# Source: src/geom/Matrix.js

    /**
    * @author       Mat Groves http://matgroves.com/ @Doormat23
    * @author       Richard Davey <rich@photonstorm.com>
    * @copyright    2016 Photon Storm Ltd.
    * @license      {@link https://github.com/photonstorm/phaser/blob/master/license.txt|MIT License}
    */

    /**
    * The Matrix is a 3x3 matrix mostly used for display transforms within the renderer.
    *
    * It is represented like so:
    *
    * | a | b | tx |
    * | c | d | ty |
    * | 0 | 0 | 1 |
    *
    * @class Phaser.Matrix
    * @constructor
    * @param {number} [a=1] - Horizontal scaling
    * @param {number} [b=0] - Horizontal skewing
    * @param {number} [c=0] - Vertical skewing
    * @param {number} [d=1] - Vertical scaling
    * @param {number} [tx=0] - Horizontal translation
    * @param {number} [ty=0] - Vertical translation
    */
    Phaser.Matrix = function (a, b, c, d, tx, ty) {

        if (a === undefined || a === null) { a = 1; }
        if (b === undefined || b === null) { b = 0; }
        if (c === undefined || c === null) { c = 0; }
        if (d === undefined || d === null) { d = 1; }
        if (tx === undefined || tx === null) { tx = 0; }
        if (ty === undefined || ty === null) { ty = 0; }

        /**
        * @property {number} a
        * @default 1
        */
        this.a = a;

        /**
        * @property {number} b
        * @default 0
        */
        this.b = b;

        /**
        * @property {number} c
        * @default 0
        */
        this.c = c;

        /**
        * @property {number} d
        * @default 1
        */
        this.d = d;

        /**
        * @property {number} tx
        * @default 0
        */
        this.tx = tx;

        /**
        * @property {number} ty
        * @default 0
        */
        this.ty = ty;

        /**
        * @property {number} type - The const type of this object.
        * @readonly
        */
        this.type = Phaser.MATRIX;

    };

    Phaser.Matrix.prototype = {

        /**
        * Sets the values of this Matrix to the values in the given array.
        *
        * The Array elements should be set as follows:
        *
        * a = array[0]
        * b = array[1]
        * c = array[3]
        * d = array[4]
        * tx = array[2]
        * ty = array[5]
        *
        * @method Phaser.Matrix#fromArray
        * @param {Array} array - The array to copy from.
        * @return {Phaser.Matrix} This Matrix object.
        */
        fromArray: function (array) {

            return this.setTo(array[0], array[1], array[3], array[4], array[2], array[5]);

        },

        /**
        * Sets the values of this Matrix to the given values.
        *
        * @method Phaser.Matrix#setTo
        * @param {number} a - Horizontal scaling
        * @param {number} b - Horizontal skewing
        * @param {number} c - Vertical skewing
        * @param {number} d - Vertical scaling
        * @param {number} tx - Horizontal translation
        * @param {number} ty - Vertical translation
        * @return {Phaser.Matrix} This Matrix object.
        */
        setTo: function (a, b, c, d, tx, ty) {

            this.a = a;
            this.b = b;
            this.c = c;
            this.d = d;
            this.tx = tx;
            this.ty = ty;

            return this;

        },

        /**
         * Creates a new Matrix object based on the values of this Matrix.
         * If you provide the output parameter the values of this Matrix will be copied over to it.
         * If the output parameter is blank a new Matrix object will be created.
         *
         * @method Phaser.Matrix#clone
         * @param {Phaser.Matrix} [output] - If provided the values of this Matrix will be copied to it, otherwise a new Matrix object is created.
         * @return {Phaser.Matrix} A clone of this Matrix.
         */
        clone: function (output) {

            if (output === undefined || output === null)
            {
                output = new Phaser.Matrix(this.a, this.b, this.c, this.d, this.tx, this.ty);
            }
            else
            {
                output.a = this.a;
                output.b = this.b;
                output.c = this.c;
                output.d = this.d;
                output.tx = this.tx;
                output.ty = this.ty;
            }

            return output;

        },

        /**
        * Copies the properties from this Matrix to the given Matrix.
        *
        * @method Phaser.Matrix#copyTo
        * @param {Phaser.Matrix} matrix - The Matrix to copy from.
        * @return {Phaser.Matrix} The destination Matrix object.
        */
        copyTo: function (matrix) {

            matrix.copyFrom(this);

            return matrix;

        },

        /**
        * Copies the properties from the given Matrix into this Matrix.
        *
        * @method Phaser.Matrix#copyFrom
        * @param {Phaser.Matrix} matrix - The Matrix to copy from.
        * @return {Phaser.Matrix} This Matrix object.
        */
        copyFrom: function (matrix) {

            this.a = matrix.a;
            this.b = matrix.b;
            this.c = matrix.c;
            this.d = matrix.d;
            this.tx = matrix.tx;
            this.ty = matrix.ty;

            return this;

        },

        /**
        * Creates a Float32 Array with values populated from this Matrix object.
        *
        * @method Phaser.Matrix#toArray
        * @param {boolean} [transpose=false] - Whether the values in the array are transposed or not.
        * @param {PIXI.Float32Array} [array] - If provided the values will be set into this array, otherwise a new Float32Array is created.
        * @return {PIXI.Float32Array} The newly created array which contains the matrix.
        */
        toArray: function (transpose, array) {

            if (array === undefined) { array = new PIXI.Float32Array(9); }

            if (transpose)
            {
                array[0] = this.a;
                array[1] = this.b;
                array[2] = 0;
                array[3] = this.c;
                array[4] = this.d;
                array[5] = 0;
                array[6] = this.tx;
                array[7] = this.ty;
                array[8] = 1;
            }
            else
            {
                array[0] = this.a;
                array[1] = this.c;
                array[2] = this.tx;
                array[3] = this.b;
                array[4] = this.d;
                array[5] = this.ty;
                array[6] = 0;
                array[7] = 0;
                array[8] = 1;
            }

            return array;

        },

        /**
        * Get a new position with the current transformation applied.
        *
        * Can be used to go from a childs coordinate space to the world coordinate space (e.g. rendering)
        *
        * @method Phaser.Matrix#apply
        * @param {Phaser.Point} pos - The origin Point.
        * @param {Phaser.Point} [newPos] - The point that the new position is assigned to. This can be same as input point.
        * @return {Phaser.Point} The new point, transformed through this matrix.
        */
        apply: function (pos, newPos) {

            if (newPos === undefined) { newPos = new Phaser.Point(); }

            newPos.x = this.a * pos.x + this.c * pos.y + this.tx;
            newPos.y = this.b * pos.x + this.d * pos.y + this.ty;

            return newPos;

        },

        /**
        * Get a new position with the inverse of the current transformation applied.
        *
        * Can be used to go from the world coordinate space to a childs coordinate space. (e.g. input)
        *
        * @method Phaser.Matrix#applyInverse
        * @param {Phaser.Point} pos - The origin Point.
        * @param {Phaser.Point} [newPos] - The point that the new position is assigned to. This can be same as input point.
        * @return {Phaser.Point} The new point, inverse transformed through this matrix.
        */
        applyInverse: function (pos, newPos) {

            if (newPos === undefined) { newPos = new Phaser.Point(); }

            var id = 1 / (this.a * this.d + this.c * -this.b);
            var x = pos.x;
            var y = pos.y;

            newPos.x = this.d * id * x + -this.c * id * y + (this.ty * this.c - this.tx * this.d) * id;
            newPos.y = this.a * id * y + -this.b * id * x + (-this.ty * this.a + this.tx * this.b) * id;

            return newPos;

        },

        /**
        * Translates the matrix on the x and y.
        * This is the same as Matrix.tx += x.
        *
        * @method Phaser.Matrix#translate
        * @param {number} x - The x value to translate on.
        * @param {number} y - The y value to translate on.
        * @return {Phaser.Matrix} This Matrix object.
        */
        translate: function (x, y) {

            this.tx += x;
            this.ty += y;

            return this;

        },

        /**
        * Applies a scale transformation to this matrix.
        *
        * @method Phaser.Matrix#scale
        * @param {number} x - The amount to scale horizontally.
        * @param {number} y - The amount to scale vertically.
        * @return {Phaser.Matrix} This Matrix object.
        */
        scale: function (x, y) {

            this.a *= x;
            this.d *= y;
            this.c *= x;
            this.b *= y;
            this.tx *= x;
            this.ty *= y;

            return this;

        },

        /**
        * Applies a rotation transformation to this matrix.
        *
        * @method Phaser.Matrix#rotate
        * @param {number} angle - The angle to rotate by, given in radians.
        * @return {Phaser.Matrix} This Matrix object.
        */
        rotate: function (angle) {

            var cos = Math.cos(angle);
            var sin = Math.sin(angle);

            var a1 = this.a;
            var c1 = this.c;
            var tx1 = this.tx;

            this.a = a1 * cos-this.b * sin;
            this.b = a1 * sin+this.b * cos;
            this.c = c1 * cos-this.d * sin;
            this.d = c1 * sin+this.d * cos;
            this.tx = tx1 * cos - this.ty * sin;
            this.ty = tx1 * sin + this.ty * cos;

            return this;

        },

        /**
        * Appends the given Matrix to this Matrix.
        *
        * @method Phaser.Matrix#append
        * @param {Phaser.Matrix} matrix - The matrix to append to this one.
        * @return {Phaser.Matrix} This Matrix object.
        */
        append: function (matrix) {

            var a1 = this.a;
            var b1 = this.b;
            var c1 = this.c;
            var d1 = this.d;

            this.a  = matrix.a * a1 + matrix.b * c1;
            this.b  = matrix.a * b1 + matrix.b * d1;
            this.c  = matrix.c * a1 + matrix.d * c1;
            this.d  = matrix.c * b1 + matrix.d * d1;

            this.tx = matrix.tx * a1 + matrix.ty * c1 + this.tx;
            this.ty = matrix.tx * b1 + matrix.ty * d1 + this.ty;

            return this;

        },

        /**
        * Resets this Matrix to an identity (default) matrix.
        *
        * @method Phaser.Matrix#identity
        * @return {Phaser.Matrix} This Matrix object.
        */
        identity: function () {

            return this.setTo(1, 0, 0, 1, 0, 0);

        }

    };

    Phaser.identityMatrix = new Phaser.Matrix();

    //  Because PIXI uses its own type, we'll replace it with ours to avoid duplicating code or confusion.
    PIXI.Matrix = Phaser.Matrix;
    PIXI.identityMatrix = Phaser.identityMatrix;