phaser/src/math/Matrix4.js

/**
 * @author       Richard Davey <rich@photonstorm.com>
 * @copyright    2020 Photon Storm Ltd.
 * @license      {@link https://opensource.org/licenses/MIT|MIT License}
 */

//  Adapted from [gl-matrix](https://github.com/toji/gl-matrix) by toji
//  and [vecmath](https://github.com/mattdesl/vecmath) by mattdesl

var Class = require('../utils/Class');

var EPSILON = 0.000001;

/**
 * @classdesc
 * A four-dimensional matrix.
 *
 * @class Matrix4
 * @memberof Phaser.Math
 * @constructor
 * @since 3.0.0
 *
 * @param {Phaser.Math.Matrix4} [m] - Optional Matrix4 to copy values from.
 */
var Matrix4 = new Class({

    initialize:

    function Matrix4 (m)
    {
        /**
         * The matrix values.
         *
         * @name Phaser.Math.Matrix4#val
         * @type {Float32Array}
         * @since 3.0.0
         */
        this.val = new Float32Array(16);

        if (m)
        {
            //  Assume Matrix4 with val:
            this.copy(m);
        }
        else
        {
            //  Default to identity
            this.identity();
        }
    },

    /**
     * Make a clone of this Matrix4.
     *
     * @method Phaser.Math.Matrix4#clone
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix4} A clone of this Matrix4.
     */
    clone: function ()
    {
        return new Matrix4(this);
    },

    //  TODO - Should work with basic values

    /**
     * This method is an alias for `Matrix4.copy`.
     *
     * @method Phaser.Math.Matrix4#set
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} src - The Matrix to set the values of this Matrix's from.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    set: function (src)
    {
        return this.copy(src);
    },

    /**
     * Copy the values of a given Matrix into this Matrix.
     *
     * @method Phaser.Math.Matrix4#copy
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} src - The Matrix to copy the values from.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    copy: function (src)
    {
        var out = this.val;
        var a = src.val;

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

        return this;
    },

    /**
     * Set the values of this Matrix from the given array.
     *
     * @method Phaser.Math.Matrix4#fromArray
     * @since 3.0.0
     *
     * @param {array} a - The array to copy the values from.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    fromArray: function (a)
    {
        var out = this.val;

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

        return this;
    },

    /**
     * Reset this Matrix.
     *
     * Sets all values to `0`.
     *
     * @method Phaser.Math.Matrix4#zero
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    zero: function ()
    {
        var out = this.val;

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

        return this;
    },

    /**
     * Set the `x`, `y` and `z` values of this Matrix.
     *
     * @method Phaser.Math.Matrix4#xyz
     * @since 3.0.0
     *
     * @param {number} x - The x value.
     * @param {number} y - The y value.
     * @param {number} z - The z value.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    xyz: function (x, y, z)
    {
        this.identity();

        var out = this.val;

        out[12] = x;
        out[13] = y;
        out[14] = z;

        return this;
    },

    /**
     * Set the scaling values of this Matrix.
     *
     * @method Phaser.Math.Matrix4#scaling
     * @since 3.0.0
     *
     * @param {number} x - The x scaling value.
     * @param {number} y - The y scaling value.
     * @param {number} z - The z scaling value.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    scaling: function (x, y, z)
    {
        this.zero();

        var out = this.val;

        out[0] = x;
        out[5] = y;
        out[10] = z;
        out[15] = 1;

        return this;
    },

    /**
     * Reset this Matrix to an identity (default) matrix.
     *
     * @method Phaser.Math.Matrix4#identity
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    identity: function ()
    {
        var out = this.val;

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

        return this;
    },

    /**
     * Transpose this Matrix.
     *
     * @method Phaser.Math.Matrix4#transpose
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    transpose: function ()
    {
        var a = this.val;

        var a01 = a[1];
        var a02 = a[2];
        var a03 = a[3];
        var a12 = a[6];
        var a13 = a[7];
        var a23 = a[11];

        a[1] = a[4];
        a[2] = a[8];
        a[3] = a[12];
        a[4] = a01;
        a[6] = a[9];
        a[7] = a[13];
        a[8] = a02;
        a[9] = a12;
        a[11] = a[14];
        a[12] = a03;
        a[13] = a13;
        a[14] = a23;

        return this;
    },

    /**
     * Invert this Matrix.
     *
     * @method Phaser.Math.Matrix4#invert
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    invert: function ()
    {
        var a = this.val;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a03 = a[3];

        var a10 = a[4];
        var a11 = a[5];
        var a12 = a[6];
        var a13 = a[7];

        var a20 = a[8];
        var a21 = a[9];
        var a22 = a[10];
        var a23 = a[11];

        var a30 = a[12];
        var a31 = a[13];
        var a32 = a[14];
        var a33 = a[15];

        var b00 = a00 * a11 - a01 * a10;
        var b01 = a00 * a12 - a02 * a10;
        var b02 = a00 * a13 - a03 * a10;
        var b03 = a01 * a12 - a02 * a11;

        var b04 = a01 * a13 - a03 * a11;
        var b05 = a02 * a13 - a03 * a12;
        var b06 = a20 * a31 - a21 * a30;
        var b07 = a20 * a32 - a22 * a30;

        var b08 = a20 * a33 - a23 * a30;
        var b09 = a21 * a32 - a22 * a31;
        var b10 = a21 * a33 - a23 * a31;
        var b11 = a22 * a33 - a23 * a32;

        // Calculate the determinant
        var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

        if (!det)
        {
            return null;
        }

        det = 1 / det;

        a[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
        a[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
        a[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
        a[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
        a[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
        a[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
        a[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
        a[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
        a[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
        a[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
        a[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
        a[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
        a[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
        a[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
        a[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
        a[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;

        return this;
    },

    /**
     * Calculate the adjoint, or adjugate, of this Matrix.
     *
     * @method Phaser.Math.Matrix4#adjoint
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    adjoint: function ()
    {
        var a = this.val;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a03 = a[3];

        var a10 = a[4];
        var a11 = a[5];
        var a12 = a[6];
        var a13 = a[7];

        var a20 = a[8];
        var a21 = a[9];
        var a22 = a[10];
        var a23 = a[11];

        var a30 = a[12];
        var a31 = a[13];
        var a32 = a[14];
        var a33 = a[15];

        a[0] = (a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22));
        a[1] = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22));
        a[2] = (a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12));
        a[3] = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12));
        a[4] = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22));
        a[5] = (a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22));
        a[6] = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12));
        a[7] = (a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12));
        a[8] = (a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21));
        a[9] = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21));
        a[10] = (a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11));
        a[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11));
        a[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21));
        a[13] = (a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21));
        a[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11));
        a[15] = (a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11));

        return this;
    },

    /**
     * Calculate the determinant of this Matrix.
     *
     * @method Phaser.Math.Matrix4#determinant
     * @since 3.0.0
     *
     * @return {number} The determinant of this Matrix.
     */
    determinant: function ()
    {
        var a = this.val;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a03 = a[3];

        var a10 = a[4];
        var a11 = a[5];
        var a12 = a[6];
        var a13 = a[7];

        var a20 = a[8];
        var a21 = a[9];
        var a22 = a[10];
        var a23 = a[11];

        var a30 = a[12];
        var a31 = a[13];
        var a32 = a[14];
        var a33 = a[15];

        var b00 = a00 * a11 - a01 * a10;
        var b01 = a00 * a12 - a02 * a10;
        var b02 = a00 * a13 - a03 * a10;
        var b03 = a01 * a12 - a02 * a11;
        var b04 = a01 * a13 - a03 * a11;
        var b05 = a02 * a13 - a03 * a12;
        var b06 = a20 * a31 - a21 * a30;
        var b07 = a20 * a32 - a22 * a30;
        var b08 = a20 * a33 - a23 * a30;
        var b09 = a21 * a32 - a22 * a31;
        var b10 = a21 * a33 - a23 * a31;
        var b11 = a22 * a33 - a23 * a32;

        // Calculate the determinant
        return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
    },

    /**
     * Multiply this Matrix by the given Matrix.
     *
     * @method Phaser.Math.Matrix4#multiply
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} src - The Matrix to multiply this Matrix by.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    multiply: function (src)
    {
        var a = this.val;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a03 = a[3];

        var a10 = a[4];
        var a11 = a[5];
        var a12 = a[6];
        var a13 = a[7];

        var a20 = a[8];
        var a21 = a[9];
        var a22 = a[10];
        var a23 = a[11];

        var a30 = a[12];
        var a31 = a[13];
        var a32 = a[14];
        var a33 = a[15];

        var b = src.val;

        // Cache only the current line of the second matrix
        var b0 = b[0];
        var b1 = b[1];
        var b2 = b[2];
        var b3 = b[3];

        a[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
        a[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
        a[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
        a[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;

        b0 = b[4];
        b1 = b[5];
        b2 = b[6];
        b3 = b[7];

        a[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
        a[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
        a[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
        a[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;

        b0 = b[8];
        b1 = b[9];
        b2 = b[10];
        b3 = b[11];

        a[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
        a[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
        a[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
        a[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;

        b0 = b[12];
        b1 = b[13];
        b2 = b[14];
        b3 = b[15];

        a[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
        a[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
        a[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
        a[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;

        return this;
    },

    /**
     * Multiply the values of this Matrix4 by those given in the `src` argument.
     *
     * @method Phaser.Math.Matrix4#multiplyLocal
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} src - The source Matrix4 that this Matrix4 is multiplied by.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    multiplyLocal: function (src)
    {
        var a = [];
        var m1 = this.val;
        var m2 = src.val;

        a[0] = m1[0] * m2[0] + m1[1] * m2[4] + m1[2] * m2[8] + m1[3] * m2[12];
        a[1] = m1[0] * m2[1] + m1[1] * m2[5] + m1[2] * m2[9] + m1[3] * m2[13];
        a[2] = m1[0] * m2[2] + m1[1] * m2[6] + m1[2] * m2[10] + m1[3] * m2[14];
        a[3] = m1[0] * m2[3] + m1[1] * m2[7] + m1[2] * m2[11] + m1[3] * m2[15];

        a[4] = m1[4] * m2[0] + m1[5] * m2[4] + m1[6] * m2[8] + m1[7] * m2[12];
        a[5] = m1[4] * m2[1] + m1[5] * m2[5] + m1[6] * m2[9] + m1[7] * m2[13];
        a[6] = m1[4] * m2[2] + m1[5] * m2[6] + m1[6] * m2[10] + m1[7] * m2[14];
        a[7] = m1[4] * m2[3] + m1[5] * m2[7] + m1[6] * m2[11] + m1[7] * m2[15];

        a[8] = m1[8] * m2[0] + m1[9] * m2[4] + m1[10] * m2[8] + m1[11] * m2[12];
        a[9] = m1[8] * m2[1] + m1[9] * m2[5] + m1[10] * m2[9] + m1[11] * m2[13];
        a[10] = m1[8] * m2[2] + m1[9] * m2[6] + m1[10] * m2[10] + m1[11] * m2[14];
        a[11] = m1[8] * m2[3] + m1[9] * m2[7] + m1[10] * m2[11] + m1[11] * m2[15];

        a[12] = m1[12] * m2[0] + m1[13] * m2[4] + m1[14] * m2[8] + m1[15] * m2[12];
        a[13] = m1[12] * m2[1] + m1[13] * m2[5] + m1[14] * m2[9] + m1[15] * m2[13];
        a[14] = m1[12] * m2[2] + m1[13] * m2[6] + m1[14] * m2[10] + m1[15] * m2[14];
        a[15] = m1[12] * m2[3] + m1[13] * m2[7] + m1[14] * m2[11] + m1[15] * m2[15];

        return this.fromArray(a);
    },

    /**
     * Translate this Matrix using the given Vector.
     *
     * @method Phaser.Math.Matrix4#translate
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector3|Phaser.Math.Vector4)} v - The Vector to translate this Matrix with.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    translate: function (v)
    {
        var x = v.x;
        var y = v.y;
        var z = v.z;
        var a = this.val;

        a[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
        a[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
        a[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
        a[15] = a[3] * x + a[7] * y + a[11] * z + a[15];

        return this;
    },

    /**
     * Translate this Matrix using the given values.
     *
     * @method Phaser.Math.Matrix4#translateXYZ
     * @since 3.16.0
     *
     * @param {number} x - The x component.
     * @param {number} y - The y component.
     * @param {number} z - The z component.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    translateXYZ: function (x, y, z)
    {
        var a = this.val;

        a[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
        a[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
        a[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
        a[15] = a[3] * x + a[7] * y + a[11] * z + a[15];

        return this;
    },

    /**
     * Apply a scale transformation to this Matrix.
     *
     * Uses the `x`, `y` and `z` components of the given Vector to scale the Matrix.
     *
     * @method Phaser.Math.Matrix4#scale
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector3|Phaser.Math.Vector4)} v - The Vector to scale this Matrix with.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    scale: function (v)
    {
        var x = v.x;
        var y = v.y;
        var z = v.z;
        var a = this.val;

        a[0] = a[0] * x;
        a[1] = a[1] * x;
        a[2] = a[2] * x;
        a[3] = a[3] * x;

        a[4] = a[4] * y;
        a[5] = a[5] * y;
        a[6] = a[6] * y;
        a[7] = a[7] * y;

        a[8] = a[8] * z;
        a[9] = a[9] * z;
        a[10] = a[10] * z;
        a[11] = a[11] * z;

        return this;
    },

    /**
     * Apply a scale transformation to this Matrix.
     *
     * @method Phaser.Math.Matrix4#scaleXYZ
     * @since 3.16.0
     *
     * @param {number} x - The x component.
     * @param {number} y - The y component.
     * @param {number} z - The z component.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    scaleXYZ: function (x, y, z)
    {
        var a = this.val;

        a[0] = a[0] * x;
        a[1] = a[1] * x;
        a[2] = a[2] * x;
        a[3] = a[3] * x;

        a[4] = a[4] * y;
        a[5] = a[5] * y;
        a[6] = a[6] * y;
        a[7] = a[7] * y;

        a[8] = a[8] * z;
        a[9] = a[9] * z;
        a[10] = a[10] * z;
        a[11] = a[11] * z;

        return this;
    },

    /**
     * Derive a rotation matrix around the given axis.
     *
     * @method Phaser.Math.Matrix4#makeRotationAxis
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector3|Phaser.Math.Vector4)} axis - The rotation axis.
     * @param {number} angle - The rotation angle in radians.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    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;
        var y = axis.y;
        var z = axis.z;
        var tx = t * x;
        var ty = t * y;

        this.fromArray([
            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;
    },

    /**
     * Apply a rotation transformation to this Matrix.
     *
     * @method Phaser.Math.Matrix4#rotate
     * @since 3.0.0
     *
     * @param {number} rad - The angle in radians to rotate by.
     * @param {Phaser.Math.Vector3} axis - The axis to rotate upon.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    rotate: function (rad, axis)
    {
        var a = this.val;
        var x = axis.x;
        var y = axis.y;
        var z = axis.z;
        var len = Math.sqrt(x * x + y * y + z * z);

        if (Math.abs(len) < EPSILON)
        {
            return null;
        }

        len = 1 / len;
        x *= len;
        y *= len;
        z *= len;

        var s = Math.sin(rad);
        var c = Math.cos(rad);
        var t = 1 - c;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a03 = a[3];

        var a10 = a[4];
        var a11 = a[5];
        var a12 = a[6];
        var a13 = a[7];

        var a20 = a[8];
        var a21 = a[9];
        var a22 = a[10];
        var a23 = a[11];

        // Construct the elements of the rotation matrix
        var b00 = x * x * t + c;
        var b01 = y * x * t + z * s;
        var b02 = z * x * t - y * s;

        var b10 = x * y * t - z * s;
        var b11 = y * y * t + c;
        var b12 = z * y * t + x * s;

        var b20 = x * z * t + y * s;
        var b21 = y * z * t - x * s;
        var b22 = z * z * t + c;

        // Perform rotation-specific matrix multiplication
        a[0] = a00 * b00 + a10 * b01 + a20 * b02;
        a[1] = a01 * b00 + a11 * b01 + a21 * b02;
        a[2] = a02 * b00 + a12 * b01 + a22 * b02;
        a[3] = a03 * b00 + a13 * b01 + a23 * b02;
        a[4] = a00 * b10 + a10 * b11 + a20 * b12;
        a[5] = a01 * b10 + a11 * b11 + a21 * b12;
        a[6] = a02 * b10 + a12 * b11 + a22 * b12;
        a[7] = a03 * b10 + a13 * b11 + a23 * b12;
        a[8] = a00 * b20 + a10 * b21 + a20 * b22;
        a[9] = a01 * b20 + a11 * b21 + a21 * b22;
        a[10] = a02 * b20 + a12 * b21 + a22 * b22;
        a[11] = a03 * b20 + a13 * b21 + a23 * b22;

        return this;
    },

    /**
     * Rotate this matrix on its X axis.
     *
     * @method Phaser.Math.Matrix4#rotateX
     * @since 3.0.0
     *
     * @param {number} rad - The angle in radians to rotate by.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    rotateX: function (rad)
    {
        var a = this.val;
        var s = Math.sin(rad);
        var c = Math.cos(rad);

        var a10 = a[4];
        var a11 = a[5];
        var a12 = a[6];
        var a13 = a[7];

        var a20 = a[8];
        var a21 = a[9];
        var a22 = a[10];
        var a23 = a[11];

        // Perform axis-specific matrix multiplication
        a[4] = a10 * c + a20 * s;
        a[5] = a11 * c + a21 * s;
        a[6] = a12 * c + a22 * s;
        a[7] = a13 * c + a23 * s;
        a[8] = a20 * c - a10 * s;
        a[9] = a21 * c - a11 * s;
        a[10] = a22 * c - a12 * s;
        a[11] = a23 * c - a13 * s;

        return this;
    },

    /**
     * Rotate this matrix on its Y axis.
     *
     * @method Phaser.Math.Matrix4#rotateY
     * @since 3.0.0
     *
     * @param {number} rad - The angle to rotate by, in radians.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    rotateY: function (rad)
    {
        var a = this.val;
        var s = Math.sin(rad);
        var c = Math.cos(rad);

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a03 = a[3];

        var a20 = a[8];
        var a21 = a[9];
        var a22 = a[10];
        var a23 = a[11];

        // Perform axis-specific matrix multiplication
        a[0] = a00 * c - a20 * s;
        a[1] = a01 * c - a21 * s;
        a[2] = a02 * c - a22 * s;
        a[3] = a03 * c - a23 * s;
        a[8] = a00 * s + a20 * c;
        a[9] = a01 * s + a21 * c;
        a[10] = a02 * s + a22 * c;
        a[11] = a03 * s + a23 * c;

        return this;
    },

    /**
     * Rotate this matrix on its Z axis.
     *
     * @method Phaser.Math.Matrix4#rotateZ
     * @since 3.0.0
     *
     * @param {number} rad - The angle to rotate by, in radians.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    rotateZ: function (rad)
    {
        var a = this.val;
        var s = Math.sin(rad);
        var c = Math.cos(rad);

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a03 = a[3];

        var a10 = a[4];
        var a11 = a[5];
        var a12 = a[6];
        var a13 = a[7];

        // Perform axis-specific matrix multiplication
        a[0] = a00 * c + a10 * s;
        a[1] = a01 * c + a11 * s;
        a[2] = a02 * c + a12 * s;
        a[3] = a03 * c + a13 * s;
        a[4] = a10 * c - a00 * s;
        a[5] = a11 * c - a01 * s;
        a[6] = a12 * c - a02 * s;
        a[7] = a13 * c - a03 * s;

        return this;
    },

    /**
     * Set the values of this Matrix from the given rotation Quaternion and translation Vector.
     *
     * @method Phaser.Math.Matrix4#fromRotationTranslation
     * @since 3.0.0
     *
     * @param {Phaser.Math.Quaternion} q - The Quaternion to set rotation from.
     * @param {Phaser.Math.Vector3} v - The Vector to set translation from.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    fromRotationTranslation: function (q, v)
    {
        // Quaternion math
        var out = this.val;

        var x = q.x;
        var y = q.y;
        var z = q.z;
        var w = q.w;

        var x2 = x + x;
        var y2 = y + y;
        var z2 = z + z;

        var xx = x * x2;
        var xy = x * y2;
        var xz = x * z2;

        var yy = y * y2;
        var yz = y * z2;
        var zz = z * z2;

        var wx = w * x2;
        var wy = w * y2;
        var wz = w * z2;

        out[0] = 1 - (yy + zz);
        out[1] = xy + wz;
        out[2] = xz - wy;
        out[3] = 0;

        out[4] = xy - wz;
        out[5] = 1 - (xx + zz);
        out[6] = yz + wx;
        out[7] = 0;

        out[8] = xz + wy;
        out[9] = yz - wx;
        out[10] = 1 - (xx + yy);
        out[11] = 0;

        out[12] = v.x;
        out[13] = v.y;
        out[14] = v.z;
        out[15] = 1;

        return this;
    },

    /**
     * Set the values of this Matrix from the given Quaternion.
     *
     * @method Phaser.Math.Matrix4#fromQuat
     * @since 3.0.0
     *
     * @param {Phaser.Math.Quaternion} q - The Quaternion to set the values of this Matrix from.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    fromQuat: function (q)
    {
        var out = this.val;

        var x = q.x;
        var y = q.y;
        var z = q.z;
        var w = q.w;

        var x2 = x + x;
        var y2 = y + y;
        var z2 = z + z;

        var xx = x * x2;
        var xy = x * y2;
        var xz = x * z2;

        var yy = y * y2;
        var yz = y * z2;
        var zz = z * z2;

        var wx = w * x2;
        var wy = w * y2;
        var wz = w * z2;

        out[0] = 1 - (yy + zz);
        out[1] = xy + wz;
        out[2] = xz - wy;
        out[3] = 0;

        out[4] = xy - wz;
        out[5] = 1 - (xx + zz);
        out[6] = yz + wx;
        out[7] = 0;

        out[8] = xz + wy;
        out[9] = yz - wx;
        out[10] = 1 - (xx + yy);
        out[11] = 0;

        out[12] = 0;
        out[13] = 0;
        out[14] = 0;
        out[15] = 1;

        return this;
    },

    /**
     * Generate a frustum matrix with the given bounds.
     *
     * @method Phaser.Math.Matrix4#frustum
     * @since 3.0.0
     *
     * @param {number} left - The left bound of the frustum.
     * @param {number} right - The right bound of the frustum.
     * @param {number} bottom - The bottom bound of the frustum.
     * @param {number} top - The top bound of the frustum.
     * @param {number} near - The near bound of the frustum.
     * @param {number} far - The far bound of the frustum.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    frustum: function (left, right, bottom, top, near, far)
    {
        var out = this.val;

        var rl = 1 / (right - left);
        var tb = 1 / (top - bottom);
        var nf = 1 / (near - far);

        out[0] = (near * 2) * rl;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;

        out[4] = 0;
        out[5] = (near * 2) * tb;
        out[6] = 0;
        out[7] = 0;

        out[8] = (right + left) * rl;
        out[9] = (top + bottom) * tb;
        out[10] = (far + near) * nf;
        out[11] = -1;

        out[12] = 0;
        out[13] = 0;
        out[14] = (far * near * 2) * nf;
        out[15] = 0;

        return this;
    },

    /**
     * Generate a perspective projection matrix with the given bounds.
     *
     * @method Phaser.Math.Matrix4#perspective
     * @since 3.0.0
     *
     * @param {number} fovy - Vertical field of view in radians
     * @param {number} aspect - Aspect ratio. Typically viewport width  /height.
     * @param {number} near - Near bound of the frustum.
     * @param {number} far - Far bound of the frustum.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    perspective: function (fovy, aspect, near, far)
    {
        var out = this.val;
        var f = 1.0 / Math.tan(fovy / 2);
        var nf = 1 / (near - far);

        out[0] = f / aspect;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;

        out[4] = 0;
        out[5] = f;
        out[6] = 0;
        out[7] = 0;

        out[8] = 0;
        out[9] = 0;
        out[10] = (far + near) * nf;
        out[11] = -1;

        out[12] = 0;
        out[13] = 0;
        out[14] = (2 * far * near) * nf;
        out[15] = 0;

        return this;
    },

    /**
     * Generate a perspective projection matrix with the given bounds.
     *
     * @method Phaser.Math.Matrix4#perspectiveLH
     * @since 3.0.0
     *
     * @param {number} width - The width of the frustum.
     * @param {number} height - The height of the frustum.
     * @param {number} near - Near bound of the frustum.
     * @param {number} far - Far bound of the frustum.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    perspectiveLH: function (width, height, near, far)
    {
        var out = this.val;

        out[0] = (2 * near) / width;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;

        out[4] = 0;
        out[5] = (2 * near) / height;
        out[6] = 0;
        out[7] = 0;

        out[8] = 0;
        out[9] = 0;
        out[10] = -far / (near - far);
        out[11] = 1;

        out[12] = 0;
        out[13] = 0;
        out[14] = (near * far) / (near - far);
        out[15] = 0;

        return this;
    },

    /**
     * Generate an orthogonal projection matrix with the given bounds.
     *
     * @method Phaser.Math.Matrix4#ortho
     * @since 3.0.0
     *
     * @param {number} left - The left bound of the frustum.
     * @param {number} right - The right bound of the frustum.
     * @param {number} bottom - The bottom bound of the frustum.
     * @param {number} top - The top bound of the frustum.
     * @param {number} near - The near bound of the frustum.
     * @param {number} far - The far bound of the frustum.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    ortho: function (left, right, bottom, top, near, far)
    {
        var out = this.val;
        var lr = left - right;
        var bt = bottom - top;
        var nf = near - far;

        //  Avoid division by zero
        lr = (lr === 0) ? lr : 1 / lr;
        bt = (bt === 0) ? bt : 1 / bt;
        nf = (nf === 0) ? nf : 1 / nf;

        out[0] = -2 * lr;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;

        out[4] = 0;
        out[5] = -2 * bt;
        out[6] = 0;
        out[7] = 0;

        out[8] = 0;
        out[9] = 0;
        out[10] = 2 * nf;
        out[11] = 0;

        out[12] = (left + right) * lr;
        out[13] = (top + bottom) * bt;
        out[14] = (far + near) * nf;
        out[15] = 1;

        return this;
    },

    /**
     * Generate a look-at matrix with the given eye position, focal point, and up axis.
     *
     * @method Phaser.Math.Matrix4#lookAt
     * @since 3.0.0
     *
     * @param {Phaser.Math.Vector3} eye - Position of the viewer
     * @param {Phaser.Math.Vector3} center - Point the viewer is looking at
     * @param {Phaser.Math.Vector3} up - vec3 pointing up.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    lookAt: function (eye, center, up)
    {
        var out = this.val;

        var eyex = eye.x;
        var eyey = eye.y;
        var eyez = eye.z;

        var upx = up.x;
        var upy = up.y;
        var upz = up.z;

        var centerx = center.x;
        var centery = center.y;
        var centerz = center.z;

        if (Math.abs(eyex - centerx) < EPSILON &&
            Math.abs(eyey - centery) < EPSILON &&
            Math.abs(eyez - centerz) < EPSILON)
        {
            return this.identity();
        }

        var z0 = eyex - centerx;
        var z1 = eyey - centery;
        var z2 = eyez - centerz;

        var len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);

        z0 *= len;
        z1 *= len;
        z2 *= len;

        var x0 = upy * z2 - upz * z1;
        var x1 = upz * z0 - upx * z2;
        var x2 = upx * z1 - upy * z0;

        len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);

        if (!len)
        {
            x0 = 0;
            x1 = 0;
            x2 = 0;
        }
        else
        {
            len = 1 / len;
            x0 *= len;
            x1 *= len;
            x2 *= len;
        }

        var y0 = z1 * x2 - z2 * x1;
        var y1 = z2 * x0 - z0 * x2;
        var y2 = z0 * x1 - z1 * x0;

        len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);

        if (!len)
        {
            y0 = 0;
            y1 = 0;
            y2 = 0;
        }
        else
        {
            len = 1 / len;
            y0 *= len;
            y1 *= len;
            y2 *= len;
        }

        out[0] = x0;
        out[1] = y0;
        out[2] = z0;
        out[3] = 0;

        out[4] = x1;
        out[5] = y1;
        out[6] = z1;
        out[7] = 0;

        out[8] = x2;
        out[9] = y2;
        out[10] = z2;
        out[11] = 0;

        out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
        out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
        out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
        out[15] = 1;

        return this;
    },

    /**
     * Set the values of this matrix from the given `yaw`, `pitch` and `roll` values.
     *
     * @method Phaser.Math.Matrix4#yawPitchRoll
     * @since 3.0.0
     *
     * @param {number} yaw - The yaw value.
     * @param {number} pitch - The pitch value.
     * @param {number} roll - The roll value.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    yawPitchRoll: function (yaw, pitch, roll)
    {
        this.zero();
        _tempMat1.zero();
        _tempMat2.zero();

        var m0 = this.val;
        var m1 = _tempMat1.val;
        var m2 = _tempMat2.val;

        //  Rotate Z
        var s = Math.sin(roll);
        var c = Math.cos(roll);

        m0[10] = 1;
        m0[15] = 1;
        m0[0] = c;
        m0[1] = s;
        m0[4] = -s;
        m0[5] = c;

        //  Rotate X
        s = Math.sin(pitch);
        c = Math.cos(pitch);

        m1[0] = 1;
        m1[15] = 1;
        m1[5] = c;
        m1[10] = c;
        m1[9] = -s;
        m1[6] = s;

        //  Rotate Y
        s = Math.sin(yaw);
        c = Math.cos(yaw);

        m2[5] = 1;
        m2[15] = 1;
        m2[0] = c;
        m2[2] = -s;
        m2[8] = s;
        m2[10] = c;

        this.multiplyLocal(_tempMat1);
        this.multiplyLocal(_tempMat2);

        return this;
    },

    /**
     * Generate a world matrix from the given rotation, position, scale, view matrix and projection matrix.
     *
     * @method Phaser.Math.Matrix4#setWorldMatrix
     * @since 3.0.0
     *
     * @param {Phaser.Math.Vector3} rotation - The rotation of the world matrix.
     * @param {Phaser.Math.Vector3} position - The position of the world matrix.
     * @param {Phaser.Math.Vector3} scale - The scale of the world matrix.
     * @param {Phaser.Math.Matrix4} [viewMatrix] - The view matrix.
     * @param {Phaser.Math.Matrix4} [projectionMatrix] - The projection matrix.
     *
     * @return {Phaser.Math.Matrix4} This Matrix4.
     */
    setWorldMatrix: function (rotation, position, scale, viewMatrix, projectionMatrix)
    {
        this.yawPitchRoll(rotation.y, rotation.x, rotation.z);

        _tempMat1.scaling(scale.x, scale.y, scale.z);
        _tempMat2.xyz(position.x, position.y, position.z);

        this.multiplyLocal(_tempMat1);
        this.multiplyLocal(_tempMat2);

        if (viewMatrix !== undefined)
        {
            this.multiplyLocal(viewMatrix);
        }

        if (projectionMatrix !== undefined)
        {
            this.multiplyLocal(projectionMatrix);
        }

        return this;
    }

});

var _tempMat1 = new Matrix4();
var _tempMat2 = new Matrix4();

module.exports = Matrix4;