three.js/src/math/Matrix4.js

/**
 * @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
 */

THREE.Matrix4 = function () {

	this.elements = new Float32Array( [

		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.' );

	}

};

THREE.Matrix4.prototype = {

	constructor: THREE.Matrix4,

	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 THREE.Matrix4().fromArray( this.elements );

	},

	copy: function ( m ) {

		this.elements.set( m.elements );

		return this;

	},

	copyPosition: function ( m ) {

		var te = this.elements;
		var 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;

		return function ( m ) {

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

			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 instanceof THREE.Euler === false ) {

			console.error( 'THREE.Matrix: .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, y, z;

		return function ( eye, target, up ) {

			if ( x === undefined ) x = new THREE.Vector3();
			if ( y === undefined ) y = new THREE.Vector3();
			if ( z === undefined ) z = new THREE.Vector3();

			var te = this.elements;

			z.subVectors( eye, target ).normalize();

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

				z.z = 1;

			}

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

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

				z.x += 0.0001;
				x.crossVectors( up, z ).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 );

	},

	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;

	},

	multiplyToArray: function ( a, b, r ) {

		var te = this.elements;

		this.multiplyMatrices( a, b );

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

		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;

	},

	applyToVector3Array: function () {

		var v1;

		return function ( array, offset, length ) {

			if ( v1 === undefined ) v1 = new THREE.Vector3();
			if ( offset === undefined ) offset = 0;
			if ( length === undefined ) length = array.length;

			for ( var i = 0, j = offset; i < length; i += 3, j += 3 ) {

				v1.fromArray( array, j );
				v1.applyMatrix4( this );
				v1.toArray( array, j );

			}

			return array;

		};

	}(),

	applyToBuffer: function () {

		var v1;

		return function applyToBuffer( buffer, offset, length ) {

			if ( v1 === undefined ) v1 = new THREE.Vector3();
			if ( offset === undefined ) offset = 0;
			if ( length === undefined ) length = buffer.length / buffer.itemSize;

			for ( var i = 0, j = offset; i < length; i ++, j ++ ) {

				v1.x = buffer.getX( j );
				v1.y = buffer.getY( j );
				v1.z = buffer.getZ( j );

				v1.applyMatrix4( this );

				buffer.setXYZ( v1.x, v1.y, v1.z );

			}

			return buffer;

		};

	}(),

	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;

	},

	flattenToArrayOffset: function ( array, offset ) {

		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;

	},

	getPosition: function () {

		var v1;

		return function () {

			if ( v1 === undefined ) v1 = new THREE.Vector3();
			console.warn( 'THREE.Matrix4: .getPosition() has been removed. Use Vector3.setFromMatrixPosition( matrix ) instead.' );

			return v1.setFromMatrixColumn( this, 3 );

		};

	}(),

	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 || false ) {

				throw new Error( msg );

			} else {

				console.warn( msg );

			}

			return this.identity();

		}

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

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

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

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

		return this.multiplyScalar( 1 / det );

	},

	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;

	},

	compose: function ( position, quaternion, scale ) {

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

		return this;

	},

	decompose: function () {

		var vector, matrix;

		return function ( position, quaternion, scale ) {

			if ( vector === undefined ) vector = new THREE.Vector3();
			if ( matrix === undefined ) matrix = new THREE.Matrix4();

			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.elements.set( this.elements ); // at this point matrix is incomplete so we can't use .copy()

			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;

		};

	}(),

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

		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;

	},

	makePerspective: function ( fov, aspect, near, far ) {

		var ymax = near * Math.tan( THREE.Math.DEG2RAD * fov * 0.5 );
		var ymin = - ymax;
		var xmin = ymin * aspect;
		var xmax = ymax * aspect;

		return this.makeFrustum( xmin, xmax, ymin, ymax, near, far );

	},

	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 ) {

		this.elements.set( array );

		return this;

	},

	toArray: function () {

		var te = this.elements;

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

	}

};