# Source: src/geom/Line.js

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

    /**
    * Creates a new Line object with a start and an end point.
    *
    * @class Phaser.Line
    * @constructor
    * @param {number} [x1=0] - The x coordinate of the start of the line.
    * @param {number} [y1=0] - The y coordinate of the start of the line.
    * @param {number} [x2=0] - The x coordinate of the end of the line.
    * @param {number} [y2=0] - The y coordinate of the end of the line.
    */
    Phaser.Line = function (x1, y1, x2, y2) {

        x1 = x1 || 0;
        y1 = y1 || 0;
        x2 = x2 || 0;
        y2 = y2 || 0;

        /**
        * @property {Phaser.Point} start - The start point of the line.
        */
        this.start = new Phaser.Point(x1, y1);

        /**
        * @property {Phaser.Point} end - The end point of the line.
        */
        this.end = new Phaser.Point(x2, y2);

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

    };

    Phaser.Line.prototype = {

        /**
        * Sets the components of the Line to the specified values.
        *
        * @method Phaser.Line#setTo
        * @param {number} [x1=0] - The x coordinate of the start of the line.
        * @param {number} [y1=0] - The y coordinate of the start of the line.
        * @param {number} [x2=0] - The x coordinate of the end of the line.
        * @param {number} [y2=0] - The y coordinate of the end of the line.
        * @return {Phaser.Line} This line object
        */
        setTo: function (x1, y1, x2, y2) {

            this.start.setTo(x1, y1);
            this.end.setTo(x2, y2);

            return this;

        },

        /**
        * Sets the line to match the x/y coordinates of the two given sprites.
        * Can optionally be calculated from their center coordinates.
        *
        * @method Phaser.Line#fromSprite
        * @param {Phaser.Sprite} startSprite - The coordinates of this Sprite will be set to the Line.start point.
        * @param {Phaser.Sprite} endSprite - The coordinates of this Sprite will be set to the Line.start point.
        * @param {boolean} [useCenter=false] - If true it will use startSprite.center.x, if false startSprite.x. Note that Sprites don't have a center property by default, so only enable if you've over-ridden your Sprite with a custom class.
        * @return {Phaser.Line} This line object
        */
        fromSprite: function (startSprite, endSprite, useCenter) {

            if (useCenter === undefined) { useCenter = false; }

            if (useCenter)
            {
                return this.setTo(startSprite.center.x, startSprite.center.y, endSprite.center.x, endSprite.center.y);
            }

            return this.setTo(startSprite.x, startSprite.y, endSprite.x, endSprite.y);

        },

        /**
        * Sets this line to start at the given `x` and `y` coordinates and for the segment to extend at `angle` for the given `length`.
        *
        * @method Phaser.Line#fromAngle
        * @param {number} x - The x coordinate of the start of the line.
        * @param {number} y - The y coordinate of the start of the line.
        * @param {number} angle - The angle of the line in radians.
        * @param {number} length - The length of the line in pixels.
        * @return {Phaser.Line} This line object
        */
        fromAngle: function (x, y, angle, length) {

            this.start.setTo(x, y);
            this.end.setTo(x + (Math.cos(angle) * length), y + (Math.sin(angle) * length));

            return this;

        },

        /**
        * Rotates the line by the amount specified in `angle`.
        *
        * Rotation takes place from the center of the line.
        * If you wish to rotate around a different point see Line.rotateAround.
        *
        * If you wish to rotate the ends of the Line then see Line.start.rotate or Line.end.rotate.
        *
        * @method Phaser.Line#rotate
        * @param {number} angle - The angle in radians (unless asDegrees is true) to rotate the line by.
        * @param {boolean} [asDegrees=false] - Is the given angle in radians (false) or degrees (true)?
        * @return {Phaser.Line} This line object
        */
        rotate: function (angle, asDegrees) {

            var cx = (this.start.x + this.end.x) / 2;
            var cy = (this.start.y + this.end.y) / 2;

            this.start.rotate(cx, cy, angle, asDegrees);
            this.end.rotate(cx, cy, angle, asDegrees);

            return this;

        },

        /**
        * Rotates the line by the amount specified in `angle`.
        *
        * Rotation takes place around the coordinates given.
        *
        * @method Phaser.Line#rotateAround
        * @param {number} x - The x coordinate to offset the rotation from.
        * @param {number} y - The y coordinate to offset the rotation from.
        * @param {number} angle - The angle in radians (unless asDegrees is true) to rotate the line by.
        * @param {boolean} [asDegrees=false] - Is the given angle in radians (false) or degrees (true)?
        * @return {Phaser.Line} This line object
        */
        rotateAround: function (x, y, angle, asDegrees) {

            this.start.rotate(x, y, angle, asDegrees);
            this.end.rotate(x, y, angle, asDegrees);

            return this;

        },

        /**
        * Checks for intersection between this line and another Line.
        * If asSegment is true it will check for segment intersection. If asSegment is false it will check for line intersection.
        * Returns the intersection segment of AB and EF as a Point, or null if there is no intersection.
        *
        * @method Phaser.Line#intersects
        * @param {Phaser.Line} line - The line to check against this one.
        * @param {boolean} [asSegment=true] - If true it will check for segment intersection, otherwise full line intersection.
        * @param {Phaser.Point} [result] - A Point object to store the result in, if not given a new one will be created.
        * @return {Phaser.Point} The intersection segment of the two lines as a Point, or null if there is no intersection.
        */
        intersects: function (line, asSegment, result) {

            return Phaser.Line.intersectsPoints(this.start, this.end, line.start, line.end, asSegment, result);

        },

        /**
        * Returns the reflected angle between two lines.
        * This is the outgoing angle based on the angle of this line and the normalAngle of the given line.
        *
        * @method Phaser.Line#reflect
        * @param {Phaser.Line} line - The line to reflect off this line.
        * @return {number} The reflected angle in radians.
        */
        reflect: function (line) {

            return Phaser.Line.reflect(this, line);

        },

        /**
        * Returns a Point object where the x and y values correspond to the center (or midpoint) of the Line segment.
        *
        * @method Phaser.Line#midPoint
        * @param {Phaser.Point} [out] - A Phaser.Point object into which the result will be populated. If not given a new Point object is created.
        * @return {Phaser.Point} A Phaser.Point object with the x and y values set to the center of the line segment.
        */
        midPoint: function (out) {

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

            out.x = (this.start.x + this.end.x) / 2;
            out.y = (this.start.y + this.end.y) / 2;

            return out;

        },

        /**
        * Centers this Line on the given coordinates.
        *
        * The line is centered by positioning the start and end points so that the lines midpoint matches
        * the coordinates given.
        *
        * @method Phaser.Line#centerOn
        * @param {number} x - The x position to center the line on.
        * @param {number} y - The y position to center the line on.
        * @return {Phaser.Line} This line object
        */
        centerOn: function (x, y) {

            var cx = (this.start.x + this.end.x) / 2;
            var cy = (this.start.y + this.end.y) / 2;

            var tx = x - cx;
            var ty = y - cy;

            this.start.add(tx, ty);
            this.end.add(tx, ty);

        },

        /**
        * Tests if the given coordinates fall on this line. See pointOnSegment to test against just the line segment.
        *
        * @method Phaser.Line#pointOnLine
        * @param {number} x - The line to check against this one.
        * @param {number} y - The line to check against this one.
        * @return {boolean} True if the point is on the line, false if not.
        */
        pointOnLine: function (x, y) {

            return ((x - this.start.x) * (this.end.y - this.start.y) === (this.end.x - this.start.x) * (y - this.start.y));

        },

        /**
        * Tests if the given coordinates fall on this line and within the segment. See pointOnLine to test against just the line.
        *
        * @method Phaser.Line#pointOnSegment
        * @param {number} x - The line to check against this one.
        * @param {number} y - The line to check against this one.
        * @return {boolean} True if the point is on the line and segment, false if not.
        */
        pointOnSegment: function (x, y) {

            var xMin = Math.min(this.start.x, this.end.x);
            var xMax = Math.max(this.start.x, this.end.x);
            var yMin = Math.min(this.start.y, this.end.y);
            var yMax = Math.max(this.start.y, this.end.y);

            return (this.pointOnLine(x, y) && (x >= xMin && x <= xMax) && (y >= yMin && y <= yMax));

        },

        /**
        * Picks a random point from anywhere on the Line segment and returns it.
        *
        * @method Phaser.Line#random
        * @param {Phaser.Point|object} [out] - A Phaser.Point, or any object with public x/y properties, that the values will be set in.
        *     If no object is provided a new Phaser.Point object will be created. In high performance areas avoid this by re-using an object.
        * @return {Phaser.Point} An object containing the random point in its `x` and `y` properties.
        */
        random: function (out) {

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

            var t = Math.random();

            out.x = this.start.x + t * (this.end.x - this.start.x);
            out.y = this.start.y + t * (this.end.y - this.start.y);

            return out;

        },

        /**
        * Using Bresenham's line algorithm this will return an array of all coordinates on this line.
        * The start and end points are rounded before this runs as the algorithm works on integers.
        *
        * @method Phaser.Line#coordinatesOnLine
        * @param {number} [stepRate=1] - How many steps will we return? 1 = every coordinate on the line, 2 = every other coordinate, etc.
        * @param {array} [results] - The array to store the results in. If not provided a new one will be generated.
        * @return {array} An array of coordinates.
        */
        coordinatesOnLine: function (stepRate, results) {

            if (stepRate === undefined) { stepRate = 1; }
            if (results === undefined) { results = []; }

            var x1 = Math.round(this.start.x);
            var y1 = Math.round(this.start.y);
            var x2 = Math.round(this.end.x);
            var y2 = Math.round(this.end.y);

            var dx = Math.abs(x2 - x1);
            var dy = Math.abs(y2 - y1);
            var sx = (x1 < x2) ? 1 : -1;
            var sy = (y1 < y2) ? 1 : -1;
            var err = dx - dy;

            results.push([x1, y1]);

            var i = 1;

            while (!((x1 === x2) && (y1 === y2)))
            {
                var e2 = err << 1;

                if (e2 > -dy)
                {
                    err -= dy;
                    x1 += sx;
                }

                if (e2 < dx)
                {
                    err += dx;
                    y1 += sy;
                }

                if (i % stepRate === 0)
                {
                    results.push([x1, y1]);
                }

                i++;

            }

            return results;

        },

        /**
         * Returns a new Line object with the same values for the start and end properties as this Line object.
         * @method Phaser.Line#clone
         * @param {Phaser.Line} output - Optional Line object. If given the values will be set into the object, otherwise a brand new Line object will be created and returned.
         * @return {Phaser.Line} The cloned Line object.
         */
        clone: function (output) {

            if (output === undefined || output === null)
            {
                output = new Phaser.Line(this.start.x, this.start.y, this.end.x, this.end.y);
            }
            else
            {
                output.setTo(this.start.x, this.start.y, this.end.x, this.end.y);
            }

            return output;

        }

    };

    /**
    * @name Phaser.Line#length
    * @property {number} length - Gets the length of the line segment.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "length", {

        get: function () {
            return Math.sqrt((this.end.x - this.start.x) * (this.end.x - this.start.x) + (this.end.y - this.start.y) * (this.end.y - this.start.y));
        }

    });

    /**
    * @name Phaser.Line#angle
    * @property {number} angle - Gets the angle of the line in radians.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "angle", {

        get: function () {
            return Math.atan2(this.end.y - this.start.y, this.end.x - this.start.x);
        }

    });

    /**
    * @name Phaser.Line#slope
    * @property {number} slope - Gets the slope of the line (y/x).
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "slope", {

        get: function () {
            return (this.end.y - this.start.y) / (this.end.x - this.start.x);
        }

    });

    /**
    * @name Phaser.Line#perpSlope
    * @property {number} perpSlope - Gets the perpendicular slope of the line (x/y).
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "perpSlope", {

        get: function () {
            return -((this.end.x - this.start.x) / (this.end.y - this.start.y));
        }

    });

    /**
    * @name Phaser.Line#x
    * @property {number} x - Gets the x coordinate of the top left of the bounds around this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "x", {

        get: function () {
            return Math.min(this.start.x, this.end.x);
        }

    });

    /**
    * @name Phaser.Line#y
    * @property {number} y - Gets the y coordinate of the top left of the bounds around this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "y", {

        get: function () {
            return Math.min(this.start.y, this.end.y);
        }

    });

    /**
    * @name Phaser.Line#left
    * @property {number} left - Gets the left-most point of this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "left", {

        get: function () {
            return Math.min(this.start.x, this.end.x);
        }

    });

    /**
    * @name Phaser.Line#right
    * @property {number} right - Gets the right-most point of this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "right", {

        get: function () {
            return Math.max(this.start.x, this.end.x);
        }

    });

    /**
    * @name Phaser.Line#top
    * @property {number} top - Gets the top-most point of this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "top", {

        get: function () {
            return Math.min(this.start.y, this.end.y);
        }

    });

    /**
    * @name Phaser.Line#bottom
    * @property {number} bottom - Gets the bottom-most point of this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "bottom", {

        get: function () {
            return Math.max(this.start.y, this.end.y);
        }

    });

    /**
    * @name Phaser.Line#width
    * @property {number} width - Gets the width of this bounds of this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "width", {

        get: function () {
            return Math.abs(this.start.x - this.end.x);
        }

    });

    /**
    * @name Phaser.Line#height
    * @property {number} height - Gets the height of this bounds of this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "height", {

        get: function () {
            return Math.abs(this.start.y - this.end.y);
        }

    });

    /**
    * @name Phaser.Line#normalX
    * @property {number} normalX - Gets the x component of the left-hand normal of this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "normalX", {

        get: function () {
            return Math.cos(this.angle - 1.5707963267948966);
        }

    });

    /**
    * @name Phaser.Line#normalY
    * @property {number} normalY - Gets the y component of the left-hand normal of this line.
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "normalY", {

        get: function () {
            return Math.sin(this.angle - 1.5707963267948966);
        }

    });

    /**
    * @name Phaser.Line#normalAngle
    * @property {number} normalAngle - Gets the angle in radians of the normal of this line (line.angle - 90 degrees.)
    * @readonly
    */
    Object.defineProperty(Phaser.Line.prototype, "normalAngle", {

        get: function () {
            return Phaser.Math.wrap(this.angle - 1.5707963267948966, -Math.PI, Math.PI);
        }

    });

    /**
    * Checks for intersection between two lines as defined by the given start and end points.
    * If asSegment is true it will check for line segment intersection. If asSegment is false it will check for line intersection.
    * Returns the intersection segment of AB and EF as a Point, or null if there is no intersection.
    * Adapted from code by Keith Hair
    *
    * @method Phaser.Line.intersectsPoints
    * @param {Phaser.Point} a - The start of the first Line to be checked.
    * @param {Phaser.Point} b - The end of the first line to be checked.
    * @param {Phaser.Point} e - The start of the second Line to be checked.
    * @param {Phaser.Point} f - The end of the second line to be checked.
    * @param {boolean} [asSegment=true] - If true it will check for segment intersection, otherwise full line intersection.
    * @param {Phaser.Point|object} [result] - A Point object to store the result in, if not given a new one will be created.
    * @return {Phaser.Point} The intersection segment of the two lines as a Point, or null if there is no intersection.
    */
    Phaser.Line.intersectsPoints = function (a, b, e, f, asSegment, result) {

        if (asSegment === undefined) { asSegment = true; }
        if (result === undefined) { result = new Phaser.Point(); }

        var a1 = b.y - a.y;
        var a2 = f.y - e.y;
        var b1 = a.x - b.x;
        var b2 = e.x - f.x;
        var c1 = (b.x * a.y) - (a.x * b.y);
        var c2 = (f.x * e.y) - (e.x * f.y);
        var denom = (a1 * b2) - (a2 * b1);

        if (denom === 0)
        {
            return null;
        }

        result.x = ((b1 * c2) - (b2 * c1)) / denom;
        result.y = ((a2 * c1) - (a1 * c2)) / denom;

        if (asSegment)
        {
            var uc = ((f.y - e.y) * (b.x - a.x) - (f.x - e.x) * (b.y - a.y));
            var ua = (((f.x - e.x) * (a.y - e.y)) - (f.y - e.y) * (a.x - e.x)) / uc;
            var ub = (((b.x - a.x) * (a.y - e.y)) - ((b.y - a.y) * (a.x - e.x))) / uc;

            if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1)
            {
                return result;
            }
            else
            {
                return null;
            }
        }

        return result;

    };

    /**
    * Checks for intersection between two lines.
    * If asSegment is true it will check for segment intersection.
    * If asSegment is false it will check for line intersection.
    * Returns the intersection segment of AB and EF as a Point, or null if there is no intersection.
    * Adapted from code by Keith Hair
    *
    * @method Phaser.Line.intersects
    * @param {Phaser.Line} a - The first Line to be checked.
    * @param {Phaser.Line} b - The second Line to be checked.
    * @param {boolean} [asSegment=true] - If true it will check for segment intersection, otherwise full line intersection.
    * @param {Phaser.Point} [result] - A Point object to store the result in, if not given a new one will be created.
    * @return {Phaser.Point} The intersection segment of the two lines as a Point, or null if there is no intersection.
    */
    Phaser.Line.intersects = function (a, b, asSegment, result) {

        return Phaser.Line.intersectsPoints(a.start, a.end, b.start, b.end, asSegment, result);

    };

    /**
    * Checks for intersection between the Line and a Rectangle shape, or a rectangle-like
    * object, with public `x`, `y`, `right` and `bottom` properties, such as a Sprite or Body.
    *
    * An intersection is considered valid if:
    *
    * The line starts within, or ends within, the Rectangle.
    * The line segment intersects one of the 4 rectangle edges.
    *
    * The for the purposes of this function rectangles are considered 'solid'.
    *
    * @method Phaser.Line.intersectsRectangle
    * @param {Phaser.Line} line - The line to check for intersection with.
    * @param {Phaser.Rectangle|object} rect - The rectangle, or rectangle-like object, to check for intersection with.
    * @return {boolean} True if the line intersects with the rectangle edges, or starts or ends within the rectangle.
    */
    Phaser.Line.intersectsRectangle = function (line, rect) {

        //  Quick bail out of the Line and Rect bounds don't intersect
        if (!Phaser.Rectangle.intersects(line, rect))
        {
            return false;
        }

        var x1 = line.start.x;
        var y1 = line.start.y;

        var x2 = line.end.x;
        var y2 = line.end.y;

        var bx1 = rect.x;
        var by1 = rect.y;
        var bx2 = rect.right;
        var by2 = rect.bottom;

        var t = 0;

        //  If the start or end of the line is inside the rect then we assume
        //  collision, as rects are solid for our use-case.

        if ((x1 >= bx1 && x1 <= bx2 && y1 >= by1 && y1 <= by2) ||
            (x2 >= bx1 && x2 <= bx2 && y2 >= by1 && y2 <= by2))
        {
            return true;
        }

        if (x1 < bx1 && x2 >= bx1)
        {
            //  Left edge
            t = y1 + (y2 - y1) * (bx1 - x1) / (x2 - x1);

            if (t > by1 && t <= by2)
            {
                return true;
            }
        }
        else if (x1 > bx2 && x2 <= bx2)
        {
            //  Right edge
            t = y1 + (y2 - y1) * (bx2 - x1) / (x2 - x1);

            if (t >= by1 && t <= by2)
            {
                return true;
            }
        }

        if (y1 < by1 && y2 >= by1)
        {
            //  Top edge
            t = x1 + (x2 - x1) * (by1 - y1) / (y2 - y1);

            if (t >= bx1 && t <= bx2)
            {
                return true;
            }
        }
        else if (y1 > by2 && y2 <= by2)
        {
            //  Bottom edge
            t = x1 + (x2 - x1) * (by2 - y1) / (y2 - y1);

            if (t >= bx1 && t <= bx2)
            {
                return true;
            }
        }

        return false;

    };

    /**
    * Returns the reflected angle between two lines.
    * This is the outgoing angle based on the angle of Line 1 and the normalAngle of Line 2.
    *
    * @method Phaser.Line.reflect
    * @param {Phaser.Line} a - The base line.
    * @param {Phaser.Line} b - The line to be reflected from the base line.
    * @return {number} The reflected angle in radians.
    */
    Phaser.Line.reflect = function (a, b) {

        return 2 * b.normalAngle - 3.141592653589793 - a.angle;

    };