
1655 |       node = node.next;
1656 |     }
1657 |     return arr;
1658 |   }
1659 | };
1660 | 
1661 | Sylvester.LinkedList.prototype.each = Sylvester.LinkedList.prototype.forEach;
1662 | 
1663 | Sylvester.LinkedList.Node = function(data) {
1664 |   this.prev = null; this.next = null;
1665 |   this.data = data;
1666 | };
1667 | 
1668 | Sylvester.LinkedList.Circular = function() {};
1669 | Sylvester.LinkedList.Circular.Methods = {
1670 |   append: function(node) {
1671 |     if (this.first === null) {
1672 |       node.prev = node;
1673 |       node.next = node;
1674 |       this.first = node;
1675 |       this.last = node;
1676 |     } else {
1677 |       node.prev = this.last;
1678 |       node.next = this.first;
1679 |       this.first.prev = node;
1680 |       this.last.next = node;
1681 |       this.last = node;
1682 |     }
1683 |     this.length++;
1684 |   },
1685 | 
1686 |   prepend: function(node) {
1687 |     if (this.first === null) {
1688 |       this.append(node);
1689 |       return;
1690 |     } else {
1691 |       node.prev = this.last;
1692 |       node.next = this.first;
1693 |       this.first.prev = node;
1694 |       this.last.next = node;
1695 |       this.first = node;
1696 |     }
1697 |     this.length++;
1698 |   },
1699 | 
1700 |   insertAfter: function(node, newNode) {
1701 |     newNode.prev = node;
1702 |     newNode.next = node.next;
1703 |     node.next.prev = newNode;
1704 |     node.next = newNode;
1705 |     if (newNode.prev === this.last) { this.last = newNode; }
1706 |     this.length++;
1707 |   },
1708 | 
1709 |   insertBefore: function(node, newNode) {
1710 |     newNode.prev = node.prev;
1711 |     newNode.next = node;
1712 |     node.prev.next = newNode;
1713 |     node.prev = newNode;
1714 |     if (newNode.next === this.first) { this.first = newNode; }
1715 |     this.length++;
1716 |   },
1717 | 
1718 |   remove: function(node) {
1719 |     if (this.length > 1) {
1720 |       node.prev.next = node.next;
1721 |       node.next.prev = node.prev;
1722 |       if (node === this.first) { this.first = node.next; }
1723 |       if (node === this.last) { this.last = node.prev; }
1724 |     } else {
1725 |       this.first = null;
1726 |       this.last = null;
1727 |     }
1728 |     node.prev = null;
1729 |     node.next = null;
1730 |     this.length--;
1731 |   },
1732 | 
1733 |   withData: function(data) {
1734 |     var nodeFromStart = this.first, nodeFromEnd = this.last, n = Math.ceil(this.length / 2);
1735 |     while (n--) {
1736 |       if (nodeFromStart.data === data) { return nodeFromStart; }
1737 |       if (nodeFromEnd.data === data) { return nodeFromEnd; }
1738 |       nodeFromStart = nodeFromStart.next;
1739 |       nodeFromEnd = nodeFromEnd.prev;
1740 |     }
1741 |     return null;
1742 |   }
1743 | };
1744 | 
1745 | Sylvester.LinkedList.Circular.prototype = new Sylvester.LinkedList;
1746 | for (var method in Sylvester.LinkedList.Circular.Methods) {
1747 |   Sylvester.LinkedList.Circular.prototype[method] = Sylvester.LinkedList.Circular.Methods[method];
1748 | }
1749 | 
1750 | Sylvester.LinkedList.Circular.fromArray = function(list, useNodes) {
1751 |   var linked = new Sylvester.LinkedList.Circular();
1752 |   var n = list.length;
1753 |   while (n--) { linked.prepend(useNodes ? new Sylvester.LinkedList.Node(list[n]) : list[n]); }
1754 |   return linked;
1755 | };
1756 | 
1757 | (function() {
1758 |   var api = (typeof require === 'function' && typeof exports === 'object')
1759 |           ? exports
1760 |           : this;
1761 |   
1762 |   api.Line    = Sylvester.Line;
1763 |   api.Matrix  = Sylvester.Matrix;
1764 |   api.Plane   = Sylvester.Plane;
1765 |   api.Polygon = Sylvester.Polygon;
1766 |   api.Vector  = Sylvester.Vector;
1767 |   
1768 |   if (typeof WScript !== 'undefined')
1769 |     this.Sylvester = Sylvester;
1770 | })();
1771 | 


--------------------------------------------------------------------------------
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