1 /**
  2  * @author mrdoob / http://mrdoob.com/
  3  * @author supereggbert / http://www.paulbrunt.co.uk/
  4  * @author philogb / http://blog.thejit.org/
  5  * @author jordi_ros / http://plattsoft.com
  6  * @author D1plo1d / http://github.com/D1plo1d
  7  * @author alteredq / http://alteredqualia.com/
  8  * @author mikael emtinger / http://gomo.se/
  9  * @author timknip / http://www.floorplanner.com/
 10  */
 11 
 12 
 13 /**@constructor*/
 14 THREE.Matrix4 = function ( n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 ) {
 15 
 16 	this.elements = new Float32Array( 16 );
 17 
 18 	this.set(
 19 
 20 		( n11 !== undefined ) ? n11 : 1, n12 || 0, n13 || 0, n14 || 0,
 21 		n21 || 0, ( n22 !== undefined ) ? n22 : 1, n23 || 0, n24 || 0,
 22 		n31 || 0, n32 || 0, ( n33 !== undefined ) ? n33 : 1, n34 || 0,
 23 		n41 || 0, n42 || 0, n43 || 0, ( n44 !== undefined ) ? n44 : 1
 24 
 25 	);
 26 
 27 };
 28 
 29 THREE.Matrix4.prototype = {
 30 
 31 	constructor: THREE.Matrix4,
 32 
 33 	set: function ( n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 ) {
 34 
 35 		var te = this.elements;
 36 
 37 		te[0] = n11; te[4] = n12; te[8] = n13; te[12] = n14;
 38 		te[1] = n21; te[5] = n22; te[9] = n23; te[13] = n24;
 39 		te[2] = n31; te[6] = n32; te[10] = n33; te[14] = n34;
 40 		te[3] = n41; te[7] = n42; te[11] = n43; te[15] = n44;
 41 
 42 		return this;
 43 
 44 	},
 45 
 46 	identity: function () {
 47 
 48 		this.set(
 49 
 50 			1, 0, 0, 0,
 51 			0, 1, 0, 0,
 52 			0, 0, 1, 0,
 53 			0, 0, 0, 1
 54 
 55 		);
 56 
 57 		return this;
 58 
 59 	},
 60 
 61 	copy: function ( m ) {
 62 
 63 		var me = m.elements;
 64 
 65 		this.set(
 66 
 67 			me[0], me[4], me[8], me[12],
 68 			me[1], me[5], me[9], me[13],
 69 			me[2], me[6], me[10], me[14],
 70 			me[3], me[7], me[11], me[15]
 71 
 72 		);
 73 
 74 		return this;
 75 
 76 	},
 77 
 78 	lookAt: function ( eye, target, up ) {
 79 
 80 		var te = this.elements;
 81 
 82 		var x = THREE.Matrix4.__v1;
 83 		var y = THREE.Matrix4.__v2;
 84 		var z = THREE.Matrix4.__v3;
 85 
 86 		z.sub( eye, target ).normalize();
 87 
 88 		if ( z.length() === 0 ) {
 89 
 90 			z.z = 1;
 91 
 92 		}
 93 
 94 		x.cross( up, z ).normalize();
 95 
 96 		if ( x.length() === 0 ) {
 97 
 98 			z.x += 0.0001;
 99 			x.cross( up, z ).normalize();
100 
101 		}
102 
103 		y.cross( z, x );
104 
105 
106 		te[0] = x.x; te[4] = y.x; te[8] = z.x;
107 		te[1] = x.y; te[5] = y.y; te[9] = z.y;
108 		te[2] = x.z; te[6] = y.z; te[10] = z.z;
109 
110 		return this;
111 
112 	},
113 
114 	multiply: function ( a, b ) {
115 
116 		var ae = a.elements;
117 		var be = b.elements;
118 		var te = this.elements;
119 
120 		var a11 = ae[0], a12 = ae[4], a13 = ae[8], a14 = ae[12];
121 		var a21 = ae[1], a22 = ae[5], a23 = ae[9], a24 = ae[13];
122 		var a31 = ae[2], a32 = ae[6], a33 = ae[10], a34 = ae[14];
123 		var a41 = ae[3], a42 = ae[7], a43 = ae[11], a44 = ae[15];
124 
125 		var b11 = be[0], b12 = be[4], b13 = be[8], b14 = be[12];
126 		var b21 = be[1], b22 = be[5], b23 = be[9], b24 = be[13];
127 		var b31 = be[2], b32 = be[6], b33 = be[10], b34 = be[14];
128 		var b41 = be[3], b42 = be[7], b43 = be[11], b44 = be[15];
129 
130 		te[0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
131 		te[4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
132 		te[8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
133 		te[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
134 
135 		te[1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
136 		te[5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
137 		te[9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
138 		te[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
139 
140 		te[2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
141 		te[6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
142 		te[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
143 		te[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
144 
145 		te[3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
146 		te[7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
147 		te[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
148 		te[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
149 
150 		return this;
151 
152 	},
153 
154 	multiplySelf: function ( m ) {
155 
156 		return this.multiply( this, m );
157 
158 	},
159 
160 	multiplyToArray: function ( a, b, r ) {
161 
162 		var te = this.elements;
163 
164 		this.multiply( a, b );
165 
166 		r[ 0 ] = te[0]; r[ 1 ] = te[1]; r[ 2 ] = te[2]; r[ 3 ] = te[3];
167 		r[ 4 ] = te[4]; r[ 5 ] = te[5]; r[ 6 ] = te[6]; r[ 7 ] = te[7];
168 		r[ 8 ]  = te[8]; r[ 9 ]  = te[9]; r[ 10 ] = te[10]; r[ 11 ] = te[11];
169 		r[ 12 ] = te[12]; r[ 13 ] = te[13]; r[ 14 ] = te[14]; r[ 15 ] = te[15];
170 
171 		return this;
172 
173 	},
174 
175 	multiplyScalar: function ( s ) {
176 
177 		var te = this.elements;
178 
179 		te[0] *= s; te[4] *= s; te[8] *= s; te[12] *= s;
180 		te[1] *= s; te[5] *= s; te[9] *= s; te[13] *= s;
181 		te[2] *= s; te[6] *= s; te[10] *= s; te[14] *= s;
182 		te[3] *= s; te[7] *= s; te[11] *= s; te[15] *= s;
183 
184 		return this;
185 
186 	},
187 
188 	multiplyVector3: function ( v ) {
189 
190 		var te = this.elements;
191 
192 		var vx = v.x, vy = v.y, vz = v.z;
193 		var d = 1 / ( te[3] * vx + te[7] * vy + te[11] * vz + te[15] );
194 
195 		v.x = ( te[0] * vx + te[4] * vy + te[8] * vz + te[12] ) * d;
196 		v.y = ( te[1] * vx + te[5] * vy + te[9] * vz + te[13] ) * d;
197 		v.z = ( te[2] * vx + te[6] * vy + te[10] * vz + te[14] ) * d;
198 
199 		return v;
200 
201 	},
202 
203 	multiplyVector4: function ( v ) {
204 
205 		var te = this.elements;
206 		var vx = v.x, vy = v.y, vz = v.z, vw = v.w;
207 
208 		v.x = te[0] * vx + te[4] * vy + te[8] * vz + te[12] * vw;
209 		v.y = te[1] * vx + te[5] * vy + te[9] * vz + te[13] * vw;
210 		v.z = te[2] * vx + te[6] * vy + te[10] * vz + te[14] * vw;
211 		v.w = te[3] * vx + te[7] * vy + te[11] * vz + te[15] * vw;
212 
213 		return v;
214 
215 	},
216 
217 	multiplyVector3Array: function ( a ) {
218 
219 		var tmp = THREE.Matrix4.__v1;
220 
221 		for ( var i = 0, il = a.length; i < il; i += 3 ) {
222 
223 			tmp.x = a[ i ];
224 			tmp.y = a[ i + 1 ];
225 			tmp.z = a[ i + 2 ];
226 
227 			this.multiplyVector3( tmp );
228 
229 			a[ i ]     = tmp.x;
230 			a[ i + 1 ] = tmp.y;
231 			a[ i + 2 ] = tmp.z;
232 
233 		}
234 
235 		return a;
236 
237 	},
238 
239 	rotateAxis: function ( v ) {
240 
241 		var te = this.elements;
242 		var vx = v.x, vy = v.y, vz = v.z;
243 
244 		v.x = vx * te[0] + vy * te[4] + vz * te[8];
245 		v.y = vx * te[1] + vy * te[5] + vz * te[9];
246 		v.z = vx * te[2] + vy * te[6] + vz * te[10];
247 
248 		v.normalize();
249 
250 		return v;
251 
252 	},
253 
254 	crossVector: function ( a ) {
255 
256 		var te = this.elements;
257 		var v = new THREE.Vector4();
258 
259 		v.x = te[0] * a.x + te[4] * a.y + te[8] * a.z + te[12] * a.w;
260 		v.y = te[1] * a.x + te[5] * a.y + te[9] * a.z + te[13] * a.w;
261 		v.z = te[2] * a.x + te[6] * a.y + te[10] * a.z + te[14] * a.w;
262 
263 		v.w = ( a.w ) ? te[3] * a.x + te[7] * a.y + te[11] * a.z + te[15] * a.w : 1;
264 
265 		return v;
266 
267 	},
268 
269 	determinant: function () {
270 
271 		var te = this.elements;
272 
273 		var n11 = te[0], n12 = te[4], n13 = te[8], n14 = te[12];
274 		var n21 = te[1], n22 = te[5], n23 = te[9], n24 = te[13];
275 		var n31 = te[2], n32 = te[6], n33 = te[10], n34 = te[14];
276 		var n41 = te[3], n42 = te[7], n43 = te[11], n44 = te[15];
277 
278 		//TODO: make this more efficient
279 		//( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )
280 
281 		return (
282 			n14 * n23 * n32 * n41-
283 			n13 * n24 * n32 * n41-
284 			n14 * n22 * n33 * n41+
285 			n12 * n24 * n33 * n41+
286 
287 			n13 * n22 * n34 * n41-
288 			n12 * n23 * n34 * n41-
289 			n14 * n23 * n31 * n42+
290 			n13 * n24 * n31 * n42+
291 
292 			n14 * n21 * n33 * n42-
293 			n11 * n24 * n33 * n42-
294 			n13 * n21 * n34 * n42+
295 			n11 * n23 * n34 * n42+
296 
297 			n14 * n22 * n31 * n43-
298 			n12 * n24 * n31 * n43-
299 			n14 * n21 * n32 * n43+
300 			n11 * n24 * n32 * n43+
301 
302 			n12 * n21 * n34 * n43-
303 			n11 * n22 * n34 * n43-
304 			n13 * n22 * n31 * n44+
305 			n12 * n23 * n31 * n44+
306 
307 			n13 * n21 * n32 * n44-
308 			n11 * n23 * n32 * n44-
309 			n12 * n21 * n33 * n44+
310 			n11 * n22 * n33 * n44
311 		);
312 
313 	},
314 
315 	transpose: function () {
316 
317 		var te = this.elements;
318 		var tmp;
319 
320 		tmp = te[1]; te[1] = te[4]; te[4] = tmp;
321 		tmp = te[2]; te[2] = te[8]; te[8] = tmp;
322 		tmp = te[6]; te[6] = te[9]; te[9] = tmp;
323 
324 		tmp = te[3]; te[3] = te[12]; te[12] = tmp;
325 		tmp = te[7]; te[7] = te[13]; te[13] = tmp;
326 		tmp = te[11]; te[11] = te[14]; te[14] = tmp;
327 
328 		return this;
329 
330 	},
331 
332 	flattenToArray: function ( flat ) {
333 
334 		var te = this.elements;
335 		flat[ 0 ] = te[0]; flat[ 1 ] = te[1]; flat[ 2 ] = te[2]; flat[ 3 ] = te[3];
336 		flat[ 4 ] = te[4]; flat[ 5 ] = te[5]; flat[ 6 ] = te[6]; flat[ 7 ] = te[7];
337 		flat[ 8 ]  = te[8]; flat[ 9 ]  = te[9]; flat[ 10 ] = te[10]; flat[ 11 ] = te[11];
338 		flat[ 12 ] = te[12]; flat[ 13 ] = te[13]; flat[ 14 ] = te[14]; flat[ 15 ] = te[15];
339 
340 		return flat;
341 
342 	},
343 
344 	flattenToArrayOffset: function( flat, offset ) {
345 
346 		var te = this.elements;
347 		flat[ offset ] = te[0];
348 		flat[ offset + 1 ] = te[1];
349 		flat[ offset + 2 ] = te[2];
350 		flat[ offset + 3 ] = te[3];
351 
352 		flat[ offset + 4 ] = te[4];
353 		flat[ offset + 5 ] = te[5];
354 		flat[ offset + 6 ] = te[6];
355 		flat[ offset + 7 ] = te[7];
356 
357 		flat[ offset + 8 ]  = te[8];
358 		flat[ offset + 9 ]  = te[9];
359 		flat[ offset + 10 ] = te[10];
360 		flat[ offset + 11 ] = te[11];
361 
362 		flat[ offset + 12 ] = te[12];
363 		flat[ offset + 13 ] = te[13];
364 		flat[ offset + 14 ] = te[14];
365 		flat[ offset + 15 ] = te[15];
366 
367 		return flat;
368 
369 	},
370 
371 	getPosition: function () {
372 
373 		var te = this.elements;
374 		return THREE.Matrix4.__v1.set( te[12], te[13], te[14] );
375 
376 	},
377 
378 	setPosition: function ( v ) {
379 
380 		var te = this.elements;
381 
382 		te[12] = v.x;
383 		te[13] = v.y;
384 		te[14] = v.z;
385 
386 		return this;
387 
388 	},
389 
390 	getColumnX: function () {
391 
392 		var te = this.elements;
393 		return THREE.Matrix4.__v1.set( te[0], te[1], te[2] );
394 
395 	},
396 
397 	getColumnY: function () {
398 
399 		var te = this.elements;
400 		return THREE.Matrix4.__v1.set( te[4], te[5], te[6] );
401 
402 	},
403 
404 	getColumnZ: function() {
405 
406 		var te = this.elements;
407 		return THREE.Matrix4.__v1.set( te[8], te[9], te[10] );
408 
409 	},
410 
411 	getInverse: function ( m ) {
412 
413 		// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
414 		var te = this.elements;
415 		var me = m.elements;
416 
417 		var n11 = me[0], n12 = me[4], n13 = me[8], n14 = me[12];
418 		var n21 = me[1], n22 = me[5], n23 = me[9], n24 = me[13];
419 		var n31 = me[2], n32 = me[6], n33 = me[10], n34 = me[14];
420 		var n41 = me[3], n42 = me[7], n43 = me[11], n44 = me[15];
421 
422 		te[0] = n23*n34*n42 - n24*n33*n42 + n24*n32*n43 - n22*n34*n43 - n23*n32*n44 + n22*n33*n44;
423 		te[4] = n14*n33*n42 - n13*n34*n42 - n14*n32*n43 + n12*n34*n43 + n13*n32*n44 - n12*n33*n44;
424 		te[8] = n13*n24*n42 - n14*n23*n42 + n14*n22*n43 - n12*n24*n43 - n13*n22*n44 + n12*n23*n44;
425 		te[12] = n14*n23*n32 - n13*n24*n32 - n14*n22*n33 + n12*n24*n33 + n13*n22*n34 - n12*n23*n34;
426 		te[1] = n24*n33*n41 - n23*n34*n41 - n24*n31*n43 + n21*n34*n43 + n23*n31*n44 - n21*n33*n44;
427 		te[5] = n13*n34*n41 - n14*n33*n41 + n14*n31*n43 - n11*n34*n43 - n13*n31*n44 + n11*n33*n44;
428 		te[9] = n14*n23*n41 - n13*n24*n41 - n14*n21*n43 + n11*n24*n43 + n13*n21*n44 - n11*n23*n44;
429 		te[13] = n13*n24*n31 - n14*n23*n31 + n14*n21*n33 - n11*n24*n33 - n13*n21*n34 + n11*n23*n34;
430 		te[2] = n22*n34*n41 - n24*n32*n41 + n24*n31*n42 - n21*n34*n42 - n22*n31*n44 + n21*n32*n44;
431 		te[6] = n14*n32*n41 - n12*n34*n41 - n14*n31*n42 + n11*n34*n42 + n12*n31*n44 - n11*n32*n44;
432 		te[10] = n12*n24*n41 - n14*n22*n41 + n14*n21*n42 - n11*n24*n42 - n12*n21*n44 + n11*n22*n44;
433 		te[14] = n14*n22*n31 - n12*n24*n31 - n14*n21*n32 + n11*n24*n32 + n12*n21*n34 - n11*n22*n34;
434 		te[3] = n23*n32*n41 - n22*n33*n41 - n23*n31*n42 + n21*n33*n42 + n22*n31*n43 - n21*n32*n43;
435 		te[7] = n12*n33*n41 - n13*n32*n41 + n13*n31*n42 - n11*n33*n42 - n12*n31*n43 + n11*n32*n43;
436 		te[11] = n13*n22*n41 - n12*n23*n41 - n13*n21*n42 + n11*n23*n42 + n12*n21*n43 - n11*n22*n43;
437 		te[15] = n12*n23*n31 - n13*n22*n31 + n13*n21*n32 - n11*n23*n32 - n12*n21*n33 + n11*n22*n33;
438 		this.multiplyScalar( 1 / m.determinant() );
439 
440 		return this;
441 
442 	},
443 
444 	setRotationFromEuler: function ( v, order ) {
445 
446 		var te = this.elements;
447 
448 		var x = v.x, y = v.y, z = v.z;
449 		var a = Math.cos( x ), b = Math.sin( x );
450 		var c = Math.cos( y ), d = Math.sin( y );
451 		var e = Math.cos( z ), f = Math.sin( z );
452 
453 		if ( order === undefined || order === 'XYZ' ) {
454 
455 			var ae = a * e, af = a * f, be = b * e, bf = b * f;
456 
457 			te[0] = c * e;
458 			te[4] = - c * f;
459 			te[8] = d;
460 
461 			te[1] = af + be * d;
462 			te[5] = ae - bf * d;
463 			te[9] = - b * c;
464 
465 			te[2] = bf - ae * d;
466 			te[6] = be + af * d;
467 			te[10] = a * c;
468 
469 		} else if ( order === 'YXZ' ) {
470 
471 			var ce = c * e, cf = c * f, de = d * e, df = d * f;
472 
473 			te[0] = ce + df * b;
474 			te[4] = de * b - cf;
475 			te[8] = a * d;
476 
477 			te[1] = a * f;
478 			te[5] = a * e;
479 			te[9] = - b;
480 
481 			te[2] = cf * b - de;
482 			te[6] = df + ce * b;
483 			te[10] = a * c;
484 
485 		} else if ( order === 'ZXY' ) {
486 
487 			var ce = c * e, cf = c * f, de = d * e, df = d * f;
488 
489 			te[0] = ce - df * b;
490 			te[4] = - a * f;
491 			te[8] = de + cf * b;
492 
493 			te[1] = cf + de * b;
494 			te[5] = a * e;
495 			te[9] = df - ce * b;
496 
497 			te[2] = - a * d;
498 			te[6] = b;
499 			te[10] = a * c;
500 
501 		} else if ( order === 'ZYX' ) {
502 
503 			var ae = a * e, af = a * f, be = b * e, bf = b * f;
504 
505 			te[0] = c * e;
506 			te[4] = be * d - af;
507 			te[8] = ae * d + bf;
508 
509 			te[1] = c * f;
510 			te[5] = bf * d + ae;
511 			te[9] = af * d - be;
512 
513 			te[2] = - d;
514 			te[6] = b * c;
515 			te[10] = a * c;
516 
517 		} else if ( order === 'YZX' ) {
518 
519 			var ac = a * c, ad = a * d, bc = b * c, bd = b * d;
520 
521 			te[0] = c * e;
522 			te[4] = bd - ac * f;
523 			te[8] = bc * f + ad;
524 
525 			te[1] = f;
526 			te[5] = a * e;
527 			te[9] = - b * e;
528 
529 			te[2] = - d * e;
530 			te[6] = ad * f + bc;
531 			te[10] = ac - bd * f;
532 
533 		} else if ( order === 'XZY' ) {
534 
535 			var ac = a * c, ad = a * d, bc = b * c, bd = b * d;
536 
537 			te[0] = c * e;
538 			te[4] = - f;
539 			te[8] = d * e;
540 
541 			te[1] = ac * f + bd;
542 			te[5] = a * e;
543 			te[9] = ad * f - bc;
544 
545 			te[2] = bc * f - ad;
546 			te[6] = b * e;
547 			te[10] = bd * f + ac;
548 
549 		}
550 
551 		return this;
552 
553 	},
554 
555 
556 	setRotationFromQuaternion: function ( q ) {
557 
558 		var te = this.elements;
559 
560 		var x = q.x, y = q.y, z = q.z, w = q.w;
561 		var x2 = x + x, y2 = y + y, z2 = z + z;
562 		var xx = x * x2, xy = x * y2, xz = x * z2;
563 		var yy = y * y2, yz = y * z2, zz = z * z2;
564 		var wx = w * x2, wy = w * y2, wz = w * z2;
565 
566 		te[0] = 1 - ( yy + zz );
567 		te[4] = xy - wz;
568 		te[8] = xz + wy;
569 
570 		te[1] = xy + wz;
571 		te[5] = 1 - ( xx + zz );
572 		te[9] = yz - wx;
573 
574 		te[2] = xz - wy;
575 		te[6] = yz + wx;
576 		te[10] = 1 - ( xx + yy );
577 
578 		return this;
579 
580 	},
581 
582 	compose: function ( translation, rotation, scale ) {
583 
584 		var te = this.elements;
585 		var mRotation = THREE.Matrix4.__m1;
586 		var mScale = THREE.Matrix4.__m2;
587 
588 		mRotation.identity();
589 		mRotation.setRotationFromQuaternion( rotation );
590 
591 		mScale.makeScale( scale.x, scale.y, scale.z );
592 
593 		this.multiply( mRotation, mScale );
594 
595 		te[12] = translation.x;
596 		te[13] = translation.y;
597 		te[14] = translation.z;
598 
599 		return this;
600 
601 	},
602 
603 	decompose: function ( translation, rotation, scale ) {
604 
605 		var te = this.elements;
606 
607 		// grab the axis vectors
608 		var x = THREE.Matrix4.__v1;
609 		var y = THREE.Matrix4.__v2;
610 		var z = THREE.Matrix4.__v3;
611 
612 		x.set( te[0], te[1], te[2] );
613 		y.set( te[4], te[5], te[6] );
614 		z.set( te[8], te[9], te[10] );
615 
616 		translation = ( translation instanceof THREE.Vector3 ) ? translation : new THREE.Vector3();
617 		rotation = ( rotation instanceof THREE.Quaternion ) ? rotation : new THREE.Quaternion();
618 		scale = ( scale instanceof THREE.Vector3 ) ? scale : new THREE.Vector3();
619 
620 		scale.x = x.length();
621 		scale.y = y.length();
622 		scale.z = z.length();
623 
624 		translation.x = te[12];
625 		translation.y = te[13];
626 		translation.z = te[14];
627 
628 		// scale the rotation part
629 
630 		var matrix = THREE.Matrix4.__m1;
631 
632 		matrix.copy( this );
633 
634 		matrix.elements[0] /= scale.x;
635 		matrix.elements[1] /= scale.x;
636 		matrix.elements[2] /= scale.x;
637 
638 		matrix.elements[4] /= scale.y;
639 		matrix.elements[5] /= scale.y;
640 		matrix.elements[6] /= scale.y;
641 
642 		matrix.elements[8] /= scale.z;
643 		matrix.elements[9] /= scale.z;
644 		matrix.elements[10] /= scale.z;
645 
646 		rotation.setFromRotationMatrix( matrix );
647 
648 		return [ translation, rotation, scale ];
649 
650 	},
651 
652 	extractPosition: function ( m ) {
653 
654 		var te = this.elements;
655 		var me = m.elements;
656 
657 		te[12] = me[12];
658 		te[13] = me[13];
659 		te[14] = me[14];
660 
661 		return this;
662 
663 	},
664 
665 	extractRotation: function ( m ) {
666 
667 		var te = this.elements;
668 		var me = m.elements;
669 
670 		var vector = THREE.Matrix4.__v1;
671 
672 		var scaleX = 1 / vector.set( me[0], me[1], me[2] ).length();
673 		var scaleY = 1 / vector.set( me[4], me[5], me[6] ).length();
674 		var scaleZ = 1 / vector.set( me[8], me[9], me[10] ).length();
675 
676 		te[0] = me[0] * scaleX;
677 		te[1] = me[1] * scaleX;
678 		te[2] = me[2] * scaleX;
679 
680 		te[4] = me[4] * scaleY;
681 		te[5] = me[5] * scaleY;
682 		te[6] = me[6] * scaleY;
683 
684 		te[8] = me[8] * scaleZ;
685 		te[9] = me[9] * scaleZ;
686 		te[10] = me[10] * scaleZ;
687 
688 		return this;
689 
690 	},
691 
692 	//
693 
694 	translate: function ( v ) {
695 
696 		var te = this.elements;
697 		var x = v.x, y = v.y, z = v.z;
698 
699 		te[12] = te[0] * x + te[4] * y + te[8] * z + te[12];
700 		te[13] = te[1] * x + te[5] * y + te[9] * z + te[13];
701 		te[14] = te[2] * x + te[6] * y + te[10] * z + te[14];
702 		te[15] = te[3] * x + te[7] * y + te[11] * z + te[15];
703 
704 		return this;
705 
706 	},
707 
708 	rotateX: function ( angle ) {
709 
710 		var te = this.elements;
711 		var m12 = te[4];
712 		var m22 = te[5];
713 		var m32 = te[6];
714 		var m42 = te[7];
715 		var m13 = te[8];
716 		var m23 = te[9];
717 		var m33 = te[10];
718 		var m43 = te[11];
719 		var c = Math.cos( angle );
720 		var s = Math.sin( angle );
721 
722 		te[4] = c * m12 + s * m13;
723 		te[5] = c * m22 + s * m23;
724 		te[6] = c * m32 + s * m33;
725 		te[7] = c * m42 + s * m43;
726 
727 		te[8] = c * m13 - s * m12;
728 		te[9] = c * m23 - s * m22;
729 		te[10] = c * m33 - s * m32;
730 		te[11] = c * m43 - s * m42;
731 
732 		return this;
733 
734 	},
735 
736 	rotateY: function ( angle ) {
737 
738 		var te = this.elements;
739 		var m11 = te[0];
740 		var m21 = te[1];
741 		var m31 = te[2];
742 		var m41 = te[3];
743 		var m13 = te[8];
744 		var m23 = te[9];
745 		var m33 = te[10];
746 		var m43 = te[11];
747 		var c = Math.cos( angle );
748 		var s = Math.sin( angle );
749 
750 		te[0] = c * m11 - s * m13;
751 		te[1] = c * m21 - s * m23;
752 		te[2] = c * m31 - s * m33;
753 		te[3] = c * m41 - s * m43;
754 
755 		te[8] = c * m13 + s * m11;
756 		te[9] = c * m23 + s * m21;
757 		te[10] = c * m33 + s * m31;
758 		te[11] = c * m43 + s * m41;
759 
760 		return this;
761 
762 	},
763 
764 	rotateZ: function ( angle ) {
765 
766 		var te = this.elements;
767 		var m11 = te[0];
768 		var m21 = te[1];
769 		var m31 = te[2];
770 		var m41 = te[3];
771 		var m12 = te[4];
772 		var m22 = te[5];
773 		var m32 = te[6];
774 		var m42 = te[7];
775 		var c = Math.cos( angle );
776 		var s = Math.sin( angle );
777 
778 		te[0] = c * m11 + s * m12;
779 		te[1] = c * m21 + s * m22;
780 		te[2] = c * m31 + s * m32;
781 		te[3] = c * m41 + s * m42;
782 
783 		te[4] = c * m12 - s * m11;
784 		te[5] = c * m22 - s * m21;
785 		te[6] = c * m32 - s * m31;
786 		te[7] = c * m42 - s * m41;
787 
788 		return this;
789 
790 	},
791 
792 	rotateByAxis: function ( axis, angle ) {
793 
794 		var te = this.elements;
795 
796 		// optimize by checking axis
797 
798 		if ( axis.x === 1 && axis.y === 0 && axis.z === 0 ) {
799 
800 			return this.rotateX( angle );
801 
802 		} else if ( axis.x === 0 && axis.y === 1 && axis.z === 0 ) {
803 
804 			return this.rotateY( angle );
805 
806 		} else if ( axis.x === 0 && axis.y === 0 && axis.z === 1 ) {
807 
808 			return this.rotateZ( angle );
809 
810 		}
811 
812 		var x = axis.x, y = axis.y, z = axis.z;
813 		var n = Math.sqrt(x * x + y * y + z * z);
814 
815 		x /= n;
816 		y /= n;
817 		z /= n;
818 
819 		var xx = x * x, yy = y * y, zz = z * z;
820 		var c = Math.cos( angle );
821 		var s = Math.sin( angle );
822 		var oneMinusCosine = 1 - c;
823 		var xy = x * y * oneMinusCosine;
824 		var xz = x * z * oneMinusCosine;
825 		var yz = y * z * oneMinusCosine;
826 		var xs = x * s;
827 		var ys = y * s;
828 		var zs = z * s;
829 
830 		var r11 = xx + (1 - xx) * c;
831 		var r21 = xy + zs;
832 		var r31 = xz - ys;
833 		var r12 = xy - zs;
834 		var r22 = yy + (1 - yy) * c;
835 		var r32 = yz + xs;
836 		var r13 = xz + ys;
837 		var r23 = yz - xs;
838 		var r33 = zz + (1 - zz) * c;
839 
840 		var m11 = te[0], m21 = te[1], m31 = te[2], m41 = te[3];
841 		var m12 = te[4], m22 = te[5], m32 = te[6], m42 = te[7];
842 		var m13 = te[8], m23 = te[9], m33 = te[10], m43 = te[11];
843 		var m14 = te[12], m24 = te[13], m34 = te[14], m44 = te[15];
844 
845 		te[0] = r11 * m11 + r21 * m12 + r31 * m13;
846 		te[1] = r11 * m21 + r21 * m22 + r31 * m23;
847 		te[2] = r11 * m31 + r21 * m32 + r31 * m33;
848 		te[3] = r11 * m41 + r21 * m42 + r31 * m43;
849 
850 		te[4] = r12 * m11 + r22 * m12 + r32 * m13;
851 		te[5] = r12 * m21 + r22 * m22 + r32 * m23;
852 		te[6] = r12 * m31 + r22 * m32 + r32 * m33;
853 		te[7] = r12 * m41 + r22 * m42 + r32 * m43;
854 
855 		te[8] = r13 * m11 + r23 * m12 + r33 * m13;
856 		te[9] = r13 * m21 + r23 * m22 + r33 * m23;
857 		te[10] = r13 * m31 + r23 * m32 + r33 * m33;
858 		te[11] = r13 * m41 + r23 * m42 + r33 * m43;
859 
860 		return this;
861 
862 	},
863 
864 	scale: function ( v ) {
865 
866 		var te = this.elements;
867 		var x = v.x, y = v.y, z = v.z;
868 
869 		te[0] *= x; te[4] *= y; te[8] *= z;
870 		te[1] *= x; te[5] *= y; te[9] *= z;
871 		te[2] *= x; te[6] *= y; te[10] *= z;
872 		te[3] *= x; te[7] *= y; te[11] *= z;
873 
874 		return this;
875 
876 	},
877 
878 	getMaxScaleOnAxis: function () {
879 
880 		var te = this.elements;
881 
882 		var scaleXSq =  te[0] * te[0] + te[1] * te[1] + te[2] * te[2];
883 		var scaleYSq =  te[4] * te[4] + te[5] * te[5] + te[6] * te[6];
884 		var scaleZSq =  te[8] * te[8] + te[9] * te[9] + te[10] * te[10];
885 
886 		return Math.sqrt( Math.max( scaleXSq, Math.max( scaleYSq, scaleZSq ) ) );
887 
888 	},
889 
890 	//
891 
892 	makeTranslation: function ( x, y, z ) {
893 
894 		this.set(
895 
896 			1, 0, 0, x,
897 			0, 1, 0, y,
898 			0, 0, 1, z,
899 			0, 0, 0, 1
900 
901 		);
902 
903 		return this;
904 
905 	},
906 
907 	makeRotationX: function ( theta ) {
908 
909 		var c = Math.cos( theta ), s = Math.sin( theta );
910 
911 		this.set(
912 
913 			1, 0,  0, 0,
914 			0, c, -s, 0,
915 			0, s,  c, 0,
916 			0, 0,  0, 1
917 
918 		);
919 
920 		return this;
921 
922 	},
923 
924 	makeRotationY: function ( theta ) {
925 
926 		var c = Math.cos( theta ), s = Math.sin( theta );
927 
928 		this.set(
929 
930 			 c, 0, s, 0,
931 			 0, 1, 0, 0,
932 			-s, 0, c, 0,
933 			 0, 0, 0, 1
934 
935 		);
936 
937 		return this;
938 
939 	},
940 
941 	makeRotationZ: function ( theta ) {
942 
943 		var c = Math.cos( theta ), s = Math.sin( theta );
944 
945 		this.set(
946 
947 			c, -s, 0, 0,
948 			s,  c, 0, 0,
949 			0,  0, 1, 0,
950 			0,  0, 0, 1
951 
952 		);
953 
954 		return this;
955 
956 	},
957 
958 	makeRotationAxis: function ( axis, angle ) {
959 
960 		// Based on http://www.gamedev.net/reference/articles/article1199.asp
961 
962 		var c = Math.cos( angle );
963 		var s = Math.sin( angle );
964 		var t = 1 - c;
965 		var x = axis.x, y = axis.y, z = axis.z;
966 		var tx = t * x, ty = t * y;
967 
968 		this.set(
969 
970 			tx * x + c, tx * y - s * z, tx * z + s * y, 0,
971 			tx * y + s * z, ty * y + c, ty * z - s * x, 0,
972 			tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
973 			0, 0, 0, 1
974 
975 		);
976 
977 		 return this;
978 
979 	},
980 
981 	makeScale: function ( x, y, z ) {
982 
983 		this.set(
984 
985 			x, 0, 0, 0,
986 			0, y, 0, 0,
987 			0, 0, z, 0,
988 			0, 0, 0, 1
989 
990 		);
991 
992 		return this;
993 
994 	},
995 
996 	makeFrustum: function ( left, right, bottom, top, near, far ) {
997 
998 		var te = this.elements;
999 		var x = 2 * near / ( right - left );
1000 		var y = 2 * near / ( top - bottom );
1001 
1002 		var a = ( right + left ) / ( right - left );
1003 		var b = ( top + bottom ) / ( top - bottom );
1004 		var c = - ( far + near ) / ( far - near );
1005 		var d = - 2 * far * near / ( far - near );
1006 
1007 		te[0] = x;  te[4] = 0;  te[8] = a;   te[12] = 0;
1008 		te[1] = 0;  te[5] = y;  te[9] = b;   te[13] = 0;
1009 		te[2] = 0;  te[6] = 0;  te[10] = c;   te[14] = d;
1010 		te[3] = 0;  te[7] = 0;  te[11] = - 1; te[15] = 0;
1011 
1012 		return this;
1013 
1014 	},
1015 
1016 	makePerspective: function ( fov, aspect, near, far ) {
1017 
1018 		var ymax = near * Math.tan( fov * Math.PI / 360 );
1019 		var ymin = - ymax;
1020 		var xmin = ymin * aspect;
1021 		var xmax = ymax * aspect;
1022 
1023 		return this.makeFrustum( xmin, xmax, ymin, ymax, near, far );
1024 
1025 	},
1026 
1027 	makeOrthographic: function ( left, right, top, bottom, near, far ) {
1028 
1029 		var te = this.elements;
1030 		var w = right - left;
1031 		var h = top - bottom;
1032 		var p = far - near;
1033 
1034 		var x = ( right + left ) / w;
1035 		var y = ( top + bottom ) / h;
1036 		var z = ( far + near ) / p;
1037 
1038 		te[0] = 2 / w; te[4] = 0;     te[8] = 0;      te[12] = -x;
1039 		te[1] = 0;     te[5] = 2 / h; te[9] = 0;      te[13] = -y;
1040 		te[2] = 0;     te[6] = 0;     te[10] = -2 / p; te[14] = -z;
1041 		te[3] = 0;     te[7] = 0;     te[11] = 0;      te[15] = 1;
1042 
1043 		return this;
1044 
1045 	},
1046 
1047 
1048 	clone: function () {
1049 
1050 		var te = this.elements;
1051 
1052 		return new THREE.Matrix4(
1053 
1054 			te[0], te[4], te[8], te[12],
1055 			te[1], te[5], te[9], te[13],
1056 			te[2], te[6], te[10], te[14],
1057 			te[3], te[7], te[11], te[15]
1058 
1059 		);
1060 
1061 	}
1062 
1063 };
1064 
1065 THREE.Matrix4.__v1 = new THREE.Vector3();
1066 THREE.Matrix4.__v2 = new THREE.Vector3();
1067 THREE.Matrix4.__v3 = new THREE.Vector3();
1068 
1069 THREE.Matrix4.__m1 = new THREE.Matrix4();
1070 THREE.Matrix4.__m2 = new THREE.Matrix4();
1071