Matrix3.js

/**
 * @author       Richard Davey <rich@phaser.io>
 * @copyright    2013-2024 Phaser Studio Inc.
 * @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');

/**
 * @classdesc
 * A three-dimensional matrix.
 *
 * Defaults to the identity matrix when instantiated.
 *
 * @class Matrix3
 * @memberof Phaser.Math
 * @constructor
 * @since 3.0.0
 *
 * @param {Phaser.Math.Matrix3} [m] - Optional Matrix3 to copy values from.
 */
var Matrix3 = new Class({

    initialize:

    function Matrix3 (m)
    {
        /**
         * The matrix values.
         *
         * @name Phaser.Math.Matrix3#val
         * @type {Float32Array}
         * @since 3.0.0
         */
        this.val = new Float32Array(9);

        if (m)
        {
            //  Assume Matrix3 with val:
            this.copy(m);
        }
        else
        {
            //  Default to identity
            this.identity();
        }
    },

    /**
     * Make a clone of this Matrix3.
     *
     * @method Phaser.Math.Matrix3#clone
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix3} A clone of this Matrix3.
     */
    clone: function ()
    {
        return new Matrix3(this);
    },

    /**
     * This method is an alias for `Matrix3.copy`.
     *
     * @method Phaser.Math.Matrix3#set
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix3} src - The Matrix to set the values of this Matrix's from.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    set: function (src)
    {
        return this.copy(src);
    },

    /**
     * Copy the values of a given Matrix into this Matrix.
     *
     * @method Phaser.Math.Matrix3#copy
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix3} src - The Matrix to copy the values from.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    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];

        return this;
    },

    /**
     * Copy the values of a given Matrix4 into this Matrix3.
     *
     * @method Phaser.Math.Matrix3#fromMat4
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} m - The Matrix4 to copy the values from.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    fromMat4: function (m)
    {
        var a = m.val;
        var out = this.val;

        out[0] = a[0];
        out[1] = a[1];
        out[2] = a[2];
        out[3] = a[4];
        out[4] = a[5];
        out[5] = a[6];
        out[6] = a[8];
        out[7] = a[9];
        out[8] = a[10];

        return this;
    },

    /**
     * Set the values of this Matrix from the given array.
     *
     * @method Phaser.Math.Matrix3#fromArray
     * @since 3.0.0
     *
     * @param {array} a - The array to copy the values from.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    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];

        return this;
    },

    /**
     * Reset this Matrix to an identity (default) matrix.
     *
     * @method Phaser.Math.Matrix3#identity
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    identity: function ()
    {
        var out = this.val;

        out[0] = 1;
        out[1] = 0;
        out[2] = 0;
        out[3] = 0;
        out[4] = 1;
        out[5] = 0;
        out[6] = 0;
        out[7] = 0;
        out[8] = 1;

        return this;
    },

    /**
     * Transpose this Matrix.
     *
     * @method Phaser.Math.Matrix3#transpose
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    transpose: function ()
    {
        var a = this.val;
        var a01 = a[1];
        var a02 = a[2];
        var a12 = a[5];

        a[1] = a[3];
        a[2] = a[6];
        a[3] = a01;
        a[5] = a[7];
        a[6] = a02;
        a[7] = a12;

        return this;
    },

    /**
     * Invert this Matrix.
     *
     * @method Phaser.Math.Matrix3#invert
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    invert: function ()
    {
        var a = this.val;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a10 = a[3];
        var a11 = a[4];
        var a12 = a[5];
        var a20 = a[6];
        var a21 = a[7];
        var a22 = a[8];

        var b01 = a22 * a11 - a12 * a21;
        var b11 = -a22 * a10 + a12 * a20;
        var b21 = a21 * a10 - a11 * a20;

        // Calculate the determinant
        var det = a00 * b01 + a01 * b11 + a02 * b21;

        if (!det)
        {
            return null;
        }

        det = 1 / det;

        a[0] = b01 * det;
        a[1] = (-a22 * a01 + a02 * a21) * det;
        a[2] = (a12 * a01 - a02 * a11) * det;
        a[3] = b11 * det;
        a[4] = (a22 * a00 - a02 * a20) * det;
        a[5] = (-a12 * a00 + a02 * a10) * det;
        a[6] = b21 * det;
        a[7] = (-a21 * a00 + a01 * a20) * det;
        a[8] = (a11 * a00 - a01 * a10) * det;

        return this;
    },

    /**
     * Calculate the adjoint, or adjugate, of this Matrix.
     *
     * @method Phaser.Math.Matrix3#adjoint
     * @since 3.0.0
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    adjoint: function ()
    {
        var a = this.val;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a10 = a[3];
        var a11 = a[4];
        var a12 = a[5];
        var a20 = a[6];
        var a21 = a[7];
        var a22 = a[8];

        a[0] = (a11 * a22 - a12 * a21);
        a[1] = (a02 * a21 - a01 * a22);
        a[2] = (a01 * a12 - a02 * a11);
        a[3] = (a12 * a20 - a10 * a22);
        a[4] = (a00 * a22 - a02 * a20);
        a[5] = (a02 * a10 - a00 * a12);
        a[6] = (a10 * a21 - a11 * a20);
        a[7] = (a01 * a20 - a00 * a21);
        a[8] = (a00 * a11 - a01 * a10);

        return this;
    },

    /**
     * Calculate the determinant of this Matrix.
     *
     * @method Phaser.Math.Matrix3#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 a10 = a[3];
        var a11 = a[4];
        var a12 = a[5];
        var a20 = a[6];
        var a21 = a[7];
        var a22 = a[8];

        return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
    },

    /**
     * Multiply this Matrix by the given Matrix.
     *
     * @method Phaser.Math.Matrix3#multiply
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix3} src - The Matrix to multiply this Matrix by.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    multiply: function (src)
    {
        var a = this.val;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a10 = a[3];
        var a11 = a[4];
        var a12 = a[5];
        var a20 = a[6];
        var a21 = a[7];
        var a22 = a[8];

        var b = src.val;

        var b00 = b[0];
        var b01 = b[1];
        var b02 = b[2];
        var b10 = b[3];
        var b11 = b[4];
        var b12 = b[5];
        var b20 = b[6];
        var b21 = b[7];
        var b22 = b[8];

        a[0] = b00 * a00 + b01 * a10 + b02 * a20;
        a[1] = b00 * a01 + b01 * a11 + b02 * a21;
        a[2] = b00 * a02 + b01 * a12 + b02 * a22;

        a[3] = b10 * a00 + b11 * a10 + b12 * a20;
        a[4] = b10 * a01 + b11 * a11 + b12 * a21;
        a[5] = b10 * a02 + b11 * a12 + b12 * a22;

        a[6] = b20 * a00 + b21 * a10 + b22 * a20;
        a[7] = b20 * a01 + b21 * a11 + b22 * a21;
        a[8] = b20 * a02 + b21 * a12 + b22 * a22;

        return this;
    },

    /**
     * Translate this Matrix using the given Vector.
     *
     * @method Phaser.Math.Matrix3#translate
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3|Phaser.Math.Vector4)} v - The Vector to translate this Matrix with.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    translate: function (v)
    {
        var a = this.val;
        var x = v.x;
        var y = v.y;

        a[6] = x * a[0] + y * a[3] + a[6];
        a[7] = x * a[1] + y * a[4] + a[7];
        a[8] = x * a[2] + y * a[5] + a[8];

        return this;
    },

    /**
     * Apply a rotation transformation to this Matrix.
     *
     * @method Phaser.Math.Matrix3#rotate
     * @since 3.0.0
     *
     * @param {number} rad - The angle in radians to rotate by.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    rotate: function (rad)
    {
        var a = this.val;

        var a00 = a[0];
        var a01 = a[1];
        var a02 = a[2];
        var a10 = a[3];
        var a11 = a[4];
        var a12 = a[5];

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

        a[0] = c * a00 + s * a10;
        a[1] = c * a01 + s * a11;
        a[2] = c * a02 + s * a12;

        a[3] = c * a10 - s * a00;
        a[4] = c * a11 - s * a01;
        a[5] = c * a12 - s * a02;

        return this;
    },

    /**
     * Apply a scale transformation to this Matrix.
     *
     * Uses the `x` and `y` components of the given Vector to scale the Matrix.
     *
     * @method Phaser.Math.Matrix3#scale
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3|Phaser.Math.Vector4)} v - The Vector to scale this Matrix with.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    scale: function (v)
    {
        var a = this.val;
        var x = v.x;
        var y = v.y;

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

        a[3] = y * a[3];
        a[4] = y * a[4];
        a[5] = y * a[5];

        return this;
    },

    /**
     * Set the values of this Matrix from the given Quaternion.
     *
     * @method Phaser.Math.Matrix3#fromQuat
     * @since 3.0.0
     *
     * @param {Phaser.Math.Quaternion} q - The Quaternion to set the values of this Matrix from.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    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;

        var out = this.val;

        out[0] = 1 - (yy + zz);
        out[3] = xy + wz;
        out[6] = xz - wy;

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

        out[2] = xz + wy;
        out[5] = yz - wx;
        out[8] = 1 - (xx + yy);

        return this;
    },

    /**
     * Set the values of this Matrix3 to be normalized from the given Matrix4.
     *
     * @method Phaser.Math.Matrix3#normalFromMat4
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} m - The Matrix4 to normalize the values from.
     *
     * @return {Phaser.Math.Matrix3} This Matrix3.
     */
    normalFromMat4: function (m)
    {
        var a = m.val;
        var out = 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;

        out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
        out[1] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
        out[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det;

        out[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
        out[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
        out[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det;

        out[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
        out[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
        out[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det;

        return this;
    }

});

module.exports = Matrix3;