phaser/src/physics/arcade/ArcadePhysics.js

/**
* @author       Richard Davey <rich@photonstorm.com>
* @copyright    2013 Photon Storm Ltd.
* @license      {@link https://github.com/photonstorm/phaser/blob/master/license.txt|MIT License}
*/

/**
* @class Phaser.Physics
*/
Phaser.Physics = {};

/**
* Arcade Physics constructor.
*
* @class Phaser.Physics.Arcade
* @classdesc Arcade Physics Constructor
* @constructor
* @param {Phaser.Game} game reference to the current game instance.
*/
Phaser.Physics.Arcade = function (game) {
    
    /**
    * @property {Phaser.Game} game - Local reference to game.
    */
    this.game = game;

    /**
    * @property {Phaser.Point} gravity - The World gravity setting. Defaults to x: 0, y: 0, or no gravity.
    */
    this.gravity = new Phaser.Point;

    /**
    * @property {Phaser.Rectangle} bounds - The bounds inside of which the physics world exists. Defaults to match the world bounds.
    */
    this.bounds = new Phaser.Rectangle(0, 0, game.world.width, game.world.height);

    /**
    * @property {number} maxObjects - Used by the QuadTree to set the maximum number of objects per quad.
    */
    this.maxObjects = 10;

    /**
    * @property {number} maxLevels - Used by the QuadTree to set the maximum number of iteration levels.
    */
    this.maxLevels = 4;

    /**
    * @property {number} OVERLAP_BIAS - A value added to the delta values during collision checks.
    */
    this.OVERLAP_BIAS = 4;

    /**
    * @property {Phaser.QuadTree} quadTree - The world QuadTree.
    */
    this.quadTree = new Phaser.QuadTree(this, this.game.world.bounds.x, this.game.world.bounds.y, this.game.world.bounds.width, this.game.world.bounds.height, this.maxObjects, this.maxLevels);

    /**
    * @property {number} quadTreeID - The QuadTree ID.
    */
    this.quadTreeID = 0;

    //  Avoid gc spikes by caching these values for re-use

    /**
    * @property {Phaser.Rectangle} _bounds1 - Internal cache var.
    * @private
    */
    this._bounds1 = new Phaser.Rectangle;

    /**
    * @property {Phaser.Rectangle} _bounds2 - Internal cache var.
    * @private
    */
    this._bounds2 = new Phaser.Rectangle;

    /**
    * @property {number} _overlap - Internal cache var.
    * @private
    */
    this._overlap = 0;

    /**
    * @property {number} _maxOverlap - Internal cache var.
    * @private
    */
    this._maxOverlap = 0;

    /**
    * @property {number} _velocity1 - Internal cache var.
    * @private
    */
    this._velocity1 = 0;

    /**
    * @property {number} _velocity2 - Internal cache var.
    * @private
    */
    this._velocity2 = 0;

    /**
    * @property {number} _newVelocity1 - Internal cache var.
    * @private
    */
    this._newVelocity1 = 0;

    /**
    * @property {number} _newVelocity2 - Internal cache var.
    * @private
    */
    this._newVelocity2 = 0;

    /**
    * @property {number} _average - Internal cache var.
    * @private
    */
    this._average = 0;

    /**
    * @property {Array} _mapData - Internal cache var.
    * @private
    */
    this._mapData = [];

    /**
    * @property {number} _mapTiles - Internal cache var.
    * @private
    */
    this._mapTiles = 0;

    /**
    * @property {boolean} _result - Internal cache var.
    * @private
    */
    this._result = false;

    /**
    * @property {number} _total - Internal cache var.
    * @private
    */
    this._total = 0;

    /**
    * @property {number} _angle - Internal cache var.
    * @private
    */
    this._angle = 0;

    /**
    * @property {number} _dx - Internal cache var.
    * @private
    */
    this._dx = 0;

    /**
    * @property {number} _dy - Internal cache var.
    * @private
    */
    this._dy = 0;

};

Phaser.Physics.Arcade.prototype = {

    /**
    * Called automatically by a Physics body, it updates all motion related values on the Body.
    *
    * @method Phaser.Physics.Arcade#updateMotion
    * @param {Phaser.Physics.Arcade.Body} The Body object to be updated.
    */
    updateMotion: function (body) {

        //  If you're wondering why the velocity is halved and applied twice, read this: http://www.niksula.hut.fi/~hkankaan/Homepages/gravity.html

        //  Rotation
        this._velocityDelta = (this.computeVelocity(0, body, body.angularVelocity, body.angularAcceleration, body.angularDrag, body.maxAngular) - body.angularVelocity) * this.game.time.physicsElapsed * 0.5 * 60;
        body.angularVelocity += this._velocityDelta;
        body.rotation += (body.angularVelocity * this.game.time.physicsElapsed);
        body.angularVelocity += this._velocityDelta;

        //  Horizontal
        this._velocityDelta = (this.computeVelocity(1, body, body.velocity.x, body.acceleration.x, body.drag.x, body.maxVelocity.x) - body.velocity.x) * this.game.time.physicsElapsed * 0.5 * 60;
        body.velocity.x += this._velocityDelta;
        body.x += (body.velocity.x * this.game.time.physicsElapsed);
        body.velocity.x += this._velocityDelta;

        //  Vertical
        this._velocityDelta = (this.computeVelocity(2, body, body.velocity.y, body.acceleration.y, body.drag.y, body.maxVelocity.y) - body.velocity.y) * this.game.time.physicsElapsed * 0.5 * 60;
        body.velocity.y += this._velocityDelta;
        body.y += (body.velocity.y * this.game.time.physicsElapsed);
        body.velocity.y += this._velocityDelta;

    },

    /**
    * A tween-like function that takes a starting velocity and some other factors and returns an altered velocity.
    *
    * @method Phaser.Physics.Arcade#computeVelocity
    * @param {number} axis - 1 for horizontal, 2 for vertical.
    * @param {Phaser.Physics.Arcade.Body} body - The Body object to be updated.
    * @param {number} velocity - Any component of velocity (e.g. 20).
    * @param {number} acceleration - Rate at which the velocity is changing.
    * @param {number} drag - Really kind of a deceleration, this is how much the velocity changes if Acceleration is not set.
    * @param {number} mMax - An absolute value cap for the velocity.
    * @return {number} The altered Velocity value.
    */
    computeVelocity: function (axis, body, velocity, acceleration, drag, max) {

        max = max || 10000;

        if (axis == 1 && body.allowGravity)
        {
            velocity += this.gravity.x + body.gravity.x;
        }
        else if (axis == 2 && body.allowGravity)
        {
            velocity += this.gravity.y + body.gravity.y;
        }

        if (acceleration !== 0)
        {
            velocity += acceleration * this.game.time.physicsElapsed;
        }
        else if (drag !== 0)
        {
            this._drag = drag * this.game.time.physicsElapsed;

            if (velocity - this._drag > 0)
            {
                velocity -= this._drag;
            }
            else if (velocity + this._drag < 0)
            {
                velocity += this._drag;
            }
            else
            {
                velocity = 0;
            }
        }

        if (velocity > max)
        {
            velocity = max;
        }
        else if (velocity < -max)
        {
            velocity = -max;
        }

        return velocity;

    },

    /**
    * Called automatically by the core game loop.
    *
    * @method Phaser.Physics.Arcade#preUpdate
    * @protected
    */
    preUpdate: function () {

        //  Clear the tree
        this.quadTree.clear();

        //  Create our tree which all of the Physics bodies will add themselves to
        this.quadTreeID = 0;
        this.quadTree = new Phaser.QuadTree(this, this.game.world.bounds.x, this.game.world.bounds.y, this.game.world.bounds.width, this.game.world.bounds.height, this.maxObjects, this.maxLevels);

    },

    /**
    * Called automatically by the core game loop.
    *
    * @method Phaser.Physics.Arcade#postUpdate
    * @protected
    */
    postUpdate: function () {

        //  Clear the tree ready for the next update
        this.quadTree.clear();

    },

    /**
    * Checks if two Sprite objects overlap.
    *
    * @method Phaser.Physics.Arcade#overlap
    * @param {Phaser.Sprite} object1 - The first object to check. Can be an instance of Phaser.Sprite or anything that extends it.
    * @param {Phaser.Sprite} object2 - The second object to check. Can be an instance of Phaser.Sprite or anything that extends it.
    * @returns {boolean} true if the two objects overlap.
    */
    overlap: function (object1, object2) {

        //  Only test valid objects
        if (object1 && object2 && object1.exists && object2.exists)
        {
            return (Phaser.Rectangle.intersects(object1.body, object2.body));
        }

        return false;

    },

    /**
    * Checks for collision between two game objects. The objects can be Sprites, Groups, Emitters or Tilemap Layers.
    * You can perform Sprite vs. Sprite, Sprite vs. Group, Group vs. Group, Sprite vs. Tilemap Layer or Group vs. Tilemap Layer collisions.
    * The objects are also automatically separated.
    *
    * @method Phaser.Physics.Arcade#collide
    * @param {Phaser.Sprite|Phaser.Group|Phaser.Particles.Emitter|Phaser.Tilemap} object1 - The first object to check. Can be an instance of Phaser.Sprite, Phaser.Group, Phaser.Particles.Emitter, or Phaser.Tilemap
    * @param {Phaser.Sprite|Phaser.Group|Phaser.Particles.Emitter|Phaser.Tilemap} object2 - The second object to check. Can be an instance of Phaser.Sprite, Phaser.Group, Phaser.Particles.Emitter or Phaser.Tilemap
    * @param {function} [collideCallback=null] - An optional callback function that is called if the objects overlap. The two objects will be passed to this function in the same order in which you passed them to Collision.overlap.
    * @param {function} [processCallback=null] - A callback function that lets you perform additional checks against the two objects if they overlap. If this is set then collideCallback will only be called if processCallback returns true.
    * @param {object} [callbackContext] - The context in which to run the callbacks.
    * @returns {number} The number of collisions that were processed.
    */
    collide: function (object1, object2, collideCallback, processCallback, callbackContext) {

        collideCallback = collideCallback || null;
        processCallback = processCallback || null;
        callbackContext = callbackContext || collideCallback;

        this._result = false;
        this._total = 0;

        //  Only collide valid objects
        if (object1 && object2 && object1.exists && object2.exists)
        {
            //  Can expand to support Buttons, Text, etc at a later date. For now these are the essentials.

            //  SPRITES
            if (object1.type == Phaser.SPRITE)
            {
                if (object2.type == Phaser.SPRITE)
                {
                    this.collideSpriteVsSprite(object1, object2, collideCallback, processCallback, callbackContext);
                }
                else if (object2.type == Phaser.GROUP || object2.type == Phaser.EMITTER)
                {
                    this.collideSpriteVsGroup(object1, object2, collideCallback, processCallback, callbackContext);
                }
                else if (object2.type == Phaser.TILEMAPLAYER)
                {
                    this.collideSpriteVsTilemapLayer(object1, object2, collideCallback, processCallback, callbackContext);
                }
            }
            //  GROUPS
            else if (object1.type == Phaser.GROUP)
            {
                if (object2.type == Phaser.SPRITE)
                {
                    this.collideSpriteVsGroup(object2, object1, collideCallback, processCallback, callbackContext);
                }
                else if (object2.type == Phaser.GROUP || object2.type == Phaser.EMITTER)
                {
                    this.collideGroupVsGroup(object1, object2, collideCallback, processCallback, callbackContext);
                }
                else if (object2.type == Phaser.TILEMAPLAYER)
                {
                    this.collideGroupVsTilemapLayer(object1, object2, collideCallback, processCallback, callbackContext);
                }
            }
            //  TILEMAP LAYERS
            else if (object1.type == Phaser.TILEMAPLAYER)
            {
                if (object2.type == Phaser.SPRITE)
                {
                    this.collideSpriteVsTilemapLayer(object2, object1, collideCallback, processCallback, callbackContext);
                }
                else if (object2.type == Phaser.GROUP || object2.type == Phaser.EMITTER)
                {
                    this.collideGroupVsTilemapLayer(object2, object1, collideCallback, processCallback, callbackContext);
                }
            }
            //  EMITTER
            else if (object1.type == Phaser.EMITTER)
            {
                if (object2.type == Phaser.SPRITE)
                {
                    this.collideSpriteVsGroup(object2, object1, collideCallback, processCallback, callbackContext);
                }
                else if (object2.type == Phaser.GROUP || object2.type == Phaser.EMITTER)
                {
                    this.collideGroupVsGroup(object1, object2, collideCallback, processCallback, callbackContext);
                }
                else if (object2.type == Phaser.TILEMAPLAYER)
                {
                    this.collideGroupVsTilemapLayer(object1, object2, collideCallback, processCallback, callbackContext);
                }
            }
        }

        return (this._total > 0);

    },

    /**
    * An internal function. Use Phaser.Physics.Arcade.collide instead.
    *
    * @method Phaser.Physics.Arcade#collideSpriteVsTilemapLayer
    * @private
    */
    collideSpriteVsTilemapLayer: function (sprite, tilemapLayer, collideCallback, processCallback, callbackContext) {

        this._mapData = tilemapLayer.getTiles(sprite.body.x, sprite.body.y, sprite.body.width, sprite.body.height, true);

        if (this._mapData.length === 0)
        {
            return;
        }

        for (var i = 0; i < this._mapData.length; i++)
        {
            if (this.separateTile(sprite.body, this._mapData[i]))
            {
                //  They collided, is there a custom process callback?
                if (processCallback)
                {
                    if (processCallback.call(callbackContext, sprite, this._mapData[i]))
                    {
                        this._total++;

                        if (collideCallback)
                        {
                            collideCallback.call(callbackContext, sprite, this._mapData[i]);
                        }
                    }
                }
                else
                {
                    this._total++;

                    if (collideCallback)
                    {
                        collideCallback.call(callbackContext, sprite, this._mapData[i]);
                    }
                }
            }
        }

    },

    /**
    * An internal function. Use Phaser.Physics.Arcade.collide instead.
    *
    * @method Phaser.Physics.Arcade#collideGroupVsTilemapLayer
    * @private
    */
    collideGroupVsTilemapLayer: function (group, tilemapLayer, collideCallback, processCallback, callbackContext) {

        if (group.length === 0)
        {
            return;
        }

        if (group.length === 0)
        {
            return;
        }

        if (group._container.first._iNext)
        {
            var currentNode = group._container.first._iNext;
                
            do  
            {
                if (currentNode.exists)
                {
                    this.collideSpriteVsTilemapLayer(currentNode, tilemapLayer, collideCallback, processCallback, callbackContext);
                }
                currentNode = currentNode._iNext;
            }
            while (currentNode != group._container.last._iNext);
        }

    },

    /**
    * An internal function. Use Phaser.Physics.Arcade.collide instead.
    *
    * @method Phaser.Physics.Arcade#collideSpriteVsSprite
    * @private
    */
    collideSpriteVsSprite: function (sprite1, sprite2, collideCallback, processCallback, callbackContext) {

        this.separate(sprite1.body, sprite2.body);

        if (this._result)
        {
            //  They collided, is there a custom process callback?
            if (processCallback)
            {
                if (processCallback.call(callbackContext, sprite1, sprite2))
                {
                    this._total++;

                    if (collideCallback)
                    {
                        collideCallback.call(callbackContext, sprite1, sprite2);
                    }
                }
            }
            else
            {
                this._total++;

                if (collideCallback)
                {
                    collideCallback.call(callbackContext, sprite1, sprite2);
                }
            }
        }

    },

    /**
    * An internal function. Use Phaser.Physics.Arcade.collide instead.
    *
    * @method Phaser.Physics.Arcade#collideSpriteVsGroup
    * @private
    */
    collideSpriteVsGroup: function (sprite, group, collideCallback, processCallback, callbackContext) {

        if (group.length === 0)
        {
            return;
        }

        //  What is the sprite colliding with in the quadtree?
        this._potentials = this.quadTree.retrieve(sprite);

        for (var i = 0, len = this._potentials.length; i < len; i++)
        {
            //  We have our potential suspects, are they in this group?
            if (this._potentials[i].sprite.group == group)
            {
                this.separate(sprite.body, this._potentials[i]);

                if (this._result && processCallback)
                {
                    this._result = processCallback.call(callbackContext, sprite, this._potentials[i].sprite);
                }

                if (this._result)
                {
                    this._total++;

                    if (collideCallback)
                    {
                        collideCallback.call(callbackContext, sprite, this._potentials[i].sprite);
                    }
                }
            }
        }

    },

    /**
    * An internal function. Use Phaser.Physics.Arcade.collide instead.
    *
    * @method Phaser.Physics.Arcade#collideGroupVsGroup
    * @private
    */
    collideGroupVsGroup: function (group1, group2, collideCallback, processCallback, callbackContext) {

        if (group1.length === 0 || group2.length === 0)
        {
            return;
        }

        if (group1._container.first._iNext)
        {
            var currentNode = group1._container.first._iNext;
                
            do  
            {
                if (currentNode.exists)
                {
                    this.collideSpriteVsGroup(currentNode, group2, collideCallback, processCallback, callbackContext);
                }
                currentNode = currentNode._iNext;
            }
            while (currentNode != group1._container.last._iNext);
        }

    },

    /**
    * The core separation function to separate two physics bodies.
    * @method Phaser.Physics.Arcade#separate
    * @param {Phaser.Physics.Arcade.Body} body1 - The Body object to separate.
    * @param {Phaser.Physics.Arcade.Body} body2 - The Body object to separate.
    * @returns {boolean} Returns true if the bodies were separated, otherwise false.
    */
    separate: function (body1, body2) {

        this._result = (this.separateX(body1, body2) || this.separateY(body1, body2));

    },

    /**
    * The core separation function to separate two physics bodies on the x axis.
    * @method Phaser.Physics.Arcade#separateX
    * @param {Phaser.Physics.Arcade.Body} body1 - The Body object to separate.
    * @param {Phaser.Physics.Arcade.Body} body2 - The Body object to separate.
    * @returns {boolean} Returns true if the bodies were separated, otherwise false.
    */
    separateX: function (body1, body2) {

        //  Can't separate two immovable bodies
        if (body1.immovable && body2.immovable)
        {
            return false;
        }

        this._overlap = 0;

        //  Check if the hulls actually overlap
        if (Phaser.Rectangle.intersects(body1, body2))
        {
            this._maxOverlap = body1.deltaAbsX() + body2.deltaAbsX() + this.OVERLAP_BIAS;

            if (body1.deltaX() === 0 && body2.deltaX() === 0)
            {
                //  They overlap but neither of them are moving
                body1.embedded = true;
                body2.embedded = true;
            }
            else if (body1.deltaX() > body2.deltaX())
            {
                //  Body1 is moving right and/or Body2 is moving left
                this._overlap = body1.x + body1.width - body2.x;

                if ((this._overlap > this._maxOverlap) || body1.allowCollision.right === false || body2.allowCollision.left === false)
                {
                    this._overlap = 0;
                }
                else
                {
                    body1.touching.right = true;
                    body2.touching.left = true;
                }
            }
            else if (body1.deltaX() < body2.deltaX())
            {
                //  Body1 is moving left and/or Body2 is moving right
                this._overlap = body1.x - body2.width - body2.x;

                if ((-this._overlap > this._maxOverlap) || body1.allowCollision.left === false || body2.allowCollision.right === false)
                {
                    this._overlap = 0;
                }
                else
                {
                    body1.touching.left = true;
                    body2.touching.right = true;
                }
            }

            //  Then adjust their positions and velocities accordingly (if there was any overlap)
            if (this._overlap != 0)
            {
                body1.overlapX = this._overlap;
                body2.overlapX = this._overlap;

                if (body1.customSeparateX || body2.customSeparateX)
                {
                    return true;
                }

                this._velocity1 = body1.velocity.x;
                this._velocity2 = body2.velocity.x;

                if (!body1.immovable && !body2.immovable)
                {
                    this._overlap *= 0.5;

                    body1.x = body1.x - this._overlap;
                    body2.x += this._overlap;

                    this._newVelocity1 = Math.sqrt((this._velocity2 * this._velocity2 * body2.mass) / body1.mass) * ((this._velocity2 > 0) ? 1 : -1);
                    this._newVelocity2 = Math.sqrt((this._velocity1 * this._velocity1 * body1.mass) / body2.mass) * ((this._velocity1 > 0) ? 1 : -1);
                    this._average = (this._newVelocity1 + this._newVelocity2) * 0.5;
                    this._newVelocity1 -= this._average;
                    this._newVelocity2 -= this._average;

                    body1.velocity.x = this._average + this._newVelocity1 * body1.bounce.x;
                    body2.velocity.x = this._average + this._newVelocity2 * body2.bounce.x;
                }
                else if (!body1.immovable)
                {
                    body1.x = body1.x - this._overlap;
                    body1.velocity.x = this._velocity2 - this._velocity1 * body1.bounce.x;
                }
                else if (!body2.immovable)
                {
                    body2.x += this._overlap;
                    body2.velocity.x = this._velocity1 - this._velocity2 * body2.bounce.x;
                }

                return true;
            }
        }

        return false;

    },

    /**
    * The core separation function to separate two physics bodies on the y axis.
    * @method Phaser.Physics.Arcade#separateY
    * @param {Phaser.Physics.Arcade.Body} body1 - The Body object to separate.
    * @param {Phaser.Physics.Arcade.Body} body2 - The Body object to separate.
    * @returns {boolean} Returns true if the bodies were separated, otherwise false.
    */
    separateY: function (body1, body2) {

        //  Can't separate two immovable or non-existing bodys
        if (body1.immovable && body2.immovable)
        {
            return false;
        }

        this._overlap = 0;

        //  Check if the hulls actually overlap
        if (Phaser.Rectangle.intersects(body1, body2))
        {
            this._maxOverlap = body1.deltaAbsY() + body2.deltaAbsY() + this.OVERLAP_BIAS;

            if (body1.deltaY() === 0 && body2.deltaY() === 0)
            {
                //  They overlap but neither of them are moving
                body1.embedded = true;
                body2.embedded = true;
            }
            else if (body1.deltaY() > body2.deltaY())
            {
                //  Body1 is moving down and/or Body2 is moving up
                this._overlap = body1.y + body1.height - body2.y;

                if ((this._overlap > this._maxOverlap) || body1.allowCollision.down === false || body2.allowCollision.up === false)
                {
                    this._overlap = 0;
                }
                else
                {
                    body1.touching.down = true;
                    body2.touching.up = true;
                }
            }
            else if (body1.deltaY() < body2.deltaY())
            {
                //  Body1 is moving up and/or Body2 is moving down
                this._overlap = body1.y - body2.height - body2.y;

                if ((-this._overlap > this._maxOverlap) || body1.allowCollision.up === false || body2.allowCollision.down === false)
                {
                    this._overlap = 0;
                }
                else
                {
                    body1.touching.up = true;
                    body2.touching.down = true;
                }
            }

            //  Then adjust their positions and velocities accordingly (if there was any overlap)
            if (this._overlap != 0)
            {
                body1.overlapY = this._overlap;
                body2.overlapY = this._overlap;

                if (body1.customSeparateY || body2.customSeparateY)
                {
                    return true;
                }

                this._velocity1 = body1.velocity.y;
                this._velocity2 = body2.velocity.y;

                if (!body1.immovable && !body2.immovable)
                {
                    this._overlap *= 0.5;

                    body1.y = body1.y - this._overlap;
                    body2.y += this._overlap;

                    this._newVelocity1 = Math.sqrt((this._velocity2 * this._velocity2 * body2.mass) / body1.mass) * ((this._velocity2 > 0) ? 1 : -1);
                    this._newVelocity2 = Math.sqrt((this._velocity1 * this._velocity1 * body1.mass) / body2.mass) * ((this._velocity1 > 0) ? 1 : -1);
                    this._average = (this._newVelocity1 + this._newVelocity2) * 0.5;
                    this._newVelocity1 -= this._average;
                    this._newVelocity2 -= this._average;

                    body1.velocity.y = this._average + this._newVelocity1 * body1.bounce.y;
                    body2.velocity.y = this._average + this._newVelocity2 * body2.bounce.y;
                }
                else if (!body1.immovable)
                {
                    body1.y = body1.y - this._overlap;
                    body1.velocity.y = this._velocity2 - this._velocity1 * body1.bounce.y;

                    //  This is special case code that handles things like horizontal moving platforms you can ride
                    if (body2.active && body2.moves && (body1.deltaY() > body2.deltaY()))
                    {
                        body1.x += body2.x - body2.lastX;
                    }
                }
                else if (!body2.immovable)
                {
                    body2.y += this._overlap;
                    body2.velocity.y = this._velocity1 - this._velocity2 * body2.bounce.y;

                    //  This is special case code that handles things like horizontal moving platforms you can ride
                    if (body1.sprite.active && body1.moves && (body1.deltaY() < body2.deltaY()))
                    {
                        body2.x += body1.x - body1.lastX;
                    }
                }

                return true;
            }

        }

        return false;

    },

    /**
    * The core separation function to separate a physics body and a tile.
    * @method Phaser.Physics.Arcade#separateTile
    * @param {Phaser.Physics.Arcade.Body} body1 - The Body object to separate.
    * @param {Phaser.Tile} tile - The tile to collide against.
    * @returns {boolean} Returns true if the bodies were separated, otherwise false.
    */
    separateTile: function (body, tile) {

        this._result = (this.separateTileX(body, tile, true) || this.separateTileY(body, tile, true));

        return this._result;

    },

    /**
    * The core separation function to separate a physics body and a tile on the x axis.
    * @method Phaser.Physics.Arcade#separateTileX
    * @param {Phaser.Physics.Arcade.Body} body1 - The Body object to separate.
    * @param {Phaser.Tile} tile - The tile to collide against.
    * @returns {boolean} Returns true if the bodies were separated, otherwise false.
    */
    separateTileX: function (body, tile, separate) {

        //  Can't separate two immovable objects (tiles are always immovable)
        if (body.immovable || body.deltaX() === 0 || Phaser.Rectangle.intersects(body.hullX, tile) === false)
        {
            return false;
        }

        this._overlap = 0;

        //  The hulls overlap, let's process it
        // this._maxOverlap = body.deltaAbsX() + this.OVERLAP_BIAS;

        if (body.deltaX() < 0)
        {
            //  Moving left
            this._overlap = tile.right - body.hullX.x;

            // if ((this._overlap > this._maxOverlap) || body.allowCollision.left === false || tile.tile.collideRight === false)
            if (body.allowCollision.left === false || tile.tile.collideRight === false)
            {
                this._overlap = 0;
            }
            else
            {
                body.touching.left = true;
            }
        }
        else
        {
            //  Moving right
            this._overlap = body.hullX.right - tile.x;

            // if ((this._overlap > this._maxOverlap) || body.allowCollision.right === false || tile.tile.collideLeft === false)
            if (body.allowCollision.right === false || tile.tile.collideLeft === false)
            {
                this._overlap = 0;
            }
            else
            {
                body.touching.right = true;
            }
        }

        //  Then adjust their positions and velocities accordingly (if there was any overlap)
        if (this._overlap != 0)
        {
            if (separate)
            {
                if (body.deltaX() < 0)
                {
                    body.x = body.x + this._overlap;
                }
                else
                {
                    body.x = body.x - this._overlap;
                }

                if (body.bounce.x === 0)
                {
                    body.velocity.x = 0;
                }
                else
                {
                    body.velocity.x = -body.velocity.x * body.bounce.x;
                }

                body.updateHulls();
            }

            return true;
        }
        else
        {
            return false;
        }

    },

    /**
    * The core separation function to separate a physics body and a tile on the x axis.
    * @method Phaser.Physics.Arcade#separateTileY
    * @param {Phaser.Physics.Arcade.Body} body1 - The Body object to separate.
    * @param {Phaser.Tile} tile - The tile to collide against.
    * @returns {boolean} Returns true if the bodies were separated, otherwise false.
    */
    separateTileY: function (body, tile, separate) {

        //  Can't separate two immovable objects (tiles are always immovable)
        if (body.immovable || body.deltaY() === 0 || Phaser.Rectangle.intersects(body.hullY, tile) === false)
        {
            return false;
        }

        this._overlap = 0;

        //  The hulls overlap, let's process it
        // this._maxOverlap = body.deltaAbsY() + this.OVERLAP_BIAS;

        if (body.deltaY() < 0)
        {
            //  Moving up
            this._overlap = tile.bottom - body.hullY.y;

            // if ((this._overlap > this._maxOverlap) || body.allowCollision.up === false || tile.tile.collideDown === false)
            if (body.allowCollision.up === false || tile.tile.collideDown === false)
            {
                this._overlap = 0;
            }
            else
            {
                body.touching.up = true;
            }
        }
        else
        {
            //  Moving down
            this._overlap = body.hullY.bottom - tile.y;

            // if ((this._overlap > this._maxOverlap) || body.allowCollision.down === false || tile.tile.collideUp === false)
            if (body.allowCollision.down === false || tile.tile.collideUp === false)
            {
                this._overlap = 0;
            }
            else
            {
                body.touching.down = true;
            }
        }

        //  Then adjust their positions and velocities accordingly (if there was any overlap)
        if (this._overlap != 0)
        {
            if (separate)
            {
                if (body.deltaY() < 0)
                {
                    body.y = body.y + this._overlap;
                }
                else
                {
                    body.y = body.y - this._overlap;
                }

                if (body.bounce.y === 0)
                {
                    body.velocity.y = 0;
                }
                else
                {
                    body.velocity.y = -body.velocity.y * body.bounce.y;
                }

                body.updateHulls();
            }
            
            return true;
        }
        else
        {
            return false;
        }

    },

    /**
    * Move the given display object towards the destination object at a steady velocity.
    * If you specify a maxTime then it will adjust the speed (over-writing what you set) so it arrives at the destination in that number of seconds.
    * Timings are approximate due to the way browser timers work. Allow for a variance of +- 50ms.
    * Note: The display object does not continuously track the target. If the target changes location during transit the display object will not modify its course.
    * Note: The display object doesn't stop moving once it reaches the destination coordinates.
    * Note: Doesn't take into account acceleration, maxVelocity or drag (if you've set drag or acceleration too high this object may not move at all)
    * 
    * @method Phaser.Physics.Arcade#moveToObject
    * @param {any} displayObject - The display object to move.
    * @param {any} destination - The display object to move towards. Can be any object but must have visible x/y properties.
    * @param {number} [speed=60] - The speed it will move, in pixels per second (default is 60 pixels/sec)
    * @param {number} [maxTime=0] - Time given in milliseconds (1000 = 1 sec). If set the speed is adjusted so the object will arrive at destination in the given number of ms.
    * @return {number} The angle (in radians) that the object should be visually set to in order to match its new velocity.
    */
    moveToObject: function (displayObject, destination, speed, maxTime) {

        if (typeof speed === 'undefined') { speed = 60; }
        if (typeof maxTime === 'undefined') { maxTime = 0; }

        this._angle = Math.atan2(destination.y - displayObject.y, destination.x - displayObject.x);
        
        if (maxTime > 0)
        {
            //  We know how many pixels we need to move, but how fast?
            speed = this.distanceBetween(displayObject, destination) / (maxTime / 1000);
        }
        
        displayObject.body.velocity.x = Math.cos(this._angle) * speed;
        displayObject.body.velocity.y = Math.sin(this._angle) * speed;

        return this._angle;

    },

    /**
    * Move the given display object towards the pointer at a steady velocity. If no pointer is given it will use Phaser.Input.activePointer.
    * If you specify a maxTime then it will adjust the speed (over-writing what you set) so it arrives at the destination in that number of seconds.
    * Timings are approximate due to the way browser timers work. Allow for a variance of +- 50ms.
    * Note: The display object does not continuously track the target. If the target changes location during transit the display object will not modify its course.
    * Note: The display object doesn't stop moving once it reaches the destination coordinates.
    * 
    * @method Phaser.Physics.Arcade#moveToPointer
    * @param {any} displayObject - The display object to move.
    * @param {number} [speed=60] - The speed it will move, in pixels per second (default is 60 pixels/sec)
    * @param {Phaser.Pointer} [pointer] - The pointer to move towards. Defaults to Phaser.Input.activePointer.
    * @param {number} [maxTime=0] - Time given in milliseconds (1000 = 1 sec). If set the speed is adjusted so the object will arrive at destination in the given number of ms.
    * @return {number} The angle (in radians) that the object should be visually set to in order to match its new velocity.
    */
    moveToPointer: function (displayObject, speed, pointer, maxTime) {

        if (typeof speed === 'undefined') { speed = 60; }
        pointer = pointer || this.game.input.activePointer;
        if (typeof maxTime === 'undefined') { maxTime = 0; }

        this._angle = this.angleToPointer(displayObject, pointer);
        
        if (maxTime > 0)
        {
            //  We know how many pixels we need to move, but how fast?
            speed = this.distanceToPointer(displayObject, pointer) / (maxTime / 1000);
        }
        
        displayObject.body.velocity.x = Math.cos(this._angle) * speed;
        displayObject.body.velocity.y = Math.sin(this._angle) * speed;

        return this._angle;

    },

    /**
    * Move the given display object towards the x/y coordinates at a steady velocity.
    * If you specify a maxTime then it will adjust the speed (over-writing what you set) so it arrives at the destination in that number of seconds.
    * Timings are approximate due to the way browser timers work. Allow for a variance of +- 50ms.
    * Note: The display object does not continuously track the target. If the target changes location during transit the display object will not modify its course.
    * Note: The display object doesn't stop moving once it reaches the destination coordinates.
    * Note: Doesn't take into account acceleration, maxVelocity or drag (if you've set drag or acceleration too high this object may not move at all)
    * 
    * @method Phaser.Physics.Arcade#moveToXY
    * @param {any} displayObject - The display object to move.
    * @param {number} x - The x coordinate to move towards.
    * @param {number} y - The y coordinate to move towards.
    * @param {number} [speed=60] - The speed it will move, in pixels per second (default is 60 pixels/sec)
    * @param {number} [maxTime=0] - Time given in milliseconds (1000 = 1 sec). If set the speed is adjusted so the object will arrive at destination in the given number of ms.
    * @return {number} The angle (in radians) that the object should be visually set to in order to match its new velocity.
    */
    moveToXY: function (displayObject, x, y, speed, maxTime) {

        if (typeof speed === 'undefined') { speed = 60; }
        if (typeof maxTime === 'undefined') { maxTime = 0; }

        this._angle = Math.atan2(y - displayObject.y, x - displayObject.x);
        
        if (maxTime > 0)
        {
            //  We know how many pixels we need to move, but how fast?
            speed = this.distanceToXY(displayObject, x, y) / (maxTime / 1000);
        }
        
        displayObject.body.velocity.x = Math.cos(this._angle) * speed;
        displayObject.body.velocity.y = Math.sin(this._angle) * speed;

        return this._angle;

    },

    /**
    * Given the angle (in degrees) and speed calculate the velocity and return it as a Point object, or set it to the given point object.
    * One way to use this is: velocityFromAngle(angle, 200, sprite.velocity) which will set the values directly to the sprites velocity and not create a new Point object.
    * 
    * @method Phaser.Physics.Arcade#velocityFromAngle
    * @param {number} angle - The angle in degrees calculated in clockwise positive direction (down = 90 degrees positive, right = 0 degrees positive, up = 90 degrees negative)
    * @param {number} [speed=60] - The speed it will move, in pixels per second sq.
    * @param {Phaser.Point|object} [point] - The Point object in which the x and y properties will be set to the calculated velocity.
    * @return {Phaser.Point} - A Point where point.x contains the velocity x value and point.y contains the velocity y value.
    */
    velocityFromAngle: function (angle, speed, point) {

        if (typeof speed === 'undefined') { speed = 60; }
        point = point || new Phaser.Point;

        return point.setTo((Math.cos(this.game.math.degToRad(angle)) * speed), (Math.sin(this.game.math.degToRad(angle)) * speed));

    },

    /**
    * Given the rotation (in radians) and speed calculate the velocity and return it as a Point object, or set it to the given point object.
    * One way to use this is: velocityFromRotation(rotation, 200, sprite.velocity) which will set the values directly to the sprites velocity and not create a new Point object.
    * 
    * @method Phaser.Physics.Arcade#velocityFromRotation
    * @param {number} rotation - The angle in radians.
    * @param {number} [speed=60] - The speed it will move, in pixels per second sq.
    * @param {Phaser.Point|object} [point] - The Point object in which the x and y properties will be set to the calculated velocity.
    * @return {Phaser.Point} - A Point where point.x contains the velocity x value and point.y contains the velocity y value.
    */
    velocityFromRotation: function (rotation, speed, point) {

        if (typeof speed === 'undefined') { speed = 60; }
        point = point || new Phaser.Point;

        return point.setTo((Math.cos(rotation) * speed), (Math.sin(rotation) * speed));

    },

    /**
    * Given the rotation (in radians) and speed calculate the acceleration and return it as a Point object, or set it to the given point object.
    * One way to use this is: velocityFromRotation(rotation, 200, sprite.velocity) which will set the values directly to the sprites velocity and not create a new Point object.
    * 
    * @method Phaser.Physics.Arcade#accelerationFromRotation
    * @param {number} rotation - The angle in radians.
    * @param {number} [speed=60] - The speed it will move, in pixels per second sq.
    * @param {Phaser.Point|object} [point] - The Point object in which the x and y properties will be set to the calculated acceleration.
    * @return {Phaser.Point} - A Point where point.x contains the acceleration x value and point.y contains the acceleration y value.
    */
    accelerationFromRotation: function (rotation, speed, point) {

        if (typeof speed === 'undefined') { speed = 60; }
        point = point || new Phaser.Point;

        return point.setTo((Math.cos(rotation) * speed), (Math.sin(rotation) * speed));

    },

    /**
    * Sets the acceleration.x/y property on the display object so it will move towards the target at the given speed (in pixels per second sq.)
    * You must give a maximum speed value, beyond which the display object won't go any faster.
    * Note: The display object does not continuously track the target. If the target changes location during transit the display object will not modify its course.
    * Note: The display object doesn't stop moving once it reaches the destination coordinates.
    * 
    * @method Phaser.Physics.Arcade#accelerateToObject
    * @param {any} displayObject - The display object to move.
    * @param {any} destination - The display object to move towards. Can be any object but must have visible x/y properties.
    * @param {number} [speed=60] - The speed it will accelerate in pixels per second.
    * @param {number} [xSpeedMax=500] - The maximum x velocity the display object can reach.
    * @param {number} [ySpeedMax=500] - The maximum y velocity the display object can reach.
    * @return {number} The angle (in radians) that the object should be visually set to in order to match its new trajectory.
    */
    accelerateToObject: function (displayObject, destination, speed, xSpeedMax, ySpeedMax) {

        if (typeof speed === 'undefined') { speed = 60; }
        if (typeof xSpeedMax === 'undefined') { xSpeedMax = 1000; }
        if (typeof ySpeedMax === 'undefined') { ySpeedMax = 1000; }

        this._angle = this.angleBetween(displayObject, destination);

        displayObject.body.acceleration.setTo(Math.cos(this._angle) * speed, Math.sin(this._angle) * speed);
        displayObject.body.maxVelocity.setTo(xSpeedMax, ySpeedMax);

        return this._angle;

    },

    /**
    * Sets the acceleration.x/y property on the display object so it will move towards the target at the given speed (in pixels per second sq.)
    * You must give a maximum speed value, beyond which the display object won't go any faster.
    * Note: The display object does not continuously track the target. If the target changes location during transit the display object will not modify its course.
    * Note: The display object doesn't stop moving once it reaches the destination coordinates.
    * 
    * @method Phaser.Physics.Arcade#accelerateToPointer
    * @param {any} displayObject - The display object to move.
    * @param {Phaser.Pointer} [pointer] - The pointer to move towards. Defaults to Phaser.Input.activePointer.
    * @param {number} [speed=60] - The speed it will accelerate in pixels per second.
    * @param {number} [xSpeedMax=500] - The maximum x velocity the display object can reach.
    * @param {number} [ySpeedMax=500] - The maximum y velocity the display object can reach.
    * @return {number} The angle (in radians) that the object should be visually set to in order to match its new trajectory.
    */
    accelerateToPointer: function (displayObject, pointer, speed, xSpeedMax, ySpeedMax) {

        if (typeof speed === 'undefined') { speed = 60; }
        if (typeof pointer === 'undefined') { pointer = this.game.input.activePointer; }
        if (typeof xSpeedMax === 'undefined') { xSpeedMax = 1000; }
        if (typeof ySpeedMax === 'undefined') { ySpeedMax = 1000; }

        this._angle = this.angleToPointer(displayObject, pointer);
        
        displayObject.body.acceleration.setTo(Math.cos(this._angle) * speed, Math.sin(this._angle) * speed);
        displayObject.body.maxVelocity.setTo(xSpeedMax, ySpeedMax);

        return this._angle;

    },

    /**
    * Sets the acceleration.x/y property on the display object so it will move towards the x/y coordinates at the given speed (in pixels per second sq.)
    * You must give a maximum speed value, beyond which the display object won't go any faster.
    * Note: The display object does not continuously track the target. If the target changes location during transit the display object will not modify its course.
    * Note: The display object doesn't stop moving once it reaches the destination coordinates.
    * 
    * @method Phaser.Physics.Arcade#accelerateToXY
    * @param {any} displayObject - The display object to move.
    * @param {number} x - The x coordinate to accelerate towards.
    * @param {number} y - The y coordinate to accelerate towards.
    * @param {number} [speed=60] - The speed it will accelerate in pixels per second.
    * @param {number} [xSpeedMax=500] - The maximum x velocity the display object can reach.
    * @param {number} [ySpeedMax=500] - The maximum y velocity the display object can reach.
    * @return {number} The angle (in radians) that the object should be visually set to in order to match its new trajectory.
    */
    accelerateToXY: function (displayObject, x, y, speed, xSpeedMax, ySpeedMax) {

        if (typeof speed === 'undefined') { speed = 60; }
        if (typeof xSpeedMax === 'undefined') { xSpeedMax = 1000; }
        if (typeof ySpeedMax === 'undefined') { ySpeedMax = 1000; }

        this._angle = this.angleToXY(displayObject, x, y);

        displayObject.body.acceleration.setTo(Math.cos(this._angle) * speed, Math.sin(this._angle) * speed);
        displayObject.body.maxVelocity.setTo(xSpeedMax, ySpeedMax);

        return this._angle;

    },

    /**
    * Find the distance between two display objects (like Sprites).
    * 
    * @method Phaser.Physics.Arcade#distanceBetween
    * @param {any} source - The Display Object to test from.
    * @param {any} target - The Display Object to test to.
    * @return {number} The distance between the source and target objects.
    */
    distanceBetween: function (source, target) {

        this._dx = source.x - target.x;
        this._dy = source.y - target.y;
        
        return Math.sqrt(this._dx * this._dx + this._dy * this._dy);

    },

    /**
    * Find the distance between a display object (like a Sprite) and the given x/y coordinates.
    * The calculation is made from the display objects x/y coordinate. This may be the top-left if its anchor hasn't been changed.
    * If you need to calculate from the center of a display object instead use the method distanceBetweenCenters()
    * 
    * @method Phaser.Physics.Arcade#distanceToXY
    * @param {any} displayObject - The Display Object to test from.
    * @param {number} x - The x coordinate to move towards.
    * @param {number} y - The y coordinate to move towards.
    * @return {number} The distance between the object and the x/y coordinates.
    */
    distanceToXY: function (displayObject, x, y) {

        this._dx = displayObject.x - x;
        this._dy = displayObject.y - y;
        
        return Math.sqrt(this._dx * this._dx + this._dy * this._dy);

    },

    /**
    * Find the distance between a display object (like a Sprite) and a Pointer. If no Pointer is given the Input.activePointer is used.
    * The calculation is made from the display objects x/y coordinate. This may be the top-left if its anchor hasn't been changed.
    * If you need to calculate from the center of a display object instead use the method distanceBetweenCenters()
    * 
    * @method Phaser.Physics.Arcade#distanceToPointer
    * @param {any} displayObject - The Display Object to test from.
    * @param {Phaser.Pointer} [pointer] - The Phaser.Pointer to test to. If none is given then Input.activePointer is used.
    * @return {number} The distance between the object and the Pointer.
    */
    distanceToPointer: function (displayObject, pointer) {

        pointer = pointer || this.game.input.activePointer;

        this._dx = displayObject.x - pointer.x;
        this._dy = displayObject.y - pointer.y;
        
        return Math.sqrt(this._dx * this._dx + this._dy * this._dy);

    },

    /**
    * Find the angle in radians between two display objects (like Sprites).
    * 
    * @method Phaser.Physics.Arcade#angleBetween
    * @param {any} source - The Display Object to test from.
    * @param {any} target - The Display Object to test to.
    * @return {number} The angle in radians between the source and target display objects.
    */
    angleBetween: function (source, target) {

        this._dx = target.x - source.x;
        this._dy = target.y - source.y;

        return Math.atan2(this._dy, this._dx);

    },

    /**
    * Find the angle in radians between a display object (like a Sprite) and the given x/y coordinate.
    * 
    * @method Phaser.Physics.Arcade#angleToXY
    * @param {any} displayObject - The Display Object to test from.
    * @param {number} x - The x coordinate to get the angle to.
    * @param {number} y - The y coordinate to get the angle to.
    * @return {number} The angle in radians between displayObject.x/y to Pointer.x/y
    */
    angleToXY: function (displayObject, x, y) {

        this._dx = x - displayObject.x;
        this._dy = y - displayObject.y;
        
        return Math.atan2(this._dy, this._dx);

    },
    
    /**
    * Find the angle in radians between a display object (like a Sprite) and a Pointer, taking their x/y and center into account.
    * 
    * @method Phaser.Physics.Arcade#angleToPointer
    * @param {any} displayObject - The Display Object to test from.
    * @param {Phaser.Pointer} [pointer] - The Phaser.Pointer to test to. If none is given then Input.activePointer is used.
    * @return {number} The angle in radians between displayObject.x/y to Pointer.x/y
    */
    angleToPointer: function (displayObject, pointer) {

        pointer = pointer || this.game.input.activePointer;

        this._dx = pointer.worldX - displayObject.x;
        this._dy = pointer.worldY - displayObject.y;
        
        return Math.atan2(this._dy, this._dx);

    }

};