three.js/src/core/Matrix4.js

/**
 * @author mr.doob / 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/
 */

THREE.Matrix4 = function ( n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 ) {

	this.set(

		n11 || 1, n12 || 0, n13 || 0, n14 || 0,
		n21 || 0, n22 || 1, n23 || 0, n24 || 0,
		n31 || 0, n32 || 0, n33 || 1, n34 || 0,
		n41 || 0, n42 || 0, n43 || 0, n44 || 1

	);

	this.flat = new Array( 16 );
	this.m33 = new THREE.Matrix3();

};

THREE.Matrix4.prototype = {

	constructor: THREE.Matrix4,

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

		this.n11 = n11; this.n12 = n12; this.n13 = n13; this.n14 = n14;
		this.n21 = n21; this.n22 = n22; this.n23 = n23; this.n24 = n24;
		this.n31 = n31; this.n32 = n32; this.n33 = n33; this.n34 = n34;
		this.n41 = n41; this.n42 = n42; this.n43 = n43; this.n44 = 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;

	},

	copy: function ( m ) {

		this.set(

			m.n11, m.n12, m.n13, m.n14,
			m.n21, m.n22, m.n23, m.n24,
			m.n31, m.n32, m.n33, m.n34,
			m.n41, m.n42, m.n43, m.n44

		);

		return this;

	},

	lookAt: function ( eye, center, up ) {

		var x = THREE.Matrix4.__v1, y = THREE.Matrix4.__v2, z = THREE.Matrix4.__v3;

		z.sub( eye, center ).normalize();

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

			z.z = 1;

		}

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

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

			z.x += 0.0001;
			x.cross( up, z ).normalize();

		}

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


		this.n11 = x.x; this.n12 = y.x; this.n13 = z.x;
		this.n21 = x.y; this.n22 = y.y; this.n23 = z.y;
		this.n31 = x.z; this.n32 = y.z; this.n33 = z.z;

		return this;

	},

	multiplyVector3: function ( v ) {

		var vx = v.x, vy = v.y, vz = v.z,
		d = 1 / ( this.n41 * vx + this.n42 * vy + this.n43 * vz + this.n44 );

		v.x = ( this.n11 * vx + this.n12 * vy + this.n13 * vz + this.n14 ) * d;
		v.y = ( this.n21 * vx + this.n22 * vy + this.n23 * vz + this.n24 ) * d;
		v.z = ( this.n31 * vx + this.n32 * vy + this.n33 * vz + this.n34 ) * d;

		return v;

	},

	multiplyVector4: function ( v ) {

		var vx = v.x, vy = v.y, vz = v.z, vw = v.w;

		v.x = this.n11 * vx + this.n12 * vy + this.n13 * vz + this.n14 * vw;
		v.y = this.n21 * vx + this.n22 * vy + this.n23 * vz + this.n24 * vw;
		v.z = this.n31 * vx + this.n32 * vy + this.n33 * vz + this.n34 * vw;
		v.w = this.n41 * vx + this.n42 * vy + this.n43 * vz + this.n44 * vw;

		return v;

	},

	rotateAxis: function ( v ) {

		var vx = v.x, vy = v.y, vz = v.z;

		v.x = vx * this.n11 + vy * this.n12 + vz * this.n13;
		v.y = vx * this.n21 + vy * this.n22 + vz * this.n23;
		v.z = vx * this.n31 + vy * this.n32 + vz * this.n33;

		v.normalize();

		return v;

	},

	crossVector: function ( a ) {

		var v = new THREE.Vector4();

		v.x = this.n11 * a.x + this.n12 * a.y + this.n13 * a.z + this.n14 * a.w;
		v.y = this.n21 * a.x + this.n22 * a.y + this.n23 * a.z + this.n24 * a.w;
		v.z = this.n31 * a.x + this.n32 * a.y + this.n33 * a.z + this.n34 * a.w;

		v.w = ( a.w ) ? this.n41 * a.x + this.n42 * a.y + this.n43 * a.z + this.n44 * a.w : 1;

		return v;

	},

	multiply: function ( a, b ) {

		var a11 = a.n11, a12 = a.n12, a13 = a.n13, a14 = a.n14,
		a21 = a.n21, a22 = a.n22, a23 = a.n23, a24 = a.n24,
		a31 = a.n31, a32 = a.n32, a33 = a.n33, a34 = a.n34,
		a41 = a.n41, a42 = a.n42, a43 = a.n43, a44 = a.n44,

		b11 = b.n11, b12 = b.n12, b13 = b.n13, b14 = b.n14,
		b21 = b.n21, b22 = b.n22, b23 = b.n23, b24 = b.n24,
		b31 = b.n31, b32 = b.n32, b33 = b.n33, b34 = b.n34,
		b41 = b.n41, b42 = b.n42, b43 = b.n43, b44 = b.n44;

		this.n11 = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
		this.n12 = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
		this.n13 = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
		this.n14 = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;

		this.n21 = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
		this.n22 = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
		this.n23 = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
		this.n24 = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;

		this.n31 = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
		this.n32 = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
		this.n33 = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
		this.n34 = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;

		this.n41 = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
		this.n42 = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
		this.n43 = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
		this.n44 = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;

		return this;

	},

	multiplyToArray: function ( a, b, r ) {

		this.multiply( a, b );

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

		return this;

	},

	multiplySelf: function ( m ) {

		this.multiply( this, m );

		return this;

	},

	multiplyScalar: function ( s ) {

		this.n11 *= s; this.n12 *= s; this.n13 *= s; this.n14 *= s;
		this.n21 *= s; this.n22 *= s; this.n23 *= s; this.n24 *= s;
		this.n31 *= s; this.n32 *= s; this.n33 *= s; this.n34 *= s;
		this.n41 *= s; this.n42 *= s; this.n43 *= s; this.n44 *= s;

		return this;

	},

	determinant: function () {

		var n11 = this.n11, n12 = this.n12, n13 = this.n13, n14 = this.n14,
		n21 = this.n21, n22 = this.n22, n23 = this.n23, n24 = this.n24,
		n31 = this.n31, n32 = this.n32, n33 = this.n33, n34 = this.n34,
		n41 = this.n41, n42 = this.n42, n43 = this.n43, n44 = this.n44;

		//TODO: make this more efficient
		//( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )
		return (
			n14 * n23 * n32 * n41-
			n13 * n24 * n32 * n41-
			n14 * n22 * n33 * n41+
			n12 * n24 * n33 * n41+

			n13 * n22 * n34 * n41-
			n12 * n23 * n34 * n41-
			n14 * n23 * n31 * n42+
			n13 * n24 * n31 * n42+

			n14 * n21 * n33 * n42-
			n11 * n24 * n33 * n42-
			n13 * n21 * n34 * n42+
			n11 * n23 * n34 * n42+

			n14 * n22 * n31 * n43-
			n12 * n24 * n31 * n43-
			n14 * n21 * n32 * n43+
			n11 * n24 * n32 * n43+

			n12 * n21 * n34 * n43-
			n11 * n22 * n34 * n43-
			n13 * n22 * n31 * n44+
			n12 * n23 * n31 * n44+

			n13 * n21 * n32 * n44-
			n11 * n23 * n32 * n44-
			n12 * n21 * n33 * n44+
			n11 * n22 * n33 * n44
		);

	},

	transpose: function () {

		var tmp;

		tmp = this.n21; this.n21 = this.n12; this.n12 = tmp;
		tmp = this.n31; this.n31 = this.n13; this.n13 = tmp;
		tmp = this.n32; this.n32 = this.n23; this.n23 = tmp;

		tmp = this.n41; this.n41 = this.n14; this.n14 = tmp;
		tmp = this.n42; this.n42 = this.n24; this.n24 = tmp;
		tmp = this.n43; this.n43 = this.n34; this.n43 = tmp;

		return this;

	},

	clone: function () {

		var m = new THREE.Matrix4();

		m.n11 = this.n11; m.n12 = this.n12; m.n13 = this.n13; m.n14 = this.n14;
		m.n21 = this.n21; m.n22 = this.n22; m.n23 = this.n23; m.n24 = this.n24;
		m.n31 = this.n31; m.n32 = this.n32; m.n33 = this.n33; m.n34 = this.n34;
		m.n41 = this.n41; m.n42 = this.n42; m.n43 = this.n43; m.n44 = this.n44;

		return m;

	},

	flatten: function () {

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

		return this.flat;

	},

	flattenToArray: function ( flat ) {

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

		return flat;

	},

	flattenToArrayOffset: function( flat, offset ) {

		flat[ offset ] = this.n11;
		flat[ offset + 1 ] = this.n21;
		flat[ offset + 2 ] = this.n31;
		flat[ offset + 3 ] = this.n41;

		flat[ offset + 4 ] = this.n12;
		flat[ offset + 5 ] = this.n22;
		flat[ offset + 6 ] = this.n32;
		flat[ offset + 7 ] = this.n42;

		flat[ offset + 8 ]  = this.n13;
		flat[ offset + 9 ]  = this.n23;
		flat[ offset + 10 ] = this.n33;
		flat[ offset + 11 ] = this.n43;

		flat[ offset + 12 ] = this.n14;
		flat[ offset + 13 ] = this.n24;
		flat[ offset + 14 ] = this.n34;
		flat[ offset + 15 ] = this.n44;

		return flat;

	},

	setTranslation: function( x, y, z ) {

		this.set(

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

		);

		return this;

	},

	setScale: function ( x, y, z ) {

		this.set(

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

		);

		return this;

	},

	setRotationX: 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;

	},

	setRotationY: 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;

	},

	setRotationZ: 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;

	},

	setRotationAxis: function( axis, angle ) {

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

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

	},

	setPosition: function( v ) {

		this.n14 = v.x;
		this.n24 = v.y;
		this.n34 = v.z;

		return this;

	},

	getPosition: function() {

		if ( ! this.position ) {

			this.position = new THREE.Vector3();

		}

		this.position.set( this.n14, this.n24, this.n34 );

		return this.position;

	},

	getColumnX: function() {

		if ( ! this.columnX ) {

			this.columnX = new THREE.Vector3();

		}

		this.columnX.set( this.n11, this.n21, this.n31 );

		return this.columnX;
	},

	getColumnY: function() {

		if ( ! this.columnY ) {

			this.columnY = new THREE.Vector3();

		}

		this.columnY.set( this.n12, this.n22, this.n32 );

		return this.columnY;

	},

	getColumnZ: function() {

		if ( ! this.columnZ ) {

			this.columnZ = new THREE.Vector3();

		}

		this.columnZ.set( this.n13, this.n23, this.n33 );

		return this.columnZ;

	},

	setRotationFromEuler: function( v, order ) {

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

		switch ( order ) {

			case 'YXZ':

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

				this.n11 = ce + df * b;
				this.n12 = de * b - cf;
				this.n13 = a * d;

				this.n21 = a * f;
				this.n22 = a * e;
				this.n23 = - b;

				this.n31 = cf * b - de;
				this.n32 = df + ce * b;
				this.n33 = a * c;
				break;

			case 'ZXY':

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

				this.n11 = ce - df * b;
				this.n12 = - a * f;
				this.n13 = de + cf * b;

				this.n21 = cf + de * b;
				this.n22 = a * e;
				this.n23 = df - ce * b;

				this.n31 = - a * d;
				this.n32 = b;
				this.n33 = a * c;
				break;

			case 'ZYX':

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

				this.n11 = c * e;
				this.n12 = be * d - af;
				this.n13 = ae * d + bf;

				this.n21 = c * f;
				this.n22 = bf * d + ae;
				this.n23 = af * d - be;

				this.n31 = - d;
				this.n32 = b * c;
				this.n33 = a * c;
				break;

			case 'YZX':

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

				this.n11 = c * e;
				this.n12 = bd - ac * f;
				this.n13 = bc * f + ad;

				this.n21 = f;
				this.n22 = a * e;
				this.n23 = - b * e;

				this.n31 = - d * e;
				this.n32 = ad * f + bc;
				this.n33 = ac - bd * f;
				break;

			case 'XZY':

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

				this.n11 = c * e;
				this.n12 = - f;
				this.n13 = d * e;

				this.n21 = ac * f + bd;
				this.n22 = a * e;
				this.n23 = ad * f - bc;

				this.n31 = bc * f - ad;
				this.n32 = b * e;
				this.n33 = bd * f + ac;
				break;

			default: // 'XYZ'

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

				this.n11 = c * e;
				this.n12 = - c * f;
				this.n13 = d;

				this.n21 = af + be * d;
				this.n22 = ae - bf * d;
				this.n23 = - b * c;

				this.n31 = bf - ae * d;
				this.n32 = be + af * d;
				this.n33 = a * c;
				break;

		}

		return this;

	},


	setRotationFromQuaternion: function( q ) {

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

		this.n11 = 1 - ( yy + zz );
		this.n12 = xy - wz;
		this.n13 = xz + wy;

		this.n21 = xy + wz;
		this.n22 = 1 - ( xx + zz );
		this.n23 = yz - wx;

		this.n31 = xz - wy;
		this.n32 = yz + wx;
		this.n33 = 1 - ( xx + yy );

		return this;

	},

	scale: function ( v ) {

		var x = v.x, y = v.y, z = v.z;

		this.n11 *= x; this.n12 *= y; this.n13 *= z;
		this.n21 *= x; this.n22 *= y; this.n23 *= z;
		this.n31 *= x; this.n32 *= y; this.n33 *= z;
		this.n41 *= x; this.n42 *= y; this.n43 *= z;

		return this;

	},

	extractPosition: function ( m ) {

		this.n14 = m.n14;
		this.n24 = m.n24;
		this.n34 = m.n34;

	},

	extractRotation: function ( m, s ) {

		var invScaleX = 1 / s.x, invScaleY = 1 / s.y, invScaleZ = 1 / s.z;

		this.n11 = m.n11 * invScaleX;
		this.n21 = m.n21 * invScaleX;
		this.n31 = m.n31 * invScaleX;

		this.n12 = m.n12 * invScaleY;
		this.n22 = m.n22 * invScaleY;
		this.n32 = m.n32 * invScaleY;

		this.n13 = m.n13 * invScaleZ;
		this.n23 = m.n23 * invScaleZ;
		this.n33 = m.n33 * invScaleZ;

	}

};

THREE.Matrix4.makeInvert = function ( m1, m2 ) {

	// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm

	var n11 = m1.n11, n12 = m1.n12, n13 = m1.n13, n14 = m1.n14,
	n21 = m1.n21, n22 = m1.n22, n23 = m1.n23, n24 = m1.n24,
	n31 = m1.n31, n32 = m1.n32, n33 = m1.n33, n34 = m1.n34,
	n41 = m1.n41, n42 = m1.n42, n43 = m1.n43, n44 = m1.n44;

	if ( m2 === undefined ) m2 = new THREE.Matrix4();

	m2.n11 = n23*n34*n42 - n24*n33*n42 + n24*n32*n43 - n22*n34*n43 - n23*n32*n44 + n22*n33*n44;
	m2.n12 = n14*n33*n42 - n13*n34*n42 - n14*n32*n43 + n12*n34*n43 + n13*n32*n44 - n12*n33*n44;
	m2.n13 = n13*n24*n42 - n14*n23*n42 + n14*n22*n43 - n12*n24*n43 - n13*n22*n44 + n12*n23*n44;
	m2.n14 = n14*n23*n32 - n13*n24*n32 - n14*n22*n33 + n12*n24*n33 + n13*n22*n34 - n12*n23*n34;
	m2.n21 = n24*n33*n41 - n23*n34*n41 - n24*n31*n43 + n21*n34*n43 + n23*n31*n44 - n21*n33*n44;
	m2.n22 = n13*n34*n41 - n14*n33*n41 + n14*n31*n43 - n11*n34*n43 - n13*n31*n44 + n11*n33*n44;
	m2.n23 = n14*n23*n41 - n13*n24*n41 - n14*n21*n43 + n11*n24*n43 + n13*n21*n44 - n11*n23*n44;
	m2.n24 = n13*n24*n31 - n14*n23*n31 + n14*n21*n33 - n11*n24*n33 - n13*n21*n34 + n11*n23*n34;
	m2.n31 = n22*n34*n41 - n24*n32*n41 + n24*n31*n42 - n21*n34*n42 - n22*n31*n44 + n21*n32*n44;
	m2.n32 = n14*n32*n41 - n12*n34*n41 - n14*n31*n42 + n11*n34*n42 + n12*n31*n44 - n11*n32*n44;
	m2.n33 = n13*n24*n41 - n14*n22*n41 + n14*n21*n42 - n11*n24*n42 - n12*n21*n44 + n11*n22*n44;
	m2.n34 = n14*n22*n31 - n12*n24*n31 - n14*n21*n32 + n11*n24*n32 + n12*n21*n34 - n11*n22*n34;
	m2.n41 = n23*n32*n41 - n22*n33*n41 - n23*n31*n42 + n21*n33*n42 + n22*n31*n43 - n21*n32*n43;
	m2.n42 = n12*n33*n41 - n13*n32*n41 + n13*n31*n42 - n11*n33*n42 - n12*n31*n43 + n11*n32*n43;
	m2.n43 = n13*n22*n41 - n12*n23*n41 - n13*n21*n42 + n11*n23*n42 + n12*n21*n43 - n11*n22*n43;
	m2.n44 = n12*n23*n31 - n13*n22*n31 + n13*n21*n32 - n11*n23*n32 - n12*n21*n33 + n11*n22*n33;
	m2.multiplyScalar( 1 / m1.determinant() );

	return m2;

};

THREE.Matrix4.makeInvert3x3 = function ( m1 ) {

	// input:  THREE.Matrix4, output: THREE.Matrix3
	// ( based on http://code.google.com/p/webgl-mjs/ )

	var m33 = m1.m33, m33m = m33.m,
	a11 =   m1.n33 * m1.n22 - m1.n32 * m1.n23,
	a21 = - m1.n33 * m1.n21 + m1.n31 * m1.n23,
	a31 =   m1.n32 * m1.n21 - m1.n31 * m1.n22,
	a12 = - m1.n33 * m1.n12 + m1.n32 * m1.n13,
	a22 =   m1.n33 * m1.n11 - m1.n31 * m1.n13,
	a32 = - m1.n32 * m1.n11 + m1.n31 * m1.n12,
	a13 =   m1.n23 * m1.n12 - m1.n22 * m1.n13,
	a23 = - m1.n23 * m1.n11 + m1.n21 * m1.n13,
	a33 =   m1.n22 * m1.n11 - m1.n21 * m1.n12,

	det = m1.n11 * a11 + m1.n21 * a12 + m1.n31 * a13,

	idet;

	// no inverse
	if ( det == 0 ) {

		console.error( 'THREE.Matrix4.makeInvert3x3: Matrix not invertible.' );

	}

	idet = 1.0 / det;

	m33m[ 0 ] = idet * a11; m33m[ 1 ] = idet * a21; m33m[ 2 ] = idet * a31;
	m33m[ 3 ] = idet * a12; m33m[ 4 ] = idet * a22; m33m[ 5 ] = idet * a32;
	m33m[ 6 ] = idet * a13; m33m[ 7 ] = idet * a23; m33m[ 8 ] = idet * a33;

	return m33;

}

THREE.Matrix4.makeFrustum = function ( left, right, bottom, top, near, far ) {

	var m, x, y, a, b, c, d;

	m = new THREE.Matrix4();
	x = 2 * near / ( right - left );
	y = 2 * near / ( top - bottom );
	a = ( right + left ) / ( right - left );
	b = ( top + bottom ) / ( top - bottom );
	c = - ( far + near ) / ( far - near );
	d = - 2 * far * near / ( far - near );

	m.n11 = x;  m.n12 = 0;  m.n13 = a;   m.n14 = 0;
	m.n21 = 0;  m.n22 = y;  m.n23 = b;   m.n24 = 0;
	m.n31 = 0;  m.n32 = 0;  m.n33 = c;   m.n34 = d;
	m.n41 = 0;  m.n42 = 0;  m.n43 = - 1; m.n44 = 0;

	return m;

};

THREE.Matrix4.makePerspective = function ( fov, aspect, near, far ) {

	var ymax, ymin, xmin, xmax;

	ymax = near * Math.tan( fov * Math.PI / 360 );
	ymin = - ymax;
	xmin = ymin * aspect;
	xmax = ymax * aspect;

	return THREE.Matrix4.makeFrustum( xmin, xmax, ymin, ymax, near, far );

};

THREE.Matrix4.makeOrtho = function ( left, right, top, bottom, near, far ) {

	var m, x, y, z, w, h, p;

	m = new THREE.Matrix4();
	w = right - left;
	h = top - bottom;
	p = far - near;
	x = ( right + left ) / w;
	y = ( top + bottom ) / h;
	z = ( far + near ) / p;

	m.n11 = 2 / w; m.n12 = 0;     m.n13 = 0;      m.n14 = -x;
	m.n21 = 0;     m.n22 = 2 / h; m.n23 = 0;      m.n24 = -y;
	m.n31 = 0;     m.n32 = 0;     m.n33 = -2 / p; m.n34 = -z;
	m.n41 = 0;     m.n42 = 0;     m.n43 = 0;      m.n44 = 1;

	return m;

};

THREE.Matrix4.__v1 = new THREE.Vector3();
THREE.Matrix4.__v2 = new THREE.Vector3();
THREE.Matrix4.__v3 = new THREE.Vector3();