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
 */

THREE.Matrix4 = function () {

	this._x = new THREE.Vector3();
	this._y = new THREE.Vector3();
	this._z = new THREE.Vector3();

};

THREE.Matrix4.prototype = {

	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,

	identity: function () {

		this.n11 = 1; this.n12 = 0; this.n13 = 0; this.n14 = 0;
		this.n21 = 0; this.n22 = 1; this.n23 = 0; this.n24 = 0;
		this.n31 = 0; this.n32 = 0; this.n33 = 1; this.n34 = 0;
		this.n41 = 0; this.n42 = 0; this.n43 = 0; this.n44 = 1;

	},

	copy: function ( m ) {

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

	},

	lookAt: function ( eye, center, up ) {

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

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

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

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

		this.n11 = x.x; this.n12 = x.y; this.n13 = x.z; this.n14 = - x.dot( eye );
		this.n21 = y.x; this.n22 = y.y; this.n23 = y.z; this.n24 = - y.dot( eye );
		this.n31 = z.x; this.n32 = z.y; this.n33 = z.z; this.n34 = - z.dot( eye );
		this.n41 = 0; this.n42 = 0; this.n43 = 0; this.
n44 = 1;
	},

	transform: function ( v ) {

		var vx = v.x, vy = v.y, vz = v.z, vw = v.w ? v.w : 1.0;

		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;

		vw = this.n41 * vx + this.n42 * vy + this.n43 * vz + this.n44 * vw;

		if( v.w ) {

			v.w = vw;

		} else {

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

		}

		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 ) {

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

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

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

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

	},

	multiplySelf: function ( m ) {

		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;

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

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

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

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

	},

	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;

	},

	determinant: function () {

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

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

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

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

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

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

	},

	transpose: function () {

		function swap( obj, p1, p2 ) {

			var aux = obj[ p1 ];
			obj[ p1 ] = obj[ p2 ];
			obj[ p2 ] = aux;

		}

		swap( this, 'n21', 'n12' );
		swap( this, 'n31', 'n13' );
		swap( this, 'n32', 'n23' );
		swap( this, 'n41', 'n14' );
		swap( this, 'n42', 'n24' );
		swap( this, 'n43', 'n34' );

		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() {

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

	},

	toString: function() {

		return  "| " + this.n11 + " " + this.n12 + " " + this.n13 + " " + this.n14 + " |\n" +
			"| " + this.n21 + " " + this.n22 + " " + this.n23 + " " + this.n24 + " |\n" +
			"| " + this.n31 + " " + this.n32 + " " + this.n33 + " " + this.n34 + " |\n" +
			"| " + this.n41 + " " + this.n42 + " " + this.n43 + " " + this.n44 + " |";

	}

};

THREE.Matrix4.translationMatrix = function ( x, y, z ) {

	var m = new THREE.Matrix4();

	m.n14 = x;
	m.n24 = y;
	m.n34 = z;

	return m;

};

THREE.Matrix4.scaleMatrix = function ( x, y, z ) {

	var m = new THREE.Matrix4();

	m.n11 = x;
	m.n22 = y;
	m.n33 = z;

	return m;

};

THREE.Matrix4.rotationXMatrix = function ( theta ) {

	var rot = new THREE.Matrix4();

	rot.n22 = rot.n33 = Math.cos( theta );
	rot.n32 = Math.sin( theta );
	rot.n23 = - rot.n32;

	return rot;

};

THREE.Matrix4.rotationYMatrix = function ( theta ) {

	var rot = new THREE.Matrix4();

	rot.n11 = rot.n33 = Math.cos( theta );
	rot.n13 = Math.sin( theta );
	rot.n31 = - rot.n13;

	return rot;

};

THREE.Matrix4.rotationZMatrix = function ( theta ) {

	var rot = new THREE.Matrix4();

	rot.n11 = rot.n22 = Math.cos( theta );
	rot.n21 = Math.sin( theta );
	rot.n12 = - rot.n21;

	return rot;

};

THREE.Matrix4.rotationAxisAngleMatrix = function ( axis, angle ) {

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

	var rot = new THREE.Matrix4(),
	c = Math.cos( angle ),
	s = Math.sin( angle ),
	t = 1 - c,
	x = axis.x, y = axis.y, z = axis.z;

	rot.n11 = t * x * x + c;
	rot.n12 = t * x * y - s * z;
	rot.n13 = t * x * z + s * y;
	rot.n21 = t * x * y + s * z;
	rot.n22 = t * y * y + c;
	rot.n23 = t * y * z - s * x;
	rot.n31 = t * x * z - s * y;
	rot.n32 = t * y * z + s * x;
	rot.n33 = t * z * z + c;

	return rot;

};

THREE.Matrix4.makeInvert = function ( m1 ) {

	//TODO: make this more efficient
	//( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )
	var m2 = new THREE.Matrix4();

	m2.n11 = m1.n23*m1.n34*m1.n42 - m1.n24*m1.n33*m1.n42 + m1.n24*m1.n32*m1.n43 - m1.n22*m1.n34*m1.n43 - m1.n23*m1.n32*m1.n44 + m1.n22*m1.n33*m1.n44;
	m2.n12 = m1.n14*m1.n33*m1.n42 - m1.n13*m1.n34*m1.n42 - m1.n14*m1.n32*m1.n43 + m1.n12*m1.n34*m1.n43 + m1.n13*m1.n32*m1.n44 - m1.n12*m1.n33*m1.n44;
	m2.n13 = m1.n13*m1.n24*m1.n42 - m1.n14*m1.n23*m1.n42 + m1.n14*m1.n22*m1.n43 - m1.n12*m1.n24*m1.n43 - m1.n13*m1.n22*m1.n44 + m1.n12*m1.n23*m1.n44;
	m2.n14 = m1.n14*m1.n23*m1.n32 - m1.n13*m1.n24*m1.n32 - m1.n14*m1.n22*m1.n33 + m1.n12*m1.n24*m1.n33 + m1.n13*m1.n22*m1.n34 - m1.n12*m1.n23*m1.n34;
	m2.n21 = m1.n24*m1.n33*m1.n41 - m1.n23*m1.n34*m1.n41 - m1.n24*m1.n31*m1.n43 + m1.n21*m1.n34*m1.n43 + m1.n23*m1.n31*m1.n44 - m1.n21*m1.n33*m1.n44;
	m2.n22 = m1.n13*m1.n34*m1.n41 - m1.n14*m1.n33*m1.n41 + m1.n14*m1.n31*m1.n43 - m1.n11*m1.n34*m1.n43 - m1.n13*m1.n31*m1.n44 + m1.n11*m1.n33*m1.n44;
	m2.n23 = m1.n14*m1.n23*m1.n41 - m1.n13*m1.n24*m1.n41 - m1.n14*m1.n21*m1.n43 + m1.n11*m1.n24*m1.n43 + m1.n13*m1.n21*m1.n44 - m1.n11*m1.n23*m1.n44;
	m2.n24 = m1.n13*m1.n24*m1.n31 - m1.n14*m1.n23*m1.n31 + m1.n14*m1.n21*m1.n33 - m1.n11*m1.n24*m1.n33 - m1.n13*m1.n21*m1.n34 + m1.n11*m1.n23*m1.n34;
	m2.n31 = m1.n22*m1.n34*m1.n41 - m1.n24*m1.n32*m1.n41 + m1.n24*m1.n31*m1.n42 - m1.n21*m1.n34*m1.n42 - m1.n22*m1.n31*m1.n44 + m1.n21*m1.n32*m1.n44;
	m2.n32 = m1.n14*m1.n32*m1.n41 - m1.n12*m1.n34*m1.n41 - m1.n14*m1.n31*m1.n42 + m1.n11*m1.n34*m1.n42 + m1.n12*m1.n31*m1.n44 - m1.n11*m1.n32*m1.n44;
	m2.n33 = m1.n13*m1.n24*m1.n41 - m1.n14*m1.n22*m1.n41 + m1.n14*m1.n21*m1.n42 - m1.n11*m1.n24*m1.n42 - m1.n12*m1.n21*m1.n44 + m1.n11*m1.n22*m1.n44;
	m2.n34 = m1.n14*m1.n22*m1.n31 - m1.n12*m1.n24*m1.n31 - m1.n14*m1.n21*m1.n32 + m1.n11*m1.n24*m1.n32 + m1.n12*m1.n21*m1.n34 - m1.n11*m1.n22*m1.n34;
	m2.n41 = m1.n23*m1.n32*m1.n41 - m1.n22*m1.n33*m1.n41 - m1.n23*m1.n31*m1.n42 + m1.n21*m1.n33*m1.n42 + m1.n22*m1.n31*m1.n43 - m1.n21*m1.n32*m1.n43;
	m2.n42 = m1.n12*m1.n33*m1.n41 - m1.n13*m1.n32*m1.n41 + m1.n13*m1.n31*m1.n42 - m1.n11*m1.n33*m1.n42 - m1.n12*m1.n31*m1.n43 + m1.n11*m1.n32*m1.n43;
	m2.n43 = m1.n13*m1.n22*m1.n41 - m1.n12*m1.n23*m1.n41 - m1.n13*m1.n21*m1.n42 + m1.n11*m1.n23*m1.n42 + m1.n12*m1.n21*m1.n43 - m1.n11*m1.n22*m1.n43;
	m2.n44 = m1.n12*m1.n23*m1.n31 - m1.n13*m1.n22*m1.n31 + m1.n13*m1.n21*m1.n32 - m1.n11*m1.n23*m1.n32 - m1.n12*m1.n21*m1.n33 + m1.n11*m1.n22*m1.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 m = m1.flatten(),
	m2 = new THREE.Matrix3(),

	a11 = m[ 10 ] * m[ 5 ] - m[ 6 ] * m[ 9 ],
	a21 = - m[ 10 ] * m[ 1 ] + m[ 2 ] * m[ 9 ],
	a31 = m[ 6 ] * m[ 1 ] - m[ 2 ] * m[ 5 ],
	a12 = - m[ 10 ] * m[ 4 ] + m[ 6 ] * m[ 8 ],
	a22 = m[ 10 ] * m[ 0 ] - m[ 2 ] * m[ 8 ],
	a32 = - m[ 6 ] * m[ 0 ] + m[ 2 ] * m[ 4 ],
	a13 = m[ 9 ] * m[ 4 ] - m[ 5 ] * m[ 8 ],
	a23 = - m[ 9 ] * m[ 0 ] + m[ 1 ] * m[ 8 ],
	a33 = m[ 5 ] * m[ 0 ] - m[ 1 ] * m[ 4 ],
	det = m[ 0 ] * ( a11 ) + m[ 1 ] * ( a12 ) + m[ 2 ] * ( a13 ),
	idet;

	// no inverse
	if (det == 0) throw "matrix not invertible";

	idet = 1.0 / det;

	m2.m[ 0 ] = idet * a11; m2.m[ 1 ] = idet * a21; m2.m[ 2 ] = idet * a31;
	m2.m[ 3 ] = idet * a12; m2.m[ 4 ] = idet * a22; m2.m[ 5 ] = idet * a32;
	m2.m[ 6 ] = idet * a13; m2.m[ 7 ] = idet * a23; m2.m[ 8 ] = idet * a33;

	return m2;

}

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 = bottom - top;
	p = far - near;
	x = ( right + left ) / w;
	y = ( bottom + top ) / 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;

};