Matrix4.js

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

var Class = require('../utils/Class');
var Vector3 = require('./Vector3');

/**
 * @ignore
 */
var EPSILON = 0.000001;

/**
 * @classdesc
 * A four-dimensional matrix.
 *
 * Adapted from [gl-matrix](https://github.com/toji/gl-matrix) by toji
 * and [vecmath](https://github.com/mattdesl/vecmath) by mattdesl
 *
 * @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);
    },

    /**
     * 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 {this} This Matrix4.
     */
    set: function (src)
    {
        return this.copy(src);
    },

    /**
     * Sets all values of this Matrix4.
     *
     * @method Phaser.Math.Matrix4#setValues
     * @since 3.50.0
     *
     * @param {number} m00 - The m00 value.
     * @param {number} m01 - The m01 value.
     * @param {number} m02 - The m02 value.
     * @param {number} m03 - The m03 value.
     * @param {number} m10 - The m10 value.
     * @param {number} m11 - The m11 value.
     * @param {number} m12 - The m12 value.
     * @param {number} m13 - The m13 value.
     * @param {number} m20 - The m20 value.
     * @param {number} m21 - The m21 value.
     * @param {number} m22 - The m22 value.
     * @param {number} m23 - The m23 value.
     * @param {number} m30 - The m30 value.
     * @param {number} m31 - The m31 value.
     * @param {number} m32 - The m32 value.
     * @param {number} m33 - The m33 value.
     *
     * @return {this} This Matrix4 instance.
     */
    setValues: function (m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33)
    {
        var out = this.val;

        out[0] = m00;
        out[1] = m01;
        out[2] = m02;
        out[3] = m03;
        out[4] = m10;
        out[5] = m11;
        out[6] = m12;
        out[7] = m13;
        out[8] = m20;
        out[9] = m21;
        out[10] = m22;
        out[11] = m23;
        out[12] = m30;
        out[13] = m31;
        out[14] = m32;
        out[15] = m33;

        return this;
    },

    /**
     * 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 {this} This Matrix4.
     */
    copy: function (src)
    {
        var a = src.val;

        return this.setValues(a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], a[11], a[12], a[13], a[14], a[15]);
    },

    /**
     * Set the values of this Matrix from the given array.
     *
     * @method Phaser.Math.Matrix4#fromArray
     * @since 3.0.0
     *
     * @param {number[]} a - The array to copy the values from. Must have at least 16 elements.
     *
     * @return {this} This Matrix4.
     */
    fromArray: function (a)
    {
        return this.setValues(a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], a[11], a[12], a[13], a[14], a[15]);
    },

    /**
     * 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 ()
    {
        return this.setValues(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
    },

    /**
     * Generates a transform matrix based on the given position, scale and rotation.
     *
     * @method Phaser.Math.Matrix4#transform
     * @since 3.50.0
     *
     * @param {Phaser.Math.Vector3} position - The position vector.
     * @param {Phaser.Math.Vector3} scale - The scale vector.
     * @param {Phaser.Math.Quaternion} rotation - The rotation quaternion.
     *
     * @return {this} This Matrix4.
     */
    transform: function (position, scale, rotation)
    {
        var rotMatrix = _tempMat1.fromQuat(rotation);

        var rm = rotMatrix.val;

        var sx = scale.x;
        var sy = scale.y;
        var sz = scale.z;

        return this.setValues(
            rm[0] * sx,
            rm[1] * sx,
            rm[2] * sx,
            0,

            rm[4] * sy,
            rm[5] * sy,
            rm[6] * sy,
            0,

            rm[8] * sz,
            rm[9] * sz,
            rm[10] * sz,
            0,

            position.x,
            position.y,
            position.z,
            1
        );
    },

    /**
     * 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 {this} 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 {this} 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 {this} This Matrix4.
     */
    identity: function ()
    {
        return this.setValues(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);
    },

    /**
     * Transpose this Matrix.
     *
     * @method Phaser.Math.Matrix4#transpose
     * @since 3.0.0
     *
     * @return {this} 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;
    },

    /**
     * Copies the given Matrix4 into this Matrix and then inverses it.
     *
     * @method Phaser.Math.Matrix4#getInverse
     * @since 3.50.0
     *
     * @param {Phaser.Math.Matrix4} m - The Matrix4 to invert into this Matrix4.
     *
     * @return {this} This Matrix4.
     */
    getInverse: function (m)
    {
        this.copy(m);

        return this.invert();
    },

    /**
     * Invert this Matrix.
     *
     * @method Phaser.Math.Matrix4#invert
     * @since 3.0.0
     *
     * @return {this} 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 this;
        }

        det = 1 / det;

        return this.setValues(
            (a11 * b11 - a12 * b10 + a13 * b09) * det,
            (a02 * b10 - a01 * b11 - a03 * b09) * det,
            (a31 * b05 - a32 * b04 + a33 * b03) * det,
            (a22 * b04 - a21 * b05 - a23 * b03) * det,
            (a12 * b08 - a10 * b11 - a13 * b07) * det,
            (a00 * b11 - a02 * b08 + a03 * b07) * det,
            (a32 * b02 - a30 * b05 - a33 * b01) * det,
            (a20 * b05 - a22 * b02 + a23 * b01) * det,
            (a10 * b10 - a11 * b08 + a13 * b06) * det,
            (a01 * b08 - a00 * b10 - a03 * b06) * det,
            (a30 * b04 - a31 * b02 + a33 * b00) * det,
            (a21 * b02 - a20 * b04 - a23 * b00) * det,
            (a11 * b07 - a10 * b09 - a12 * b06) * det,
            (a00 * b09 - a01 * b07 + a02 * b06) * det,
            (a31 * b01 - a30 * b03 - a32 * b00) * det,
            (a20 * b03 - a21 * b01 + a22 * b00) * det
        );
    },

    /**
     * Calculate the adjoint, or adjugate, of this Matrix.
     *
     * @method Phaser.Math.Matrix4#adjoint
     * @since 3.0.0
     *
     * @return {this} 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];

        return this.setValues(
            (a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22)),
            -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22)),
            (a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12)),
            -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12)),
            -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22)),
            (a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22)),
            -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12)),
            (a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12)),
            (a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21)),
            -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21)),
            (a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11)),
            -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11)),
            -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21)),
            (a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21)),
            -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11)),
            (a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11))
        );
    },

    /**
     * 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 {this} 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 {this} This Matrix4.
     */
    multiplyLocal: function (src)
    {
        var a = this.val;
        var b = src.val;

        return this.setValues(
            a[0] * b[0] + a[1] * b[4] + a[2] * b[8] + a[3] * b[12],
            a[0] * b[1] + a[1] * b[5] + a[2] * b[9] + a[3] * b[13],
            a[0] * b[2] + a[1] * b[6] + a[2] * b[10] + a[3] * b[14],
            a[0] * b[3] + a[1] * b[7] + a[2] * b[11] + a[3] * b[15],

            a[4] * b[0] + a[5] * b[4] + a[6] * b[8] + a[7] * b[12],
            a[4] * b[1] + a[5] * b[5] + a[6] * b[9] + a[7] * b[13],
            a[4] * b[2] + a[5] * b[6] + a[6] * b[10] + a[7] * b[14],
            a[4] * b[3] + a[5] * b[7] + a[6] * b[11] + a[7] * b[15],

            a[8] * b[0] + a[9] * b[4] + a[10] * b[8] + a[11] * b[12],
            a[8] * b[1] + a[9] * b[5] + a[10] * b[9] + a[11] * b[13],
            a[8] * b[2] + a[9] * b[6] + a[10] * b[10] + a[11] * b[14],
            a[8] * b[3] + a[9] * b[7] + a[10] * b[11] + a[11] * b[15],

            a[12] * b[0] + a[13] * b[4] + a[14] * b[8] + a[15] * b[12],
            a[12] * b[1] + a[13] * b[5] + a[14] * b[9] + a[15] * b[13],
            a[12] * b[2] + a[13] * b[6] + a[14] * b[10] + a[15] * b[14],
            a[12] * b[3] + a[13] * b[7] + a[14] * b[11] + a[15] * b[15]
        );
    },

    /**
     * Multiplies the given Matrix4 object with this Matrix.
     *
     * This is the same as calling `multiplyMatrices(m, this)`.
     *
     * @method Phaser.Math.Matrix4#premultiply
     * @since 3.50.0
     *
     * @param {Phaser.Math.Matrix4} m - The Matrix4 to multiply with this one.
     *
     * @return {this} This Matrix4.
     */
    premultiply: function (m)
    {
        return this.multiplyMatrices(m, this);
    },

    /**
     * Multiplies the two given Matrix4 objects and stores the results in this Matrix.
     *
     * @method Phaser.Math.Matrix4#multiplyMatrices
     * @since 3.50.0
     *
     * @param {Phaser.Math.Matrix4} a - The first Matrix4 to multiply.
     * @param {Phaser.Math.Matrix4} b - The second Matrix4 to multiply.
     *
     * @return {this} This Matrix4.
     */
    multiplyMatrices: function (a, b)
    {
        var am = a.val;
        var bm = b.val;

        var a11 = am[0];
        var a12 = am[4];
        var a13 = am[8];
        var a14 = am[12];
        var a21 = am[1];
        var a22 = am[5];
        var a23 = am[9];
        var a24 = am[13];
        var a31 = am[2];
        var a32 = am[6];
        var a33 = am[10];
        var a34 = am[14];
        var a41 = am[3];
        var a42 = am[7];
        var a43 = am[11];
        var a44 = am[15];

        var b11 = bm[0];
        var b12 = bm[4];
        var b13 = bm[8];
        var b14 = bm[12];
        var b21 = bm[1];
        var b22 = bm[5];
        var b23 = bm[9];
        var b24 = bm[13];
        var b31 = bm[2];
        var b32 = bm[6];
        var b33 = bm[10];
        var b34 = bm[14];
        var b41 = bm[3];
        var b42 = bm[7];
        var b43 = bm[11];
        var b44 = bm[15];

        return this.setValues(
            a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41,
            a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41,
            a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41,
            a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41,
            a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42,
            a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42,
            a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42,
            a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42,
            a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43,
            a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43,
            a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43,
            a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43,
            a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44,
            a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44,
            a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44,
            a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44
        );
    },

    /**
     * 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 {this} This Matrix4.
     */
    translate: function (v)
    {
        return this.translateXYZ(v.x, v.y, v.z);
    },

    /**
     * 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 {this} 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 {this} This Matrix4.
     */
    scale: function (v)
    {
        return this.scaleXYZ(v.x, v.y, v.z);
    },

    /**
     * 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 {this} 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 {this} 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;

        return this.setValues(
            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
        );
    },

    /**
     * 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 {this} 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 this;
        }

        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];

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

        //  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
        return this.setValues(
            a00 * b00 + a10 * b01 + a20 * b02,
            a01 * b00 + a11 * b01 + a21 * b02,
            a02 * b00 + a12 * b01 + a22 * b02,
            a03 * b00 + a13 * b01 + a23 * b02,
            a00 * b10 + a10 * b11 + a20 * b12,
            a01 * b10 + a11 * b11 + a21 * b12,
            a02 * b10 + a12 * b11 + a22 * b12,
            a03 * b10 + a13 * b11 + a23 * b12,
            a00 * b20 + a10 * b21 + a20 * b22,
            a01 * b20 + a11 * b21 + a21 * b22,
            a02 * b20 + a12 * b21 + a22 * b22,
            a03 * b20 + a13 * b21 + a23 * b22,
            a30, a31, a32, a33
        );
    },

    /**
     * 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 {this} 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 {this} 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 {this} 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 {this} This Matrix4.
     */
    fromRotationTranslation: function (q, v)
    {
        //  Quaternion math
        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;

        return this.setValues(
            1 - (yy + zz),
            xy + wz,
            xz - wy,
            0,

            xy - wz,
            1 - (xx + zz),
            yz + wx,
            0,

            xz + wy,
            yz - wx,
            1 - (xx + yy),
            0,

            v.x,
            v.y,
            v.z,
            1
        );
    },

    /**
     * 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 {this} This Matrix4.
     */
    fromQuat: function (q)
    {
        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;

        return this.setValues(
            1 - (yy + zz),
            xy + wz,
            xz - wy,
            0,

            xy - wz,
            1 - (xx + zz),
            yz + wx,
            0,

            xz + wy,
            yz - wx,
            1 - (xx + yy),
            0,

            0,
            0,
            0,
            1
        );
    },

    /**
     * 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 {this} This Matrix4.
     */
    frustum: function (left, right, bottom, top, near, far)
    {
        var rl = 1 / (right - left);
        var tb = 1 / (top - bottom);
        var nf = 1 / (near - far);

        return this.setValues(
            (near * 2) * rl,
            0,
            0,
            0,

            0,
            (near * 2) * tb,
            0,
            0,

            (right + left) * rl,
            (top + bottom) * tb,
            (far + near) * nf,
            -1,

            0,
            0,
            (far * near * 2) * nf,
            0
        );
    },

    /**
     * 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 {this} This Matrix4.
     */
    perspective: function (fovy, aspect, near, far)
    {
        var f = 1.0 / Math.tan(fovy / 2);
        var nf = 1 / (near - far);

        return this.setValues(
            f / aspect,
            0,
            0,
            0,

            0,
            f,
            0,
            0,

            0,
            0,
            (far + near) * nf,
            -1,

            0,
            0,
            (2 * far * near) * nf,
            0
        );
    },

    /**
     * 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 {this} This Matrix4.
     */
    perspectiveLH: function (width, height, near, far)
    {
        return this.setValues(
            (2 * near) / width,
            0,
            0,
            0,

            0,
            (2 * near) / height,
            0,
            0,

            0,
            0,
            -far / (near - far),
            1,

            0,
            0,
            (near * far) / (near - far),
            0
        );
    },

    /**
     * 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 {this} This Matrix4.
     */
    ortho: function (left, right, bottom, top, near, far)
    {
        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;

        return this.setValues(
            -2 * lr,
            0,
            0,
            0,

            0,
            -2 * bt,
            0,
            0,

            0,
            0,
            2 * nf,
            0,

            (left + right) * lr,
            (top + bottom) * bt,
            (far + near) * nf,
            1
        );
    },

    /**
     * Generate a right-handed look-at matrix with the given eye position, target and up axis.
     *
     * @method Phaser.Math.Matrix4#lookAtRH
     * @since 3.50.0
     *
     * @param {Phaser.Math.Vector3} eye - Position of the viewer.
     * @param {Phaser.Math.Vector3} target - Point the viewer is looking at.
     * @param {Phaser.Math.Vector3} up - vec3 pointing up.
     *
     * @return {this} This Matrix4.
     */
    lookAtRH: function (eye, target, up)
    {
        var m = this.val;

        _z.subVectors(eye, target);

        if (_z.getLengthSquared() === 0)
        {
            // eye and target are in the same position
            _z.z = 1;
        }

        _z.normalize();
        _x.crossVectors(up, _z);

        if (_x.getLengthSquared() === 0)
        {
            // up and z are parallel

            if (Math.abs(up.z) === 1)
            {
                _z.x += 0.0001;
            }
            else
            {
                _z.z += 0.0001;
            }

            _z.normalize();
            _x.crossVectors(up, _z);
        }

        _x.normalize();
        _y.crossVectors(_z, _x);

        m[0] = _x.x;
        m[1] = _x.y;
        m[2] = _x.z;
        m[4] = _y.x;
        m[5] = _y.y;
        m[6] = _y.z;
        m[8] = _z.x;
        m[9] = _z.y;
        m[10] = _z.z;

        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 {this} This Matrix4.
     */
    lookAt: function (eye, center, up)
    {
        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;
        }

        return this.setValues(
            x0,
            y0,
            z0,
            0,

            x1,
            y1,
            z1,
            0,

            x2,
            y2,
            z2,
            0,

            -(x0 * eyex + x1 * eyey + x2 * eyez),
            -(y0 * eyex + y1 * eyey + y2 * eyez),
            -(z0 * eyex + z1 * eyey + z2 * eyez),
            1
        );
    },

    /**
     * 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 {this} 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 {this} 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)
        {
            this.multiplyLocal(viewMatrix);
        }

        if (projectionMatrix)
        {
            this.multiplyLocal(projectionMatrix);
        }

        return this;
    },

    /**
     * Multiplies this Matrix4 by the given `src` Matrix4 and stores the results in the `out` Matrix4.
     *
     * @method Phaser.Math.Matrix4#multiplyToMat4
     * @since 3.50.0
     *
     * @param {Phaser.Math.Matrix4} src - The Matrix4 to multiply with this one.
     * @param {Phaser.Math.Matrix4} out - The receiving Matrix.
     *
     * @return {Phaser.Math.Matrix4} This `out` Matrix4.
     */
    multiplyToMat4: function (src, out)
    {
        var a = this.val;
        var b = src.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 = b[0];
        var b01 = b[1];
        var b02 = b[2];
        var b03 = b[3];
        var b10 = b[4];
        var b11 = b[5];
        var b12 = b[6];
        var b13 = b[7];
        var b20 = b[8];
        var b21 = b[9];
        var b22 = b[10];
        var b23 = b[11];
        var b30 = b[12];
        var b31 = b[13];
        var b32 = b[14];
        var b33 = b[15];

        return out.setValues(
            b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30,
            b01 * a01 + b01 * a11 + b02 * a21 + b03 * a31,
            b02 * a02 + b01 * a12 + b02 * a22 + b03 * a32,
            b03 * a03 + b01 * a13 + b02 * a23 + b03 * a33,

            b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30,
            b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31,
            b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32,
            b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33,

            b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30,
            b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31,
            b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32,
            b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33,

            b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30,
            b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31,
            b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32,
            b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33
        );
    },

    /**
     * Takes the rotation and position vectors and builds this Matrix4 from them.
     *
     * @method Phaser.Math.Matrix4#fromRotationXYTranslation
     * @since 3.50.0
     *
     * @param {Phaser.Math.Vector3} rotation - The rotation vector.
     * @param {Phaser.Math.Vector3} position - The position vector.
     * @param {boolean} translateFirst - Should the operation translate then rotate (`true`), or rotate then translate? (`false`)
     *
     * @return {this} This Matrix4.
     */
    fromRotationXYTranslation: function (rotation, position, translateFirst)
    {
        var x = position.x;
        var y = position.y;
        var z = position.z;

        var sx = Math.sin(rotation.x);
        var cx = Math.cos(rotation.x);

        var sy = Math.sin(rotation.y);
        var cy = Math.cos(rotation.y);

        var a30 = x;
        var a31 = y;
        var a32 = z;

        //  Rotate X

        var b21 = -sx;

        //  Rotate Y

        var c01 = 0 - b21 * sy;

        var c02 = 0 - cx * sy;

        var c21 = b21 * cy;

        var c22 = cx * cy;

        //  Translate
        if (!translateFirst)
        {
            // a30 = cy * x + 0 * y + sy * z;
            a30 = cy * x + sy * z;
            a31 = c01 * x + cx * y + c21 * z;
            a32 = c02 * x + sx * y + c22 * z;
        }

        return this.setValues(
            cy,
            c01,
            c02,
            0,
            0,
            cx,
            sx,
            0,
            sy,
            c21,
            c22,
            0,
            a30,
            a31,
            a32,
            1
        );
    },

    /**
     * Returns the maximum axis scale from this Matrix4.
     *
     * @method Phaser.Math.Matrix4#getMaxScaleOnAxis
     * @since 3.50.0
     *
     * @return {number} The maximum axis scale.
     */
    getMaxScaleOnAxis: function ()
    {
        var m = this.val;

        var scaleXSq = m[0] * m[0] + m[1] * m[1] + m[2] * m[2];
        var scaleYSq = m[4] * m[4] + m[5] * m[5] + m[6] * m[6];
        var scaleZSq = m[8] * m[8] + m[9] * m[9] + m[10] * m[10];

        return Math.sqrt(Math.max(scaleXSq, scaleYSq, scaleZSq));
    }

});

/**
 * @ignore
 */
var _tempMat1 = new Matrix4();

/**
 * @ignore
 */
var _tempMat2 = new Matrix4();

/**
 * @ignore
 */
var _x = new Vector3();

/**
 * @ignore
 */
var _y = new Vector3();

/**
 * @ignore
 */
var _z = new Vector3();

module.exports = Matrix4;