/**
 * @author alteredq / http://alteredqualia.com/
 * @author mrdoob / http://mrdoob.com/
 */

var _Math = {

	DEG2RAD: Math.PI / 180,
	RAD2DEG: 180 / Math.PI,

	generateUUID: ( function () {

		// http://stackoverflow.com/questions/105034/how-to-create-a-guid-uuid-in-javascript/21963136#21963136

		var lut = [];

		for ( var i = 0; i < 256; i ++ ) {

			lut[ i ] = ( i < 16 ? '0' : '' ) + ( i ).toString( 16 ).toUpperCase();

		}

		return function generateUUID() {

			var d0 = Math.random() * 0xffffffff | 0;
			var d1 = Math.random() * 0xffffffff | 0;
			var d2 = Math.random() * 0xffffffff | 0;
			var d3 = Math.random() * 0xffffffff | 0;
			return lut[ d0 & 0xff ] + lut[ d0 >> 8 & 0xff ] + lut[ d0 >> 16 & 0xff ] + lut[ d0 >> 24 & 0xff ] + '-' +
				lut[ d1 & 0xff ] + lut[ d1 >> 8 & 0xff ] + '-' + lut[ d1 >> 16 & 0x0f | 0x40 ] + lut[ d1 >> 24 & 0xff ] + '-' +
				lut[ d2 & 0x3f | 0x80 ] + lut[ d2 >> 8 & 0xff ] + '-' + lut[ d2 >> 16 & 0xff ] + lut[ d2 >> 24 & 0xff ] +
				lut[ d3 & 0xff ] + lut[ d3 >> 8 & 0xff ] + lut[ d3 >> 16 & 0xff ] + lut[ d3 >> 24 & 0xff ];

		};

	} )(),

	clamp: function ( value, min, max ) {

		return Math.max( min, Math.min( max, value ) );

	},

	// compute euclidian modulo of m % n
	// https://en.wikipedia.org/wiki/Modulo_operation

	euclideanModulo: function ( n, m ) {

		return ( ( n % m ) + m ) % m;

	},

	// Linear mapping from range <a1, a2> to range <b1, b2>

	mapLinear: function ( x, a1, a2, b1, b2 ) {

		return b1 + ( x - a1 ) * ( b2 - b1 ) / ( a2 - a1 );

	},

	// https://en.wikipedia.org/wiki/Linear_interpolation

	lerp: function ( x, y, t ) {

		return ( 1 - t ) * x + t * y;

	},

	// http://en.wikipedia.org/wiki/Smoothstep

	smoothstep: function ( x, min, max ) {

		if ( x <= min ) return 0;
		if ( x >= max ) return 1;

		x = ( x - min ) / ( max - min );

		return x * x * ( 3 - 2 * x );

	},

	smootherstep: function ( x, min, max ) {

		if ( x <= min ) return 0;
		if ( x >= max ) return 1;

		x = ( x - min ) / ( max - min );

		return x * x * x * ( x * ( x * 6 - 15 ) + 10 );

	},

	// Random integer from <low, high> interval

	randInt: function ( low, high ) {

		return low + Math.floor( Math.random() * ( high - low + 1 ) );

	},

	// Random float from <low, high> interval

	randFloat: function ( low, high ) {

		return low + Math.random() * ( high - low );

	},

	// Random float from <-range/2, range/2> interval

	randFloatSpread: function ( range ) {

		return range * ( 0.5 - Math.random() );

	},

	degToRad: function ( degrees ) {

		return degrees * _Math.DEG2RAD;

	},

	radToDeg: function ( radians ) {

		return radians * _Math.RAD2DEG;

	},

	isPowerOfTwo: function ( value ) {

		return ( value & ( value - 1 ) ) === 0 && value !== 0;

	},

	ceilPowerOfTwo: function ( value ) {

		return Math.pow( 2, Math.ceil( Math.log( value ) / Math.LN2 ) );

	},

	floorPowerOfTwo: function ( value ) {

		return Math.pow( 2, Math.floor( Math.log( value ) / Math.LN2 ) );

	}

};




/**
 * @author mrdoob / http://mrdoob.com/
 * @author philogb / http://blog.thejit.org/
 * @author egraether / http://egraether.com/
 * @author zz85 / http://www.lab4games.net/zz85/blog
 */

function Vector2( x, y ) {

	this.x = x || 0;
	this.y = y || 0;

}

Object.defineProperties( Vector2.prototype, {

	"width": {

		get: function () {

			return this.x;

		},

		set: function ( value ) {

			this.x = value;

		}

	},

	"height": {

		get: function () {

			return this.y;

		},

		set: function ( value ) {

			this.y = value;

		}

	}

} );

Object.assign( Vector2.prototype, {

	isVector2: true,

	set: function ( x, y ) {

		this.x = x;
		this.y = y;

		return this;

	},

	setScalar: function ( scalar ) {

		this.x = scalar;
		this.y = scalar;

		return this;

	},

	setX: function ( x ) {

		this.x = x;

		return this;

	},

	setY: function ( y ) {

		this.y = y;

		return this;

	},

	setComponent: function ( index, value ) {

		switch ( index ) {

			case 0: this.x = value; break;
			case 1: this.y = value; break;
			default: throw new Error( 'index is out of range: ' + index );

		}

		return this;

	},

	getComponent: function ( index ) {

		switch ( index ) {

			case 0: return this.x;
			case 1: return this.y;
			default: throw new Error( 'index is out of range: ' + index );

		}

	},

	clone: function () {

		return new this.constructor( this.x, this.y );

	},

	copy: function ( v ) {

		this.x = v.x;
		this.y = v.y;

		return this;

	},

	add: function ( v, w ) {

		if ( w !== undefined ) {

			console.warn( 'THREE.Vector2: .add() now only accepts one argument. Use .addVectors( a, b ) instead.' );
			return this.addVectors( v, w );

		}

		this.x += v.x;
		this.y += v.y;

		return this;

	},

	addScalar: function ( s ) {

		this.x += s;
		this.y += s;

		return this;

	},

	addVectors: function ( a, b ) {

		this.x = a.x + b.x;
		this.y = a.y + b.y;

		return this;

	},

	addScaledVector: function ( v, s ) {

		this.x += v.x * s;
		this.y += v.y * s;

		return this;

	},

	sub: function ( v, w ) {

		if ( w !== undefined ) {

			console.warn( 'THREE.Vector2: .sub() now only accepts one argument. Use .subVectors( a, b ) instead.' );
			return this.subVectors( v, w );

		}

		this.x -= v.x;
		this.y -= v.y;

		return this;

	},

	subScalar: function ( s ) {

		this.x -= s;
		this.y -= s;

		return this;

	},

	subVectors: function ( a, b ) {

		this.x = a.x - b.x;
		this.y = a.y - b.y;

		return this;

	},

	multiply: function ( v ) {

		this.x *= v.x;
		this.y *= v.y;

		return this;

	},

	multiplyScalar: function ( scalar ) {

		this.x *= scalar;
		this.y *= scalar;

		return this;

	},

	divide: function ( v ) {

		this.x /= v.x;
		this.y /= v.y;

		return this;

	},

	divideScalar: function ( scalar ) {

		return this.multiplyScalar( 1 / scalar );

	},

	applyMatrix3: function ( m ) {

		var x = this.x, y = this.y;
		var e = m.elements;

		this.x = e[ 0 ] * x + e[ 3 ] * y + e[ 6 ];
		this.y = e[ 1 ] * x + e[ 4 ] * y + e[ 7 ];

		return this;

	},

	min: function ( v ) {

		this.x = Math.min( this.x, v.x );
		this.y = Math.min( this.y, v.y );

		return this;

	},

	max: function ( v ) {

		this.x = Math.max( this.x, v.x );
		this.y = Math.max( this.y, v.y );

		return this;

	},

	clamp: function ( min, max ) {

		// assumes min < max, componentwise

		this.x = Math.max( min.x, Math.min( max.x, this.x ) );
		this.y = Math.max( min.y, Math.min( max.y, this.y ) );

		return this;

	},

	clampScalar: function () {

		var min = new Vector2();
		var max = new Vector2();

		return function clampScalar( minVal, maxVal ) {

			min.set( minVal, minVal );
			max.set( maxVal, maxVal );

			return this.clamp( min, max );

		};

	}(),

	clampLength: function ( min, max ) {

		var length = this.length();

		return this.divideScalar( length || 1 ).multiplyScalar( Math.max( min, Math.min( max, length ) ) );

	},

	floor: function () {

		this.x = Math.floor( this.x );
		this.y = Math.floor( this.y );

		return this;

	},

	ceil: function () {

		this.x = Math.ceil( this.x );
		this.y = Math.ceil( this.y );

		return this;

	},

	round: function () {

		this.x = Math.round( this.x );
		this.y = Math.round( this.y );

		return this;

	},

	roundToZero: function () {

		this.x = ( this.x < 0 ) ? Math.ceil( this.x ) : Math.floor( this.x );
		this.y = ( this.y < 0 ) ? Math.ceil( this.y ) : Math.floor( this.y );

		return this;

	},

	negate: function () {

		this.x = - this.x;
		this.y = - this.y;

		return this;

	},

	dot: function ( v ) {

		return this.x * v.x + this.y * v.y;

	},

	lengthSq: function () {

		return this.x * this.x + this.y * this.y;

	},

	length: function () {

		return Math.sqrt( this.x * this.x + this.y * this.y );

	},

	manhattanLength: function () {

		return Math.abs( this.x ) + Math.abs( this.y );

	},

	normalize: function () {

		return this.divideScalar( this.length() || 1 );

	},

	angle: function () {

		// computes the angle in radians with respect to the positive x-axis

		var angle = Math.atan2( this.y, this.x );

		if ( angle < 0 ) angle += 2 * Math.PI;

		return angle;

	},

	distanceTo: function ( v ) {

		return Math.sqrt( this.distanceToSquared( v ) );

	},

	distanceToSquared: function ( v ) {

		var dx = this.x - v.x, dy = this.y - v.y;
		return dx * dx + dy * dy;

	},

	manhattanDistanceTo: function ( v ) {

		return Math.abs( this.x - v.x ) + Math.abs( this.y - v.y );

	},

	setLength: function ( length ) {

		return this.normalize().multiplyScalar( length );

	},

	lerp: function ( v, alpha ) {

		this.x += ( v.x - this.x ) * alpha;
		this.y += ( v.y - this.y ) * alpha;

		return this;

	},

	lerpVectors: function ( v1, v2, alpha ) {

		return this.subVectors( v2, v1 ).multiplyScalar( alpha ).add( v1 );

	},

	equals: function ( v ) {

		return ( ( v.x === this.x ) && ( v.y === this.y ) );

	},

	fromArray: function ( array, offset ) {

		if ( offset === undefined ) offset = 0;

		this.x = array[ offset ];
		this.y = array[ offset + 1 ];

		return this;

	},

	toArray: function ( array, offset ) {

		if ( array === undefined ) array = [];
		if ( offset === undefined ) offset = 0;

		array[ offset ] = this.x;
		array[ offset + 1 ] = this.y;

		return array;

	},

	fromBufferAttribute: function ( attribute, index, offset ) {

		if ( offset !== undefined ) {

			console.warn( 'THREE.Vector2: offset has been removed from .fromBufferAttribute().' );

		}

		this.x = attribute.getX( index );
		this.y = attribute.getY( index );

		return this;

	},

	rotateAround: function ( center, angle ) {

		var c = Math.cos( angle ), s = Math.sin( angle );

		var x = this.x - center.x;
		var y = this.y - center.y;

		this.x = x * c - y * s + center.x;
		this.y = x * s + y * c + center.y;

		return this;

	}

} );


/**
 * @author mrdoob / http://mrdoob.com/
 * @author kile / http://kile.stravaganza.org/
 * @author philogb / http://blog.thejit.org/
 * @author mikael emtinger / http://gomo.se/
 * @author egraether / http://egraether.com/
 * @author WestLangley / http://github.com/WestLangley
 */

function Vector3( x, y, z ) {

	this.x = x || 0;
	this.y = y || 0;
	this.z = z || 0;

}

Object.assign( Vector3.prototype, {

	isVector3: true,

	set: function ( x, y, z ) {

		this.x = x;
		this.y = y;
		this.z = z;

		return this;

	},

	setScalar: function ( scalar ) {

		this.x = scalar;
		this.y = scalar;
		this.z = scalar;

		return this;

	},

	setX: function ( x ) {

		this.x = x;

		return this;

	},

	setY: function ( y ) {

		this.y = y;

		return this;

	},

	setZ: function ( z ) {

		this.z = z;

		return this;

	},

	setComponent: function ( index, value ) {

		switch ( index ) {

			case 0: this.x = value; break;
			case 1: this.y = value; break;
			case 2: this.z = value; break;
			default: throw new Error( 'index is out of range: ' + index );

		}

		return this;

	},

	getComponent: function ( index ) {

		switch ( index ) {

			case 0: return this.x;
			case 1: return this.y;
			case 2: return this.z;
			default: throw new Error( 'index is out of range: ' + index );

		}

	},

	clone: function () {

		return new this.constructor( this.x, this.y, this.z );

	},

	copy: function ( v ) {

		this.x = v.x;
		this.y = v.y;
		this.z = v.z;

		return this;

	},

	add: function ( v, w ) {

		if ( w !== undefined ) {

			console.warn( 'THREE.Vector3: .add() now only accepts one argument. Use .addVectors( a, b ) instead.' );
			return this.addVectors( v, w );

		}

		this.x += v.x;
		this.y += v.y;
		this.z += v.z;

		return this;

	},

	addScalar: function ( s ) {

		this.x += s;
		this.y += s;
		this.z += s;

		return this;

	},

	addVectors: function ( a, b ) {

		this.x = a.x + b.x;
		this.y = a.y + b.y;
		this.z = a.z + b.z;

		return this;

	},

	addScaledVector: function ( v, s ) {

		this.x += v.x * s;
		this.y += v.y * s;
		this.z += v.z * s;

		return this;

	},

	sub: function ( v, w ) {

		if ( w !== undefined ) {

			console.warn( 'THREE.Vector3: .sub() now only accepts one argument. Use .subVectors( a, b ) instead.' );
			return this.subVectors( v, w );

		}

		this.x -= v.x;
		this.y -= v.y;
		this.z -= v.z;

		return this;

	},

	subScalar: function ( s ) {

		this.x -= s;
		this.y -= s;
		this.z -= s;

		return this;

	},

	subVectors: function ( a, b ) {

		this.x = a.x - b.x;
		this.y = a.y - b.y;
		this.z = a.z - b.z;

		return this;

	},

	multiply: function ( v, w ) {

		if ( w !== undefined ) {

			console.warn( 'THREE.Vector3: .multiply() now only accepts one argument. Use .multiplyVectors( a, b ) instead.' );
			return this.multiplyVectors( v, w );

		}

		this.x *= v.x;
		this.y *= v.y;
		this.z *= v.z;

		return this;

	},

	multiplyScalar: function ( scalar ) {

		this.x *= scalar;
		this.y *= scalar;
		this.z *= scalar;

		return this;

	},

	multiplyVectors: function ( a, b ) {

		this.x = a.x * b.x;
		this.y = a.y * b.y;
		this.z = a.z * b.z;

		return this;

	},

	applyEuler: function () {

		var quaternion = new Quaternion();

		return function applyEuler( euler ) {

			if ( ! ( euler && euler.isEuler ) ) {

				console.error( 'THREE.Vector3: .applyEuler() now expects an Euler rotation rather than a Vector3 and order.' );

			}

			return this.applyQuaternion( quaternion.setFromEuler( euler ) );

		};

	}(),

	applyAxisAngle: function () {

		var quaternion = new Quaternion();

		return function applyAxisAngle( axis, angle ) {

			return this.applyQuaternion( quaternion.setFromAxisAngle( axis, angle ) );

		};

	}(),

	applyMatrix3: function ( m ) {

		var x = this.x, y = this.y, z = this.z;
		var e = m.elements;

		this.x = e[ 0 ] * x + e[ 3 ] * y + e[ 6 ] * z;
		this.y = e[ 1 ] * x + e[ 4 ] * y + e[ 7 ] * z;
		this.z = e[ 2 ] * x + e[ 5 ] * y + e[ 8 ] * z;

		return this;

	},

	applyMatrix4: function ( m ) {

		var x = this.x, y = this.y, z = this.z;
		var e = m.elements;

		var w = 1 / ( e[ 3 ] * x + e[ 7 ] * y + e[ 11 ] * z + e[ 15 ] );

		this.x = ( e[ 0 ] * x + e[ 4 ] * y + e[ 8 ] * z + e[ 12 ] ) * w;
		this.y = ( e[ 1 ] * x + e[ 5 ] * y + e[ 9 ] * z + e[ 13 ] ) * w;
		this.z = ( e[ 2 ] * x + e[ 6 ] * y + e[ 10 ] * z + e[ 14 ] ) * w;

		return this;

	},

	applyQuaternion: function ( q ) {

		var x = this.x, y = this.y, z = this.z;
		var qx = q.x, qy = q.y, qz = q.z, qw = q.w;

		// calculate quat * vector

		var ix = qw * x + qy * z - qz * y;
		var iy = qw * y + qz * x - qx * z;
		var iz = qw * z + qx * y - qy * x;
		var iw = - qx * x - qy * y - qz * z;

		// calculate result * inverse quat

		this.x = ix * qw + iw * - qx + iy * - qz - iz * - qy;
		this.y = iy * qw + iw * - qy + iz * - qx - ix * - qz;
		this.z = iz * qw + iw * - qz + ix * - qy - iy * - qx;

		return this;

	},

	project: function () {

		var matrix = new Matrix4();

		return function project( camera ) {

			matrix.multiplyMatrices( camera.projectionMatrix, matrix.getInverse( camera.matrixWorld ) );
			return this.applyMatrix4( matrix );

		};

	}(),

	unproject: function () {

		var matrix = new Matrix4();

		return function unproject( camera ) {

			matrix.multiplyMatrices( camera.matrixWorld, matrix.getInverse( camera.projectionMatrix ) );
			return this.applyMatrix4( matrix );

		};

	}(),

	transformDirection: function ( m ) {

		// input: THREE.Matrix4 affine matrix
		// vector interpreted as a direction

		var x = this.x, y = this.y, z = this.z;
		var e = m.elements;

		this.x = e[ 0 ] * x + e[ 4 ] * y + e[ 8 ] * z;
		this.y = e[ 1 ] * x + e[ 5 ] * y + e[ 9 ] * z;
		this.z = e[ 2 ] * x + e[ 6 ] * y + e[ 10 ] * z;

		return this.normalize();

	},

	divide: function ( v ) {

		this.x /= v.x;
		this.y /= v.y;
		this.z /= v.z;

		return this;

	},

	divideScalar: function ( scalar ) {

		return this.multiplyScalar( 1 / scalar );

	},

	min: function ( v ) {

		this.x = Math.min( this.x, v.x );
		this.y = Math.min( this.y, v.y );
		this.z = Math.min( this.z, v.z );

		return this;

	},

	max: function ( v ) {

		this.x = Math.max( this.x, v.x );
		this.y = Math.max( this.y, v.y );
		this.z = Math.max( this.z, v.z );

		return this;

	},

	clamp: function ( min, max ) {

		// assumes min < max, componentwise

		this.x = Math.max( min.x, Math.min( max.x, this.x ) );
		this.y = Math.max( min.y, Math.min( max.y, this.y ) );
		this.z = Math.max( min.z, Math.min( max.z, this.z ) );

		return this;

	},

	clampScalar: function () {

		var min = new Vector3();
		var max = new Vector3();

		return function clampScalar( minVal, maxVal ) {

			min.set( minVal, minVal, minVal );
			max.set( maxVal, maxVal, maxVal );

			return this.clamp( min, max );

		};

	}(),

	clampLength: function ( min, max ) {

		var length = this.length();

		return this.divideScalar( length || 1 ).multiplyScalar( Math.max( min, Math.min( max, length ) ) );

	},

	floor: function () {

		this.x = Math.floor( this.x );
		this.y = Math.floor( this.y );
		this.z = Math.floor( this.z );

		return this;

	},

	ceil: function () {

		this.x = Math.ceil( this.x );
		this.y = Math.ceil( this.y );
		this.z = Math.ceil( this.z );

		return this;

	},

	round: function () {

		this.x = Math.round( this.x );
		this.y = Math.round( this.y );
		this.z = Math.round( this.z );

		return this;

	},

	roundToZero: function () {

		this.x = ( this.x < 0 ) ? Math.ceil( this.x ) : Math.floor( this.x );
		this.y = ( this.y < 0 ) ? Math.ceil( this.y ) : Math.floor( this.y );
		this.z = ( this.z < 0 ) ? Math.ceil( this.z ) : Math.floor( this.z );

		return this;

	},

	negate: function () {

		this.x = - this.x;
		this.y = - this.y;
		this.z = - this.z;

		return this;

	},

	dot: function ( v ) {

		return this.x * v.x + this.y * v.y + this.z * v.z;

	},

	// TODO lengthSquared?

	lengthSq: function () {

		return this.x * this.x + this.y * this.y + this.z * this.z;

	},

	length: function () {

		return Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z );

	},

	manhattanLength: function () {

		return Math.abs( this.x ) + Math.abs( this.y ) + Math.abs( this.z );

	},

	normalize: function () {

		return this.divideScalar( this.length() || 1 );

	},

	setLength: function ( length ) {

		return this.normalize().multiplyScalar( length );

	},

	lerp: function ( v, alpha ) {

		this.x += ( v.x - this.x ) * alpha;
		this.y += ( v.y - this.y ) * alpha;
		this.z += ( v.z - this.z ) * alpha;

		return this;

	},

	lerpVectors: function ( v1, v2, alpha ) {

		return this.subVectors( v2, v1 ).multiplyScalar( alpha ).add( v1 );

	},

	cross: function ( v, w ) {

		if ( w !== undefined ) {

			console.warn( 'THREE.Vector3: .cross() now only accepts one argument. Use .crossVectors( a, b ) instead.' );
			return this.crossVectors( v, w );

		}

		return this.crossVectors( this, v );

	},

	crossVectors: function ( a, b ) {

		var ax = a.x, ay = a.y, az = a.z;
		var bx = b.x, by = b.y, bz = b.z;

		this.x = ay * bz - az * by;
		this.y = az * bx - ax * bz;
		this.z = ax * by - ay * bx;

		return this;

	},

	projectOnVector: function ( vector ) {

		var scalar = vector.dot( this ) / vector.lengthSq();

		return this.copy( vector ).multiplyScalar( scalar );

	},

	projectOnPlane: function () {

		var v1 = new Vector3();

		return function projectOnPlane( planeNormal ) {

			v1.copy( this ).projectOnVector( planeNormal );

			return this.sub( v1 );

		};

	}(),

	reflect: function () {

		// reflect incident vector off plane orthogonal to normal
		// normal is assumed to have unit length

		var v1 = new Vector3();

		return function reflect( normal ) {

			return this.sub( v1.copy( normal ).multiplyScalar( 2 * this.dot( normal ) ) );

		};

	}(),

	angleTo: function ( v ) {

		var theta = this.dot( v ) / ( Math.sqrt( this.lengthSq() * v.lengthSq() ) );

		// clamp, to handle numerical problems

		return Math.acos( _Math.clamp( theta, - 1, 1 ) );

	},

	distanceTo: function ( v ) {

		return Math.sqrt( this.distanceToSquared( v ) );

	},

	distanceToSquared: function ( v ) {

		var dx = this.x - v.x, dy = this.y - v.y, dz = this.z - v.z;

		return dx * dx + dy * dy + dz * dz;

	},

	manhattanDistanceTo: function ( v ) {

		return Math.abs( this.x - v.x ) + Math.abs( this.y - v.y ) + Math.abs( this.z - v.z );

	},

	setFromSpherical: function ( s ) {

		var sinPhiRadius = Math.sin( s.phi ) * s.radius;

		this.x = sinPhiRadius * Math.sin( s.theta );
		this.y = Math.cos( s.phi ) * s.radius;
		this.z = sinPhiRadius * Math.cos( s.theta );

		return this;

	},

	setFromCylindrical: function ( c ) {

		this.x = c.radius * Math.sin( c.theta );
		this.y = c.y;
		this.z = c.radius * Math.cos( c.theta );

		return this;

	},

	setFromMatrixPosition: function ( m ) {

		var e = m.elements;

		this.x = e[ 12 ];
		this.y = e[ 13 ];
		this.z = e[ 14 ];

		return this;

	},

	setFromMatrixScale: function ( m ) {

		var sx = this.setFromMatrixColumn( m, 0 ).length();
		var sy = this.setFromMatrixColumn( m, 1 ).length();
		var sz = this.setFromMatrixColumn( m, 2 ).length();

		this.x = sx;
		this.y = sy;
		this.z = sz;

		return this;

	},

	setFromMatrixColumn: function ( m, index ) {

		return this.fromArray( m.elements, index * 4 );

	},

	equals: function ( v ) {

		return ( ( v.x === this.x ) && ( v.y === this.y ) && ( v.z === this.z ) );

	},

	fromArray: function ( array, offset ) {

		if ( offset === undefined ) offset = 0;

		this.x = array[ offset ];
		this.y = array[ offset + 1 ];
		this.z = array[ offset + 2 ];

		return this;

	},

	toArray: function ( array, offset ) {

		if ( array === undefined ) array = [];
		if ( offset === undefined ) offset = 0;

		array[ offset ] = this.x;
		array[ offset + 1 ] = this.y;
		array[ offset + 2 ] = this.z;

		return array;

	},

	fromBufferAttribute: function ( attribute, index, offset ) {

		if ( offset !== undefined ) {

			console.warn( 'THREE.Vector3: offset has been removed from .fromBufferAttribute().' );

		}

		this.x = attribute.getX( index );
		this.y = attribute.getY( index );
		this.z = attribute.getZ( index );

		return this;

	}

} );



/**
 * @author mikael emtinger / http://gomo.se/
 * @author alteredq / http://alteredqualia.com/
 * @author WestLangley / http://github.com/WestLangley
 * @author bhouston / http://clara.io
 */

function Quaternion( x, y, z, w ) {

	this._x = x || 0;
	this._y = y || 0;
	this._z = z || 0;
	this._w = ( w !== undefined ) ? w : 1;

}

Object.assign( Quaternion, {

	slerp: function ( qa, qb, qm, t ) {

		return qm.copy( qa ).slerp( qb, t );

	},

	slerpFlat: function ( dst, dstOffset, src0, srcOffset0, src1, srcOffset1, t ) {

		// fuzz-free, array-based Quaternion SLERP operation

		var x0 = src0[ srcOffset0 + 0 ],
			y0 = src0[ srcOffset0 + 1 ],
			z0 = src0[ srcOffset0 + 2 ],
			w0 = src0[ srcOffset0 + 3 ],

			x1 = src1[ srcOffset1 + 0 ],
			y1 = src1[ srcOffset1 + 1 ],
			z1 = src1[ srcOffset1 + 2 ],
			w1 = src1[ srcOffset1 + 3 ];

		if ( w0 !== w1 || x0 !== x1 || y0 !== y1 || z0 !== z1 ) {

			var s = 1 - t,

				cos = x0 * x1 + y0 * y1 + z0 * z1 + w0 * w1,

				dir = ( cos >= 0 ? 1 : - 1 ),
				sqrSin = 1 - cos * cos;

			// Skip the Slerp for tiny steps to avoid numeric problems:
			if ( sqrSin > Number.EPSILON ) {

				var sin = Math.sqrt( sqrSin ),
					len = Math.atan2( sin, cos * dir );

				s = Math.sin( s * len ) / sin;
				t = Math.sin( t * len ) / sin;

			}

			var tDir = t * dir;

			x0 = x0 * s + x1 * tDir;
			y0 = y0 * s + y1 * tDir;
			z0 = z0 * s + z1 * tDir;
			w0 = w0 * s + w1 * tDir;

			// Normalize in case we just did a lerp:
			if ( s === 1 - t ) {

				var f = 1 / Math.sqrt( x0 * x0 + y0 * y0 + z0 * z0 + w0 * w0 );

				x0 *= f;
				y0 *= f;
				z0 *= f;
				w0 *= f;

			}

		}

		dst[ dstOffset ] = x0;
		dst[ dstOffset + 1 ] = y0;
		dst[ dstOffset + 2 ] = z0;
		dst[ dstOffset + 3 ] = w0;

	}

} );

Object.defineProperties( Quaternion.prototype, {

	x: {

		get: function () {

			return this._x;

		},

		set: function ( value ) {

			this._x = value;
			this.onChangeCallback();

		}

	},

	y: {

		get: function () {

			return this._y;

		},

		set: function ( value ) {

			this._y = value;
			this.onChangeCallback();

		}

	},

	z: {

		get: function () {

			return this._z;

		},

		set: function ( value ) {

			this._z = value;
			this.onChangeCallback();

		}

	},

	w: {

		get: function () {

			return this._w;

		},

		set: function ( value ) {

			this._w = value;
			this.onChangeCallback();

		}

	}

} );

Object.assign( Quaternion.prototype, {

	set: function ( x, y, z, w ) {

		this._x = x;
		this._y = y;
		this._z = z;
		this._w = w;

		this.onChangeCallback();

		return this;

	},

	clone: function () {

		return new this.constructor( this._x, this._y, this._z, this._w );

	},

	copy: function ( quaternion ) {

		this._x = quaternion.x;
		this._y = quaternion.y;
		this._z = quaternion.z;
		this._w = quaternion.w;

		this.onChangeCallback();

		return this;

	},

	setFromEuler: function ( euler, update ) {

		if ( ! ( euler && euler.isEuler ) ) {

			throw new Error( 'THREE.Quaternion: .setFromEuler() now expects an Euler rotation rather than a Vector3 and order.' );

		}

		var x = euler._x, y = euler._y, z = euler._z, order = euler.order;

		// http://www.mathworks.com/matlabcentral/fileexchange/
		// 	20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/
		//	content/SpinCalc.m

		var cos = Math.cos;
		var sin = Math.sin;

		var c1 = cos( x / 2 );
		var c2 = cos( y / 2 );
		var c3 = cos( z / 2 );

		var s1 = sin( x / 2 );
		var s2 = sin( y / 2 );
		var s3 = sin( z / 2 );

		if ( order === 'XYZ' ) {

			this._x = s1 * c2 * c3 + c1 * s2 * s3;
			this._y = c1 * s2 * c3 - s1 * c2 * s3;
			this._z = c1 * c2 * s3 + s1 * s2 * c3;
			this._w = c1 * c2 * c3 - s1 * s2 * s3;

		} else if ( order === 'YXZ' ) {

			this._x = s1 * c2 * c3 + c1 * s2 * s3;
			this._y = c1 * s2 * c3 - s1 * c2 * s3;
			this._z = c1 * c2 * s3 - s1 * s2 * c3;
			this._w = c1 * c2 * c3 + s1 * s2 * s3;

		} else if ( order === 'ZXY' ) {

			this._x = s1 * c2 * c3 - c1 * s2 * s3;
			this._y = c1 * s2 * c3 + s1 * c2 * s3;
			this._z = c1 * c2 * s3 + s1 * s2 * c3;
			this._w = c1 * c2 * c3 - s1 * s2 * s3;

		} else if ( order === 'ZYX' ) {

			this._x = s1 * c2 * c3 - c1 * s2 * s3;
			this._y = c1 * s2 * c3 + s1 * c2 * s3;
			this._z = c1 * c2 * s3 - s1 * s2 * c3;
			this._w = c1 * c2 * c3 + s1 * s2 * s3;

		} else if ( order === 'YZX' ) {

			this._x = s1 * c2 * c3 + c1 * s2 * s3;
			this._y = c1 * s2 * c3 + s1 * c2 * s3;
			this._z = c1 * c2 * s3 - s1 * s2 * c3;
			this._w = c1 * c2 * c3 - s1 * s2 * s3;

		} else if ( order === 'XZY' ) {

			this._x = s1 * c2 * c3 - c1 * s2 * s3;
			this._y = c1 * s2 * c3 - s1 * c2 * s3;
			this._z = c1 * c2 * s3 + s1 * s2 * c3;
			this._w = c1 * c2 * c3 + s1 * s2 * s3;

		}

		if ( update !== false ) this.onChangeCallback();

		return this;

	},

	setFromAxisAngle: function ( axis, angle ) {

		// http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm

		// assumes axis is normalized

		var halfAngle = angle / 2, s = Math.sin( halfAngle );

		this._x = axis.x * s;
		this._y = axis.y * s;
		this._z = axis.z * s;
		this._w = Math.cos( halfAngle );

		this.onChangeCallback();

		return this;

	},

	setFromRotationMatrix: function ( m ) {

		// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm

		// assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)

		var te = m.elements,

			m11 = te[ 0 ], m12 = te[ 4 ], m13 = te[ 8 ],
			m21 = te[ 1 ], m22 = te[ 5 ], m23 = te[ 9 ],
			m31 = te[ 2 ], m32 = te[ 6 ], m33 = te[ 10 ],

			trace = m11 + m22 + m33,
			s;

		if ( trace > 0 ) {

			s = 0.5 / Math.sqrt( trace + 1.0 );

			this._w = 0.25 / s;
			this._x = ( m32 - m23 ) * s;
			this._y = ( m13 - m31 ) * s;
			this._z = ( m21 - m12 ) * s;

		} else if ( m11 > m22 && m11 > m33 ) {

			s = 2.0 * Math.sqrt( 1.0 + m11 - m22 - m33 );

			this._w = ( m32 - m23 ) / s;
			this._x = 0.25 * s;
			this._y = ( m12 + m21 ) / s;
			this._z = ( m13 + m31 ) / s;

		} else if ( m22 > m33 ) {

			s = 2.0 * Math.sqrt( 1.0 + m22 - m11 - m33 );

			this._w = ( m13 - m31 ) / s;
			this._x = ( m12 + m21 ) / s;
			this._y = 0.25 * s;
			this._z = ( m23 + m32 ) / s;

		} else {

			s = 2.0 * Math.sqrt( 1.0 + m33 - m11 - m22 );

			this._w = ( m21 - m12 ) / s;
			this._x = ( m13 + m31 ) / s;
			this._y = ( m23 + m32 ) / s;
			this._z = 0.25 * s;

		}

		this.onChangeCallback();

		return this;

	},

	setFromUnitVectors: function () {

		// assumes direction vectors vFrom and vTo are normalized

		var v1 = new Vector3();
		var r;

		var EPS = 0.000001;

		return function setFromUnitVectors( vFrom, vTo ) {

			if ( v1 === undefined ) v1 = new Vector3();

			r = vFrom.dot( vTo ) + 1;

			if ( r < EPS ) {

				r = 0;

				if ( Math.abs( vFrom.x ) > Math.abs( vFrom.z ) ) {

					v1.set( - vFrom.y, vFrom.x, 0 );

				} else {

					v1.set( 0, - vFrom.z, vFrom.y );

				}

			} else {

				v1.crossVectors( vFrom, vTo );

			}

			this._x = v1.x;
			this._y = v1.y;
			this._z = v1.z;
			this._w = r;

			return this.normalize();

		};

	}(),

	inverse: function () {

		// quaternion is assumed to have unit length

		return this.conjugate();

	},

	conjugate: function () {

		this._x *= - 1;
		this._y *= - 1;
		this._z *= - 1;

		this.onChangeCallback();

		return this;

	},

	dot: function ( v ) {

		return this._x * v._x + this._y * v._y + this._z * v._z + this._w * v._w;

	},

	lengthSq: function () {

		return this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w;

	},

	length: function () {

		return Math.sqrt( this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w );

	},

	normalize: function () {

		var l = this.length();

		if ( l === 0 ) {

			this._x = 0;
			this._y = 0;
			this._z = 0;
			this._w = 1;

		} else {

			l = 1 / l;

			this._x = this._x * l;
			this._y = this._y * l;
			this._z = this._z * l;
			this._w = this._w * l;

		}

		this.onChangeCallback();

		return this;

	},

	multiply: function ( q, p ) {

		if ( p !== undefined ) {

			console.warn( 'THREE.Quaternion: .multiply() now only accepts one argument. Use .multiplyQuaternions( a, b ) instead.' );
			return this.multiplyQuaternions( q, p );

		}

		return this.multiplyQuaternions( this, q );

	},

	premultiply: function ( q ) {

		return this.multiplyQuaternions( q, this );

	},

	multiplyQuaternions: function ( a, b ) {

		// from http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm

		var qax = a._x, qay = a._y, qaz = a._z, qaw = a._w;
		var qbx = b._x, qby = b._y, qbz = b._z, qbw = b._w;

		this._x = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
		this._y = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
		this._z = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
		this._w = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;

		this.onChangeCallback();

		return this;

	},

	slerp: function ( qb, t ) {

		if ( t === 0 ) return this;
		if ( t === 1 ) return this.copy( qb );

		var x = this._x, y = this._y, z = this._z, w = this._w;

		// http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/

		var cosHalfTheta = w * qb._w + x * qb._x + y * qb._y + z * qb._z;

		if ( cosHalfTheta < 0 ) {

			this._w = - qb._w;
			this._x = - qb._x;
			this._y = - qb._y;
			this._z = - qb._z;

			cosHalfTheta = - cosHalfTheta;

		} else {

			this.copy( qb );

		}

		if ( cosHalfTheta >= 1.0 ) {

			this._w = w;
			this._x = x;
			this._y = y;
			this._z = z;

			return this;

		}

		var sinHalfTheta = Math.sqrt( 1.0 - cosHalfTheta * cosHalfTheta );

		if ( Math.abs( sinHalfTheta ) < 0.001 ) {

			this._w = 0.5 * ( w + this._w );
			this._x = 0.5 * ( x + this._x );
			this._y = 0.5 * ( y + this._y );
			this._z = 0.5 * ( z + this._z );

			return this;

		}

		var halfTheta = Math.atan2( sinHalfTheta, cosHalfTheta );
		var ratioA = Math.sin( ( 1 - t ) * halfTheta ) / sinHalfTheta,
			ratioB = Math.sin( t * halfTheta ) / sinHalfTheta;

		this._w = ( w * ratioA + this._w * ratioB );
		this._x = ( x * ratioA + this._x * ratioB );
		this._y = ( y * ratioA + this._y * ratioB );
		this._z = ( z * ratioA + this._z * ratioB );

		this.onChangeCallback();

		return this;

	},

	equals: function ( quaternion ) {

		return ( quaternion._x === this._x ) && ( quaternion._y === this._y ) && ( quaternion._z === this._z ) && ( quaternion._w === this._w );

	},

	fromArray: function ( array, offset ) {

		if ( offset === undefined ) offset = 0;

		this._x = array[ offset ];
		this._y = array[ offset + 1 ];
		this._z = array[ offset + 2 ];
		this._w = array[ offset + 3 ];

		this.onChangeCallback();

		return this;

	},

	toArray: function ( array, offset ) {

		if ( array === undefined ) array = [];
		if ( offset === undefined ) offset = 0;

		array[ offset ] = this._x;
		array[ offset + 1 ] = this._y;
		array[ offset + 2 ] = this._z;
		array[ offset + 3 ] = this._w;

		return array;

	},

	onChange: function ( callback ) {

		this.onChangeCallback = callback;

		return this;

	},

	onChangeCallback: function () {}

} );



/**
 * @author mrdoob / http://mrdoob.com/
 * @author supereggbert / http://www.paulbrunt.co.uk/
 * @author philogb / http://blog.thejit.org/
 * @author jordi_ros / http://plattsoft.com
 * @author D1plo1d / http://github.com/D1plo1d
 * @author alteredq / http://alteredqualia.com/
 * @author mikael emtinger / http://gomo.se/
 * @author timknip / http://www.floorplanner.com/
 * @author bhouston / http://clara.io
 * @author WestLangley / http://github.com/WestLangley
 */

function Matrix4() {

	this.elements = [

		1, 0, 0, 0,
		0, 1, 0, 0,
		0, 0, 1, 0,
		0, 0, 0, 1

	];

	if ( arguments.length > 0 ) {

		console.error( 'THREE.Matrix4: the constructor no longer reads arguments. use .set() instead.' );

	}

}

Object.assign( Matrix4.prototype, {

	isMatrix4: true,

	set: function ( n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 ) {

		var te = this.elements;

		te[ 0 ] = n11; te[ 4 ] = n12; te[ 8 ] = n13; te[ 12 ] = n14;
		te[ 1 ] = n21; te[ 5 ] = n22; te[ 9 ] = n23; te[ 13 ] = n24;
		te[ 2 ] = n31; te[ 6 ] = n32; te[ 10 ] = n33; te[ 14 ] = n34;
		te[ 3 ] = n41; te[ 7 ] = n42; te[ 11 ] = n43; te[ 15 ] = n44;

		return this;

	},

	identity: function () {

		this.set(

			1, 0, 0, 0,
			0, 1, 0, 0,
			0, 0, 1, 0,
			0, 0, 0, 1

		);

		return this;

	},

	clone: function () {

		return new Matrix4().fromArray( this.elements );

	},

	copy: function ( m ) {

		var te = this.elements;
		var me = m.elements;

		te[ 0 ] = me[ 0 ]; te[ 1 ] = me[ 1 ]; te[ 2 ] = me[ 2 ]; te[ 3 ] = me[ 3 ];
		te[ 4 ] = me[ 4 ]; te[ 5 ] = me[ 5 ]; te[ 6 ] = me[ 6 ]; te[ 7 ] = me[ 7 ];
		te[ 8 ] = me[ 8 ]; te[ 9 ] = me[ 9 ]; te[ 10 ] = me[ 10 ]; te[ 11 ] = me[ 11 ];
		te[ 12 ] = me[ 12 ]; te[ 13 ] = me[ 13 ]; te[ 14 ] = me[ 14 ]; te[ 15 ] = me[ 15 ];

		return this;

	},

	copyPosition: function ( m ) {

		var te = this.elements, me = m.elements;

		te[ 12 ] = me[ 12 ];
		te[ 13 ] = me[ 13 ];
		te[ 14 ] = me[ 14 ];

		return this;

	},

	extractBasis: function ( xAxis, yAxis, zAxis ) {

		xAxis.setFromMatrixColumn( this, 0 );
		yAxis.setFromMatrixColumn( this, 1 );
		zAxis.setFromMatrixColumn( this, 2 );

		return this;

	},

	makeBasis: function ( xAxis, yAxis, zAxis ) {

		this.set(
			xAxis.x, yAxis.x, zAxis.x, 0,
			xAxis.y, yAxis.y, zAxis.y, 0,
			xAxis.z, yAxis.z, zAxis.z, 0,
			0, 0, 0, 1
		);

		return this;

	},

	extractRotation: function () {

		var v1 = new Vector3();

		return function extractRotation( m ) {

			var te = this.elements;
			var me = m.elements;

			var scaleX = 1 / v1.setFromMatrixColumn( m, 0 ).length();
			var scaleY = 1 / v1.setFromMatrixColumn( m, 1 ).length();
			var scaleZ = 1 / v1.setFromMatrixColumn( m, 2 ).length();

			te[ 0 ] = me[ 0 ] * scaleX;
			te[ 1 ] = me[ 1 ] * scaleX;
			te[ 2 ] = me[ 2 ] * scaleX;

			te[ 4 ] = me[ 4 ] * scaleY;
			te[ 5 ] = me[ 5 ] * scaleY;
			te[ 6 ] = me[ 6 ] * scaleY;

			te[ 8 ] = me[ 8 ] * scaleZ;
			te[ 9 ] = me[ 9 ] * scaleZ;
			te[ 10 ] = me[ 10 ] * scaleZ;

			return this;

		};

	}(),

	makeRotationFromEuler: function ( euler ) {

		if ( ! ( euler && euler.isEuler ) ) {

			console.error( 'THREE.Matrix4: .makeRotationFromEuler() now expects a Euler rotation rather than a Vector3 and order.' );

		}

		var te = this.elements;

		var x = euler.x, y = euler.y, z = euler.z;
		var a = Math.cos( x ), b = Math.sin( x );
		var c = Math.cos( y ), d = Math.sin( y );
		var e = Math.cos( z ), f = Math.sin( z );

		if ( euler.order === 'XYZ' ) {

			var ae = a * e, af = a * f, be = b * e, bf = b * f;

			te[ 0 ] = c * e;
			te[ 4 ] = - c * f;
			te[ 8 ] = d;

			te[ 1 ] = af + be * d;
			te[ 5 ] = ae - bf * d;
			te[ 9 ] = - b * c;

			te[ 2 ] = bf - ae * d;
			te[ 6 ] = be + af * d;
			te[ 10 ] = a * c;

		} else if ( euler.order === 'YXZ' ) {

			var ce = c * e, cf = c * f, de = d * e, df = d * f;

			te[ 0 ] = ce + df * b;
			te[ 4 ] = de * b - cf;
			te[ 8 ] = a * d;

			te[ 1 ] = a * f;
			te[ 5 ] = a * e;
			te[ 9 ] = - b;

			te[ 2 ] = cf * b - de;
			te[ 6 ] = df + ce * b;
			te[ 10 ] = a * c;

		} else if ( euler.order === 'ZXY' ) {

			var ce = c * e, cf = c * f, de = d * e, df = d * f;

			te[ 0 ] = ce - df * b;
			te[ 4 ] = - a * f;
			te[ 8 ] = de + cf * b;

			te[ 1 ] = cf + de * b;
			te[ 5 ] = a * e;
			te[ 9 ] = df - ce * b;

			te[ 2 ] = - a * d;
			te[ 6 ] = b;
			te[ 10 ] = a * c;

		} else if ( euler.order === 'ZYX' ) {

			var ae = a * e, af = a * f, be = b * e, bf = b * f;

			te[ 0 ] = c * e;
			te[ 4 ] = be * d - af;
			te[ 8 ] = ae * d + bf;

			te[ 1 ] = c * f;
			te[ 5 ] = bf * d + ae;
			te[ 9 ] = af * d - be;

			te[ 2 ] = - d;
			te[ 6 ] = b * c;
			te[ 10 ] = a * c;

		} else if ( euler.order === 'YZX' ) {

			var ac = a * c, ad = a * d, bc = b * c, bd = b * d;

			te[ 0 ] = c * e;
			te[ 4 ] = bd - ac * f;
			te[ 8 ] = bc * f + ad;

			te[ 1 ] = f;
			te[ 5 ] = a * e;
			te[ 9 ] = - b * e;

			te[ 2 ] = - d * e;
			te[ 6 ] = ad * f + bc;
			te[ 10 ] = ac - bd * f;

		} else if ( euler.order === 'XZY' ) {

			var ac = a * c, ad = a * d, bc = b * c, bd = b * d;

			te[ 0 ] = c * e;
			te[ 4 ] = - f;
			te[ 8 ] = d * e;

			te[ 1 ] = ac * f + bd;
			te[ 5 ] = a * e;
			te[ 9 ] = ad * f - bc;

			te[ 2 ] = bc * f - ad;
			te[ 6 ] = b * e;
			te[ 10 ] = bd * f + ac;

		}

		// last column
		te[ 3 ] = 0;
		te[ 7 ] = 0;
		te[ 11 ] = 0;

		// bottom row
		te[ 12 ] = 0;
		te[ 13 ] = 0;
		te[ 14 ] = 0;
		te[ 15 ] = 1;

		return this;

	},

	makeRotationFromQuaternion: function ( q ) {

		var te = this.elements;

		var x = q._x, y = q._y, z = q._z, w = q._w;
		var x2 = x + x, y2 = y + y, z2 = z + z;
		var xx = x * x2, xy = x * y2, xz = x * z2;
		var yy = y * y2, yz = y * z2, zz = z * z2;
		var wx = w * x2, wy = w * y2, wz = w * z2;

		te[ 0 ] = 1 - ( yy + zz );
		te[ 4 ] = xy - wz;
		te[ 8 ] = xz + wy;

		te[ 1 ] = xy + wz;
		te[ 5 ] = 1 - ( xx + zz );
		te[ 9 ] = yz - wx;

		te[ 2 ] = xz - wy;
		te[ 6 ] = yz + wx;
		te[ 10 ] = 1 - ( xx + yy );

		// last column
		te[ 3 ] = 0;
		te[ 7 ] = 0;
		te[ 11 ] = 0;

		// bottom row
		te[ 12 ] = 0;
		te[ 13 ] = 0;
		te[ 14 ] = 0;
		te[ 15 ] = 1;

		return this;

	},

	lookAt: function () {

		var x = new Vector3();
		var y = new Vector3();
		var z = new Vector3();

		return function lookAt( eye, target, up ) {

			var te = this.elements;

			z.subVectors( eye, target );

			if ( z.lengthSq() === 0 ) {

				// eye and target are in the same position

				z.z = 1;

			}

			z.normalize();
			x.crossVectors( up, z );

			if ( x.lengthSq() === 0 ) {

				// up and z are parallel

				if ( Math.abs( up.z ) === 1 ) {

					z.x += 0.0001;

				} else {

					z.z += 0.0001;

				}

				z.normalize();
				x.crossVectors( up, z );

			}

			x.normalize();
			y.crossVectors( z, x );

			te[ 0 ] = x.x; te[ 4 ] = y.x; te[ 8 ] = z.x;
			te[ 1 ] = x.y; te[ 5 ] = y.y; te[ 9 ] = z.y;
			te[ 2 ] = x.z; te[ 6 ] = y.z; te[ 10 ] = z.z;

			return this;

		};

	}(),

	multiply: function ( m, n ) {

		if ( n !== undefined ) {

			console.warn( 'THREE.Matrix4: .multiply() now only accepts one argument. Use .multiplyMatrices( a, b ) instead.' );
			return this.multiplyMatrices( m, n );

		}

		return this.multiplyMatrices( this, m );

	},

	premultiply: function ( m ) {

		return this.multiplyMatrices( m, this );

	},

	multiplyMatrices: function ( a, b ) {

		var ae = a.elements;
		var be = b.elements;
		var te = this.elements;

		var a11 = ae[ 0 ], a12 = ae[ 4 ], a13 = ae[ 8 ], a14 = ae[ 12 ];
		var a21 = ae[ 1 ], a22 = ae[ 5 ], a23 = ae[ 9 ], a24 = ae[ 13 ];
		var a31 = ae[ 2 ], a32 = ae[ 6 ], a33 = ae[ 10 ], a34 = ae[ 14 ];
		var a41 = ae[ 3 ], a42 = ae[ 7 ], a43 = ae[ 11 ], a44 = ae[ 15 ];

		var b11 = be[ 0 ], b12 = be[ 4 ], b13 = be[ 8 ], b14 = be[ 12 ];
		var b21 = be[ 1 ], b22 = be[ 5 ], b23 = be[ 9 ], b24 = be[ 13 ];
		var b31 = be[ 2 ], b32 = be[ 6 ], b33 = be[ 10 ], b34 = be[ 14 ];
		var b41 = be[ 3 ], b42 = be[ 7 ], b43 = be[ 11 ], b44 = be[ 15 ];

		te[ 0 ] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
		te[ 4 ] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
		te[ 8 ] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
		te[ 12 ] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;

		te[ 1 ] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
		te[ 5 ] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
		te[ 9 ] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
		te[ 13 ] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;

		te[ 2 ] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
		te[ 6 ] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
		te[ 10 ] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
		te[ 14 ] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;

		te[ 3 ] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
		te[ 7 ] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
		te[ 11 ] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
		te[ 15 ] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;

		return this;

	},

	multiplyScalar: function ( s ) {

		var te = this.elements;

		te[ 0 ] *= s; te[ 4 ] *= s; te[ 8 ] *= s; te[ 12 ] *= s;
		te[ 1 ] *= s; te[ 5 ] *= s; te[ 9 ] *= s; te[ 13 ] *= s;
		te[ 2 ] *= s; te[ 6 ] *= s; te[ 10 ] *= s; te[ 14 ] *= s;
		te[ 3 ] *= s; te[ 7 ] *= s; te[ 11 ] *= s; te[ 15 ] *= s;

		return this;

	},

	applyToBufferAttribute: function () {

		var v1 = new Vector3();

		return function applyToBufferAttribute( attribute ) {

			for ( var i = 0, l = attribute.count; i < l; i ++ ) {

				v1.x = attribute.getX( i );
				v1.y = attribute.getY( i );
				v1.z = attribute.getZ( i );

				v1.applyMatrix4( this );

				attribute.setXYZ( i, v1.x, v1.y, v1.z );

			}

			return attribute;

		};

	}(),

	determinant: function () {

		var te = this.elements;

		var n11 = te[ 0 ], n12 = te[ 4 ], n13 = te[ 8 ], n14 = te[ 12 ];
		var n21 = te[ 1 ], n22 = te[ 5 ], n23 = te[ 9 ], n24 = te[ 13 ];
		var n31 = te[ 2 ], n32 = te[ 6 ], n33 = te[ 10 ], n34 = te[ 14 ];
		var n41 = te[ 3 ], n42 = te[ 7 ], n43 = te[ 11 ], n44 = te[ 15 ];

		//TODO: make this more efficient
		//( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )

		return (
			n41 * (
				+ n14 * n23 * n32
				 - n13 * n24 * n32
				 - n14 * n22 * n33
				 + n12 * n24 * n33
				 + n13 * n22 * n34
				 - n12 * n23 * n34
			) +
			n42 * (
				+ n11 * n23 * n34
				 - n11 * n24 * n33
				 + n14 * n21 * n33
				 - n13 * n21 * n34
				 + n13 * n24 * n31
				 - n14 * n23 * n31
			) +
			n43 * (
				+ n11 * n24 * n32
				 - n11 * n22 * n34
				 - n14 * n21 * n32
				 + n12 * n21 * n34
				 + n14 * n22 * n31
				 - n12 * n24 * n31
			) +
			n44 * (
				- n13 * n22 * n31
				 - n11 * n23 * n32
				 + n11 * n22 * n33
				 + n13 * n21 * n32
				 - n12 * n21 * n33
				 + n12 * n23 * n31
			)

		);

	},

	transpose: function () {

		var te = this.elements;
		var tmp;

		tmp = te[ 1 ]; te[ 1 ] = te[ 4 ]; te[ 4 ] = tmp;
		tmp = te[ 2 ]; te[ 2 ] = te[ 8 ]; te[ 8 ] = tmp;
		tmp = te[ 6 ]; te[ 6 ] = te[ 9 ]; te[ 9 ] = tmp;

		tmp = te[ 3 ]; te[ 3 ] = te[ 12 ]; te[ 12 ] = tmp;
		tmp = te[ 7 ]; te[ 7 ] = te[ 13 ]; te[ 13 ] = tmp;
		tmp = te[ 11 ]; te[ 11 ] = te[ 14 ]; te[ 14 ] = tmp;

		return this;

	},

	setPosition: function ( v ) {

		var te = this.elements;

		te[ 12 ] = v.x;
		te[ 13 ] = v.y;
		te[ 14 ] = v.z;

		return this;

	},

	getInverse: function ( m, throwOnDegenerate ) {

		// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
		var te = this.elements,
			me = m.elements,

			n11 = me[ 0 ], n21 = me[ 1 ], n31 = me[ 2 ], n41 = me[ 3 ],
			n12 = me[ 4 ], n22 = me[ 5 ], n32 = me[ 6 ], n42 = me[ 7 ],
			n13 = me[ 8 ], n23 = me[ 9 ], n33 = me[ 10 ], n43 = me[ 11 ],
			n14 = me[ 12 ], n24 = me[ 13 ], n34 = me[ 14 ], n44 = me[ 15 ],

			t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44,
			t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44,
			t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44,
			t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;

		var det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;

		if ( det === 0 ) {

			var msg = "THREE.Matrix4: .getInverse() can't invert matrix, determinant is 0";

			if ( throwOnDegenerate === true ) {

				throw new Error( msg );

			} else {

				console.warn( msg );

			}

			return this.identity();

		}

		var detInv = 1 / det;

		te[ 0 ] = t11 * detInv;
		te[ 1 ] = ( n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44 ) * detInv;
		te[ 2 ] = ( n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44 ) * detInv;
		te[ 3 ] = ( n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43 ) * detInv;

		te[ 4 ] = t12 * detInv;
		te[ 5 ] = ( n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44 ) * detInv;
		te[ 6 ] = ( n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44 ) * detInv;
		te[ 7 ] = ( n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43 ) * detInv;

		te[ 8 ] = t13 * detInv;
		te[ 9 ] = ( n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44 ) * detInv;
		te[ 10 ] = ( n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44 ) * detInv;
		te[ 11 ] = ( n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43 ) * detInv;

		te[ 12 ] = t14 * detInv;
		te[ 13 ] = ( n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34 ) * detInv;
		te[ 14 ] = ( n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34 ) * detInv;
		te[ 15 ] = ( n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33 ) * detInv;

		return this;

	},

	scale: function ( v ) {

		var te = this.elements;
		var x = v.x, y = v.y, z = v.z;

		te[ 0 ] *= x; te[ 4 ] *= y; te[ 8 ] *= z;
		te[ 1 ] *= x; te[ 5 ] *= y; te[ 9 ] *= z;
		te[ 2 ] *= x; te[ 6 ] *= y; te[ 10 ] *= z;
		te[ 3 ] *= x; te[ 7 ] *= y; te[ 11 ] *= z;

		return this;

	},

	getMaxScaleOnAxis: function () {

		var te = this.elements;

		var scaleXSq = te[ 0 ] * te[ 0 ] + te[ 1 ] * te[ 1 ] + te[ 2 ] * te[ 2 ];
		var scaleYSq = te[ 4 ] * te[ 4 ] + te[ 5 ] * te[ 5 ] + te[ 6 ] * te[ 6 ];
		var scaleZSq = te[ 8 ] * te[ 8 ] + te[ 9 ] * te[ 9 ] + te[ 10 ] * te[ 10 ];

		return Math.sqrt( Math.max( scaleXSq, scaleYSq, scaleZSq ) );

	},

	makeTranslation: function ( x, y, z ) {

		this.set(

			1, 0, 0, x,
			0, 1, 0, y,
			0, 0, 1, z,
			0, 0, 0, 1

		);

		return this;

	},

	makeRotationX: function ( theta ) {

		var c = Math.cos( theta ), s = Math.sin( theta );

		this.set(

			1, 0, 0, 0,
			0, c, - s, 0,
			0, s, c, 0,
			0, 0, 0, 1

		);

		return this;

	},

	makeRotationY: function ( theta ) {

		var c = Math.cos( theta ), s = Math.sin( theta );

		this.set(

			 c, 0, s, 0,
			 0, 1, 0, 0,
			- s, 0, c, 0,
			 0, 0, 0, 1

		);

		return this;

	},

	makeRotationZ: function ( theta ) {

		var c = Math.cos( theta ), s = Math.sin( theta );

		this.set(

			c, - s, 0, 0,
			s, c, 0, 0,
			0, 0, 1, 0,
			0, 0, 0, 1

		);

		return this;

	},

	makeRotationAxis: function ( axis, angle ) {

		// Based on http://www.gamedev.net/reference/articles/article1199.asp

		var c = Math.cos( angle );
		var s = Math.sin( angle );
		var t = 1 - c;
		var x = axis.x, y = axis.y, z = axis.z;
		var tx = t * x, ty = t * y;

		this.set(

			tx * x + c, tx * y - s * z, tx * z + s * y, 0,
			tx * y + s * z, ty * y + c, ty * z - s * x, 0,
			tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
			0, 0, 0, 1

		);

		 return this;

	},

	makeScale: function ( x, y, z ) {

		this.set(

			x, 0, 0, 0,
			0, y, 0, 0,
			0, 0, z, 0,
			0, 0, 0, 1

		);

		return this;

	},

	makeShear: function ( x, y, z ) {

		this.set(

			1, y, z, 0,
			x, 1, z, 0,
			x, y, 1, 0,
			0, 0, 0, 1

		);

		return this;

	},

	compose: function ( position, quaternion, scale ) {

		this.makeRotationFromQuaternion( quaternion );
		this.scale( scale );
		this.setPosition( position );

		return this;

	},

	decompose: function () {

		var vector = new Vector3();
		var matrix = new Matrix4();

		return function decompose( position, quaternion, scale ) {

			var te = this.elements;

			var sx = vector.set( te[ 0 ], te[ 1 ], te[ 2 ] ).length();
			var sy = vector.set( te[ 4 ], te[ 5 ], te[ 6 ] ).length();
			var sz = vector.set( te[ 8 ], te[ 9 ], te[ 10 ] ).length();

			// if determine is negative, we need to invert one scale
			var det = this.determinant();
			if ( det < 0 ) sx = - sx;

			position.x = te[ 12 ];
			position.y = te[ 13 ];
			position.z = te[ 14 ];

			// scale the rotation part
			matrix.copy( this );

			var invSX = 1 / sx;
			var invSY = 1 / sy;
			var invSZ = 1 / sz;

			matrix.elements[ 0 ] *= invSX;
			matrix.elements[ 1 ] *= invSX;
			matrix.elements[ 2 ] *= invSX;

			matrix.elements[ 4 ] *= invSY;
			matrix.elements[ 5 ] *= invSY;
			matrix.elements[ 6 ] *= invSY;

			matrix.elements[ 8 ] *= invSZ;
			matrix.elements[ 9 ] *= invSZ;
			matrix.elements[ 10 ] *= invSZ;

			quaternion.setFromRotationMatrix( matrix );

			scale.x = sx;
			scale.y = sy;
			scale.z = sz;

			return this;

		};

	}(),

	makePerspective: function ( left, right, top, bottom, near, far ) {

		if ( far === undefined ) {

			console.warn( 'THREE.Matrix4: .makePerspective() has been redefined and has a new signature. Please check the docs.' );

		}

		var te = this.elements;
		var x = 2 * near / ( right - left );
		var y = 2 * near / ( top - bottom );

		var a = ( right + left ) / ( right - left );
		var b = ( top + bottom ) / ( top - bottom );
		var c = - ( far + near ) / ( far - near );
		var d = - 2 * far * near / ( far - near );

		te[ 0 ] = x;	te[ 4 ] = 0;	te[ 8 ] = a;	te[ 12 ] = 0;
		te[ 1 ] = 0;	te[ 5 ] = y;	te[ 9 ] = b;	te[ 13 ] = 0;
		te[ 2 ] = 0;	te[ 6 ] = 0;	te[ 10 ] = c;	te[ 14 ] = d;
		te[ 3 ] = 0;	te[ 7 ] = 0;	te[ 11 ] = - 1;	te[ 15 ] = 0;

		return this;

	},

	makeOrthographic: function ( left, right, top, bottom, near, far ) {

		var te = this.elements;
		var w = 1.0 / ( right - left );
		var h = 1.0 / ( top - bottom );
		var p = 1.0 / ( far - near );

		var x = ( right + left ) * w;
		var y = ( top + bottom ) * h;
		var z = ( far + near ) * p;

		te[ 0 ] = 2 * w;	te[ 4 ] = 0;	te[ 8 ] = 0;	te[ 12 ] = - x;
		te[ 1 ] = 0;	te[ 5 ] = 2 * h;	te[ 9 ] = 0;	te[ 13 ] = - y;
		te[ 2 ] = 0;	te[ 6 ] = 0;	te[ 10 ] = - 2 * p;	te[ 14 ] = - z;
		te[ 3 ] = 0;	te[ 7 ] = 0;	te[ 11 ] = 0;	te[ 15 ] = 1;

		return this;

	},

	equals: function ( matrix ) {

		var te = this.elements;
		var me = matrix.elements;

		for ( var i = 0; i < 16; i ++ ) {

			if ( te[ i ] !== me[ i ] ) return false;

		}

		return true;

	},

	fromArray: function ( array, offset ) {

		if ( offset === undefined ) offset = 0;

		for ( var i = 0; i < 16; i ++ ) {

			this.elements[ i ] = array[ i + offset ];

		}

		return this;

	},

	toArray: function ( array, offset ) {

		if ( array === undefined ) array = [];
		if ( offset === undefined ) offset = 0;

		var te = this.elements;

		array[ offset ] = te[ 0 ];
		array[ offset + 1 ] = te[ 1 ];
		array[ offset + 2 ] = te[ 2 ];
		array[ offset + 3 ] = te[ 3 ];

		array[ offset + 4 ] = te[ 4 ];
		array[ offset + 5 ] = te[ 5 ];
		array[ offset + 6 ] = te[ 6 ];
		array[ offset + 7 ] = te[ 7 ];

		array[ offset + 8 ] = te[ 8 ];
		array[ offset + 9 ] = te[ 9 ];
		array[ offset + 10 ] = te[ 10 ];
		array[ offset + 11 ] = te[ 11 ];

		array[ offset + 12 ] = te[ 12 ];
		array[ offset + 13 ] = te[ 13 ];
		array[ offset + 14 ] = te[ 14 ];
		array[ offset + 15 ] = te[ 15 ];

		return array;

	}

} );

