three.js/src/core/Matrix4.js

/**
 * @author supereggbert / http://www.paulbrunt.co.uk/
 * @author mr.doob / http://mrdoob.com/
 */

THREE.Matrix4 = function () {

	var x, y, z;

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

	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;

	this.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;
	};

	this.lookAt = function ( eye, center, up ) {

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

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

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

		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.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;

		}
	};

	this.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;

	};

	this.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;

	};

	this.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;

	};

	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;

	};

	this.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.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.n13 = a;
	m.n22 = y; m.n23 = b;
	m.n33 = c; m.n34 = d;
	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 );

};