liabru-matter-js/build/matter.js

/**
* matter.js 0.8.0-edge 2015-01-21
* http://brm.io/matter-js/
* License: MIT
*/

/**
 * The MIT License (MIT)
 * 
 * Copyright (c) 2014 Liam Brummitt
 * 
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 * 
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

(function() {

var Matter = {};

// Begin Matter namespace closure

// All Matter modules are included below during build
// Outro.js then closes at the end of the file


// Begin src/body/Body.js

/**
* The `Matter.Body` module contains methods for creating and manipulating body models.
* A `Matter.Body` is a rigid body that can be simulated by a `Matter.Engine`.
* Factories for commonly used body configurations (such as rectangles, circles and other polygons) can be found in the module `Matter.Bodies`.
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.

* @class Body
*/

var Body = {};

(function() {

    Body._inertiaScale = 4;

    var _nextCollidingGroupId = 1,
        _nextNonCollidingGroupId = -1,
        _nextCategory = 0x0001;

    /**
     * Creates a new rigid body model. The options parameter is an object that specifies any properties you wish to override the defaults.
     * All properties have default values, and many are pre-calculated automatically based on other properties.
     * See the properites section below for detailed information on what you can pass via the `options` object.
     * @method create
     * @param {} options
     * @return {body} body
     */
    Body.create = function(options) {
        var defaults = {
            id: Common.nextId(),
            type: 'body',
            label: 'Body',
            angle: 0,
            vertices: Vertices.fromPath('L 0 0 L 40 0 L 40 40 L 0 40'),
            position: { x: 0, y: 0 },
            force: { x: 0, y: 0 },
            torque: 0,
            positionImpulse: { x: 0, y: 0 },
            constraintImpulse: { x: 0, y: 0, angle: 0 },
            speed: 0,
            angularSpeed: 0,
            velocity: { x: 0, y: 0 },
            angularVelocity: 0,
            isStatic: false,
            isSleeping: false,
            motion: 0,
            sleepThreshold: 60,
            density: 0.001,
            restitution: 0,
            friction: 0.1,
            frictionAir: 0.01,
            collisionFilter: {
                category: 0x0001,
                mask: 0xFFFFFFFF,
                group: 0
            },
            slop: 0.05,
            timeScale: 1,
            render: {
                visible: true,
                sprite: {
                    xScale: 1,
                    yScale: 1
                },
                lineWidth: 1.5
            }
        };

        var body = Common.extend(defaults, options);

        _initProperties(body, options);

        return body;
    };

    /**
     * Returns the next unique group index for which bodies will collide.
     * If `isNonColliding` is `true`, returns the next unique group index for which bodies will _not_ collide.
     * See `body.collisionFilter` for more information.
     * @method nextGroup
     * @param {bool} [isNonColliding=false]
     * @return {Number} Unique group index
     */
    Body.nextGroup = function(isNonColliding) {
        if (isNonColliding)
            return _nextNonCollidingGroupId--;

        return _nextCollidingGroupId++;
    };

    /**
     * Returns the next unique category bitfield (starting after the initial default category `0x0001`).
     * There are 32 available. See `body.collisionFilter` for more information.
     * @method nextCategory
     * @return {Number} Unique category bitfield
     */
    Body.nextCategory = function() {
        _nextCategory = _nextCategory << 1;
        return _nextCategory;
    };

    /**
     * Initialises body properties.
     * @method _initProperties
     * @private
     * @param {body} body
     * @param {} options
     */
    var _initProperties = function(body, options) {
        // init required properties
        Body.set(body, {
            bounds: body.bounds || Bounds.create(body.vertices),
            positionPrev: body.positionPrev || Vector.clone(body.position),
            anglePrev: body.anglePrev || body.angle,
            vertices: body.vertices,
            isStatic: body.isStatic,
            isSleeping: body.isSleeping
        });

        Vertices.rotate(body.vertices, body.angle, body.position);
        Axes.rotate(body.axes, body.angle);
        Bounds.update(body.bounds, body.vertices, body.velocity);

        // allow options to override the automatically calculated properties
        Body.set(body, {
            axes: options.axes || body.axes,
            area: options.area || body.area,
            mass: options.mass || body.mass,
            inertia: options.inertia || body.inertia
        });

        // render properties
        var defaultFillStyle = (body.isStatic ? '#eeeeee' : Common.choose(['#556270', '#4ECDC4', '#C7F464', '#FF6B6B', '#C44D58'])),
            defaultStrokeStyle = Common.shadeColor(defaultFillStyle, -20);
        body.render.fillStyle = body.render.fillStyle || defaultFillStyle;
        body.render.strokeStyle = body.render.strokeStyle || defaultStrokeStyle;
    };

    /**
     * Given a property and a value (or map of), sets the property(s) on the body, using the appropriate setter functions if they exist.
     * Prefer to use the actual setter functions in performance critical situations.
     * @method set
     * @param {body} body
     * @param {} settings A property name (or map of properties and values) to set on the body.
     * @param {} value The value to set if `settings` is a single property name.
     */
    Body.set = function(body, settings, value) {
        var property;

        if (typeof settings === 'string') {
            property = settings;
            settings = {};
            settings[property] = value;
        }

        for (property in settings) {
            value = settings[property];

            if (!settings.hasOwnProperty(property))
                continue;

            switch (property) {

            case 'isStatic':
                Body.setStatic(body, value);
                break;
            case 'isSleeping':
                Sleeping.set(body, value);
                break;
            case 'mass':
                Body.setMass(body, value);
                break;
            case 'density':
                Body.setDensity(body, value);
                break;
            case 'inertia':
                Body.setInertia(body, value);
                break;
            case 'vertices':
                Body.setVertices(body, value);
                break;
            case 'position':
                Body.setPosition(body, value);
                break;
            case 'angle':
                Body.setAngle(body, value);
                break;
            case 'velocity':
                Body.setVelocity(body, value);
                break;
            case 'angularVelocity':
                Body.setAngularVelocity(body, value);
                break;
            default:
                body[property] = value;

            }
        }
    };

    /**
     * Sets the body as static, including isStatic flag and setting mass and inertia to Infinity.
     * @method setStatic
     * @param {body} body
     * @param {bool} isStatic
     */
    Body.setStatic = function(body, isStatic) {
        body.isStatic = isStatic;

        if (isStatic) {
            body.restitution = 0;
            body.friction = 1;
            body.mass = body.inertia = body.density = Infinity;
            body.inverseMass = body.inverseInertia = 0;

            body.positionPrev.x = body.position.x;
            body.positionPrev.y = body.position.y;
            body.anglePrev = body.angle;
            body.angularVelocity = 0;
            body.speed = 0;
            body.angularSpeed = 0;
            body.motion = 0;
        }
    };

    /**
     * Sets the mass of the body. Inverse mass and density are automatically updated to reflect the change.
     * @method setMass
     * @param {body} body
     * @param {number} mass
     */
    Body.setMass = function(body, mass) {
        body.mass = mass;
        body.inverseMass = 1 / body.mass;
        body.density = body.mass / body.area;
    };

    /**
     * Sets the density of the body. Mass is automatically updated to reflect the change.
     * @method setDensity
     * @param {body} body
     * @param {number} density
     */
    Body.setDensity = function(body, density) {
        Body.setMass(body, density * body.area);
        body.density = density;
    };

    /**
     * Sets the moment of inertia (i.e. second moment of area) of the body of the body. 
     * Inverse inertia is automatically updated to reflect the change. Mass is not changed.
     * @method setInertia
     * @param {body} body
     * @param {number} inertia
     */
    Body.setInertia = function(body, inertia) {
        body.inertia = inertia;
        body.inverseInertia = 1 / body.inertia;
    };

    /**
     * Sets the body's vertices and updates body properties accordingly, including inertia, area and mass (with respect to `body.density`).
     * Vertices will be automatically transformed to be orientated around their centre of mass as the origin.
     * They are then automatically translated to world space based on `body.position`.
     *
     * The `vertices` argument should be passed as an array of `Matter.Vector` points (or a `Matter.Vertices` array).
     * Vertices must form a convex hull, concave hulls are not supported.
     *
     * @method setVertices
     * @param {body} body
     * @param {vector[]} vertices
     */
    Body.setVertices = function(body, vertices) {
        // change vertices
        if (vertices[0].body === body) {
            body.vertices = vertices;
        } else {
            body.vertices = Vertices.create(vertices, body);
        }

        // update properties
        body.axes = Axes.fromVertices(body.vertices);
        body.area = Vertices.area(body.vertices);
        Body.setMass(body, body.density * body.area);

        // orient vertices around the centre of mass at origin (0, 0)
        var centre = Vertices.centre(body.vertices);
        Vertices.translate(body.vertices, centre, -1);

        // update inertia while vertices are at origin (0, 0)
        Body.setInertia(body, Body._inertiaScale * Vertices.inertia(body.vertices, body.mass));

        // update geometry
        Vertices.translate(body.vertices, body.position);
        Bounds.update(body.bounds, body.vertices, body.velocity);
    };

    /**
     * Sets the position of the body instantly. Velocity, angle, force etc. are unchanged.
     * @method setPosition
     * @param {body} body
     * @param {vector} position
     */
    Body.setPosition = function(body, position) {
        var delta = Vector.sub(position, body.position);

        body.position.x = position.x;
        body.position.y = position.y;
        body.positionPrev.x += delta.x;
        body.positionPrev.y += delta.y;

        Vertices.translate(body.vertices, delta);
        Bounds.update(body.bounds, body.vertices, body.velocity);
    };

    /**
     * Sets the angle of the body instantly. Angular velocity, position, force etc. are unchanged.
     * @method setAngle
     * @param {body} body
     * @param {number} angle
     */
    Body.setAngle = function(body, angle) {
        var delta = angle - body.angle;

        body.angle = angle;
        body.anglePrev += delta;

        Vertices.rotate(body.vertices, delta, body.position);
        Axes.rotate(body.axes, delta);
        Bounds.update(body.bounds, body.vertices, body.velocity);
    };

    /**
     * Sets the linear velocity of the body instantly. Position, angle, force etc. are unchanged. See also `Body.applyForce`.
     * @method setVelocity
     * @param {body} body
     * @param {vector} velocity
     */
    Body.setVelocity = function(body, velocity) {
        body.positionPrev.x = body.position.x - velocity.x;
        body.positionPrev.y = body.position.y - velocity.y;
        body.velocity.x = velocity.x;
        body.velocity.y = velocity.y;
        body.speed = Vector.magnitude(body.velocity);
    };

    /**
     * Sets the angular velocity of the body instantly. Position, angle, force etc. are unchanged. See also `Body.applyForce`.
     * @method setAngularVelocity
     * @param {body} body
     * @param {number} velocity
     */
    Body.setAngularVelocity = function(body, velocity) {
        body.anglePrev = body.angle - velocity;
        body.angularVelocity = velocity;
        body.angularSpeed = Math.abs(body.angularVelocity);
    };

    /**
     * Moves a body by a given vector relative to its current position, without imparting any velocity.
     * @method translate
     * @param {body} body
     * @param {vector} translation
     */
    Body.translate = function(body, translation) {
        Body.setPosition(body, Vector.add(body.position, translation));
    };

    /**
     * Rotates a body by a given angle relative to its current angle, without imparting any angular velocity.
     * @method rotate
     * @param {body} body
     * @param {number} rotation
     */
    Body.rotate = function(body, rotation) {
        Body.setAngle(body, body.angle + rotation);
    };

    /**
     * Scales the body, including updating physical properties (mass, area, axes, inertia), from a world-space point (default is body centre).
     * @method scale
     * @param {body} body
     * @param {number} scaleX
     * @param {number} scaleY
     * @param {vector} [point]
     */
    Body.scale = function(body, scaleX, scaleY, point) {
        // scale vertices
        Vertices.scale(body.vertices, scaleX, scaleY, point);

        // update properties
        body.axes = Axes.fromVertices(body.vertices);
        body.area = Vertices.area(body.vertices);
        Body.setMass(body, body.density * body.area);

        // update inertia (requires vertices to be at origin)
        Vertices.translate(body.vertices, { x: -body.position.x, y: -body.position.y });
        Body.setInertia(body, Vertices.inertia(body.vertices, body.mass));
        Vertices.translate(body.vertices, { x: body.position.x, y: body.position.y });

        // update bounds
        Bounds.update(body.bounds, body.vertices, body.velocity);
    };

    /**
     * Performs a simulation step for the given `body`, including updating position and angle using Verlet integration.
     * @method update
     * @param {body} body
     * @param {number} deltaTime
     * @param {number} timeScale
     * @param {number} correction
     */
    Body.update = function(body, deltaTime, timeScale, correction) {
        var deltaTimeSquared = Math.pow(deltaTime * timeScale * body.timeScale, 2);

        // from the previous step
        var frictionAir = 1 - body.frictionAir * timeScale * body.timeScale,
            velocityPrevX = body.position.x - body.positionPrev.x,
            velocityPrevY = body.position.y - body.positionPrev.y;

        // update velocity with verlet integration
        body.velocity.x = (velocityPrevX * frictionAir * correction) + (body.force.x / body.mass) * deltaTimeSquared;
        body.velocity.y = (velocityPrevY * frictionAir * correction) + (body.force.y / body.mass) * deltaTimeSquared;

        body.positionPrev.x = body.position.x;
        body.positionPrev.y = body.position.y;
        body.position.x += body.velocity.x;
        body.position.y += body.velocity.y;

        // update angular velocity with verlet integration
        body.angularVelocity = ((body.angle - body.anglePrev) * frictionAir * correction) + (body.torque / body.inertia) * deltaTimeSquared;
        body.anglePrev = body.angle;
        body.angle += body.angularVelocity;

        // track speed and acceleration
        body.speed = Vector.magnitude(body.velocity);
        body.angularSpeed = Math.abs(body.angularVelocity);

        // transform the body geometry
        Vertices.translate(body.vertices, body.velocity);
        if (body.angularVelocity !== 0) {
            Vertices.rotate(body.vertices, body.angularVelocity, body.position);
            Axes.rotate(body.axes, body.angularVelocity);
        }
        Bounds.update(body.bounds, body.vertices, body.velocity);
    };

    /**
     * Applies a force to a body from a given world-space position, including resulting torque.
     * @method applyForce
     * @param {body} body
     * @param {vector} position
     * @param {vector} force
     */
    Body.applyForce = function(body, position, force) {
        body.force.x += force.x;
        body.force.y += force.y;
        var offset = { x: position.x - body.position.x, y: position.y - body.position.y };
        body.torque += (offset.x * force.y - offset.y * force.x) * body.inverseInertia;
    };

    /*
    *
    *  Properties Documentation
    *
    */

    /**
     * An integer `Number` uniquely identifying number generated in `Body.create` by `Common.nextId`.
     *
     * @property id
     * @type number
     */

    /**
     * A `String` denoting the type of object.
     *
     * @property type
     * @type string
     * @default "body"
     */

    /**
     * An arbitrary `String` name to help the user identify and manage bodies.
     *
     * @property label
     * @type string
     * @default "Body"
     */

    /**
     * A `Number` specifying the angle of the body, in radians.
     *
     * @property angle
     * @type number
     * @default 0
     */

    /**
     * An array of `Vector` objects that specify the convex hull of the rigid body.
     * These should be provided about the origin `(0, 0)`. E.g.
     *
     *     [{ x: 0, y: 0 }, { x: 25, y: 50 }, { x: 50, y: 0 }]
     *
     * When passed via `Body.create`, the verticies are translated relative to `body.position` (i.e. world-space, and constantly updated by `Body.update` during simulation).
     * The `Vector` objects are also augmented with additional properties required for efficient collision detection. 
     *
     * Other properties such as `inertia` and `bounds` are automatically calculated from the passed vertices (unless provided via `options`).
     * Concave hulls are not currently supported. The module `Matter.Vertices` contains useful methods for working with vertices.
     *
     * @property vertices
     * @type vector[]
     */

    /**
     * A `Vector` that specifies the current world-space position of the body.
     *
     * @property position
     * @type vector
     * @default { x: 0, y: 0 }
     */

    /**
     * A `Vector` that specifies the force to apply in the current step. It is zeroed after every `Body.update`. See also `Body.applyForce`.
     *
     * @property force
     * @type vector
     * @default { x: 0, y: 0 }
     */

    /**
     * A `Number` that specifies the torque (turning force) to apply in the current step. It is zeroed after every `Body.update`.
     *
     * @property torque
     * @type number
     * @default 0
     */

    /**
     * A `Number` that _measures_ the current speed of the body after the last `Body.update`. It is read-only and always positive (it's the magnitude of `body.velocity`).
     *
     * @readOnly
     * @property speed
     * @type number
     * @default 0
     */

    /**
     * A `Number` that _measures_ the current angular speed of the body after the last `Body.update`. It is read-only and always positive (it's the magnitude of `body.angularVelocity`).
     *
     * @readOnly
     * @property angularSpeed
     * @type number
     * @default 0
     */

    /**
     * A `Vector` that _measures_ the current velocity of the body after the last `Body.update`. It is read-only. 
     * If you need to modify a body's velocity directly, you should either apply a force or simply change the body's `position` (as the engine uses position-Verlet integration).
     *
     * @readOnly
     * @property velocity
     * @type vector
     * @default { x: 0, y: 0 }
     */

    /**
     * A `Number` that _measures_ the current angular velocity of the body after the last `Body.update`. It is read-only. 
     * If you need to modify a body's angular velocity directly, you should apply a torque or simply change the body's `angle` (as the engine uses position-Verlet integration).
     *
     * @readOnly
     * @property angularVelocity
     * @type number
     * @default 0
     */

    /**
     * A flag that indicates whether a body is considered static. A static body can never change position or angle and is completely fixed.
     * If you need to set a body as static after its creation, you should use `Body.setStatic` as this requires more than just setting this flag.
     *
     * @property isStatic
     * @type boolean
     * @default false
     */

    /**
     * A flag that indicates whether the body is considered sleeping. A sleeping body acts similar to a static body, except it is only temporary and can be awoken.
     * If you need to set a body as sleeping, you should use `Sleeping.set` as this requires more than just setting this flag.
     *
     * @property isSleeping
     * @type boolean
     * @default false
     */

    /**
     * A `Number` that _measures_ the amount of movement a body currently has (a combination of `speed` and `angularSpeed`). It is read-only and always positive.
     * It is used and updated by the `Matter.Sleeping` module during simulation to decide if a body has come to rest.
     *
     * @readOnly
     * @property motion
     * @type number
     * @default 0
     */

    /**
     * A `Number` that defines the number of updates in which this body must have near-zero velocity before it is set as sleeping by the `Matter.Sleeping` module (if sleeping is enabled by the engine).
     *
     * @property sleepThreshold
     * @type number
     * @default 60
     */

    /**
     * A `Number` that defines the density of the body, that is its mass per unit area.
     * If you pass the density via `Body.create` the `mass` property is automatically calculated for you based on the size (area) of the object.
     * This is generally preferable to simply setting mass and allows for more intuitive definition of materials (e.g. rock has a higher density than wood).
     *
     * @property density
     * @type number
     * @default 0.001
     */

    /**
     * A `Number` that defines the mass of the body, although it may be more appropriate to specify the `density` property instead.
     * If you modify this value, you must also modify the `body.inverseMass` property (`1 / mass`).
     *
     * @property mass
     * @type number
     */

    /**
     * A `Number` that defines the inverse mass of the body (`1 / mass`).
     * If you modify this value, you must also modify the `body.mass` property.
     *
     * @property inverseMass
     * @type number
     */

    /**
     * A `Number` that defines the moment of inertia (i.e. second moment of area) of the body.
     * It is automatically calculated from the given convex hull (`vertices` array) and density in `Body.create`.
     * If you modify this value, you must also modify the `body.inverseInertia` property (`1 / inertia`).
     *
     * @property inertia
     * @type number
     */

    /**
     * A `Number` that defines the inverse moment of inertia of the body (`1 / inertia`).
     * If you modify this value, you must also modify the `body.inertia` property.
     *
     * @property inverseInertia
     * @type number
     */

    /**
     * A `Number` that defines the restitution (elasticity) of the body. The value is always positive and is in the range `(0, 1)`.
     * A value of `0` means collisions may be perfectly inelastic and no bouncing may occur. 
     * A value of `0.8` means the body may bounce back with approximately 80% of its kinetic energy.
     * Note that collision response is based on _pairs_ of bodies, and that `restitution` values are _combined_ with the following formula:
     *
     *     Math.max(bodyA.restitution, bodyB.restitution)
     *
     * @property restitution
     * @type number
     * @default 0
     */

    /**
     * A `Number` that defines the friction of the body. The value is always positive and is in the range `(0, 1)`.
     * A value of `0` means that the body may slide indefinitely.
     * A value of `1` means the body may come to a stop almost instantly after a force is applied.
     *
     * The effects of the value may be non-linear. 
     * High values may be unstable depending on the body.
     * The engine uses a Coulomb friction model including static and kinetic friction.
     * Note that collision response is based on _pairs_ of bodies, and that `friction` values are _combined_ with the following formula:
     *
     *     Math.min(bodyA.friction, bodyB.friction)
     *
     * @property friction
     * @type number
     * @default 0.1
     */

    /**
     * A `Number` that defines the air friction of the body (air resistance). 
     * A value of `0` means the body will never slow as it moves through space.
     * The higher the value, the faster a body slows when moving through space.
     * The effects of the value are non-linear. 
     *
     * @property frictionAir
     * @type number
     * @default 0.01
     */

    /**
     * An `Object` that specifies the collision filtering properties of this body.
     *
     * Collisions between two bodies will obey the following rules:
     * - If the two bodies have the same non-zero value of `collisionFilter.group`,
     *   they will always collide if the value is positive, and they will never collide
     *   if the value is negative.
     * - If the two bodies have different values of `collisionFilter.group` or if one
     *   (or both) of the bodies has a value of 0, then the category/mask rules apply as follows:
     *
     * Each body belongs to a collision category, given by `collisionFilter.category`. This
     * value is used as a bit field and the category should have only one bit set, meaning that
     * the value of this property is a power of two in the range [1, 2^31]. Thus, there are 32
     * different collision categories available.
     *
     * Each body also defines a collision bitmask, given by `collisionFilter.mask` which specifies
     * the categories it collides with (the value is the bitwise AND value of all these categories).
     *
     * Using the category/mask rules, two bodies `A` and `B` collide if each includes the other's
     * category in its mask, i.e. `(categoryA & maskB) !== 0` and `(categoryB & maskA) !== 0`
     * are both true.
     *
     * @property collisionFilter
     * @type object
     */

    /**
     * An Integer `Number`, that specifies the collision group this body belongs to.
     * See `body.collisionFilter` for more information.
     *
     * @property collisionFilter.group
     * @type object
     * @default 0
     */

    /**
     * A bit field that specifies the collision category this body belongs to.
     * The category value should have only one bit set, for example `0x0001`.
     * This means there are up to 32 unique collision categories available.
     * See `body.collisionFilter` for more information.
     *
     * @property collisionFilter.category
     * @type object
     * @default 1
     */

    /**
     * A bit mask that specifies the collision categories this body may collide with.
     * See `body.collisionFilter` for more information.
     *
     * @property collisionFilter.mask
     * @type object
     * @default -1
     */

    /**
     * A `Number` that specifies a tolerance on how far a body is allowed to 'sink' or rotate into other bodies.
     * Avoid changing this value unless you understand the purpose of `slop` in physics engines.
     * The default should generally suffice, although very large bodies may require larger values for stable stacking.
     *
     * @property slop
     * @type number
     * @default 0.05
     */

    /**
     * A `Number` that allows per-body time scaling, e.g. a force-field where bodies inside are in slow-motion, while others are at full speed.
     *
     * @property timeScale
     * @type number
     * @default 1
     */

    /**
     * An `Object` that defines the rendering properties to be consumed by the module `Matter.Render`.
     *
     * @property render
     * @type object
     */

    /**
     * A flag that indicates if the body should be rendered.
     *
     * @property render.visible
     * @type boolean
     * @default true
     */

    /**
     * An `Object` that defines the sprite properties to use when rendering, if any.
     *
     * @property render.sprite
     * @type object
     */

    /**
     * An `String` that defines the path to the image to use as the sprite texture, if any.
     *
     * @property render.sprite.texture
     * @type string
     */
     
    /**
     * A `Number` that defines the scaling in the x-axis for the sprite, if any.
     *
     * @property render.sprite.xScale
     * @type number
     * @default 1
     */

    /**
     * A `Number` that defines the scaling in the y-axis for the sprite, if any.
     *
     * @property render.sprite.yScale
     * @type number
     * @default 1
     */

    /**
     * A `Number` that defines the line width to use when rendering the body outline (if a sprite is not defined).
     * A value of `0` means no outline will be rendered.
     *
     * @property render.lineWidth
     * @type number
     * @default 1.5
     */

    /**
     * A `String` that defines the fill style to use when rendering the body (if a sprite is not defined).
     * It is the same as when using a canvas, so it accepts CSS style property values.
     *
     * @property render.fillStyle
     * @type string
     * @default a random colour
     */

    /**
     * A `String` that defines the stroke style to use when rendering the body outline (if a sprite is not defined).
     * It is the same as when using a canvas, so it accepts CSS style property values.
     *
     * @property render.strokeStyle
     * @type string
     * @default a random colour
     */

    /**
     * An array of unique axis vectors (edge normals) used for collision detection.
     * These are automatically calculated from the given convex hull (`vertices` array) in `Body.create`.
     * They are constantly updated by `Body.update` during the simulation.
     *
     * @property axes
     * @type vector[]
     */
     
    /**
     * A `Number` that _measures_ the area of the body's convex hull, calculated at creation by `Body.create`.
     *
     * @property area
     * @type string
     * @default 
     */

    /**
     * A `Bounds` object that defines the AABB region for the body.
     * It is automatically calculated from the given convex hull (`vertices` array) in `Body.create` and constantly updated by `Body.update` during simulation.
     *
     * @property bounds
     * @type bounds
     */

})();


;   // End src/body/Body.js


// Begin src/body/Composite.js

/**
* The `Matter.Composite` module contains methods for creating and manipulating composite bodies.
* A composite body is a collection of `Matter.Body`, `Matter.Constraint` and other `Matter.Composite`, therefore composites form a tree structure.
* It is important to use the functions in this module to modify composites, rather than directly modifying their properties.
* Note that the `Matter.World` object is also a type of `Matter.Composite` and as such all composite methods here can also operate on a `Matter.World`.
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Composite
*/

var Composite = {};

(function() {

    /**
     * Creates a new composite. The options parameter is an object that specifies any properties you wish to override the defaults.
     * See the properites section below for detailed information on what you can pass via the `options` object.
     * @method create
     * @param {} [options]
     * @return {composite} A new composite
     */
    Composite.create = function(options) {
        return Common.extend({ 
            id: Common.nextId(),
            type: 'composite',
            parent: null,
            isModified: false,
            bodies: [], 
            constraints: [], 
            composites: [],
            label: 'Composite'
        }, options);
    };

    /**
     * Sets the composite's `isModified` flag. 
     * If `updateParents` is true, all parents will be set (default: false).
     * If `updateChildren` is true, all children will be set (default: false).
     * @method setModified
     * @param {composite} composite
     * @param {boolean} isModified
     * @param {boolean} [updateParents=false]
     * @param {boolean} [updateChildren=false]
     */
    Composite.setModified = function(composite, isModified, updateParents, updateChildren) {
        composite.isModified = isModified;

        if (updateParents && composite.parent) {
            Composite.setModified(composite.parent, isModified, updateParents, updateChildren);
        }

        if (updateChildren) {
            for(var i = 0; i < composite.composites.length; i++) {
                var childComposite = composite.composites[i];
                Composite.setModified(childComposite, isModified, updateParents, updateChildren);
            }
        }
    };

    /**
     * Generic add function. Adds one or many body(s), constraint(s) or a composite(s) to the given composite.
     * Triggers `beforeAdd` and `afterAdd` events on the `composite`.
     * @method add
     * @param {composite} composite
     * @param {} object
     * @return {composite} The original composite with the objects added
     */
    Composite.add = function(composite, object) {
        var objects = [].concat(object);

        Events.trigger(composite, 'beforeAdd', { object: object });

        for (var i = 0; i < objects.length; i++) {
            var obj = objects[i];

            switch (obj.type) {

            case 'body':
                Composite.addBody(composite, obj);
                break;
            case 'constraint':
                Composite.addConstraint(composite, obj);
                break;
            case 'composite':
                Composite.addComposite(composite, obj);
                break;
            case 'mouseConstraint':
                Composite.addConstraint(composite, obj.constraint);
                break;

            }
        }

        Events.trigger(composite, 'afterAdd', { object: object });

        return composite;
    };

    /**
     * Generic remove function. Removes one or many body(s), constraint(s) or a composite(s) to the given composite.
     * Optionally searching its children recursively.
     * Triggers `beforeRemove` and `afterRemove` events on the `composite`.
     * @method remove
     * @param {composite} composite
     * @param {} object
     * @param {boolean} [deep=false]
     * @return {composite} The original composite with the objects removed
     */
    Composite.remove = function(composite, object, deep) {
        var objects = [].concat(object);

        Events.trigger(composite, 'beforeRemove', { object: object });

        for (var i = 0; i < objects.length; i++) {
            var obj = objects[i];

            switch (obj.type) {

            case 'body':
                Composite.removeBody(composite, obj, deep);
                break;
            case 'constraint':
                Composite.removeConstraint(composite, obj, deep);
                break;
            case 'composite':
                Composite.removeComposite(composite, obj, deep);
                break;
            case 'mouseConstraint':
                Composite.removeConstraint(composite, obj.constraint);
                break;

            }
        }

        Events.trigger(composite, 'afterRemove', { object: object });

        return composite;
    };

    /**
     * Adds a composite to the given composite
     * @private
     * @method addComposite
     * @param {composite} compositeA
     * @param {composite} compositeB
     * @return {composite} The original compositeA with the objects from compositeB added
     */
    Composite.addComposite = function(compositeA, compositeB) {
        compositeA.composites.push(compositeB);
        compositeB.parent = compositeA;
        Composite.setModified(compositeA, true, true, false);
        return compositeA;
    };

    /**
     * Removes a composite from the given composite, and optionally searching its children recursively
     * @private
     * @method removeComposite
     * @param {composite} compositeA
     * @param {composite} compositeB
     * @param {boolean} [deep=false]
     * @return {composite} The original compositeA with the composite removed
     */
    Composite.removeComposite = function(compositeA, compositeB, deep) {
        var position = Common.indexOf(compositeA.composites, compositeB);
        if (position !== -1) {
            Composite.removeCompositeAt(compositeA, position);
            Composite.setModified(compositeA, true, true, false);
        }

        if (deep) {
            for (var i = 0; i < compositeA.composites.length; i++){
                Composite.removeComposite(compositeA.composites[i], compositeB, true);
            }
        }

        return compositeA;
    };

    /**
     * Removes a composite from the given composite
     * @private
     * @method removeCompositeAt
     * @param {composite} composite
     * @param {number} position
     * @return {composite} The original composite with the composite removed
     */
    Composite.removeCompositeAt = function(composite, position) {
        composite.composites.splice(position, 1);
        Composite.setModified(composite, true, true, false);
        return composite;
    };

    /**
     * Adds a body to the given composite
     * @private
     * @method addBody
     * @param {composite} composite
     * @param {body} body
     * @return {composite} The original composite with the body added
     */
    Composite.addBody = function(composite, body) {
        composite.bodies.push(body);
        Composite.setModified(composite, true, true, false);
        return composite;
    };

    /**
     * Removes a body from the given composite, and optionally searching its children recursively
     * @private
     * @method removeBody
     * @param {composite} composite
     * @param {body} body
     * @param {boolean} [deep=false]
     * @return {composite} The original composite with the body removed
     */
    Composite.removeBody = function(composite, body, deep) {
        var position = Common.indexOf(composite.bodies, body);
        if (position !== -1) {
            Composite.removeBodyAt(composite, position);
            Composite.setModified(composite, true, true, false);
        }

        if (deep) {
            for (var i = 0; i < composite.composites.length; i++){
                Composite.removeBody(composite.composites[i], body, true);
            }
        }

        return composite;
    };

    /**
     * Removes a body from the given composite
     * @private
     * @method removeBodyAt
     * @param {composite} composite
     * @param {number} position
     * @return {composite} The original composite with the body removed
     */
    Composite.removeBodyAt = function(composite, position) {
        composite.bodies.splice(position, 1);
        Composite.setModified(composite, true, true, false);
        return composite;
    };

    /**
     * Adds a constraint to the given composite
     * @private
     * @method addConstraint
     * @param {composite} composite
     * @param {constraint} constraint
     * @return {composite} The original composite with the constraint added
     */
    Composite.addConstraint = function(composite, constraint) {
        composite.constraints.push(constraint);
        Composite.setModified(composite, true, true, false);
        return composite;
    };

    /**
     * Removes a constraint from the given composite, and optionally searching its children recursively
     * @private
     * @method removeConstraint
     * @param {composite} composite
     * @param {constraint} constraint
     * @param {boolean} [deep=false]
     * @return {composite} The original composite with the constraint removed
     */
    Composite.removeConstraint = function(composite, constraint, deep) {
        var position = Common.indexOf(composite.constraints, constraint);
        if (position !== -1) {
            Composite.removeConstraintAt(composite, position);
        }

        if (deep) {
            for (var i = 0; i < composite.composites.length; i++){
                Composite.removeConstraint(composite.composites[i], constraint, true);
            }
        }

        return composite;
    };

    /**
     * Removes a body from the given composite
     * @private
     * @method removeConstraintAt
     * @param {composite} composite
     * @param {number} position
     * @return {composite} The original composite with the constraint removed
     */
    Composite.removeConstraintAt = function(composite, position) {
        composite.constraints.splice(position, 1);
        Composite.setModified(composite, true, true, false);
        return composite;
    };

    /**
     * Removes all bodies, constraints and composites from the given composite
     * Optionally clearing its children recursively
     * @method clear
     * @param {world} world
     * @param {boolean} keepStatic
     * @param {boolean} [deep=false]
     */
    Composite.clear = function(composite, keepStatic, deep) {
        if (deep) {
            for (var i = 0; i < composite.composites.length; i++){
                Composite.clear(composite.composites[i], keepStatic, true);
            }
        }
        
        if (keepStatic) {
            composite.bodies = composite.bodies.filter(function(body) { return body.isStatic; });
        } else {
            composite.bodies.length = 0;
        }

        composite.constraints.length = 0;
        composite.composites.length = 0;
        Composite.setModified(composite, true, true, false);

        return composite;
    };

    /**
     * Returns all bodies in the given composite, including all bodies in its children, recursively
     * @method allBodies
     * @param {composite} composite
     * @return {body[]} All the bodies
     */
    Composite.allBodies = function(composite) {
        var bodies = [].concat(composite.bodies);

        for (var i = 0; i < composite.composites.length; i++)
            bodies = bodies.concat(Composite.allBodies(composite.composites[i]));

        return bodies;
    };

    /**
     * Returns all constraints in the given composite, including all constraints in its children, recursively
     * @method allConstraints
     * @param {composite} composite
     * @return {constraint[]} All the constraints
     */
    Composite.allConstraints = function(composite) {
        var constraints = [].concat(composite.constraints);

        for (var i = 0; i < composite.composites.length; i++)
            constraints = constraints.concat(Composite.allConstraints(composite.composites[i]));

        return constraints;
    };

    /**
     * Returns all composites in the given composite, including all composites in its children, recursively
     * @method allComposites
     * @param {composite} composite
     * @return {composite[]} All the composites
     */
    Composite.allComposites = function(composite) {
        var composites = [].concat(composite.composites);

        for (var i = 0; i < composite.composites.length; i++)
            composites = composites.concat(Composite.allComposites(composite.composites[i]));

        return composites;
    };

    /**
     * Searches the composite recursively for an object matching the type and id supplied, null if not found
     * @method get
     * @param {composite} composite
     * @param {number} id
     * @param {string} type
     * @return {object} The requested object, if found
     */
    Composite.get = function(composite, id, type) {
        var objects,
            object;

        switch (type) {
        case 'body':
            objects = Composite.allBodies(composite);
            break;
        case 'constraint':
            objects = Composite.allConstraints(composite);
            break;
        case 'composite':
            objects = Composite.allComposites(composite).concat(composite);
            break;
        }

        if (!objects)
            return null;

        object = objects.filter(function(object) { 
            return object.id.toString() === id.toString(); 
        });

        return object.length === 0 ? null : object[0];
    };

    /**
     * Moves the given object(s) from compositeA to compositeB (equal to a remove followed by an add)
     * @method move
     * @param {compositeA} compositeA
     * @param {object[]} objects
     * @param {compositeB} compositeB
     * @return {composite} Returns compositeA
     */
    Composite.move = function(compositeA, objects, compositeB) {
        Composite.remove(compositeA, objects);
        Composite.add(compositeB, objects);
        return compositeA;
    };

    /**
     * Assigns new ids for all objects in the composite, recursively
     * @method rebase
     * @param {composite} composite
     * @return {composite} Returns composite
     */
    Composite.rebase = function(composite) {
        var objects = Composite.allBodies(composite)
                        .concat(Composite.allConstraints(composite))
                        .concat(Composite.allComposites(composite));

        for (var i = 0; i < objects.length; i++) {
            objects[i].id = Common.nextId();
        }

        Composite.setModified(composite, true, true, false);

        return composite;
    };

    /**
     * Translates all children in the composite by a given vector relative to their current positions, 
     * without imparting any velocity.
     * @method translate
     * @param {composite} composite
     * @param {vector} translation
     * @param {bool} [recursive=true]
     */
    Composite.translate = function(composite, translation, recursive) {
        var bodies = recursive ? Composite.allBodies(composite) : composite.bodies;

        for (var i = 0; i < bodies.length; i++) {
            Body.translate(bodies[i], translation);
        }

        Composite.setModified(composite, true, true, false);

        return composite;
    };

    /**
     * Rotates all children in the composite by a given angle about the given point, without imparting any angular velocity.
     * @method rotate
     * @param {composite} composite
     * @param {number} rotation
     * @param {vector} point
     * @param {bool} [recursive=true]
     */
    Composite.rotate = function(composite, rotation, point, recursive) {
        var cos = Math.cos(rotation),
            sin = Math.sin(rotation),
            bodies = recursive ? Composite.allBodies(composite) : composite.bodies;

        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i],
                dx = body.position.x - point.x,
                dy = body.position.y - point.y;
                
            Body.setPosition(body, {
                x: point.x + (dx * cos - dy * sin),
                y: point.y + (dx * sin + dy * cos)
            });

            Body.rotate(body, rotation);
        }

        Composite.setModified(composite, true, true, false);

        return composite;
    };

    /**
     * Scales all children in the composite, including updating physical properties (mass, area, axes, inertia), from a world-space point.
     * @method scale
     * @param {composite} composite
     * @param {number} scaleX
     * @param {number} scaleY
     * @param {vector} point
     * @param {bool} [recursive=true]
     */
    Composite.scale = function(composite, scaleX, scaleY, point, recursive) {
        var bodies = recursive ? Composite.allBodies(composite) : composite.bodies;

        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i],
                dx = body.position.x - point.x,
                dy = body.position.y - point.y;
                
            Body.setPosition(body, {
                x: point.x + dx * scaleX,
                y: point.y + dy * scaleY
            });

            Body.scale(body, scaleX, scaleY);
        }

        Composite.setModified(composite, true, true, false);

        return composite;
    };

    /*
    *
    *  Events Documentation
    *
    */

    /**
    * Fired when a call to `Composite.add` is made, before objects have been added.
    *
    * @event beforeAdd
    * @param {} event An event object
    * @param {} event.object The object(s) to be added (may be a single body, constraint, composite or a mixed array of these)
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired when a call to `Composite.add` is made, after objects have been added.
    *
    * @event afterAdd
    * @param {} event An event object
    * @param {} event.object The object(s) that have been added (may be a single body, constraint, composite or a mixed array of these)
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired when a call to `Composite.remove` is made, before objects have been removed.
    *
    * @event beforeRemove
    * @param {} event An event object
    * @param {} event.object The object(s) to be removed (may be a single body, constraint, composite or a mixed array of these)
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired when a call to `Composite.remove` is made, after objects have been removed.
    *
    * @event afterRemove
    * @param {} event An event object
    * @param {} event.object The object(s) that have been removed (may be a single body, constraint, composite or a mixed array of these)
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /*
    *
    *  Properties Documentation
    *
    */

    /**
     * An integer `Number` uniquely identifying number generated in `Composite.create` by `Common.nextId`.
     *
     * @property id
     * @type number
     */

    /**
     * A `String` denoting the type of object.
     *
     * @property type
     * @type string
     * @default "composite"
     */

    /**
     * An arbitrary `String` name to help the user identify and manage composites.
     *
     * @property label
     * @type string
     * @default "Composite"
     */

    /**
     * A flag that specifies whether the composite has been modified during the current step.
     * Most `Matter.Composite` methods will automatically set this flag to `true` to inform the engine of changes to be handled.
     * If you need to change it manually, you should use the `Composite.setModified` method.
     *
     * @property isModified
     * @type boolean
     * @default false
     */

    /**
     * The `Composite` that is the parent of this composite. It is automatically managed by the `Matter.Composite` methods.
     *
     * @property parent
     * @type composite
     * @default null
     */

    /**
     * An array of `Body` that are _direct_ children of this composite.
     * To add or remove bodies you should use `Composite.add` and `Composite.remove` methods rather than directly modifying this property.
     * If you wish to recursively find all descendants, you should use the `Composite.allBodies` method.
     *
     * @property bodies
     * @type body[]
     * @default []
     */

    /**
     * An array of `Constraint` that are _direct_ children of this composite.
     * To add or remove constraints you should use `Composite.add` and `Composite.remove` methods rather than directly modifying this property.
     * If you wish to recursively find all descendants, you should use the `Composite.allConstraints` method.
     *
     * @property constraints
     * @type constraint[]
     * @default []
     */

    /**
     * An array of `Composite` that are _direct_ children of this composite.
     * To add or remove composites you should use `Composite.add` and `Composite.remove` methods rather than directly modifying this property.
     * If you wish to recursively find all descendants, you should use the `Composite.allComposites` method.
     *
     * @property composites
     * @type composite[]
     * @default []
     */

})();

;   // End src/body/Composite.js


// Begin src/body/World.js

/**
* The `Matter.World` module contains methods for creating and manipulating the world composite.
* A `Matter.World` is a `Matter.Composite` body, which is a collection of `Matter.Body`, `Matter.Constraint` and other `Matter.Composite`.
* A `Matter.World` has a few additional properties including `gravity` and `bounds`.
* It is important to use the functions in the `Matter.Composite` module to modify the world composite, rather than directly modifying its properties.
* There are also a few methods here that alias those in `Matter.Composite` for easier readability.
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class World
*/

var World = {};

(function() {

    /**
     * Creates a new world composite. The options parameter is an object that specifies any properties you wish to override the defaults.
     * See the properites section below for detailed information on what you can pass via the `options` object.
     * @method create
     * @constructor
     * @param {} options
     * @return {world} A new world
     */
    World.create = function(options) {
        var composite = Composite.create();

        var defaults = {
            label: 'World',
            gravity: { x: 0, y: 1 },
            bounds: { 
                min: { x: 0, y: 0 }, 
                max: { x: 800, y: 600 } 
            }
        };
        
        return Common.extend(composite, defaults, options);
    };

    // World is a Composite body
    // see src/module/Outro.js for these aliases:
    
    /**
     * An alias for Composite.clear since World is also a Composite
     * @method clear
     * @param {world} world
     * @param {boolean} keepStatic
     */

    /**
     * An alias for Composite.add since World is also a Composite
     * @method addComposite
     * @param {world} world
     * @param {composite} composite
     * @return {world} The original world with the objects from composite added
     */
    
     /**
      * An alias for Composite.addBody since World is also a Composite
      * @method addBody
      * @param {world} world
      * @param {body} body
      * @return {world} The original world with the body added
      */

     /**
      * An alias for Composite.addConstraint since World is also a Composite
      * @method addConstraint
      * @param {world} world
      * @param {constraint} constraint
      * @return {world} The original world with the constraint added
      */

})();

;   // End src/body/World.js


// Begin src/collision/Contact.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Contact
*/

var Contact = {};

(function() {

    /**
     * Description
     * @method create
     * @param {vertex} vertex
     * @return {contact} A new contact
     */
    Contact.create = function(vertex) {
        return {
            id: Contact.id(vertex),
            vertex: vertex,
            normalImpulse: 0,
            tangentImpulse: 0
        };
    };
    
    /**
     * Description
     * @method id
     * @param {vertex} vertex
     * @return {string} Unique contactID
     */
    Contact.id = function(vertex) {
        return vertex.body.id + '_' + vertex.index;
    };

})();


;   // End src/collision/Contact.js


// Begin src/collision/Detector.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Detector
*/

// TODO: speculative contacts

var Detector = {};

(function() {

    /**
     * Description
     * @method collisions
     * @param {pair[]} broadphasePairs
     * @param {engine} engine
     * @return {array} collisions
     */
    Detector.collisions = function(broadphasePairs, engine) {
        var collisions = [],
            metrics = engine.metrics,
            pairsTable = engine.pairs.table;

        for (var i = 0; i < broadphasePairs.length; i++) {
            var bodyA = broadphasePairs[i][0], 
                bodyB = broadphasePairs[i][1];

            if ((bodyA.isStatic || bodyA.isSleeping) && (bodyB.isStatic || bodyB.isSleeping))
                continue;
            
            if (!Detector.canCollide(bodyA.collisionFilter, bodyB.collisionFilter))
                continue;

            metrics.midphaseTests += 1;

            // mid phase
            if (Bounds.overlaps(bodyA.bounds, bodyB.bounds)) {

                // find a previous collision we could reuse
                var pairId = Pair.id(bodyA, bodyB),
                    pair = pairsTable[pairId],
                    previousCollision;

                if (pair && pair.isActive) {
                    previousCollision = pair.collision;
                } else {
                    previousCollision = null;
                }

                // narrow phase
                var collision = SAT.collides(bodyA, bodyB, previousCollision);

                metrics.narrowphaseTests += 1;

                if (collision.reused)
                    metrics.narrowReuseCount += 1;

                if (collision.collided) {
                    collisions.push(collision);
                    metrics.narrowDetections += 1;
                }
            }
        }

        return collisions;
    };

    /**
     * Description
     * @method bruteForce
     * @param {body[]} bodies
     * @param {engine} engine
     * @return {array} collisions
     */
    Detector.bruteForce = function(bodies, engine) {
        var collisions = [],
            metrics = engine.metrics,
            pairsTable = engine.pairs.table;

        for (var i = 0; i < bodies.length; i++) {
            for (var j = i + 1; j < bodies.length; j++) {
                var bodyA = bodies[i], 
                    bodyB = bodies[j];

                // NOTE: could share a function for the below, but may drop performance?

                if ((bodyA.isStatic || bodyA.isSleeping) && (bodyB.isStatic || bodyB.isSleeping))
                    continue;
                
                if (!Detector.canCollide(bodyA.collisionFilter, bodyB.collisionFilter))
                    continue;

                metrics.midphaseTests += 1;

                // mid phase
                if (Bounds.overlaps(bodyA.bounds, bodyB.bounds)) {

                    // find a previous collision we could reuse
                    var pairId = Pair.id(bodyA, bodyB),
                        pair = pairsTable[pairId],
                        previousCollision;

                    if (pair && pair.isActive) {
                        previousCollision = pair.collision;
                    } else {
                        previousCollision = null;
                    }

                    // narrow phase
                    var collision = SAT.collides(bodyA, bodyB, previousCollision);

                    metrics.narrowphaseTests += 1;

                    if (collision.reused)
                        metrics.narrowReuseCount += 1;

                    if (collision.collided) {
                        collisions.push(collision);
                        metrics.narrowDetections += 1;
                    }
                }
            }
        }

        return collisions;
    };

    /**
     * Returns `true` if both supplied collision filters will allow a collision to occur.
     * See `body.collisionFilter` for more information.
     * @method canCollide
     * @param {} filterA
     * @param {} filterB
     * @return {bool} `true` if collision can occur
     */
    Detector.canCollide = function(filterA, filterB) {
        if (filterA.group === filterB.group && filterA.group !== 0)
            return filterA.group > 0;

        return (filterA.mask & filterB.category) !== 0 && (filterB.mask & filterA.category) !== 0;
    };

})();


;   // End src/collision/Detector.js


// Begin src/collision/Grid.js

/**
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Grid
*/

var Grid = {};

(function() {

    /**
     * Description
     * @method create
     * @param {} options
     * @return {grid} A new grid
     */
    Grid.create = function(options) {
        var defaults = {
            controller: Grid,
            detector: Detector.collisions,
            buckets: {},
            pairs: {},
            pairsList: [],
            bucketWidth: 48,
            bucketHeight: 48
        };

        return Common.extend(defaults, options);
    };

    /**
     * Description
     * @method update
     * @param {grid} grid
     * @param {body[]} bodies
     * @param {engine} engine
     * @param {boolean} forceUpdate
     */
    Grid.update = function(grid, bodies, engine, forceUpdate) {
        var i, col, row,
            world = engine.world,
            buckets = grid.buckets,
            bucket,
            bucketId,
            metrics = engine.metrics,
            gridChanged = false;

        metrics.broadphaseTests = 0;

        for (i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (body.isSleeping && !forceUpdate)
                continue;

            // don't update out of world bodies
            if (body.bounds.max.x < 0 || body.bounds.min.x > world.bounds.width
                || body.bounds.max.y < 0 || body.bounds.min.y > world.bounds.height)
                continue;

            var newRegion = _getRegion(grid, body);

            // if the body has changed grid region
            if (!body.region || newRegion.id !== body.region.id || forceUpdate) {

                metrics.broadphaseTests += 1;

                if (!body.region || forceUpdate)
                    body.region = newRegion;

                var union = _regionUnion(newRegion, body.region);

                // update grid buckets affected by region change
                // iterate over the union of both regions
                for (col = union.startCol; col <= union.endCol; col++) {
                    for (row = union.startRow; row <= union.endRow; row++) {
                        bucketId = _getBucketId(col, row);
                        bucket = buckets[bucketId];

                        var isInsideNewRegion = (col >= newRegion.startCol && col <= newRegion.endCol
                                                && row >= newRegion.startRow && row <= newRegion.endRow);

                        var isInsideOldRegion = (col >= body.region.startCol && col <= body.region.endCol
                                                && row >= body.region.startRow && row <= body.region.endRow);

                        // remove from old region buckets
                        if (!isInsideNewRegion && isInsideOldRegion) {
                            if (isInsideOldRegion) {
                                if (bucket)
                                    _bucketRemoveBody(grid, bucket, body);
                            }
                        }

                        // add to new region buckets
                        if (body.region === newRegion || (isInsideNewRegion && !isInsideOldRegion) || forceUpdate) {
                            if (!bucket)
                                bucket = _createBucket(buckets, bucketId);
                            _bucketAddBody(grid, bucket, body);
                        }
                    }
                }

                // set the new region
                body.region = newRegion;

                // flag changes so we can update pairs
                gridChanged = true;
            }
        }

        // update pairs list only if pairs changed (i.e. a body changed region)
        if (gridChanged)
            grid.pairsList = _createActivePairsList(grid);
    };

    /**
     * Description
     * @method clear
     * @param {grid} grid
     */
    Grid.clear = function(grid) {
        grid.buckets = {};
        grid.pairs = {};
        grid.pairsList = [];
    };

    /**
     * Description
     * @method _regionUnion
     * @private
     * @param {} regionA
     * @param {} regionB
     * @return CallExpression
     */
    var _regionUnion = function(regionA, regionB) {
        var startCol = Math.min(regionA.startCol, regionB.startCol),
            endCol = Math.max(regionA.endCol, regionB.endCol),
            startRow = Math.min(regionA.startRow, regionB.startRow),
            endRow = Math.max(regionA.endRow, regionB.endRow);

        return _createRegion(startCol, endCol, startRow, endRow);
    };

    /**
     * Description
     * @method _getRegion
     * @private
     * @param {} grid
     * @param {} body
     * @return CallExpression
     */
    var _getRegion = function(grid, body) {
        var bounds = body.bounds,
            startCol = Math.floor(bounds.min.x / grid.bucketWidth),
            endCol = Math.floor(bounds.max.x / grid.bucketWidth),
            startRow = Math.floor(bounds.min.y / grid.bucketHeight),
            endRow = Math.floor(bounds.max.y / grid.bucketHeight);

        return _createRegion(startCol, endCol, startRow, endRow);
    };

    /**
     * Description
     * @method _createRegion
     * @private
     * @param {} startCol
     * @param {} endCol
     * @param {} startRow
     * @param {} endRow
     * @return ObjectExpression
     */
    var _createRegion = function(startCol, endCol, startRow, endRow) {
        return { 
            id: startCol + ',' + endCol + ',' + startRow + ',' + endRow,
            startCol: startCol, 
            endCol: endCol, 
            startRow: startRow, 
            endRow: endRow 
        };
    };

    /**
     * Description
     * @method _getBucketId
     * @private
     * @param {} column
     * @param {} row
     * @return BinaryExpression
     */
    var _getBucketId = function(column, row) {
        return column + ',' + row;
    };

    /**
     * Description
     * @method _createBucket
     * @private
     * @param {} buckets
     * @param {} bucketId
     * @return bucket
     */
    var _createBucket = function(buckets, bucketId) {
        var bucket = buckets[bucketId] = [];
        return bucket;
    };

    /**
     * Description
     * @method _bucketAddBody
     * @private
     * @param {} grid
     * @param {} bucket
     * @param {} body
     */
    var _bucketAddBody = function(grid, bucket, body) {
        // add new pairs
        for (var i = 0; i < bucket.length; i++) {
            var bodyB = bucket[i];

            if (body.id === bodyB.id || (body.isStatic && bodyB.isStatic))
                continue;

            // keep track of the number of buckets the pair exists in
            // important for Grid.update to work
            var pairId = Pair.id(body, bodyB),
                pair = grid.pairs[pairId];

            if (pair) {
                pair[2] += 1;
            } else {
                grid.pairs[pairId] = [body, bodyB, 1];
            }
        }

        // add to bodies (after pairs, otherwise pairs with self)
        bucket.push(body);
    };

    /**
     * Description
     * @method _bucketRemoveBody
     * @private
     * @param {} grid
     * @param {} bucket
     * @param {} body
     */
    var _bucketRemoveBody = function(grid, bucket, body) {
        // remove from bucket
        bucket.splice(Common.indexOf(bucket, body), 1);

        // update pair counts
        for (var i = 0; i < bucket.length; i++) {
            // keep track of the number of buckets the pair exists in
            // important for _createActivePairsList to work
            var bodyB = bucket[i],
                pairId = Pair.id(body, bodyB),
                pair = grid.pairs[pairId];

            if (pair)
                pair[2] -= 1;
        }
    };

    /**
     * Description
     * @method _createActivePairsList
     * @private
     * @param {} grid
     * @return pairs
     */
    var _createActivePairsList = function(grid) {
        var pairKeys,
            pair,
            pairs = [];

        // grid.pairs is used as a hashmap
        pairKeys = Common.keys(grid.pairs);

        // iterate over grid.pairs
        for (var k = 0; k < pairKeys.length; k++) {
            pair = grid.pairs[pairKeys[k]];

            // if pair exists in at least one bucket
            // it is a pair that needs further collision testing so push it
            if (pair[2] > 0) {
                pairs.push(pair);
            } else {
                delete grid.pairs[pairKeys[k]];
            }
        }

        return pairs;
    };
    
})();

;   // End src/collision/Grid.js


// Begin src/collision/Pair.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Pair
*/

var Pair = {};

(function() {
    
    /**
     * Description
     * @method create
     * @param {collision} collision
     * @return {pair} A new pair
     */
    Pair.create = function(collision, timestamp) {
        var bodyA = collision.bodyA,
            bodyB = collision.bodyB;

        var pair = {
            id: Pair.id(bodyA, bodyB),
            bodyA: bodyA,
            bodyB: bodyB,
            contacts: {},
            activeContacts: [],
            separation: 0,
            isActive: true,
            timeCreated: timestamp,
            timeUpdated: timestamp,
            inverseMass: bodyA.inverseMass + bodyB.inverseMass,
            friction: Math.min(bodyA.friction, bodyB.friction),
            restitution: Math.max(bodyA.restitution, bodyB.restitution),
            slop: Math.max(bodyA.slop, bodyB.slop)
        };

        Pair.update(pair, collision, timestamp);

        return pair;
    };

    /**
     * Description
     * @method update
     * @param {pair} pair
     * @param {collision} collision
     */
    Pair.update = function(pair, collision, timestamp) {
        var contacts = pair.contacts,
            supports = collision.supports,
            activeContacts = pair.activeContacts;
        
        pair.collision = collision;
        pair.inverseMass = collision.bodyA.inverseMass + collision.bodyB.inverseMass;
        pair.friction = Math.min(collision.bodyA.friction, collision.bodyB.friction);
        pair.restitution = Math.max(collision.bodyA.restitution, collision.bodyB.restitution);
        pair.slop = Math.max(collision.bodyA.slop, collision.bodyB.slop);
        activeContacts.length = 0;
        
        if (collision.collided) {
            for (var i = 0; i < supports.length; i++) {
                var support = supports[i],
                    contactId = Contact.id(support),
                    contact = contacts[contactId];

                if (contact) {
                    activeContacts.push(contact);
                } else {
                    activeContacts.push(contacts[contactId] = Contact.create(support));
                }
            }

            pair.separation = collision.depth;
            Pair.setActive(pair, true, timestamp);
        } else {
            if (pair.isActive === true)
                Pair.setActive(pair, false, timestamp);
        }
    };
    
    /**
     * Description
     * @method setActive
     * @param {pair} pair
     * @param {bool} isActive
     */
    Pair.setActive = function(pair, isActive, timestamp) {
        if (isActive) {
            pair.isActive = true;
            pair.timeUpdated = timestamp;
        } else {
            pair.isActive = false;
            pair.activeContacts.length = 0;
        }
    };

    /**
     * Description
     * @method id
     * @param {body} bodyA
     * @param {body} bodyB
     * @return {string} Unique pairId
     */
    Pair.id = function(bodyA, bodyB) {
        if (bodyA.id < bodyB.id) {
            return bodyA.id + '_' + bodyB.id;
        } else {
            return bodyB.id + '_' + bodyA.id;
        }
    };

})();


;   // End src/collision/Pair.js


// Begin src/collision/Pairs.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Pairs
*/

var Pairs = {};

(function() {
    
    var _pairMaxIdleLife = 1000;

    /**
     * Creates a new pairs structure
     * @method create
     * @param {object} options
     * @return {pairs} A new pairs structure
     */
    Pairs.create = function(options) {
        return Common.extend({ 
            table: {},
            list: [],
            collisionStart: [],
            collisionActive: [],
            collisionEnd: []
        }, options);
    };

    /**
     * Description
     * @method update
     * @param {object} pairs
     * @param {collision[]} collisions
     */
    Pairs.update = function(pairs, collisions, timestamp) {
        var pairsList = pairs.list,
            pairsTable = pairs.table,
            collisionStart = pairs.collisionStart,
            collisionEnd = pairs.collisionEnd,
            collisionActive = pairs.collisionActive,
            activePairIds = [],
            collision,
            pairId,
            pair,
            i;

        // clear collision state arrays, but maintain old reference
        collisionStart.length = 0;
        collisionEnd.length = 0;
        collisionActive.length = 0;

        for (i = 0; i < collisions.length; i++) {
            collision = collisions[i];

            if (collision.collided) {
                pairId = Pair.id(collision.bodyA, collision.bodyB);
                activePairIds.push(pairId);

                pair = pairsTable[pairId];
                
                if (pair) {
                    // pair already exists (but may or may not be active)
                    if (pair.isActive) {
                        // pair exists and is active
                        collisionActive.push(pair);
                    } else {
                        // pair exists but was inactive, so a collision has just started again
                        collisionStart.push(pair);
                    }

                    // update the pair
                    Pair.update(pair, collision, timestamp);
                } else {
                    // pair did not exist, create a new pair
                    pair = Pair.create(collision, timestamp);
                    pairsTable[pairId] = pair;

                    // push the new pair
                    collisionStart.push(pair);
                    pairsList.push(pair);
                }
            }
        }

        // deactivate previously active pairs that are now inactive
        for (i = 0; i < pairsList.length; i++) {
            pair = pairsList[i];
            if (pair.isActive && Common.indexOf(activePairIds, pair.id) === -1) {
                Pair.setActive(pair, false, timestamp);
                collisionEnd.push(pair);
            }
        }
    };
    
    /**
     * Description
     * @method removeOld
     * @param {object} pairs
     */
    Pairs.removeOld = function(pairs, timestamp) {
        var pairsList = pairs.list,
            pairsTable = pairs.table,
            indexesToRemove = [],
            pair,
            collision,
            pairIndex,
            i;

        for (i = 0; i < pairsList.length; i++) {
            pair = pairsList[i];
            collision = pair.collision;
            
            // never remove sleeping pairs
            if (collision.bodyA.isSleeping || collision.bodyB.isSleeping) {
                pair.timeUpdated = timestamp;
                continue;
            }

            // if pair is inactive for too long, mark it to be removed
            if (timestamp - pair.timeUpdated > _pairMaxIdleLife) {
                indexesToRemove.push(i);
            }
        }

        // remove marked pairs
        for (i = 0; i < indexesToRemove.length; i++) {
            pairIndex = indexesToRemove[i] - i;
            pair = pairsList[pairIndex];
            delete pairsTable[pair.id];
            pairsList.splice(pairIndex, 1);
        }
    };

    /**
     * Clears the given pairs structure
     * @method create
     * @param {object} options
     * @param {pairs} pairs
     */
    Pairs.clear = function(pairs) {
        pairs.table = {};
        pairs.list.length = 0;
        pairs.collisionStart.length = 0;
        pairs.collisionActive.length = 0;
        pairs.collisionEnd.length = 0;
        return pairs;
    };

})();

;   // End src/collision/Pairs.js


// Begin src/collision/Query.js

/**
* The `Matter.Query` module contains methods for performing collision queries.
*
* @class Query
*/

var Query = {};

(function() {

    /**
     * Casts a ray segment against a set of bodies and returns all collisions, ray width is optional. Intersection points are not provided.
     * @method ray
     * @param {body[]} bodies
     * @param {vector} startPoint
     * @param {vector} endPoint
     * @param {number} [rayWidth]
     * @return {object[]} Collisions
     */
    Query.ray = function(bodies, startPoint, endPoint, rayWidth) {
        rayWidth = rayWidth || Number.MIN_VALUE;

        var rayAngle = Vector.angle(startPoint, endPoint),
            rayLength = Vector.magnitude(Vector.sub(startPoint, endPoint)),
            rayX = (endPoint.x + startPoint.x) * 0.5,
            rayY = (endPoint.y + startPoint.y) * 0.5,
            ray = Bodies.rectangle(rayX, rayY, rayLength, rayWidth, { angle: rayAngle }),
            collisions = [];

        for (var i = 0; i < bodies.length; i++) {
            var bodyA = bodies[i];

            if (Bounds.overlaps(bodyA.bounds, ray.bounds)) {
                var collision = SAT.collides(bodyA, ray);
                if (collision.collided) {
                    collision.body = collision.bodyA = collision.bodyB = bodyA;
                    collisions.push(collision);
                }
            }
        }

        return collisions;
    };

    /**
     * Returns all bodies whose bounds are inside (or outside if set) the given set of bounds, from the given set of bodies.
     * @method region
     * @param {body[]} bodies
     * @param {bounds} bounds
     * @param {bool} [outside=false]
     * @return {body[]} The bodies matching the query
     */
    Query.region = function(bodies, bounds, outside) {
        var result = [];

        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i],
                overlaps = Bounds.overlaps(body.bounds, bounds);
            if ((overlaps && !outside) || (!overlaps && outside))
                result.push(body);
        }

        return result;
    };

})();

;   // End src/collision/Query.js


// Begin src/collision/Resolver.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Resolver
*/

var Resolver = {};

(function() {

    var _restingThresh = 4,
        _positionDampen = 0.2,
        _positionWarming = 0.6;

    /**
     * Description
     * @method solvePosition
     * @param {pair[]} pairs
     * @param {number} timeScale
     */
    Resolver.solvePosition = function(pairs, timeScale) {
        var i,
            pair,
            collision,
            bodyA,
            bodyB,
            vertex,
            vertexCorrected,
            normal,
            bodyBtoA;

        // find impulses required to resolve penetration
        for (i = 0; i < pairs.length; i++) {
            pair = pairs[i];
            
            if (!pair.isActive)
                continue;
            
            collision = pair.collision;
            bodyA = collision.bodyA;
            bodyB = collision.bodyB;
            vertex = collision.supports[0];
            vertexCorrected = collision.supportCorrected;
            normal = collision.normal;

            // get current separation between body edges involved in collision
            bodyBtoA = Vector.sub(Vector.add(bodyB.positionImpulse, vertex), 
                                    Vector.add(bodyA.positionImpulse, vertexCorrected));

            pair.separation = Vector.dot(normal, bodyBtoA);
        }
        
        for (i = 0; i < pairs.length; i++) {
            pair = pairs[i];
            
            if (!pair.isActive)
                continue;
            
            collision = pair.collision;
            bodyA = collision.bodyA;
            bodyB = collision.bodyB;
            normal = collision.normal;
            positionImpulse = ((pair.separation * _positionDampen) - pair.slop) * timeScale;
        
            if (bodyA.isStatic || bodyB.isStatic)
                positionImpulse *= 2;
            
            if (!(bodyA.isStatic || bodyA.isSleeping)) {
                bodyA.positionImpulse.x += normal.x * positionImpulse;
                bodyA.positionImpulse.y += normal.y * positionImpulse;
            }

            if (!(bodyB.isStatic || bodyB.isSleeping)) {
                bodyB.positionImpulse.x -= normal.x * positionImpulse;
                bodyB.positionImpulse.y -= normal.y * positionImpulse;
            }
        }
    };

    /**
     * Description
     * @method postSolvePosition
     * @param {body[]} bodies
     */
    Resolver.postSolvePosition = function(bodies) {
        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (body.positionImpulse.x !== 0 || body.positionImpulse.y !== 0) {
                // move the body without changing velocity
                body.position.x += body.positionImpulse.x;
                body.position.y += body.positionImpulse.y;
                body.positionPrev.x += body.positionImpulse.x;
                body.positionPrev.y += body.positionImpulse.y;

                // update body geometry
                Vertices.translate(body.vertices, body.positionImpulse);
                Bounds.update(body.bounds, body.vertices, body.velocity);
                
                // dampen accumulator to warm the next step
                body.positionImpulse.x *= _positionWarming;
                body.positionImpulse.y *= _positionWarming;
            }
        }
    };

    /**
     * Description
     * @method preSolveVelocity
     * @param {pair[]} pairs
     */
    Resolver.preSolveVelocity = function(pairs) {
        var impulse = {},
            i,
            j,
            pair,
            contacts,
            collision,
            bodyA,
            bodyB,
            normal,
            tangent,
            contact,
            contactVertex,
            normalImpulse,
            tangentImpulse,
            offset;
        
        for (i = 0; i < pairs.length; i++) {
            pair = pairs[i];
            
            if (!pair.isActive)
                continue;
            
            contacts = pair.activeContacts;
            collision = pair.collision;
            bodyA = collision.bodyA;
            bodyB = collision.bodyB;
            normal = collision.normal;
            tangent = collision.tangent;
                
            // resolve each contact
            for (j = 0; j < contacts.length; j++) {
                contact = contacts[j];
                contactVertex = contact.vertex;
                normalImpulse = contact.normalImpulse;
                tangentImpulse = contact.tangentImpulse;
                
                // total impulse from contact
                impulse.x = (normal.x * normalImpulse) + (tangent.x * tangentImpulse);
                impulse.y = (normal.y * normalImpulse) + (tangent.y * tangentImpulse);
                
                // apply impulse from contact
                if (!(bodyA.isStatic || bodyA.isSleeping)) {
                    offset = Vector.sub(contactVertex, bodyA.position);
                    bodyA.positionPrev.x += impulse.x * bodyA.inverseMass;
                    bodyA.positionPrev.y += impulse.y * bodyA.inverseMass;
                    bodyA.anglePrev += Vector.cross(offset, impulse) * bodyA.inverseInertia;
                }

                if (!(bodyB.isStatic || bodyB.isSleeping)) {
                    offset = Vector.sub(contactVertex, bodyB.position);
                    bodyB.positionPrev.x -= impulse.x * bodyB.inverseMass;
                    bodyB.positionPrev.y -= impulse.y * bodyB.inverseMass;
                    bodyB.anglePrev -= Vector.cross(offset, impulse) * bodyB.inverseInertia;
                }
            }
        }
    };

    /**
     * Description
     * @method solveVelocity
     * @param {pair[]} pairs
     */
    Resolver.solveVelocity = function(pairs, timeScale) {
        var impulse = {},
            timeScaleSquared = timeScale * timeScale;
        
        for (var i = 0; i < pairs.length; i++) {
            var pair = pairs[i];
            
            if (!pair.isActive)
                continue;
            
            var collision = pair.collision,
                bodyA = collision.bodyA,
                bodyB = collision.bodyB,
                normal = collision.normal,
                tangent = collision.tangent,
                contacts = pair.activeContacts,
                contactShare = 1 / contacts.length;

            // update body velocities
            bodyA.velocity.x = bodyA.position.x - bodyA.positionPrev.x;
            bodyA.velocity.y = bodyA.position.y - bodyA.positionPrev.y;
            bodyB.velocity.x = bodyB.position.x - bodyB.positionPrev.x;
            bodyB.velocity.y = bodyB.position.y - bodyB.positionPrev.y;
            bodyA.angularVelocity = bodyA.angle - bodyA.anglePrev;
            bodyB.angularVelocity = bodyB.angle - bodyB.anglePrev;

            // resolve each contact
            for (var j = 0; j < contacts.length; j++) {
                var contact = contacts[j],
                    contactVertex = contact.vertex,
                    offsetA = Vector.sub(contactVertex, bodyA.position),
                    offsetB = Vector.sub(contactVertex, bodyB.position),
                    velocityPointA = Vector.add(bodyA.velocity, Vector.mult(Vector.perp(offsetA), bodyA.angularVelocity)),
                    velocityPointB = Vector.add(bodyB.velocity, Vector.mult(Vector.perp(offsetB), bodyB.angularVelocity)), 
                    relativeVelocity = Vector.sub(velocityPointA, velocityPointB),
                    normalVelocity = Vector.dot(normal, relativeVelocity);

                var tangentVelocity = Vector.dot(tangent, relativeVelocity),
                    tangentSpeed = Math.abs(tangentVelocity),
                    tangentVelocityDirection = Common.sign(tangentVelocity);

                // raw impulses
                var normalImpulse = (1 + pair.restitution) * normalVelocity,
                    normalForce = Common.clamp(pair.separation + normalVelocity, 0, 1);

                // coulomb friction
                var tangentImpulse = tangentVelocity;
                if (tangentSpeed > normalForce * pair.friction * timeScaleSquared)
                    tangentImpulse = normalForce * pair.friction * timeScaleSquared * tangentVelocityDirection;

                // modify impulses accounting for mass, inertia and offset
                var oAcN = Vector.cross(offsetA, normal),
                    oBcN = Vector.cross(offsetB, normal),
                    share = contactShare / (pair.inverseMass + bodyA.inverseInertia * oAcN * oAcN  + bodyB.inverseInertia * oBcN * oBcN);
                normalImpulse *= share;
                tangentImpulse *= share;
                
                // handle high velocity and resting collisions separately
                if (normalVelocity < 0 && normalVelocity * normalVelocity > _restingThresh * timeScaleSquared) {
                    // high velocity so clear cached contact impulse
                    contact.normalImpulse = 0;
                    contact.tangentImpulse = 0;
                } else {
                    // solve resting collision constraints using Erin Catto's method (GDC08)

                    // impulse constraint, tends to 0
                    var contactNormalImpulse = contact.normalImpulse;
                    contact.normalImpulse = Math.min(contact.normalImpulse + normalImpulse, 0);
                    normalImpulse = contact.normalImpulse - contactNormalImpulse;
                    
                    // tangent impulse, tends to -maxFriction or maxFriction
                    var contactTangentImpulse = contact.tangentImpulse;
                    contact.tangentImpulse = Common.clamp(contact.tangentImpulse + tangentImpulse, -tangentSpeed, tangentSpeed);
                    tangentImpulse = contact.tangentImpulse - contactTangentImpulse;
                }
                
                // total impulse from contact
                impulse.x = (normal.x * normalImpulse) + (tangent.x * tangentImpulse);
                impulse.y = (normal.y * normalImpulse) + (tangent.y * tangentImpulse);
                
                // apply impulse from contact
                if (!(bodyA.isStatic || bodyA.isSleeping)) {
                    bodyA.positionPrev.x += impulse.x * bodyA.inverseMass;
                    bodyA.positionPrev.y += impulse.y * bodyA.inverseMass;
                    bodyA.anglePrev += Vector.cross(offsetA, impulse) * bodyA.inverseInertia;
                }

                if (!(bodyB.isStatic || bodyB.isSleeping)) {
                    bodyB.positionPrev.x -= impulse.x * bodyB.inverseMass;
                    bodyB.positionPrev.y -= impulse.y * bodyB.inverseMass;
                    bodyB.anglePrev -= Vector.cross(offsetB, impulse) * bodyB.inverseInertia;
                }
            }
        }
    };

})();

;   // End src/collision/Resolver.js


// Begin src/collision/SAT.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class SAT
*/

// TODO: true circles and curves

var SAT = {};

(function() {

    /**
     * Description
     * @method collides
     * @param {body} bodyA
     * @param {body} bodyB
     * @param {collision} previousCollision
     * @return {collision} collision
     */
    SAT.collides = function(bodyA, bodyB, previousCollision) {
        var overlapAB,
            overlapBA, 
            minOverlap,
            collision,
            prevCol = previousCollision,
            canReusePrevCol = false;

        if (prevCol) {
            // estimate total motion
            var motion = bodyA.speed * bodyA.speed + bodyA.angularSpeed * bodyA.angularSpeed
                       + bodyB.speed * bodyB.speed + bodyB.angularSpeed * bodyB.angularSpeed;

            // we may be able to (partially) reuse collision result 
            // but only safe if collision was resting
            canReusePrevCol = prevCol && prevCol.collided && motion < 0.2;

            // reuse collision object
            collision = prevCol;
        } else {
            collision = { collided: false, bodyA: bodyA, bodyB: bodyB };
        }

        if (prevCol && canReusePrevCol) {
            // if we can reuse the collision result
            // we only need to test the previously found axis
            var axes = [prevCol.bodyA.axes[prevCol.axisNumber]];

            minOverlap = _overlapAxes(prevCol.bodyA.vertices, prevCol.bodyB.vertices, axes);
            collision.reused = true;

            if (minOverlap.overlap <= 0) {
                collision.collided = false;
                return collision;
            }
        } else {
            // if we can't reuse a result, perform a full SAT test

            overlapAB = _overlapAxes(bodyA.vertices, bodyB.vertices, bodyA.axes);

            if (overlapAB.overlap <= 0) {
                collision.collided = false;
                return collision;
            }

            overlapBA = _overlapAxes(bodyB.vertices, bodyA.vertices, bodyB.axes);

            if (overlapBA.overlap <= 0) {
                collision.collided = false;
                return collision;
            }

            if (overlapAB.overlap < overlapBA.overlap) {
                minOverlap = overlapAB;
                collision.bodyA = bodyA;
                collision.bodyB = bodyB;
            } else {
                minOverlap = overlapBA;
                collision.bodyA = bodyB;
                collision.bodyB = bodyA;
            }

            // important for reuse later
            collision.axisNumber = minOverlap.axisNumber;
        }

        collision.collided = true;
        collision.normal = minOverlap.axis;
        collision.depth = minOverlap.overlap;
        
        bodyA = collision.bodyA;
        bodyB = collision.bodyB;

        // ensure normal is facing away from bodyA
        if (Vector.dot(collision.normal, Vector.sub(bodyB.position, bodyA.position)) > 0) 
            collision.normal = Vector.neg(collision.normal);

        collision.tangent = Vector.perp(collision.normal);

        collision.penetration = { 
            x: collision.normal.x * collision.depth, 
            y: collision.normal.y * collision.depth 
        };

        // find support points, there is always either exactly one or two
        var verticesB = _findSupports(bodyA, bodyB, collision.normal),
            supports = collision.supports || [];
        supports.length = 0;

        // find the supports from bodyB that are inside bodyA
        if (Vertices.contains(bodyA.vertices, verticesB[0]))
            supports.push(verticesB[0]);

        if (Vertices.contains(bodyA.vertices, verticesB[1]))
            supports.push(verticesB[1]);

        // find the supports from bodyA that are inside bodyB
        if (supports.length < 2) {
            var verticesA = _findSupports(bodyB, bodyA, Vector.neg(collision.normal));
                
            if (Vertices.contains(bodyB.vertices, verticesA[0]))
                supports.push(verticesA[0]);

            if (supports.length < 2 && Vertices.contains(bodyB.vertices, verticesA[1]))
                supports.push(verticesA[1]);
        }

        // account for the edge case of overlapping but no vertex containment
        if (supports.length < 2)
            supports = [verticesB[0]];
        
        collision.supports = supports;
        collision.supportCorrected = Vector.sub(supports[0], collision.penetration);

        return collision;
    };

    /**
     * Description
     * @method _overlapAxes
     * @private
     * @param {} verticesA
     * @param {} verticesB
     * @param {} axes
     * @return result
     */
    var _overlapAxes = function(verticesA, verticesB, axes) {
        var projectionA = {}, 
            projectionB = {},
            result = { overlap: Number.MAX_VALUE },
            overlap,
            axis;

        for (var i = 0; i < axes.length; i++) {
            axis = axes[i];

            _projectToAxis(projectionA, verticesA, axis);
            _projectToAxis(projectionB, verticesB, axis);

            overlap = projectionA.min < projectionB.min 
                        ? projectionA.max - projectionB.min 
                        : projectionB.max - projectionA.min;

            if (overlap <= 0) {
                result.overlap = overlap;
                return result;
            }

            if (overlap < result.overlap) {
                result.overlap = overlap;
                result.axis = axis;
                result.axisNumber = i;
            }
        }

        return result;
    };

    /**
     * Description
     * @method _projectToAxis
     * @private
     * @param {} projection
     * @param {} vertices
     * @param {} axis
     */
    var _projectToAxis = function(projection, vertices, axis) {
        var min = Vector.dot(vertices[0], axis),
            max = min;

        for (var i = 1; i < vertices.length; i += 1) {
            var dot = Vector.dot(vertices[i], axis);

            if (dot > max) { 
                max = dot; 
            } else if (dot < min) { 
                min = dot; 
            }
        }

        projection.min = min;
        projection.max = max;
    };
    
    /**
     * Description
     * @method _findSupports
     * @private
     * @param {} bodyA
     * @param {} bodyB
     * @param {} normal
     * @return ArrayExpression
     */
    var _findSupports = function(bodyA, bodyB, normal) {
        var nearestDistance = Number.MAX_VALUE,
            vertexToBody = { x: 0, y: 0 },
            vertices = bodyB.vertices,
            bodyAPosition = bodyA.position,
            distance,
            vertex,
            vertexA = vertices[0],
            vertexB = vertices[1];

        // find closest vertex on bodyB
        for (var i = 0; i < vertices.length; i++) {
            vertex = vertices[i];
            vertexToBody.x = vertex.x - bodyAPosition.x;
            vertexToBody.y = vertex.y - bodyAPosition.y;
            distance = -Vector.dot(normal, vertexToBody);

            if (distance < nearestDistance) {
                nearestDistance = distance;
                vertexA = vertex;
            }
        }

        // find next closest vertex using the two connected to it
        var prevIndex = vertexA.index - 1 >= 0 ? vertexA.index - 1 : vertices.length - 1;
        vertex = vertices[prevIndex];
        vertexToBody.x = vertex.x - bodyAPosition.x;
        vertexToBody.y = vertex.y - bodyAPosition.y;
        nearestDistance = -Vector.dot(normal, vertexToBody);
        vertexB = vertex;

        var nextIndex = (vertexA.index + 1) % vertices.length;
        vertex = vertices[nextIndex];
        vertexToBody.x = vertex.x - bodyAPosition.x;
        vertexToBody.y = vertex.y - bodyAPosition.y;
        distance = -Vector.dot(normal, vertexToBody);
        if (distance < nearestDistance) {
            vertexB = vertex;
        }

        return [vertexA, vertexB];
    };

})();


;   // End src/collision/SAT.js


// Begin src/constraint/Constraint.js

/**
* The `Matter.Constraint` module contains methods for creating and manipulating constraints.
* Constraints are used for specifying that a fixed distance must be maintained between two bodies (or a body and a fixed world-space position).
* The stiffness of constraints can be modified to create springs or elastic.
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Constraint
*/

// TODO: fix instabillity issues with torque
// TODO: linked constraints
// TODO: breakable constraints
// TODO: collidable constraints
// TODO: allow constrained bodies to sleep
// TODO: handle 0 length constraints properly
// TODO: impulse caching and warming

var Constraint = {};

(function() {

    var _minLength = 0.000001,
        _minDifference = 0.001;

    /**
     * Creates a new constraint.
     * All properties have default values, and many are pre-calculated automatically based on other properties.
     * See the properites section below for detailed information on what you can pass via the `options` object.
     * @method create
     * @param {} options
     * @return {constraint} constraint
     */
    Constraint.create = function(options) {
        var constraint = options;

        // if bodies defined but no points, use body centre
        if (constraint.bodyA && !constraint.pointA)
            constraint.pointA = { x: 0, y: 0 };
        if (constraint.bodyB && !constraint.pointB)
            constraint.pointB = { x: 0, y: 0 };

        // calculate static length using initial world space points
        var initialPointA = constraint.bodyA ? Vector.add(constraint.bodyA.position, constraint.pointA) : constraint.pointA,
            initialPointB = constraint.bodyB ? Vector.add(constraint.bodyB.position, constraint.pointB) : constraint.pointB,
            length = Vector.magnitude(Vector.sub(initialPointA, initialPointB));
    
        constraint.length = constraint.length || length || _minLength;

        // render
        var render = {
            visible: true,
            lineWidth: 2,
            strokeStyle: '#666'
        };
        
        constraint.render = Common.extend(render, constraint.render);

        // option defaults
        constraint.id = constraint.id || Common.nextId();
        constraint.label = constraint.label || 'Constraint';
        constraint.type = 'constraint';
        constraint.stiffness = constraint.stiffness || 1;
        constraint.angularStiffness = constraint.angularStiffness || 0;
        constraint.angleA = constraint.bodyA ? constraint.bodyA.angle : constraint.angleA;
        constraint.angleB = constraint.bodyB ? constraint.bodyB.angle : constraint.angleB;

        return constraint;
    };

    /**
     * Description
     * @private
     * @method solveAll
     * @param {constraint[]} constraints
     * @param {number} timeScale
     */
    Constraint.solveAll = function(constraints, timeScale) {
        for (var i = 0; i < constraints.length; i++) {
            Constraint.solve(constraints[i], timeScale);
        }
    };

    /**
     * Description
     * @private
     * @method solve
     * @param {constraint} constraint
     * @param {number} timeScale
     */
    Constraint.solve = function(constraint, timeScale) {
        var bodyA = constraint.bodyA,
            bodyB = constraint.bodyB,
            pointA = constraint.pointA,
            pointB = constraint.pointB;

        // update reference angle
        if (bodyA && !bodyA.isStatic) {
            constraint.pointA = Vector.rotate(pointA, bodyA.angle - constraint.angleA);
            constraint.angleA = bodyA.angle;
        }
        
        // update reference angle
        if (bodyB && !bodyB.isStatic) {
            constraint.pointB = Vector.rotate(pointB, bodyB.angle - constraint.angleB);
            constraint.angleB = bodyB.angle;
        }

        var pointAWorld = pointA,
            pointBWorld = pointB;

        if (bodyA) pointAWorld = Vector.add(bodyA.position, pointA);
        if (bodyB) pointBWorld = Vector.add(bodyB.position, pointB);

        if (!pointAWorld || !pointBWorld)
            return;

        var delta = Vector.sub(pointAWorld, pointBWorld),
            currentLength = Vector.magnitude(delta);

        // prevent singularity
        if (currentLength === 0)
            currentLength = _minLength;

        // solve distance constraint with Gauss-Siedel method
        var difference = (currentLength - constraint.length) / currentLength,
            normal = Vector.div(delta, currentLength),
            force = Vector.mult(delta, difference * 0.5 * constraint.stiffness * timeScale * timeScale);
        
        // if difference is very small, we can skip
        if (Math.abs(1 - (currentLength / constraint.length)) < _minDifference * timeScale)
            return;

        var velocityPointA,
            velocityPointB,
            offsetA,
            offsetB,
            oAn,
            oBn,
            bodyADenom,
            bodyBDenom;
    
        if (bodyA && !bodyA.isStatic) {
            // point body offset
            offsetA = { 
                x: pointAWorld.x - bodyA.position.x + force.x, 
                y: pointAWorld.y - bodyA.position.y + force.y
            };
            
            // update velocity
            bodyA.velocity.x = bodyA.position.x - bodyA.positionPrev.x;
            bodyA.velocity.y = bodyA.position.y - bodyA.positionPrev.y;
            bodyA.angularVelocity = bodyA.angle - bodyA.anglePrev;
            
            // find point velocity and body mass
            velocityPointA = Vector.add(bodyA.velocity, Vector.mult(Vector.perp(offsetA), bodyA.angularVelocity));
            oAn = Vector.dot(offsetA, normal);
            bodyADenom = bodyA.inverseMass + bodyA.inverseInertia * oAn * oAn;
        } else {
            velocityPointA = { x: 0, y: 0 };
            bodyADenom = bodyA ? bodyA.inverseMass : 0;
        }
            
        if (bodyB && !bodyB.isStatic) {
            // point body offset
            offsetB = { 
                x: pointBWorld.x - bodyB.position.x - force.x, 
                y: pointBWorld.y - bodyB.position.y - force.y 
            };
            
            // update velocity
            bodyB.velocity.x = bodyB.position.x - bodyB.positionPrev.x;
            bodyB.velocity.y = bodyB.position.y - bodyB.positionPrev.y;
            bodyB.angularVelocity = bodyB.angle - bodyB.anglePrev;

            // find point velocity and body mass
            velocityPointB = Vector.add(bodyB.velocity, Vector.mult(Vector.perp(offsetB), bodyB.angularVelocity));
            oBn = Vector.dot(offsetB, normal);
            bodyBDenom = bodyB.inverseMass + bodyB.inverseInertia * oBn * oBn;
        } else {
            velocityPointB = { x: 0, y: 0 };
            bodyBDenom = bodyB ? bodyB.inverseMass : 0;
        }
        
        var relativeVelocity = Vector.sub(velocityPointB, velocityPointA),
            normalImpulse = Vector.dot(normal, relativeVelocity) / (bodyADenom + bodyBDenom);
    
        if (normalImpulse > 0) normalImpulse = 0;
    
        var normalVelocity = {
            x: normal.x * normalImpulse, 
            y: normal.y * normalImpulse
        };

        var torque;
 
        if (bodyA && !bodyA.isStatic) {
            torque = Vector.cross(offsetA, normalVelocity) * bodyA.inverseInertia * (1 - constraint.angularStiffness);

            Sleeping.set(bodyA, false);
            
            // clamp to prevent instabillity
            // TODO: solve this properlly
            torque = Common.clamp(torque, -0.01, 0.01);

            // keep track of applied impulses for post solving
            bodyA.constraintImpulse.x -= force.x;
            bodyA.constraintImpulse.y -= force.y;
            bodyA.constraintImpulse.angle += torque;

            // apply forces
            bodyA.position.x -= force.x;
            bodyA.position.y -= force.y;
            bodyA.angle += torque;
        }

        if (bodyB && !bodyB.isStatic) {
            torque = Vector.cross(offsetB, normalVelocity) * bodyB.inverseInertia * (1 - constraint.angularStiffness);

            Sleeping.set(bodyB, false);
            
            // clamp to prevent instabillity
            // TODO: solve this properlly
            torque = Common.clamp(torque, -0.01, 0.01);

            // keep track of applied impulses for post solving
            bodyB.constraintImpulse.x += force.x;
            bodyB.constraintImpulse.y += force.y;
            bodyB.constraintImpulse.angle -= torque;
            
            // apply forces
            bodyB.position.x += force.x;
            bodyB.position.y += force.y;
            bodyB.angle -= torque;
        }

    };

    /**
     * Performs body updates required after solving constraints
     * @private
     * @method postSolveAll
     * @param {body[]} bodies
     */
    Constraint.postSolveAll = function(bodies) {
        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i],
                impulse = body.constraintImpulse;

            // update geometry and reset
            Vertices.translate(body.vertices, impulse);

            if (impulse.angle !== 0) {
                Vertices.rotate(body.vertices, impulse.angle, body.position);
                Axes.rotate(body.axes, impulse.angle);
                impulse.angle = 0;
            }

            Bounds.update(body.bounds, body.vertices);

            impulse.x = 0;
            impulse.y = 0;
        }
    };

    /*
    *
    *  Properties Documentation
    *
    */

    /**
     * An integer `Number` uniquely identifying number generated in `Composite.create` by `Common.nextId`.
     *
     * @property id
     * @type number
     */

    /**
     * A `String` denoting the type of object.
     *
     * @property type
     * @type string
     * @default "constraint"
     */

    /**
     * An arbitrary `String` name to help the user identify and manage bodies.
     *
     * @property label
     * @type string
     * @default "Constraint"
     */

    /**
     * An `Object` that defines the rendering properties to be consumed by the module `Matter.Render`.
     *
     * @property render
     * @type object
     */

    /**
     * A flag that indicates if the constraint should be rendered.
     *
     * @property render.visible
     * @type boolean
     * @default true
     */

    /**
     * A `Number` that defines the line width to use when rendering the constraint outline.
     * A value of `0` means no outline will be rendered.
     *
     * @property render.lineWidth
     * @type number
     * @default 2
     */

    /**
     * A `String` that defines the stroke style to use when rendering the constraint outline.
     * It is the same as when using a canvas, so it accepts CSS style property values.
     *
     * @property render.strokeStyle
     * @type string
     * @default a random colour
     */

    /**
     * The first possible `Body` that this constraint is attached to.
     *
     * @property bodyA
     * @type body
     * @default null
     */

    /**
     * The second possible `Body` that this constraint is attached to.
     *
     * @property bodyB
     * @type body
     * @default null
     */

    /**
     * A `Vector` that specifies the offset of the constraint from center of the `constraint.bodyA` if defined, otherwise a world-space position.
     *
     * @property pointA
     * @type vector
     * @default { x: 0, y: 0 }
     */

    /**
     * A `Vector` that specifies the offset of the constraint from center of the `constraint.bodyA` if defined, otherwise a world-space position.
     *
     * @property pointB
     * @type vector
     * @default { x: 0, y: 0 }
     */

    /**
     * A `Number` that specifies the stiffness of the constraint, i.e. the rate at which it returns to its resting `constraint.length`.
     * A value of `1` means the constraint should be very stiff.
     * A value of `0.2` means the constraint acts like a soft spring.
     *
     * @property stiffness
     * @type number
     * @default 1
     */

    /**
     * A `Number` that specifies the target resting length of the constraint. 
     * It is calculated automatically in `Constraint.create` from intial positions of the `constraint.bodyA` and `constraint.bodyB`.
     *
     * @property length
     * @type number
     */

})();

;   // End src/constraint/Constraint.js


// Begin src/constraint/MouseConstraint.js

/**
* The `Matter.MouseConstraint` module contains methods for creating mouse constraints.
* Mouse constraints are used for allowing user interaction, providing the ability to move bodies via the mouse or touch.
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class MouseConstraint
*/

var MouseConstraint = {};

(function() {

    /**
     * Creates a new mouse constraint.
     * All properties have default values, and many are pre-calculated automatically based on other properties.
     * See the properites section below for detailed information on what you can pass via the `options` object.
     * @method create
     * @param {engine} engine
     * @param {} options
     * @return {MouseConstraint} A new MouseConstraint
     */
    MouseConstraint.create = function(engine, options) {
        var mouse = (engine ? engine.mouse : null) || (options ? options.mouse : null);

        if (!mouse && engine && engine.render && engine.render.canvas) {
            mouse = Mouse.create(engine.render.canvas);
        } else {
            mouse = Mouse.create();
            Common.log('MouseConstraint.create: options.mouse was undefined, engine.render.canvas was undefined, may not function as expected', 'warn');
        }

        var constraint = Constraint.create({ 
            label: 'Mouse Constraint',
            pointA: mouse.position,
            pointB: { x: 0, y: 0 },
            length: 0.01, 
            stiffness: 0.1,
            angularStiffness: 1,
            render: {
                strokeStyle: '#90EE90',
                lineWidth: 3
            }
        });

        var defaults = {
            type: 'mouseConstraint',
            mouse: mouse,
            body: null,
            constraint: constraint,
            collisionFilter: {
                category: 0x0001,
                mask: 0xFFFFFFFF,
                group: 0
            }
        };

        var mouseConstraint = Common.extend(defaults, options);

        Events.on(engine, 'tick', function() {
            var allBodies = Composite.allBodies(engine.world);
            MouseConstraint.update(mouseConstraint, allBodies);
            _triggerEvents(mouseConstraint);
        });

        return mouseConstraint;
    };

    /**
     * Updates the given mouse constraint.
     * @private
     * @method update
     * @param {MouseConstraint} mouseConstraint
     * @param {body[]} bodies
     */
    MouseConstraint.update = function(mouseConstraint, bodies) {
        var mouse = mouseConstraint.mouse,
            constraint = mouseConstraint.constraint,
            body = mouseConstraint.body;

        if (mouse.button === 0) {
            if (!constraint.bodyB) {
                for (var i = 0; i < bodies.length; i++) {
                    body = bodies[i];
                    if (Bounds.contains(body.bounds, mouse.position) 
                            && Vertices.contains(body.vertices, mouse.position)
                            && Detector.canCollide(body.collisionFilter, mouseConstraint.collisionFilter)) {
                       
                        constraint.pointA = mouse.position;
                        constraint.bodyB = mouseConstraint.body = body;
                        constraint.pointB = { x: mouse.position.x - body.position.x, y: mouse.position.y - body.position.y };
                        constraint.angleB = body.angle;

                        Sleeping.set(body, false);
                        Events.trigger(mouseConstraint, 'startdrag', { mouse: mouse, body: body });
                    }
                }
            } else {
                Sleeping.set(constraint.bodyB, false);
                constraint.pointA = mouse.position;
            }
        } else {
            constraint.bodyB = mouseConstraint.body = null;
            constraint.pointB = null;

            if (body)
                Events.trigger(mouseConstraint, 'enddrag', { mouse: mouse, body: body });
        }
    };

    /**
     * Triggers mouse constraint events
     * @method _triggerEvents
     * @private
     * @param {mouse} mouse
     */
    var _triggerEvents = function(mouseConstraint) {
        var mouse = mouseConstraint.mouse,
            mouseEvents = mouse.sourceEvents;

        if (mouseEvents.mousemove)
            Events.trigger(mouseConstraint, 'mousemove', { mouse: mouse });

        if (mouseEvents.mousedown)
            Events.trigger(mouseConstraint, 'mousedown', { mouse: mouse });

        if (mouseEvents.mouseup)
            Events.trigger(mouseConstraint, 'mouseup', { mouse: mouse });

        // reset the mouse state ready for the next step
        Mouse.clearSourceEvents(mouse);
    };

    /*
    *
    *  Events Documentation
    *
    */

    /**
    * Fired when the mouse has moved (or a touch moves) during the last step
    *
    * @event mousemove
    * @param {} event An event object
    * @param {mouse} event.mouse The engine's mouse instance
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired when the mouse is down (or a touch has started) during the last step
    *
    * @event mousedown
    * @param {} event An event object
    * @param {mouse} event.mouse The engine's mouse instance
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired when the mouse is up (or a touch has ended) during the last step
    *
    * @event mouseup
    * @param {} event An event object
    * @param {mouse} event.mouse The engine's mouse instance
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired when the user starts dragging a body
    *
    * @event startdrag
    * @param {} event An event object
    * @param {mouse} event.mouse The engine's mouse instance
    * @param {body} event.body The body being dragged
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired when the user ends dragging a body
    *
    * @event enddrag
    * @param {} event An event object
    * @param {mouse} event.mouse The engine's mouse instance
    * @param {body} event.body The body that has stopped being dragged
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /*
    *
    *  Properties Documentation
    *
    */

    /**
     * A `String` denoting the type of object.
     *
     * @property type
     * @type string
     * @default "constraint"
     */

    /**
     * The `Mouse` instance in use. If not supplied in `MouseConstraint.create`, one will be created.
     *
     * @property mouse
     * @type mouse
     * @default mouse
     */

    /**
     * The `Body` that is currently being moved by the user, or `null` if no body.
     *
     * @property body
     * @type body
     * @default null
     */

    /**
     * The `Constraint` object that is used to move the body during interaction.
     *
     * @property constraint
     * @type constraint
     */

    /**
     * An `Object` that specifies the collision filter properties.
     * The collision filter allows the user to define which types of body this mouse constraint can interact with.
     * See `body.collisionFilter` for more information.
     *
     * @property collisionFilter
     * @type object
     */

})();


;   // End src/constraint/MouseConstraint.js


// Begin src/core/Common.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Common
*/

var Common = {};

(function() {

    Common._nextId = 0;
    Common._seed = 0;

    /**
     * Description
     * @method extend
     * @param {} obj
     * @param {boolean} deep
     * @return {} obj extended
     */
    Common.extend = function(obj, deep) {
        var argsStart,
            args,
            deepClone;

        if (typeof deep === 'boolean') {
            argsStart = 2;
            deepClone = deep;
        } else {
            argsStart = 1;
            deepClone = true;
        }

        args = Array.prototype.slice.call(arguments, argsStart);

        for (var i = 0; i < args.length; i++) {
            var source = args[i];

            if (source) {
                for (var prop in source) {
                    if (deepClone && source[prop] && source[prop].constructor === Object) {
                        if (!obj[prop] || obj[prop].constructor === Object) {
                            obj[prop] = obj[prop] || {};
                            Common.extend(obj[prop], deepClone, source[prop]);
                        } else {
                            obj[prop] = source[prop];
                        }
                    } else {
                        obj[prop] = source[prop];
                    }
                }
            }
        }
        
        return obj;
    };

    /**
     * Creates a new clone of the object, if deep is true references will also be cloned
     * @method clone
     * @param {} obj
     * @param {bool} deep
     * @return {} obj cloned
     */
    Common.clone = function(obj, deep) {
        return Common.extend({}, deep, obj);
    };

    /**
     * Description
     * @method keys
     * @param {} obj
     * @return {string[]} keys
     */
    Common.keys = function(obj) {
        if (Object.keys)
            return Object.keys(obj);

        // avoid hasOwnProperty for performance
        var keys = [];
        for (var key in obj)
            keys.push(key);
        return keys;
    };

    /**
     * Description
     * @method values
     * @param {} obj
     * @return {array} Array of the objects property values
     */
    Common.values = function(obj) {
        var values = [];
        
        if (Object.keys) {
            var keys = Object.keys(obj);
            for (var i = 0; i < keys.length; i++) {
                values.push(obj[keys[i]]);
            }
            return values;
        }
        
        // avoid hasOwnProperty for performance
        for (var key in obj)
            values.push(obj[key]);
        return values;
    };

    /**
     * Description
     * @method shadeColor
     * @param {string} color
     * @param {number} percent
     * @return {string} A hex colour string made by lightening or darkening color by percent
     */
    Common.shadeColor = function(color, percent) {   
        // http://stackoverflow.com/questions/5560248/programmatically-lighten-or-darken-a-hex-color
        var colorInteger = parseInt(color.slice(1),16), 
            amount = Math.round(2.55 * percent), 
            R = (colorInteger >> 16) + amount, 
            B = (colorInteger >> 8 & 0x00FF) + amount, 
            G = (colorInteger & 0x0000FF) + amount;
        return "#" + (0x1000000 + (R < 255 ? R < 1 ? 0 : R :255) * 0x10000 
                + (B < 255 ? B < 1 ? 0 : B : 255) * 0x100 
                + (G < 255 ? G < 1 ? 0 : G : 255)).toString(16).slice(1);
    };

    /**
     * Description
     * @method shuffle
     * @param {array} array
     * @return {array} array shuffled randomly
     */
    Common.shuffle = function(array) {
        for (var i = array.length - 1; i > 0; i--) {
            var j = Math.floor(Common.random() * (i + 1));
            var temp = array[i];
            array[i] = array[j];
            array[j] = temp;
        }
        return array;
    };

    /**
     * Description
     * @method choose
     * @param {array} choices
     * @return {object} A random choice object from the array
     */
    Common.choose = function(choices) {
        return choices[Math.floor(Common.random() * choices.length)];
    };

    /**
     * Description
     * @method isElement
     * @param {object} obj
     * @return {boolean} True if the object is a HTMLElement, otherwise false
     */
    Common.isElement = function(obj) {
        // http://stackoverflow.com/questions/384286/javascript-isdom-how-do-you-check-if-a-javascript-object-is-a-dom-object
        try {
            return obj instanceof HTMLElement;
        }
        catch(e){
            return (typeof obj==="object") &&
              (obj.nodeType===1) && (typeof obj.style === "object") &&
              (typeof obj.ownerDocument ==="object");
        }
    };
    
    /**
     * Description
     * @method clamp
     * @param {number} value
     * @param {number} min
     * @param {number} max
     * @return {number} The value clamped between min and max inclusive
     */
    Common.clamp = function(value, min, max) {
        if (value < min)
            return min;
        if (value > max)
            return max;
        return value;
    };
    
    /**
     * Description
     * @method sign
     * @param {number} value
     * @return {number} -1 if negative, +1 if 0 or positive
     */
    Common.sign = function(value) {
        return value < 0 ? -1 : 1;
    };
    
    /**
     * Description
     * @method now
     * @return {number} the current timestamp (high-res if avaliable)
     */
    Common.now = function() {
        // http://stackoverflow.com/questions/221294/how-do-you-get-a-timestamp-in-javascript
        // https://gist.github.com/davidwaterston/2982531
        
        var perf = window.performance;

        if (perf) {
            perf.now = perf.now || perf.webkitNow || perf.msNow || perf.oNow || perf.mozNow;
            return +(perf.now());
        }
        
        return +(new Date());
    };

    
    /**
     * Description
     * @method random
     * @param {number} min
     * @param {number} max
     * @return {number} A random number between min and max inclusive
     */
    Common.random = function(min, max) {
        min = (typeof min !== "undefined") ? min : 0;
        max = (typeof max !== "undefined") ? max : 1;
        return min + _seededRandom() * (max - min);
    };

    /**
     * Converts a CSS hex colour string into an integer
     * @method colorToNumber
     * @param {string} colorString
     * @return {number} An integer representing the CSS hex string
     */
    Common.colorToNumber = function(colorString) {
        colorString = colorString.replace('#','');

        if (colorString.length == 3) {
            colorString = colorString.charAt(0) + colorString.charAt(0)
                        + colorString.charAt(1) + colorString.charAt(1)
                        + colorString.charAt(2) + colorString.charAt(2);
        }

        return parseInt(colorString, 16);
    };

    /**
     * A wrapper for console.log, for providing errors and warnings
     * @method log
     * @param {string} message
     * @param {string} type
     */
    Common.log = function(message, type) {
        if (!console || !console.log || !console.warn)
            return;

        var style;

        switch (type) {

        case 'warn':
            console.warn('Matter.js:', message);
            break;
        case 'error':
            console.log('Matter.js:', message);
            break;

        }
    };

    /**
     * Returns the next unique sequential ID
     * @method nextId
     * @return {Number} Unique sequential ID
     */
    Common.nextId = function() {
        return Common._nextId++;
    };

    /**
     * A cross browser compatible indexOf implementation
     * @method indexOf
     * @param {array} haystack
     * @param {object} needle
     */
    Common.indexOf = function(haystack, needle) {
        if (haystack.indexOf)
            return haystack.indexOf(needle);

        for (var i = 0; i < haystack.length; i++) {
            if (haystack[i] === needle)
                return i;
        }

        return -1;
    };

    var _seededRandom = function() {
        // https://gist.github.com/ngryman/3830489
        Common._seed = (Common._seed * 9301 + 49297) % 233280;
        return Common._seed / 233280;
    };

})();

;   // End src/core/Common.js


// Begin src/core/Engine.js

/**
* The `Matter.Engine` module contains methods for creating and manipulating engines.
* An engine is a controller that manages updating and rendering the simulation of the world.
* See `Matter.Runner` for an optional game loop utility.
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Engine
*/

var Engine = {};

(function() {

    var _fps = 60,
        _delta = 1000 / _fps;

    /**
     * Creates a new engine. The options parameter is an object that specifies any properties you wish to override the defaults.
     * All properties have default values, and many are pre-calculated automatically based on other properties.
     * See the properites section below for detailed information on what you can pass via the `options` object.
     * @method create
     * @param {HTMLElement} element
     * @param {object} [options]
     * @return {engine} engine
     */
    Engine.create = function(element, options) {

        // options may be passed as the first (and only) argument
        options = Common.isElement(element) ? options : element;
        element = Common.isElement(element) ? element : null;

        var defaults = {
            enabled: true,
            positionIterations: 6,
            velocityIterations: 4,
            constraintIterations: 2,
            enableSleeping: false,
            events: [],
            timing: {
                fps: _fps,
                timestamp: 0,
                delta: _delta,
                correction: 1,
                deltaMin: 1000 / _fps,
                deltaMax: 1000 / (_fps * 0.5),
                timeScale: 1,
                isFixed: false,
                frameRequestId: 0
            },
            render: {
                element: element,
                controller: Render
            },
            broadphase: {
                controller: Grid
            }
        };
        
        var engine = Common.extend(defaults, options);

        engine.render = engine.render.controller.create(engine.render);
        engine.world = World.create(engine.world);
        engine.pairs = Pairs.create();
        engine.metrics = engine.metrics || Metrics.create();
        engine.broadphase = engine.broadphase.controller.create(engine.broadphase);

        return engine;
    };

    /**
     * Moves the simulation forward in time by `delta` ms. 
     * Triggers `beforeUpdate` and `afterUpdate` events.
     * Triggers `collisionStart`, `collisionActive` and `collisionEnd` events.
     * @method update
     * @param {engine} engine
     * @param {number} delta
     * @param {number} [correction]
     */
    Engine.update = function(engine, delta, correction) {
        correction = (typeof correction !== 'undefined') ? correction : 1;

        var world = engine.world,
            timing = engine.timing,
            broadphase = engine.broadphase,
            broadphasePairs = [],
            i;

        // increment timestamp
        timing.timestamp += delta * timing.timeScale;
        timing.correction = correction;

        // create an event object
        var event = {
            timestamp: engine.timing.timestamp
        };

        Events.trigger(engine, 'beforeUpdate', event);

        // get lists of all bodies and constraints, no matter what composites they are in
        var allBodies = Composite.allBodies(world),
            allConstraints = Composite.allConstraints(world);

        // reset metrics logging
        Metrics.reset(engine.metrics);

        // if sleeping enabled, call the sleeping controller
        if (engine.enableSleeping)
            Sleeping.update(allBodies, timing.timeScale);

        // applies gravity to all bodies
        _bodiesApplyGravity(allBodies, world.gravity);

        // update all body position and rotation by integration
        _bodiesUpdate(allBodies, delta, timing.timeScale, correction, world.bounds);

        // update all constraints
        for (i = 0; i < engine.constraintIterations; i++) {
            Constraint.solveAll(allConstraints, timing.timeScale);
        }
        Constraint.postSolveAll(allBodies);

        // broadphase pass: find potential collision pairs
        if (broadphase.controller) {

            // if world is dirty, we must flush the whole grid
            if (world.isModified)
                broadphase.controller.clear(broadphase);

            // update the grid buckets based on current bodies
            broadphase.controller.update(broadphase, allBodies, engine, world.isModified);
            broadphasePairs = broadphase.pairsList;
        } else {

            // if no broadphase set, we just pass all bodies
            broadphasePairs = allBodies;
        }

        // narrowphase pass: find actual collisions, then create or update collision pairs
        var collisions = broadphase.detector(broadphasePairs, engine);

        // update collision pairs
        var pairs = engine.pairs,
            timestamp = timing.timestamp;
        Pairs.update(pairs, collisions, timestamp);
        Pairs.removeOld(pairs, timestamp);

        // wake up bodies involved in collisions
        if (engine.enableSleeping)
            Sleeping.afterCollisions(pairs.list, timing.timeScale);

        // trigger collision events
        if (pairs.collisionStart.length > 0)
            Events.trigger(engine, 'collisionStart', { pairs: pairs.collisionStart });

        // iteratively resolve velocity between collisions
        Resolver.preSolveVelocity(pairs.list);
        for (i = 0; i < engine.velocityIterations; i++) {
            Resolver.solveVelocity(pairs.list, timing.timeScale);
        }
        
        // iteratively resolve position between collisions
        for (i = 0; i < engine.positionIterations; i++) {
            Resolver.solvePosition(pairs.list, timing.timeScale);
        }
        Resolver.postSolvePosition(allBodies);

        // trigger collision events
        if (pairs.collisionActive.length > 0)
            Events.trigger(engine, 'collisionActive', { pairs: pairs.collisionActive });

        if (pairs.collisionEnd.length > 0)
            Events.trigger(engine, 'collisionEnd', { pairs: pairs.collisionEnd });

        // update metrics log
        Metrics.update(engine.metrics, engine);

        // clear force buffers
        _bodiesClearForces(allBodies);

        // clear all composite modified flags
        if (world.isModified)
            Composite.setModified(world, false, false, true);

        Events.trigger(engine, 'afterUpdate', event);

        return engine;
    };

    /**
     * Renders the world by calling its defined renderer `engine.render.controller`. Triggers `beforeRender` and `afterRender` events.
     * @method render
     * @param {engine} engineA
     * @param {engine} engineB
     */
    Engine.render = function(engine) {
        // create an event object
        var event = {
            timestamp: engine.timing.timestamp
        };

        Events.trigger(engine, 'beforeRender', event);
        engine.render.controller.world(engine);
        Events.trigger(engine, 'afterRender', event);
    };
    
    /**
     * Merges two engines by keeping the configuration of `engineA` but replacing the world with the one from `engineB`.
     * @method merge
     * @param {engine} engineA
     * @param {engine} engineB
     */
    Engine.merge = function(engineA, engineB) {
        Common.extend(engineA, engineB);
        
        if (engineB.world) {
            engineA.world = engineB.world;

            Engine.clear(engineA);

            var bodies = Composite.allBodies(engineA.world);

            for (var i = 0; i < bodies.length; i++) {
                var body = bodies[i];
                Sleeping.set(body, false);
                body.id = Common.nextId();
            }
        }
    };

    /**
     * Clears the engine including the world, pairs and broadphase.
     * @method clear
     * @param {engine} engine
     */
    Engine.clear = function(engine) {
        var world = engine.world;
        
        Pairs.clear(engine.pairs);

        var broadphase = engine.broadphase;
        if (broadphase.controller) {
            var bodies = Composite.allBodies(world);
            broadphase.controller.clear(broadphase);
            broadphase.controller.update(broadphase, bodies, engine, true);
        }
    };

    /**
     * Zeroes the `body.force` and `body.torque` force buffers.
     * @method bodiesClearForces
     * @private
     * @param {body[]} bodies
     */
    var _bodiesClearForces = function(bodies) {
        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            // reset force buffers
            body.force.x = 0;
            body.force.y = 0;
            body.torque = 0;
        }
    };

    /**
     * Applys a mass dependant force to all given bodies.
     * @method bodiesApplyGravity
     * @private
     * @param {body[]} bodies
     * @param {vector} gravity
     */
    var _bodiesApplyGravity = function(bodies, gravity) {
        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (body.isStatic || body.isSleeping)
                continue;

            // apply gravity
            body.force.y += body.mass * gravity.y * 0.001;
            body.force.x += body.mass * gravity.x * 0.001;
        }
    };

    /**
     * Applys `Body.update` to all given `bodies`.
     * @method updateAll
     * @private
     * @param {body[]} bodies
     * @param {number} deltaTime 
     * The amount of time elapsed between updates
     * @param {number} timeScale
     * @param {number} correction 
     * The Verlet correction factor (deltaTime / lastDeltaTime)
     * @param {bounds} worldBounds
     */
    var _bodiesUpdate = function(bodies, deltaTime, timeScale, correction, worldBounds) {
        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (body.isStatic || body.isSleeping)
                continue;

            // don't update out of world bodies
            if (body.bounds.max.x < worldBounds.min.x || body.bounds.min.x > worldBounds.max.x
                || body.bounds.max.y < worldBounds.min.y || body.bounds.min.y > worldBounds.max.y)
                continue;

            Body.update(body, deltaTime, timeScale, correction);
        }
    };

    /**
     * An alias for `Runner.run`, see `Matter.Runner` for more information.
     * @method run
     * @param {engine} engine
     */

    /*
    *
    *  Events Documentation
    *
    */

    /**
    * Fired at the start of a tick, before any updates to the engine or timing
    *
    * @event beforeTick
    * @param {} event An event object
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired after engine timing updated, but just before engine state updated
    *
    * @event tick
    * @param {} event An event object
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired just before an update
    *
    * @event beforeUpdate
    * @param {} event An event object
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired after engine update and all collision events
    *
    * @event afterUpdate
    * @param {} event An event object
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired just before rendering
    *
    * @event beforeRender
    * @param {} event An event object
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired after rendering
    *
    * @event afterRender
    * @param {} event An event object
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired after engine update and after rendering
    *
    * @event afterTick
    * @param {} event An event object
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired after engine update, provides a list of all pairs that have started to collide in the current tick (if any)
    *
    * @event collisionStart
    * @param {} event An event object
    * @param {} event.pairs List of affected pairs
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired after engine update, provides a list of all pairs that are colliding in the current tick (if any)
    *
    * @event collisionActive
    * @param {} event An event object
    * @param {} event.pairs List of affected pairs
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /**
    * Fired after engine update, provides a list of all pairs that have ended collision in the current tick (if any)
    *
    * @event collisionEnd
    * @param {} event An event object
    * @param {} event.pairs List of affected pairs
    * @param {DOMHighResTimeStamp} event.timestamp The timestamp of the current tick
    * @param {} event.source The source object of the event
    * @param {} event.name The name of the event
    */

    /*
    *
    *  Properties Documentation
    *
    */

    /**
     * A flag that specifies whether the engine is running or not.
     *
     * @property enabled
     * @type boolean
     * @default true
     */

    /**
     * An integer `Number` that specifies the number of position iterations to perform each update.
     * The higher the value, the higher quality the simulation will be at the expense of performance.
     *
     * @property positionIterations
     * @type number
     * @default 6
     */

    /**
     * An integer `Number` that specifies the number of velocity iterations to perform each update.
     * The higher the value, the higher quality the simulation will be at the expense of performance.
     *
     * @property velocityIterations
     * @type number
     * @default 4
     */

    /**
     * An integer `Number` that specifies the number of constraint iterations to perform each update.
     * The higher the value, the higher quality the simulation will be at the expense of performance.
     * The default value of `2` is usually very adequate.
     *
     * @property constraintIterations
     * @type number
     * @default 2
     */

    /**
     * A flag that specifies whether the engine should allow sleeping via the `Matter.Sleeping` module.
     * Sleeping can improve stability and performance, but often at the expense of accuracy.
     *
     * @property enableSleeping
     * @type boolean
     * @default false
     */

    /**
     * An `Object` containing properties regarding the timing systems of the engine. 
     *
     * @property timing
     * @type object
     */

    /**
     * A `Number` that specifies the global scaling factor of time for all bodies.
     * A value of `0` freezes the simulation.
     * A value of `0.1` gives a slow-motion effect.
     * A value of `1.2` gives a speed-up effect.
     *
     * @property timing.timeScale
     * @type number
     * @default 1
     */

    /**
     * A `Number` that specifies the current simulation-time in milliseconds starting from `0`. 
     * It is incremented on every `Engine.update` by the `timing.delta`. 
     *
     * @property timing.timestamp
     * @type number
     * @default 0
     */

    /**
     * A `Boolean` that specifies if the `Engine.run` game loop should use a fixed timestep (otherwise it is variable).
     * If timing is fixed, then the apparant simulation speed will change depending on the frame rate (but behaviour will be deterministic).
     * If the timing is variable, then the apparant simulation speed will be constant (approximately, but at the cost of determininism).
     *
     * @property timing.isFixed
     * @type boolean
     * @default false
     */

    /**
     * A `Number` that specifies the time step between updates in milliseconds.
     * If `engine.timing.isFixed` is set to `true`, then `delta` is fixed.
     * If it is `false`, then `delta` can dynamically change to maintain the correct apparant simulation speed.
     *
     * @property timing.delta
     * @type number
     * @default 1000 / 60
     */

    /**
     * A `Number` that specifies the time correction factor to apply to the current timestep.
     * It is automatically handled when using `Engine.run`, but is also only optional even if you use your own game loop.
     * The value is defined as `delta / lastDelta`, i.e. the percentage change of `delta` between steps.
     * This value is always `1` (no correction) when frame rate is constant or `engine.timing.isFixed` is `true`.
     * If the framerate and hence `delta` are changing, then correction should be applied to the current update to account for the change.
     * See the paper on <a href="http://lonesock.net/article/verlet.html">Time Corrected Verlet</a> for more information.
     *
     * @property timing.correction
     * @type number
     * @default 1
     */

    /**
     * An instance of a `Render` controller. The default value is a `Matter.Render` instance created by `Engine.create`.
     * One may also develop a custom renderer module based on `Matter.Render` and pass an instance of it to `Engine.create` via `options.render`.
     *
     * A minimal custom renderer object must define at least three functions: `create`, `clear` and `world` (see `Matter.Render`).
     * It is also possible to instead pass the _module_ reference via `options.render.controller` and `Engine.create` will instantiate one for you.
     *
     * @property render
     * @type render
     * @default a Matter.Render instance
     */

    /**
     * An instance of a broadphase controller. The default value is a `Matter.Grid` instance created by `Engine.create`.
     *
     * @property broadphase
     * @type grid
     * @default a Matter.Grid instance
     */

    /**
     * A `World` composite object that will contain all simulated bodies and constraints.
     *
     * @property world
     * @type world
     * @default a Matter.World instance
     */

})();

;   // End src/core/Engine.js


// Begin src/core/Events.js

/**
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Events
*/

var Events = {};

(function() {

    /**
     * Subscribes a callback function to the given object's `eventName`.
     * @method on
     * @param {} object
     * @param {string} eventNames
     * @param {function} callback
     */
    Events.on = function(object, eventNames, callback) {
        var names = eventNames.split(' '),
            name;

        for (var i = 0; i < names.length; i++) {
            name = names[i];
            object.events = object.events || {};
            object.events[name] = object.events[name] || [];
            object.events[name].push(callback);
        }

        return callback;
    };

    /**
     * Removes the given event callback. If no callback, clears all callbacks in `eventNames`. If no `eventNames`, clears all events.
     * @method off
     * @param {} object
     * @param {string} eventNames
     * @param {function} callback
     */
    Events.off = function(object, eventNames, callback) {
        if (!eventNames) {
            object.events = {};
            return;
        }

        // handle Events.off(object, callback)
        if (typeof eventNames === 'function') {
            callback = eventNames;
            eventNames = Common.keys(object.events).join(' ');
        }

        var names = eventNames.split(' ');

        for (var i = 0; i < names.length; i++) {
            var callbacks = object.events[names[i]],
                newCallbacks = [];

            if (callback) {
                for (var j = 0; j < callbacks.length; j++) {
                    if (callbacks[j] !== callback)
                        newCallbacks.push(callbacks[j]);
                }
            }

            object.events[names[i]] = newCallbacks;
        }
    };

    /**
     * Fires all the callbacks subscribed to the given object's `eventName`, in the order they subscribed, if any.
     * @method trigger
     * @param {} object
     * @param {string} eventNames
     * @param {} event
     */
    Events.trigger = function(object, eventNames, event) {
        var names,
            name,
            callbacks,
            eventClone;

        if (object.events) {
            if (!event)
                event = {};

            names = eventNames.split(' ');

            for (var i = 0; i < names.length; i++) {
                name = names[i];
                callbacks = object.events[name];

                if (callbacks) {
                    eventClone = Common.clone(event, false);
                    eventClone.name = name;
                    eventClone.source = object;

                    for (var j = 0; j < callbacks.length; j++) {
                        callbacks[j].apply(object, [eventClone]);
                    }
                }
            }
        }
    };

})();

;   // End src/core/Events.js


// Begin src/core/Metrics.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Metrics
*/

var Metrics = {};

(function() {

    /**
     * Description
     * @method create
     * @return {metrics} A new metrics
     */
    Metrics.create = function() {
        return {
            extended: false,
            narrowDetections: 0,
            narrowphaseTests: 0,
            narrowReuse: 0,
            narrowReuseCount: 0,
            midphaseTests: 0,
            broadphaseTests: 0,
            narrowEff: 0.0001,
            midEff: 0.0001,
            broadEff: 0.0001,
            collisions: 0,
            buckets: 0,
            bodies: 0,
            pairs: 0
        };
    };

    /**
     * Description
     * @method reset
     * @param {metrics} metrics
     */
    Metrics.reset = function(metrics) {
        if (metrics.extended) {
            metrics.narrowDetections = 0;
            metrics.narrowphaseTests = 0;
            metrics.narrowReuse = 0;
            metrics.narrowReuseCount = 0;
            metrics.midphaseTests = 0;
            metrics.broadphaseTests = 0;
            metrics.narrowEff = 0;
            metrics.midEff = 0;
            metrics.broadEff = 0;
            metrics.collisions = 0;
            metrics.buckets = 0;
            metrics.pairs = 0;
            metrics.bodies = 0;
        }
    };

    /**
     * Description
     * @method update
     * @param {metrics} metrics
     * @param {engine} engine
     */
    Metrics.update = function(metrics, engine) {
        if (metrics.extended) {
            var world = engine.world,
                bodies = Composite.allBodies(world);

            metrics.collisions = metrics.narrowDetections;
            metrics.pairs = engine.pairs.list.length;
            metrics.bodies = bodies.length;
            metrics.midEff = (metrics.narrowDetections / (metrics.midphaseTests || 1)).toFixed(2);
            metrics.narrowEff = (metrics.narrowDetections / (metrics.narrowphaseTests || 1)).toFixed(2);
            metrics.broadEff = (1 - (metrics.broadphaseTests / (bodies.length || 1))).toFixed(2);
            metrics.narrowReuse = (metrics.narrowReuseCount / (metrics.narrowphaseTests || 1)).toFixed(2);
            //var broadphase = engine.broadphase[engine.broadphase.current];
            //if (broadphase.instance)
            //    metrics.buckets = Common.keys(broadphase.instance.buckets).length;
        }
    };

})();


;   // End src/core/Metrics.js


// Begin src/core/Mouse.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Mouse
*/

var Mouse = {};

(function() {

    /**
     * Description
     * @method create
     * @param {HTMLElement} element
     * @return {mouse} A new mouse
     */
    Mouse.create = function(element) {
        var mouse = {};

        if (!element) {
            Common.log('Mouse.create: element was undefined, defaulting to document.body', 'warn');
        }
        
        mouse.element = element || document.body;
        mouse.absolute = { x: 0, y: 0 };
        mouse.position = { x: 0, y: 0 };
        mouse.mousedownPosition = { x: 0, y: 0 };
        mouse.mouseupPosition = { x: 0, y: 0 };
        mouse.offset = { x: 0, y: 0 };
        mouse.scale = { x: 1, y: 1 };
        mouse.wheelDelta = 0;
        mouse.button = -1;
        mouse.pixelRatio = mouse.element.getAttribute('data-pixel-ratio') || 1;

        mouse.sourceEvents = {
            mousemove: null,
            mousedown: null,
            mouseup: null,
            mousewheel: null
        };
        
        mouse.mousemove = function(event) { 
            var position = _getRelativeMousePosition(event, mouse.element, mouse.pixelRatio),
                touches = event.changedTouches;

            if (touches) {
                mouse.button = 0;
                event.preventDefault();
            }

            mouse.absolute.x = position.x;
            mouse.absolute.y = position.y;
            mouse.position.x = mouse.absolute.x * mouse.scale.x + mouse.offset.x;
            mouse.position.y = mouse.absolute.y * mouse.scale.y + mouse.offset.y;
            mouse.sourceEvents.mousemove = event;
        };
        
        mouse.mousedown = function(event) {
            var position = _getRelativeMousePosition(event, mouse.element, mouse.pixelRatio),
                touches = event.changedTouches;

            if (touches) {
                mouse.button = 0;
                event.preventDefault();
            } else {
                mouse.button = event.button;
            }

            mouse.absolute.x = position.x;
            mouse.absolute.y = position.y;
            mouse.position.x = mouse.absolute.x * mouse.scale.x + mouse.offset.x;
            mouse.position.y = mouse.absolute.y * mouse.scale.y + mouse.offset.y;
            mouse.mousedownPosition.x = mouse.position.x;
            mouse.mousedownPosition.y = mouse.position.y;
            mouse.sourceEvents.mousedown = event;
        };
        
        mouse.mouseup = function(event) {
            var position = _getRelativeMousePosition(event, mouse.element, mouse.pixelRatio),
                touches = event.changedTouches;

            if (touches) {
                event.preventDefault();
            }
            
            mouse.button = -1;
            mouse.absolute.x = position.x;
            mouse.absolute.y = position.y;
            mouse.position.x = mouse.absolute.x * mouse.scale.x + mouse.offset.x;
            mouse.position.y = mouse.absolute.y * mouse.scale.y + mouse.offset.y;
            mouse.mouseupPosition.x = mouse.position.x;
            mouse.mouseupPosition.y = mouse.position.y;
            mouse.sourceEvents.mouseup = event;
        };

        mouse.mousewheel = function(event) {
            mouse.wheelDelta = Math.max(-1, Math.min(1, event.wheelDelta || -event.detail));
            event.preventDefault();
        };

        Mouse.setElement(mouse, mouse.element);

        return mouse;
    };

    /**
     * Sets the element the mouse is bound to (and relative to)
     * @method setElement
     * @param {mouse} mouse
     * @param {HTMLElement} element
     */
    Mouse.setElement = function(mouse, element) {
        mouse.element = element;

        element.addEventListener('mousemove', mouse.mousemove);
        element.addEventListener('mousedown', mouse.mousedown);
        element.addEventListener('mouseup', mouse.mouseup);
        
        element.addEventListener("mousewheel", mouse.mousewheel);
        element.addEventListener("DOMMouseScroll", mouse.mousewheel);

        element.addEventListener('touchmove', mouse.mousemove);
        element.addEventListener('touchstart', mouse.mousedown);
        element.addEventListener('touchend', mouse.mouseup);
    };

    /**
     * Clears all captured source events
     * @method clearSourceEvents
     * @param {mouse} mouse
     */
    Mouse.clearSourceEvents = function(mouse) {
        mouse.sourceEvents.mousemove = null;
        mouse.sourceEvents.mousedown = null;
        mouse.sourceEvents.mouseup = null;
        mouse.sourceEvents.mousewheel = null;
        mouse.wheelDelta = 0;
    };

    /**
     * Sets the offset
     * @method setOffset
     * @param {mouse} mouse
     */
    Mouse.setOffset = function(mouse, offset) {
        mouse.offset.x = offset.x;
        mouse.offset.y = offset.y;
        mouse.position.x = mouse.absolute.x * mouse.scale.x + mouse.offset.x;
        mouse.position.y = mouse.absolute.y * mouse.scale.y + mouse.offset.y;
    };

    /**
     * Sets the scale
     * @method setScale
     * @param {mouse} mouse
     */
    Mouse.setScale = function(mouse, scale) {
        mouse.scale.x = scale.x;
        mouse.scale.y = scale.y;
        mouse.position.x = mouse.absolute.x * mouse.scale.x + mouse.offset.x;
        mouse.position.y = mouse.absolute.y * mouse.scale.y + mouse.offset.y;
    };
    
    /**
     * Description
     * @method _getRelativeMousePosition
     * @private
     * @param {} event
     * @param {} element
     * @param {number} pixelRatio
     * @return {}
     */
    var _getRelativeMousePosition = function(event, element, pixelRatio) {
        var elementBounds = element.getBoundingClientRect(),
            rootNode = (document.documentElement || document.body.parentNode || document.body),
            scrollX = (window.pageXOffset !== undefined) ? window.pageXOffset : rootNode.scrollLeft,
            scrollY = (window.pageYOffset !== undefined) ? window.pageYOffset : rootNode.scrollTop,
            touches = event.changedTouches,
            x, y;
        
        if (touches) {
            x = touches[0].pageX - elementBounds.left - scrollX;
            y = touches[0].pageY - elementBounds.top - scrollY;
        } else {
            x = event.pageX - elementBounds.left - scrollX;
            y = event.pageY - elementBounds.top - scrollY;
        }

        return { 
            x: x / (element.clientWidth / element.width * pixelRatio),
            y: y / (element.clientHeight / element.height * pixelRatio)
        };
    };

})();


;   // End src/core/Mouse.js


// Begin src/core/Runner.js

/**
* The `Matter.Runner` module is an optional utility which provides a game loop, 
* that handles updating and rendering a `Matter.Engine` for you within a browser.
* Note that the method `Engine.run` is an alias for `Runner.run`.
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Runner
*/

var Runner = {};

(function() {

    var _fps = 60,
        _deltaSampleSize = _fps,
        _delta = 1000 / _fps;

    var _requestAnimationFrame = window.requestAnimationFrame || window.webkitRequestAnimationFrame
                                      || window.mozRequestAnimationFrame || window.msRequestAnimationFrame 
                                      || function(callback){ window.setTimeout(function() { callback(Common.now()); }, _delta); };
   
    var _cancelAnimationFrame = window.cancelAnimationFrame || window.mozCancelAnimationFrame 
                                      || window.webkitCancelAnimationFrame || window.msCancelAnimationFrame;

    /**
     * Provides a basic game loop that handles updating the engine for you.
     * Calls `Engine.update` and `Engine.render` on the `requestAnimationFrame` event automatically.
     * Handles time correction and non-fixed dynamic timing (if enabled). 
     * Triggers `beforeTick`, `tick` and `afterTick` events.
     * @method run
     * @param {engine} engine
     */
    Runner.run = function(engine) {
        var counterTimestamp = 0,
            frameCounter = 0,
            deltaHistory = [],
            timePrev,
            timeScalePrev = 1;

        (function render(time){
            var timing = engine.timing,
                delta,
                correction = 1;

            timing.frameRequestId = _requestAnimationFrame(render);

            if (!engine.enabled)
                return;

            // create an event object
            var event = {
                timestamp: time
            };

            Events.trigger(engine, 'beforeTick', event);

            if (timing.isFixed) {
                // fixed timestep
                delta = timing.delta;
            } else {
                // dynamic timestep based on wall clock between calls
                delta = (time - timePrev) || timing.delta;
                timePrev = time;

                // optimistically filter delta over a few frames, to improve stability
                deltaHistory.push(delta);
                deltaHistory = deltaHistory.slice(-_deltaSampleSize);
                delta = Math.min.apply(null, deltaHistory);
                
                // limit delta
                delta = delta < timing.deltaMin ? timing.deltaMin : delta;
                delta = delta > timing.deltaMax ? timing.deltaMax : delta;

                // time correction for delta
                correction = delta / timing.delta;

                // update engine timing object
                timing.delta = delta;
            }

            // time correction for time scaling
            if (timeScalePrev !== 0)
                correction *= timing.timeScale / timeScalePrev;

            if (timing.timeScale === 0)
                correction = 0;

            timeScalePrev = timing.timeScale;
            
            // fps counter
            frameCounter += 1;
            if (time - counterTimestamp >= 1000) {
                timing.fps = frameCounter * ((time - counterTimestamp) / 1000);
                counterTimestamp = time;
                frameCounter = 0;
            }

            Events.trigger(engine, 'tick', event);

            // if world has been modified, clear the render scene graph
            if (engine.world.isModified && engine.render.controller.clear)
                engine.render.controller.clear(engine.render);

            // update
            Engine.update(engine, delta, correction);

            // render
            Engine.render(engine);

            Events.trigger(engine, 'afterTick', event);
        })();
    };

    /**
     * Ends execution of `Runner.run` on the given `engine`, by canceling the animation frame request event loop.
     * If you wish to only temporarily pause the engine, see `engine.enabled` instead.
     * @method stop
     * @param {engine} engine
     */
    Runner.stop = function(engine) {
        _cancelAnimationFrame(engine.timing.frameRequestId);
    };

})();


;   // End src/core/Runner.js


// Begin src/core/Sleeping.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Sleeping
*/

var Sleeping = {};

(function() {

    Sleeping._motionWakeThreshold = 0.18;
    Sleeping._motionSleepThreshold = 0.08;
    Sleeping._minBias = 0.9;

    /**
     * Puts bodies to sleep or wakes them up depending on their motion.
     * @method update
     * @param {body[]} bodies
     * @param {number} timeScale
     */
    Sleeping.update = function(bodies, timeScale) {
        var timeFactor = timeScale * timeScale * timeScale;

        // update bodies sleeping status
        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i],
                motion = body.speed * body.speed + body.angularSpeed * body.angularSpeed;

            // wake up bodies if they have a force applied
            if (body.force.x > 0 || body.force.y > 0) {
                Sleeping.set(body, false);
                continue;
            }

            var minMotion = Math.min(body.motion, motion),
                maxMotion = Math.max(body.motion, motion);
        
            // biased average motion estimation between frames
            body.motion = Sleeping._minBias * minMotion + (1 - Sleeping._minBias) * maxMotion;
            
            if (body.sleepThreshold > 0 && body.motion < Sleeping._motionSleepThreshold * timeFactor) {
                body.sleepCounter += 1;
                
                if (body.sleepCounter >= body.sleepThreshold)
                    Sleeping.set(body, true);
            } else if (body.sleepCounter > 0) {
                body.sleepCounter -= 1;
            }
        }
    };

    /**
     * Given a set of colliding pairs, wakes the sleeping bodies involved.
     * @method afterCollisions
     * @param {pair[]} pairs
     * @param {number} timeScale
     */
    Sleeping.afterCollisions = function(pairs, timeScale) {
        var timeFactor = timeScale * timeScale * timeScale;

        // wake up bodies involved in collisions
        for (var i = 0; i < pairs.length; i++) {
            var pair = pairs[i];
            
            // don't wake inactive pairs
            if (!pair.isActive)
                continue;

            var collision = pair.collision,
                bodyA = collision.bodyA, 
                bodyB = collision.bodyB;
        
            // don't wake if at least one body is static
            if ((bodyA.isSleeping && bodyB.isSleeping) || bodyA.isStatic || bodyB.isStatic)
                continue;
        
            if (bodyA.isSleeping || bodyB.isSleeping) {
                var sleepingBody = (bodyA.isSleeping && !bodyA.isStatic) ? bodyA : bodyB,
                    movingBody = sleepingBody === bodyA ? bodyB : bodyA;

                if (!sleepingBody.isStatic && movingBody.motion > Sleeping._motionWakeThreshold * timeFactor) {
                    Sleeping.set(sleepingBody, false);
                }
            }
        }
    };

    /**
     * Description
     * @method set
     * @param {body} body
     * @param {boolean} isSleeping
     */
    Sleeping.set = function(body, isSleeping) {
        if (isSleeping) {
            body.isSleeping = true;
            body.sleepCounter = body.sleepThreshold;

            body.positionImpulse.x = 0;
            body.positionImpulse.y = 0;

            body.positionPrev.x = body.position.x;
            body.positionPrev.y = body.position.y;

            body.anglePrev = body.angle;
            body.speed = 0;
            body.angularSpeed = 0;
            body.motion = 0;
        } else {
            body.isSleeping = false;
            body.sleepCounter = 0;
        }
    };

})();

;   // End src/core/Sleeping.js


// Begin src/factory/Bodies.js

/**
* The `Matter.Bodies` module contains factory methods for creating rigid body models 
* with commonly used body configurations (such as rectangles, circles and other polygons).
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Bodies
*/

// TODO: true circle bodies

var Bodies = {};

(function() {

    /**
     * Creates a new rigid body model with a rectangle hull. 
     * The options parameter is an object that specifies any properties you wish to override the defaults.
     * See the properties section of the `Matter.Body` module for detailed information on what you can pass via the `options` object.
     * @method rectangle
     * @param {number} x
     * @param {number} y
     * @param {number} width
     * @param {number} height
     * @param {object} [options]
     * @return {body} A new rectangle body
     */
    Bodies.rectangle = function(x, y, width, height, options) {
        options = options || {};

        var rectangle = { 
            label: 'Rectangle Body',
            position: { x: x, y: y },
            vertices: Vertices.fromPath('L 0 0 L ' + width + ' 0 L ' + width + ' ' + height + ' L 0 ' + height)
        };

        if (options.chamfer) {
            var chamfer = options.chamfer;
            rectangle.vertices = Vertices.chamfer(rectangle.vertices, chamfer.radius, 
                                    chamfer.quality, chamfer.qualityMin, chamfer.qualityMax);
            delete options.chamfer;
        }

        return Body.create(Common.extend({}, rectangle, options));
    };
    
    /**
     * Creates a new rigid body model with a trapezoid hull. 
     * The options parameter is an object that specifies any properties you wish to override the defaults.
     * See the properties section of the `Matter.Body` module for detailed information on what you can pass via the `options` object.
     * @method trapezoid
     * @param {number} x
     * @param {number} y
     * @param {number} width
     * @param {number} height
     * @param {number} slope
     * @param {object} [options]
     * @return {body} A new trapezoid body
     */
    Bodies.trapezoid = function(x, y, width, height, slope, options) {
        options = options || {};

        slope *= 0.5;
        var roof = (1 - (slope * 2)) * width;
        
        var x1 = width * slope,
            x2 = x1 + roof,
            x3 = x2 + x1;

        var trapezoid = { 
            label: 'Trapezoid Body',
            position: { x: x, y: y },
            vertices: Vertices.fromPath('L 0 0 L ' + x1 + ' ' + (-height) + ' L ' + x2 + ' ' + (-height) + ' L ' + x3 + ' 0')
        };

        if (options.chamfer) {
            var chamfer = options.chamfer;
            trapezoid.vertices = Vertices.chamfer(trapezoid.vertices, chamfer.radius, 
                                    chamfer.quality, chamfer.qualityMin, chamfer.qualityMax);
            delete options.chamfer;
        }

        return Body.create(Common.extend({}, trapezoid, options));
    };

    /**
     * Creates a new rigid body model with a circle hull. 
     * The options parameter is an object that specifies any properties you wish to override the defaults.
     * See the properties section of the `Matter.Body` module for detailed information on what you can pass via the `options` object.
     * @method circle
     * @param {number} x
     * @param {number} y
     * @param {number} radius
     * @param {object} [options]
     * @param {number} maxSides
     * @return {body} A new circle body
     */
    Bodies.circle = function(x, y, radius, options, maxSides) {
        options = options || {};
        options.label = 'Circle Body';
        
        // approximate circles with polygons until true circles implemented in SAT

        maxSides = maxSides || 25;
        var sides = Math.ceil(Math.max(10, Math.min(maxSides, radius)));

        // optimisation: always use even number of sides (half the number of unique axes)
        if (sides % 2 === 1)
            sides += 1;

        // flag for better rendering
        options.circleRadius = radius;

        return Bodies.polygon(x, y, sides, radius, options);
    };

    /**
     * Creates a new rigid body model with a regular polygon hull with the given number of sides. 
     * The options parameter is an object that specifies any properties you wish to override the defaults.
     * See the properties section of the `Matter.Body` module for detailed information on what you can pass via the `options` object.
     * @method polygon
     * @param {number} x
     * @param {number} y
     * @param {number} sides
     * @param {number} radius
     * @param {object} [options]
     * @return {body} A new regular polygon body
     */
    Bodies.polygon = function(x, y, sides, radius, options) {
        options = options || {};

        if (sides < 3)
            return Bodies.circle(x, y, radius, options);

        var theta = 2 * Math.PI / sides,
            path = '',
            offset = theta * 0.5;

        for (var i = 0; i < sides; i += 1) {
            var angle = offset + (i * theta),
                xx = Math.cos(angle) * radius,
                yy = Math.sin(angle) * radius;

            path += 'L ' + xx.toFixed(3) + ' ' + yy.toFixed(3) + ' ';
        }

        var polygon = { 
            label: 'Polygon Body',
            position: { x: x, y: y },
            vertices: Vertices.fromPath(path)
        };

        if (options.chamfer) {
            var chamfer = options.chamfer;
            polygon.vertices = Vertices.chamfer(polygon.vertices, chamfer.radius, 
                                    chamfer.quality, chamfer.qualityMin, chamfer.qualityMax);
            delete options.chamfer;
        }

        return Body.create(Common.extend({}, polygon, options));
    };

})();


;   // End src/factory/Bodies.js


// Begin src/factory/Composites.js

/**
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Composites
*/

var Composites = {};

(function() {

    /**
     * Description
     * @method stack
     * @param {number} xx
     * @param {number} yy
     * @param {number} columns
     * @param {number} rows
     * @param {number} columnGap
     * @param {number} rowGap
     * @param {function} callback
     * @return {composite} A new composite containing objects created in the callback
     */
    Composites.stack = function(xx, yy, columns, rows, columnGap, rowGap, callback) {
        var stack = Composite.create({ label: 'Stack' }),
            x = xx,
            y = yy,
            lastBody,
            i = 0;

        for (var row = 0; row < rows; row++) {
            var maxHeight = 0;
            
            for (var column = 0; column < columns; column++) {
                var body = callback(x, y, column, row, lastBody, i);
                    
                if (body) {
                    var bodyHeight = body.bounds.max.y - body.bounds.min.y,
                        bodyWidth = body.bounds.max.x - body.bounds.min.x; 

                    if (bodyHeight > maxHeight)
                        maxHeight = bodyHeight;
                    
                    Body.translate(body, { x: bodyWidth * 0.5, y: bodyHeight * 0.5 });

                    x = body.bounds.max.x + columnGap;

                    Composite.addBody(stack, body);
                    
                    lastBody = body;
                    i += 1;
                }
            }
            
            y += maxHeight + rowGap;
            x = xx;
        }

        return stack;
    };
    
    /**
     * Description
     * @method chain
     * @param {composite} composite
     * @param {number} xOffsetA
     * @param {number} yOffsetA
     * @param {number} xOffsetB
     * @param {number} yOffsetB
     * @param {object} options
     * @return {composite} A new composite containing objects chained together with constraints
     */
    Composites.chain = function(composite, xOffsetA, yOffsetA, xOffsetB, yOffsetB, options) {
        var bodies = composite.bodies;
        
        for (var i = 1; i < bodies.length; i++) {
            var bodyA = bodies[i - 1],
                bodyB = bodies[i],
                bodyAHeight = bodyA.bounds.max.y - bodyA.bounds.min.y,
                bodyAWidth = bodyA.bounds.max.x - bodyA.bounds.min.x, 
                bodyBHeight = bodyB.bounds.max.y - bodyB.bounds.min.y,
                bodyBWidth = bodyB.bounds.max.x - bodyB.bounds.min.x;
        
            var defaults = {
                bodyA: bodyA,
                pointA: { x: bodyAWidth * xOffsetA, y: bodyAHeight * yOffsetA },
                bodyB: bodyB,
                pointB: { x: bodyBWidth * xOffsetB, y: bodyBHeight * yOffsetB }
            };
            
            var constraint = Common.extend(defaults, options);
        
            Composite.addConstraint(composite, Constraint.create(constraint));
        }

        composite.label += ' Chain';
        
        return composite;
    };

    /**
     * Connects bodies in the composite with constraints in a grid pattern, with optional cross braces
     * @method mesh
     * @param {composite} composite
     * @param {number} columns
     * @param {number} rows
     * @param {boolean} crossBrace
     * @param {object} options
     * @return {composite} The composite containing objects meshed together with constraints
     */
    Composites.mesh = function(composite, columns, rows, crossBrace, options) {
        var bodies = composite.bodies,
            row,
            col,
            bodyA,
            bodyB,
            bodyC;
        
        for (row = 0; row < rows; row++) {
            for (col = 0; col < columns; col++) {
                if (col > 0) {
                    bodyA = bodies[(col - 1) + (row * columns)];
                    bodyB = bodies[col + (row * columns)];
                    Composite.addConstraint(composite, Constraint.create(Common.extend({ bodyA: bodyA, bodyB: bodyB }, options)));
                }
            }

            for (col = 0; col < columns; col++) {
                if (row > 0) {
                    bodyA = bodies[col + ((row - 1) * columns)];
                    bodyB = bodies[col + (row * columns)];
                    Composite.addConstraint(composite, Constraint.create(Common.extend({ bodyA: bodyA, bodyB: bodyB }, options)));

                    if (crossBrace && col > 0) {
                        bodyC = bodies[(col - 1) + ((row - 1) * columns)];
                        Composite.addConstraint(composite, Constraint.create(Common.extend({ bodyA: bodyC, bodyB: bodyB }, options)));
                    }

                    if (crossBrace && col < columns - 1) {
                        bodyC = bodies[(col + 1) + ((row - 1) * columns)];
                        Composite.addConstraint(composite, Constraint.create(Common.extend({ bodyA: bodyC, bodyB: bodyB }, options)));
                    }
                }
            }
        }

        composite.label += ' Mesh';
        
        return composite;
    };
    
    /**
     * Description
     * @method pyramid
     * @param {number} xx
     * @param {number} yy
     * @param {number} columns
     * @param {number} rows
     * @param {number} columnGap
     * @param {number} rowGap
     * @param {function} callback
     * @return {composite} A new composite containing objects created in the callback
     */
    Composites.pyramid = function(xx, yy, columns, rows, columnGap, rowGap, callback) {
        return Composites.stack(xx, yy, columns, rows, columnGap, rowGap, function(x, y, column, row, lastBody, i) {
            var actualRows = Math.min(rows, Math.ceil(columns / 2)),
                lastBodyWidth = lastBody ? lastBody.bounds.max.x - lastBody.bounds.min.x : 0;
            
            if (row > actualRows)
                return;
            
            // reverse row order
            row = actualRows - row;
            
            var start = row,
                end = columns - 1 - row;

            if (column < start || column > end)
                return;
            
            // retroactively fix the first body's position, since width was unknown
            if (i === 1) {
                Body.translate(lastBody, { x: (column + (columns % 2 === 1 ? 1 : -1)) * lastBodyWidth, y: 0 });
            }

            var xOffset = lastBody ? column * lastBodyWidth : 0;
            
            return callback(xx + xOffset + column * columnGap, y, column, row, lastBody, i);
        });
    };

    /**
     * Description
     * @method newtonsCradle
     * @param {number} xx
     * @param {number} yy
     * @param {number} number
     * @param {number} size
     * @param {number} length
     * @return {composite} A new composite newtonsCradle body
     */
    Composites.newtonsCradle = function(xx, yy, number, size, length) {
        var newtonsCradle = Composite.create({ label: 'Newtons Cradle' });

        for (var i = 0; i < number; i++) {
            var separation = 1.9,
                circle = Bodies.circle(xx + i * (size * separation), yy + length, size, 
                            { inertia: 99999, restitution: 1, friction: 0, frictionAir: 0.0001, slop: 0.01 }),
                constraint = Constraint.create({ pointA: { x: xx + i * (size * separation), y: yy }, bodyB: circle });

            Composite.addBody(newtonsCradle, circle);
            Composite.addConstraint(newtonsCradle, constraint);
        }

        return newtonsCradle;
    };
    
    /**
     * Description
     * @method car
     * @param {number} xx
     * @param {number} yy
     * @param {number} width
     * @param {number} height
     * @param {number} wheelSize
     * @return {composite} A new composite car body
     */
    Composites.car = function(xx, yy, width, height, wheelSize) {
        var group = Body.nextGroup(true),
            wheelBase = -20,
            wheelAOffset = -width * 0.5 + wheelBase,
            wheelBOffset = width * 0.5 - wheelBase,
            wheelYOffset = 0;
    
        var car = Composite.create({ label: 'Car' }),
            body = Bodies.trapezoid(xx, yy, width, height, 0.3, { 
                collisionFilter: {
                    group: group
                },
                friction: 0.01,
                chamfer: {
                    radius: 10
                }
            });
    
        var wheelA = Bodies.circle(xx + wheelAOffset, yy + wheelYOffset, wheelSize, { 
            collisionFilter: {
                group: group
            },
            restitution: 0.5, 
            friction: 0.9,
            density: 0.01
        });
                    
        var wheelB = Bodies.circle(xx + wheelBOffset, yy + wheelYOffset, wheelSize, { 
            collisionFilter: {
                group: group
            },
            restitution: 0.5, 
            friction: 0.9,
            density: 0.01
        });
                    
        var axelA = Constraint.create({
            bodyA: body,
            pointA: { x: wheelAOffset, y: wheelYOffset },
            bodyB: wheelA,
            stiffness: 0.5
        });
                        
        var axelB = Constraint.create({
            bodyA: body,
            pointA: { x: wheelBOffset, y: wheelYOffset },
            bodyB: wheelB,
            stiffness: 0.5
        });
        
        Composite.addBody(car, body);
        Composite.addBody(car, wheelA);
        Composite.addBody(car, wheelB);
        Composite.addConstraint(car, axelA);
        Composite.addConstraint(car, axelB);

        return car;
    };

    /**
     * Creates a simple soft body like object
     * @method softBody
     * @param {number} xx
     * @param {number} yy
     * @param {number} columns
     * @param {number} rows
     * @param {number} columnGap
     * @param {number} rowGap
     * @param {boolean} crossBrace
     * @param {number} particleRadius
     * @param {} particleOptions
     * @param {} constraintOptions
     * @return {composite} A new composite softBody
     */
    Composites.softBody = function(xx, yy, columns, rows, columnGap, rowGap, crossBrace, particleRadius, particleOptions, constraintOptions) {
        particleOptions = Common.extend({ inertia: Infinity }, particleOptions);
        constraintOptions = Common.extend({ stiffness: 0.4 }, constraintOptions);

        var softBody = Composites.stack(xx, yy, columns, rows, columnGap, rowGap, function(x, y) {
            return Bodies.circle(x, y, particleRadius, particleOptions);
        });

        Composites.mesh(softBody, columns, rows, crossBrace, constraintOptions);

        softBody.label = 'Soft Body';

        return softBody;
    };

})();


;   // End src/factory/Composites.js


// Begin src/geometry/Axes.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Axes
*/

var Axes = {};

(function() {

    /**
     * Description
     * @method fromVertices
     * @param {vertices} vertices
     * @return {axes} A new axes from the given vertices
     */
    Axes.fromVertices = function(vertices) {
        var axes = {};

        // find the unique axes, using edge normal gradients
        for (var i = 0; i < vertices.length; i++) {
            var j = (i + 1) % vertices.length, 
                normal = Vector.normalise({ 
                    x: vertices[j].y - vertices[i].y, 
                    y: vertices[i].x - vertices[j].x
                }),
                gradient = (normal.y === 0) ? Infinity : (normal.x / normal.y);
            
            // limit precision
            gradient = gradient.toFixed(3).toString();

            axes[gradient] = normal;
        }

        return Common.values(axes);
    };

    /**
     * Description
     * @method rotate
     * @param {axes} axes
     * @param {number} angle
     */
    Axes.rotate = function(axes, angle) {
        if (angle === 0)
            return;
        
        var cos = Math.cos(angle),
            sin = Math.sin(angle);

        for (var i = 0; i < axes.length; i++) {
            var axis = axes[i],
                xx;
            xx = axis.x * cos - axis.y * sin;
            axis.y = axis.x * sin + axis.y * cos;
            axis.x = xx;
        }
    };

})();

;   // End src/geometry/Axes.js


// Begin src/geometry/Bounds.js

/**
* _Internal Class_, not generally used outside of the engine's internals.
*
* @class Bounds
*/

var Bounds = {};

(function() {

    /**
     * Description
     * @method create
     * @param {vertices} vertices
     * @return {bounds} A new bounds object
     */
    Bounds.create = function(vertices) {
        var bounds = { 
            min: { x: 0, y: 0 }, 
            max: { x: 0, y: 0 }
        };

        if (vertices)
            Bounds.update(bounds, vertices);
        
        return bounds;
    };

    /**
     * Description
     * @method update
     * @param {bounds} bounds
     * @param {vertices} vertices
     * @param {vector} velocity
     */
    Bounds.update = function(bounds, vertices, velocity) {
        bounds.min.x = Number.MAX_VALUE;
        bounds.max.x = Number.MIN_VALUE;
        bounds.min.y = Number.MAX_VALUE;
        bounds.max.y = Number.MIN_VALUE;

        for (var i = 0; i < vertices.length; i++) {
            var vertex = vertices[i];
            if (vertex.x > bounds.max.x) bounds.max.x = vertex.x;
            if (vertex.x < bounds.min.x) bounds.min.x = vertex.x;
            if (vertex.y > bounds.max.y) bounds.max.y = vertex.y;
            if (vertex.y < bounds.min.y) bounds.min.y = vertex.y;
        }
        
        if (velocity) {
            if (velocity.x > 0) {
                bounds.max.x += velocity.x;
            } else {
                bounds.min.x += velocity.x;
            }
            
            if (velocity.y > 0) {
                bounds.max.y += velocity.y;
            } else {
                bounds.min.y += velocity.y;
            }
        }
    };

    /**
     * Description
     * @method contains
     * @param {bounds} bounds
     * @param {vector} point
     * @return {boolean} True if the bounds contain the point, otherwise false
     */
    Bounds.contains = function(bounds, point) {
        return point.x >= bounds.min.x && point.x <= bounds.max.x 
               && point.y >= bounds.min.y && point.y <= bounds.max.y;
    };

    /**
     * Description
     * @method overlaps
     * @param {bounds} boundsA
     * @param {bounds} boundsB
     * @return {boolean} True if the bounds overlap, otherwise false
     */
    Bounds.overlaps = function(boundsA, boundsB) {
        return (boundsA.min.x <= boundsB.max.x && boundsA.max.x >= boundsB.min.x
                && boundsA.max.y >= boundsB.min.y && boundsA.min.y <= boundsB.max.y);
    };

    /**
     * Translates the bounds by the given vector
     * @method translate
     * @param {bounds} bounds
     * @param {vector} vector
     */
    Bounds.translate = function(bounds, vector) {
        bounds.min.x += vector.x;
        bounds.max.x += vector.x;
        bounds.min.y += vector.y;
        bounds.max.y += vector.y;
    };

    /**
     * Shifts the bounds to the given position
     * @method shift
     * @param {bounds} bounds
     * @param {vector} position
     */
    Bounds.shift = function(bounds, position) {
        var deltaX = bounds.max.x - bounds.min.x,
            deltaY = bounds.max.y - bounds.min.y;
            
        bounds.min.x = position.x;
        bounds.max.x = position.x + deltaX;
        bounds.min.y = position.y;
        bounds.max.y = position.y + deltaY;
    };
    
})();

;   // End src/geometry/Bounds.js


// Begin src/geometry/Vector.js

/**
* The `Matter.Vector` module contains methods for creating and manipulating vectors.
* Vectors are the basis of all the geometry related operations in the engine.
* A `Matter.Vector` object is of the form `{ x: 0, y: 0 }`.
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Vector
*/

// TODO: consider params for reusing vector objects

var Vector = {};

(function() {

    /**
     * Returns a new vector with `x` and `y` copied from the given `vector`.
     * @method clone
     * @param {vector} vector
     * @return {vector} A new cloned vector
     */
    Vector.clone = function(vector) {
        return { x: vector.x, y: vector.y };
    };

    /**
     * Returns the magnitude (length) of a vector.
     * @method magnitude
     * @param {vector} vector
     * @return {number} The magnitude of the vector
     */
    Vector.magnitude = function(vector) {
        return Math.sqrt((vector.x * vector.x) + (vector.y * vector.y));
    };

    /**
     * Returns the magnitude (length) of a vector (therefore saving a `sqrt` operation).
     * @method magnitudeSquared
     * @param {vector} vector
     * @return {number} The squared magnitude of the vector
     */
    Vector.magnitudeSquared = function(vector) {
        return (vector.x * vector.x) + (vector.y * vector.y);
    };

    /**
     * Rotates the vector about (0, 0) by specified angle.
     * @method rotate
     * @param {vector} vector
     * @param {number} angle
     * @return {vector} A new vector rotated about (0, 0)
     */
    Vector.rotate = function(vector, angle) {
        var cos = Math.cos(angle), sin = Math.sin(angle);
        return {
            x: vector.x * cos - vector.y * sin,
            y: vector.x * sin + vector.y * cos
        };
    };

    /**
     * Rotates the vector about a specified point by specified angle.
     * @method rotateAbout
     * @param {vector} vector
     * @param {number} angle
     * @param {vector} point
     * @return {vector} A new vector rotated about the point
     */
    Vector.rotateAbout = function(vector, angle, point) {
        var cos = Math.cos(angle), sin = Math.sin(angle);
        return {
            x: point.x + ((vector.x - point.x) * cos - (vector.y - point.y) * sin),
            y: point.y + ((vector.x - point.x) * sin + (vector.y - point.y) * cos)
        };
    };

    /**
     * Normalises a vector (such that its magnitude is `1`).
     * @method normalise
     * @param {vector} vector
     * @return {vector} A new vector normalised
     */
    Vector.normalise = function(vector) {
        var magnitude = Vector.magnitude(vector);
        if (magnitude === 0)
            return { x: 0, y: 0 };
        return { x: vector.x / magnitude, y: vector.y / magnitude };
    };

    /**
     * Returns the dot-product of two vectors.
     * @method dot
     * @param {vector} vectorA
     * @param {vector} vectorB
     * @return {number} The dot product of the two vectors
     */
    Vector.dot = function(vectorA, vectorB) {
        return (vectorA.x * vectorB.x) + (vectorA.y * vectorB.y);
    };

    /**
     * Returns the cross-product of two vectors.
     * @method cross
     * @param {vector} vectorA
     * @param {vector} vectorB
     * @return {number} The cross product of the two vectors
     */
    Vector.cross = function(vectorA, vectorB) {
        return (vectorA.x * vectorB.y) - (vectorA.y * vectorB.x);
    };

    /**
     * Adds the two vectors.
     * @method add
     * @param {vector} vectorA
     * @param {vector} vectorB
     * @return {vector} A new vector of vectorA and vectorB added
     */
    Vector.add = function(vectorA, vectorB) {
        return { x: vectorA.x + vectorB.x, y: vectorA.y + vectorB.y };
    };

    /**
     * Subtracts the two vectors.
     * @method sub
     * @param {vector} vectorA
     * @param {vector} vectorB
     * @return {vector} A new vector of vectorA and vectorB subtracted
     */
    Vector.sub = function(vectorA, vectorB) {
        return { x: vectorA.x - vectorB.x, y: vectorA.y - vectorB.y };
    };

    /**
     * Multiplies a vector and a scalar.
     * @method mult
     * @param {vector} vector
     * @param {number} scalar
     * @return {vector} A new vector multiplied by scalar
     */
    Vector.mult = function(vector, scalar) {
        return { x: vector.x * scalar, y: vector.y * scalar };
    };

    /**
     * Divides a vector and a scalar.
     * @method div
     * @param {vector} vector
     * @param {number} scalar
     * @return {vector} A new vector divided by scalar
     */
    Vector.div = function(vector, scalar) {
        return { x: vector.x / scalar, y: vector.y / scalar };
    };

    /**
     * Returns the perpendicular vector. Set `negate` to true for the perpendicular in the opposite direction.
     * @method perp
     * @param {vector} vector
     * @param {bool} [negate=false]
     * @return {vector} The perpendicular vector
     */
    Vector.perp = function(vector, negate) {
        negate = negate === true ? -1 : 1;
        return { x: negate * -vector.y, y: negate * vector.x };
    };

    /**
     * Negates both components of a vector such that it points in the opposite direction.
     * @method neg
     * @param {vector} vector
     * @return {vector} The negated vector
     */
    Vector.neg = function(vector) {
        return { x: -vector.x, y: -vector.y };
    };

    /**
     * Returns the angle in radians between the two vectors relative to the x-axis.
     * @method angle
     * @param {vector} vectorA
     * @param {vector} vectorB
     * @return {number} The angle in radians
     */
    Vector.angle = function(vectorA, vectorB) {
        return Math.atan2(vectorB.y - vectorA.y, vectorB.x - vectorA.x);
    };

})();

;   // End src/geometry/Vector.js


// Begin src/geometry/Vertices.js

/**
* The `Matter.Vertices` module contains methods for creating and manipulating sets of vertices.
* A set of vertices is an array of `Matter.Vector` with additional indexing properties inserted by `Vertices.create`.
* A `Matter.Body` maintains a set of vertices to represent the shape of the object (its convex hull).
*
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class Vertices
*/

// TODO: convex decomposition - http://mnbayazit.com/406/bayazit

var Vertices = {};

(function() {

    /**
     * Creates a new set of `Matter.Body` compatible vertices.
     * The `points` argument accepts an array of `Matter.Vector` points orientated around the origin `(0, 0)`, for example:
     *
     *     [{ x: 0, y: 0 }, { x: 25, y: 50 }, { x: 50, y: 0 }]
     *
     * The `Vertices.create` method returns a new array of vertices, which are similar to Matter.Vector objects,
     * but with some additional references required for efficient collision detection routines.
     *
     * Note that the `body` argument is not optional, a `Matter.Body` reference must be provided.
     *
     * @method create
     * @param {vector[]} points
     * @param {body} body
     */
    Vertices.create = function(points, body) {
        var vertices = [];

        for (var i = 0; i < points.length; i++) {
            var point = points[i],
                vertex = {};

            vertex.x = point.x;
            vertex.y = point.y;
            vertex.index = i;
            vertex.body = body;

            vertices.push(vertex);
        }

        return vertices;
    };

    /**
     * Parses a _simple_ SVG-style path into a `Matter.Vertices` object for the given `Matter.Body`.
     * @method fromPath
     * @param {string} path
     * @param {body} body
     * @return {vertices} vertices
     */
    Vertices.fromPath = function(path, body) {
        var pathPattern = /L\s*([\-\d\.]*)\s*([\-\d\.]*)/ig,
            points = [];

        path.replace(pathPattern, function(match, x, y) {
            points.push({ x: parseFloat(x), y: parseFloat(y) });
        });

        return Vertices.create(points, body);
    };

    /**
     * Returns the centre (centroid) of the set of vertices.
     * @method centre
     * @param {vertices} vertices
     * @return {vector} The centre point
     */
    Vertices.centre = function(vertices) {
        var area = Vertices.area(vertices, true),
            centre = { x: 0, y: 0 },
            cross,
            temp,
            j;

        for (var i = 0; i < vertices.length; i++) {
            j = (i + 1) % vertices.length;
            cross = Vector.cross(vertices[i], vertices[j]);
            temp = Vector.mult(Vector.add(vertices[i], vertices[j]), cross);
            centre = Vector.add(centre, temp);
        }

        return Vector.div(centre, 6 * area);
    };

    /**
     * Returns the area of the set of vertices.
     * @method area
     * @param {vertices} vertices
     * @param {bool} signed
     * @return {number} The area
     */
    Vertices.area = function(vertices, signed) {
        var area = 0,
            j = vertices.length - 1;

        for (var i = 0; i < vertices.length; i++) {
            area += (vertices[j].x - vertices[i].x) * (vertices[j].y + vertices[i].y);
            j = i;
        }

        if (signed)
            return area / 2;

        return Math.abs(area) / 2;
    };

    /**
     * Returns the moment of inertia (second moment of area) of the set of vertices given the total mass.
     * @method inertia
     * @param {vertices} vertices
     * @param {number} mass
     * @return {number} The polygon's moment of inertia
     */
    Vertices.inertia = function(vertices, mass) {
        var numerator = 0,
            denominator = 0,
            v = vertices,
            cross,
            j;

        // find the polygon's moment of inertia, using second moment of area
        // http://www.physicsforums.com/showthread.php?t=25293
        for (var n = 0; n < v.length; n++) {
            j = (n + 1) % v.length;
            cross = Math.abs(Vector.cross(v[j], v[n]));
            numerator += cross * (Vector.dot(v[j], v[j]) + Vector.dot(v[j], v[n]) + Vector.dot(v[n], v[n]));
            denominator += cross;
        }

        return (mass / 6) * (numerator / denominator);
    };

    /**
     * Translates the set of vertices in-place.
     * @method translate
     * @param {vertices} vertices
     * @param {vector} vector
     * @param {number} scalar
     */
    Vertices.translate = function(vertices, vector, scalar) {
        var i;
        if (scalar) {
            for (i = 0; i < vertices.length; i++) {
                vertices[i].x += vector.x * scalar;
                vertices[i].y += vector.y * scalar;
            }
        } else {
            for (i = 0; i < vertices.length; i++) {
                vertices[i].x += vector.x;
                vertices[i].y += vector.y;
            }
        }

        return vertices;
    };

    /**
     * Rotates the set of vertices in-place.
     * @method rotate
     * @param {vertices} vertices
     * @param {number} angle
     * @param {vector} point
     */
    Vertices.rotate = function(vertices, angle, point) {
        if (angle === 0)
            return;

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

        for (var i = 0; i < vertices.length; i++) {
            var vertice = vertices[i],
                dx = vertice.x - point.x,
                dy = vertice.y - point.y;
                
            vertice.x = point.x + (dx * cos - dy * sin);
            vertice.y = point.y + (dx * sin + dy * cos);
        }

        return vertices;
    };

    /**
     * Returns `true` if the `point` is inside the set of `vertices`.
     * @method contains
     * @param {vertices} vertices
     * @param {vector} point
     * @return {boolean} True if the vertices contains point, otherwise false
     */
    Vertices.contains = function(vertices, point) {
        for (var i = 0; i < vertices.length; i++) {
            var vertice = vertices[i],
                nextVertice = vertices[(i + 1) % vertices.length];
            if ((point.x - vertice.x) * (nextVertice.y - vertice.y) + (point.y - vertice.y) * (vertice.x - nextVertice.x) > 0) {
                return false;
            }
        }

        return true;
    };

    /**
     * Scales the vertices from a point (default is centre) in-place.
     * @method scale
     * @param {vertices} vertices
     * @param {number} scaleX
     * @param {number} scaleY
     * @param {vector} point
     */
    Vertices.scale = function(vertices, scaleX, scaleY, point) {
        if (scaleX === 1 && scaleY === 1)
            return vertices;

        point = point || Vertices.centre(vertices);

        var vertex,
            delta;

        for (var i = 0; i < vertices.length; i++) {
            vertex = vertices[i];
            delta = Vector.sub(vertex, point);
            vertices[i].x = point.x + delta.x * scaleX;
            vertices[i].y = point.y + delta.y * scaleY;
        }

        return vertices;
    };

    /**
     * Chamfers a set of vertices by giving them rounded corners, returns a new set of vertices.
     * The radius parameter is a single number or an array to specify the radius for each vertex.
     * @method chamfer
     * @param {vertices} vertices
     * @param {number[]} radius
     * @param {number} quality
     * @param {number} qualityMin
     * @param {number} qualityMax
     */
    Vertices.chamfer = function(vertices, radius, quality, qualityMin, qualityMax) {
        radius = radius || [8];

        if (!radius.length)
            radius = [radius];

        // quality defaults to -1, which is auto
        quality = (typeof quality !== 'undefined') ? quality : -1;
        qualityMin = qualityMin || 2;
        qualityMax = qualityMax || 14;

        var newVertices = [];

        for (var i = 0; i < vertices.length; i++) {
            var prevVertex = vertices[i - 1 >= 0 ? i - 1 : vertices.length - 1],
                vertex = vertices[i],
                nextVertex = vertices[(i + 1) % vertices.length],
                currentRadius = radius[i < radius.length ? i : radius.length - 1];

            if (currentRadius === 0) {
                newVertices.push(vertex);
                continue;
            }

            var prevNormal = Vector.normalise({ 
                x: vertex.y - prevVertex.y, 
                y: prevVertex.x - vertex.x
            });

            var nextNormal = Vector.normalise({ 
                x: nextVertex.y - vertex.y, 
                y: vertex.x - nextVertex.x
            });

            var diagonalRadius = Math.sqrt(2 * Math.pow(currentRadius, 2)),
                radiusVector = Vector.mult(Common.clone(prevNormal), currentRadius),
                midNormal = Vector.normalise(Vector.mult(Vector.add(prevNormal, nextNormal), 0.5)),
                scaledVertex = Vector.sub(vertex, Vector.mult(midNormal, diagonalRadius));

            var precision = quality;

            if (quality === -1) {
                // automatically decide precision
                precision = Math.pow(currentRadius, 0.32) * 1.75;
            }

            precision = Common.clamp(precision, qualityMin, qualityMax);

            // use an even value for precision, more likely to reduce axes by using symmetry
            if (precision % 2 === 1)
                precision += 1;

            var alpha = Math.acos(Vector.dot(prevNormal, nextNormal)),
                theta = alpha / precision;

            for (var j = 0; j < precision; j++) {
                newVertices.push(Vector.add(Vector.rotate(radiusVector, theta * j), scaledVertex));
            }
        }

        return newVertices;
    };

})();


;   // End src/geometry/Vertices.js


// Begin src/render/Render.js

/**
* The `Matter.Render` module is the default `render.controller` used by a `Matter.Engine`.
* This renderer is HTML5 canvas based and supports a number of drawing options including sprites and viewports.
*
* It is possible develop a custom renderer module based on `Matter.Render` and pass an instance of it to `Engine.create` via `options.render`.
* A minimal custom renderer object must define at least three functions: `create`, `clear` and `world` (see `Matter.Render`).
*
* See also `Matter.RenderPixi` for an alternate WebGL, scene-graph based renderer.
*
* @class Render
*/

var Render = {};

(function() {
    
    /**
     * Creates a new renderer. The options parameter is an object that specifies any properties you wish to override the defaults.
     * All properties have default values, and many are pre-calculated automatically based on other properties.
     * See the properites section below for detailed information on what you can pass via the `options` object.
     * @method create
     * @param {object} [options]
     * @return {render} A new renderer
     */
    Render.create = function(options) {
        var defaults = {
            controller: Render,
            element: null,
            canvas: null,
            options: {
                width: 800,
                height: 600,
                pixelRatio: 1,
                background: '#fafafa',
                wireframeBackground: '#222',
                hasBounds: false,
                enabled: true,
                wireframes: true,
                showSleeping: true,
                showDebug: false,
                showBroadphase: false,
                showBounds: false,
                showVelocity: false,
                showCollisions: false,
                showAxes: false,
                showPositions: false,
                showAngleIndicator: false,
                showIds: false,
                showShadows: false
            }
        };

        var render = Common.extend(defaults, options);

        render.canvas = render.canvas || _createCanvas(render.options.width, render.options.height);
        render.context = render.canvas.getContext('2d');
        render.textures = {};

        render.bounds = render.bounds || { 
            min: { 
                x: 0,
                y: 0
            }, 
            max: { 
                x: render.options.width,
                y: render.options.height
            }
        };

        if (render.options.pixelRatio !== 1) {
            Render.setPixelRatio(render, render.options.pixelRatio);
        }

        if (Common.isElement(render.element)) {
            render.element.appendChild(render.canvas);
        } else {
            Common.log('Render.create: options.element was undefined, render.canvas was created but not appended', 'warn');
        }

        return render;
    };

    /**
     * Sets the pixel ratio of the renderer and updates the canvas.
     * To automatically detect the correct ratio, pass the string `'auto'` for `pixelRatio`.
     * @method setPixelRatio
     * @param {render} render
     * @param {number} pixelRatio
     */
    Render.setPixelRatio = function(render, pixelRatio) {
        var options = render.options,
            canvas = render.canvas;

        if (pixelRatio === 'auto') {
            pixelRatio = _getPixelRatio(canvas);
        }

        options.pixelRatio = pixelRatio;
        canvas.setAttribute('data-pixel-ratio', pixelRatio);
        canvas.width = options.width * pixelRatio;
        canvas.height = options.height * pixelRatio;
        canvas.style.width = options.width + 'px';
        canvas.style.height = options.height + 'px';
        render.context.scale(pixelRatio, pixelRatio);
    };

    /**
     * Renders the given `engine`'s `Matter.World` object.
     * This is the entry point for all rendering and should be called every time the scene changes.
     * @method world
     * @param {engine} engine
     */
    Render.world = function(engine) {
        var render = engine.render,
            world = engine.world,
            canvas = render.canvas,
            context = render.context,
            options = render.options,
            allBodies = Composite.allBodies(world),
            allConstraints = Composite.allConstraints(world),
            background = options.wireframes ? options.wireframeBackground : options.background,
            bodies = [],
            constraints = [],
            i;

        // apply background if it has changed
        if (render.currentBackground !== background)
            _applyBackground(render, background);

        // clear the canvas with a transparent fill, to allow the canvas background to show
        context.globalCompositeOperation = 'source-in';
        context.fillStyle = "transparent";
        context.fillRect(0, 0, canvas.width, canvas.height);
        context.globalCompositeOperation = 'source-over';

        // handle bounds
        if (options.hasBounds) {
            var boundsWidth = render.bounds.max.x - render.bounds.min.x,
                boundsHeight = render.bounds.max.y - render.bounds.min.y,
                boundsScaleX = boundsWidth / options.width,
                boundsScaleY = boundsHeight / options.height;

            // filter out bodies that are not in view
            for (i = 0; i < allBodies.length; i++) {
                var body = allBodies[i];
                if (Bounds.overlaps(body.bounds, render.bounds))
                    bodies.push(body);
            }

            // filter out constraints that are not in view
            for (i = 0; i < allConstraints.length; i++) {
                var constraint = allConstraints[i],
                    bodyA = constraint.bodyA,
                    bodyB = constraint.bodyB,
                    pointAWorld = constraint.pointA,
                    pointBWorld = constraint.pointB;

                if (bodyA) pointAWorld = Vector.add(bodyA.position, constraint.pointA);
                if (bodyB) pointBWorld = Vector.add(bodyB.position, constraint.pointB);

                if (!pointAWorld || !pointBWorld)
                    continue;

                if (Bounds.contains(render.bounds, pointAWorld) || Bounds.contains(render.bounds, pointBWorld))
                    constraints.push(constraint);
            }

            // transform the view
            context.scale(1 / boundsScaleX, 1 / boundsScaleY);
            context.translate(-render.bounds.min.x, -render.bounds.min.y);
        } else {
            constraints = allConstraints;
            bodies = allBodies;
        }

        if (!options.wireframes || (engine.enableSleeping && options.showSleeping)) {
            // fully featured rendering of bodies
            Render.bodies(engine, bodies, context);
        } else {
            // optimised method for wireframes only
            Render.bodyWireframes(engine, bodies, context);
        }

        if (options.showBounds)
            Render.bodyBounds(engine, bodies, context);

        if (options.showAxes || options.showAngleIndicator)
            Render.bodyAxes(engine, bodies, context);
        
        if (options.showPositions)
            Render.bodyPositions(engine, bodies, context);

        if (options.showVelocity)
            Render.bodyVelocity(engine, bodies, context);

        if (options.showIds)
            Render.bodyIds(engine, bodies, context);

        if (options.showCollisions)
            Render.collisions(engine, engine.pairs.list, context);

        Render.constraints(constraints, context);

        if (options.showBroadphase && engine.broadphase.controller === Grid)
            Render.grid(engine, engine.broadphase, context);

        if (options.showDebug)
            Render.debug(engine, context);

        if (options.hasBounds) {
            // revert view transforms
            context.setTransform(options.pixelRatio, 0, 0, options.pixelRatio, 0, 0);
        }
    };

    /**
     * Description
     * @private
     * @method debug
     * @param {engine} engine
     * @param {RenderingContext} context
     */
    Render.debug = function(engine, context) {
        var c = context,
            world = engine.world,
            render = engine.render,
            options = render.options,
            bodies = Composite.allBodies(world),
            space = "    ";

        if (engine.timing.timestamp - (render.debugTimestamp || 0) >= 500) {
            var text = "";
            text += "fps: " + Math.round(engine.timing.fps) + space;

            if (engine.metrics.extended) {
                text += "delta: " + engine.timing.delta.toFixed(3) + space;
                text += "correction: " + engine.timing.correction.toFixed(3) + space;
                text += "bodies: " + bodies.length + space;

                if (engine.broadphase.controller === Grid)
                    text += "buckets: " + engine.metrics.buckets + space;

                text += "\n";

                text += "collisions: " + engine.metrics.collisions + space;
                text += "pairs: " + engine.pairs.list.length + space;
                text += "broad: " + engine.metrics.broadEff + space;
                text += "mid: " + engine.metrics.midEff + space;
                text += "narrow: " + engine.metrics.narrowEff + space;
            }            

            render.debugString = text;
            render.debugTimestamp = engine.timing.timestamp;
        }

        if (render.debugString) {
            c.font = "12px Arial";

            if (options.wireframes) {
                c.fillStyle = 'rgba(255,255,255,0.5)';
            } else {
                c.fillStyle = 'rgba(0,0,0,0.5)';
            }

            var split = render.debugString.split('\n');

            for (var i = 0; i < split.length; i++) {
                c.fillText(split[i], 50, 50 + i * 18);
            }
        }
    };

    /**
     * Description
     * @private
     * @method constraints
     * @param {constraint[]} constraints
     * @param {RenderingContext} context
     */
    Render.constraints = function(constraints, context) {
        var c = context;

        for (var i = 0; i < constraints.length; i++) {
            var constraint = constraints[i];

            if (!constraint.render.visible || !constraint.pointA || !constraint.pointB)
                continue;

            var bodyA = constraint.bodyA,
                bodyB = constraint.bodyB;

            if (bodyA) {
                c.beginPath();
                c.moveTo(bodyA.position.x + constraint.pointA.x, bodyA.position.y + constraint.pointA.y);
            } else {
                c.beginPath();
                c.moveTo(constraint.pointA.x, constraint.pointA.y);
            }

            if (bodyB) {
                c.lineTo(bodyB.position.x + constraint.pointB.x, bodyB.position.y + constraint.pointB.y);
            } else {
                c.lineTo(constraint.pointB.x, constraint.pointB.y);
            }

            c.lineWidth = constraint.render.lineWidth;
            c.strokeStyle = constraint.render.strokeStyle;
            c.stroke();
        }
    };
    
    /**
     * Description
     * @private
     * @method bodyShadows
     * @param {engine} engine
     * @param {body[]} bodies
     * @param {RenderingContext} context
     */
    Render.bodyShadows = function(engine, bodies, context) {
        var c = context,
            render = engine.render;

        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (!body.render.visible)
                continue;

            if (body.circleRadius) {
                c.beginPath();
                c.arc(body.position.x, body.position.y, body.circleRadius, 0, 2 * Math.PI);
                c.closePath();
            } else {
                c.beginPath();
                c.moveTo(body.vertices[0].x, body.vertices[0].y);
                for (var j = 1; j < body.vertices.length; j++) {
                    c.lineTo(body.vertices[j].x, body.vertices[j].y);
                }
                c.closePath();
            }

            var distanceX = body.position.x - render.options.width * 0.5,
                distanceY = body.position.y - render.options.height * 0.2,
                distance = Math.abs(distanceX) + Math.abs(distanceY);

            c.shadowColor = 'rgba(0,0,0,0.15)';
            c.shadowOffsetX = 0.05 * distanceX;
            c.shadowOffsetY = 0.05 * distanceY;
            c.shadowBlur = 1 + 12 * Math.min(1, distance / 1000);

            c.fill();

            c.shadowColor = null;
            c.shadowOffsetX = null;
            c.shadowOffsetY = null;
            c.shadowBlur = null;
        }
    };

    /**
     * Description
     * @private
     * @method bodies
     * @param {engine} engine
     * @param {body[]} bodies
     * @param {RenderingContext} context
     */
    Render.bodies = function(engine, bodies, context) {
        var c = context,
            render = engine.render,
            options = render.options,
            i;

        for (i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (!body.render.visible)
                continue;

            if (body.render.sprite && body.render.sprite.texture && !options.wireframes) {
                // body sprite
                var sprite = body.render.sprite,
                    texture = _getTexture(render, sprite.texture);

                if (options.showSleeping && body.isSleeping) 
                    c.globalAlpha = 0.5;

                c.translate(body.position.x, body.position.y); 
                c.rotate(body.angle);

                c.drawImage(texture, texture.width * -0.5 * sprite.xScale, texture.height * -0.5 * sprite.yScale, 
                            texture.width * sprite.xScale, texture.height * sprite.yScale);

                // revert translation, hopefully faster than save / restore
                c.rotate(-body.angle);
                c.translate(-body.position.x, -body.position.y); 

                if (options.showSleeping && body.isSleeping) 
                    c.globalAlpha = 1;
            } else {
                // body polygon
                if (body.circleRadius) {
                    c.beginPath();
                    c.arc(body.position.x, body.position.y, body.circleRadius, 0, 2 * Math.PI);
                } else {
                    c.beginPath();
                    c.moveTo(body.vertices[0].x, body.vertices[0].y);
                    for (var j = 1; j < body.vertices.length; j++) {
                        c.lineTo(body.vertices[j].x, body.vertices[j].y);
                    }
                    c.closePath();
                }

                if (!options.wireframes) {
                    if (options.showSleeping && body.isSleeping) {
                        c.fillStyle = Common.shadeColor(body.render.fillStyle, 50);
                    } else {
                        c.fillStyle = body.render.fillStyle;
                    }

                    c.lineWidth = body.render.lineWidth;
                    c.strokeStyle = body.render.strokeStyle;
                    c.fill();
                    c.stroke();
                } else {
                    c.lineWidth = 1;
                    c.strokeStyle = '#bbb';
                    if (options.showSleeping && body.isSleeping)
                        c.strokeStyle = 'rgba(255,255,255,0.2)';
                    c.stroke();
                }
            }
        }

    };

    /**
     * Optimised method for drawing body wireframes in one pass
     * @private
     * @method bodyWireframes
     * @param {engine} engine
     * @param {body[]} bodies
     * @param {RenderingContext} context
     */
    Render.bodyWireframes = function(engine, bodies, context) {
        var c = context,
            i,
            j;

        c.beginPath();

        for (i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (!body.render.visible)
                continue;

            c.moveTo(body.vertices[0].x, body.vertices[0].y);

            for (j = 1; j < body.vertices.length; j++) {
                c.lineTo(body.vertices[j].x, body.vertices[j].y);
            }
            
            c.lineTo(body.vertices[0].x, body.vertices[0].y);
        }

        c.lineWidth = 1;
        c.strokeStyle = '#bbb';
        c.stroke();
    };

    /**
     * Draws body bounds
     * @private
     * @method bodyBounds
     * @param {engine} engine
     * @param {body[]} bodies
     * @param {RenderingContext} context
     */
    Render.bodyBounds = function(engine, bodies, context) {
        var c = context,
            render = engine.render,
            options = render.options;

        c.beginPath();

        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (body.render.visible)
                c.rect(body.bounds.min.x, body.bounds.min.y, body.bounds.max.x - body.bounds.min.x, body.bounds.max.y - body.bounds.min.y);
        }

        if (options.wireframes) {
            c.strokeStyle = 'rgba(255,255,255,0.08)';
        } else {
            c.strokeStyle = 'rgba(0,0,0,0.1)';
        }

        c.lineWidth = 1;
        c.stroke();
    };

    /**
     * Draws body angle indicators and axes
     * @private
     * @method bodyAxes
     * @param {engine} engine
     * @param {body[]} bodies
     * @param {RenderingContext} context
     */
    Render.bodyAxes = function(engine, bodies, context) {
        var c = context,
            render = engine.render,
            options = render.options,
            i,
            j;

        c.beginPath();

        for (i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (!body.render.visible)
                continue;

            if (options.showAxes) {
                // render all axes
                for (j = 0; j < body.axes.length; j++) {
                    var axis = body.axes[j];
                    c.moveTo(body.position.x, body.position.y);
                    c.lineTo(body.position.x + axis.x * 20, body.position.y + axis.y * 20);
                }
            } else {
                // render a single axis indicator
                c.moveTo(body.position.x, body.position.y);
                c.lineTo((body.vertices[0].x + body.vertices[body.vertices.length-1].x) / 2, 
                         (body.vertices[0].y + body.vertices[body.vertices.length-1].y) / 2);
            }
        }

        if (options.wireframes) {
            c.strokeStyle = 'indianred';
        } else {
            c.strokeStyle = 'rgba(0,0,0,0.3)';
        }

        c.lineWidth = 1;
        c.stroke();
    };

    /**
     * Draws body positions
     * @private
     * @method bodyPositions
     * @param {engine} engine
     * @param {body[]} bodies
     * @param {RenderingContext} context
     */
    Render.bodyPositions = function(engine, bodies, context) {
        var c = context,
            render = engine.render,
            options = render.options,
            body,
            i;

        c.beginPath();

        // render current positions
        for (i = 0; i < bodies.length; i++) {
            body = bodies[i];
            if (body.render.visible) {
                c.arc(body.position.x, body.position.y, 3, 0, 2 * Math.PI, false);
                c.closePath();
            }
        }

        if (options.wireframes) {
            c.fillStyle = 'indianred';
        } else {
            c.fillStyle = 'rgba(0,0,0,0.5)';
        }
        c.fill();

        c.beginPath();

        // render previous positions
        for (i = 0; i < bodies.length; i++) {
            body = bodies[i];
            if (body.render.visible) {
                c.arc(body.positionPrev.x, body.positionPrev.y, 2, 0, 2 * Math.PI, false);
                c.closePath();
            }
        }

        c.fillStyle = 'rgba(255,165,0,0.8)';
        c.fill();
    };

    /**
     * Draws body velocity
     * @private
     * @method bodyVelocity
     * @param {engine} engine
     * @param {body[]} bodies
     * @param {RenderingContext} context
     */
    Render.bodyVelocity = function(engine, bodies, context) {
        var c = context;

        c.beginPath();

        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (!body.render.visible)
                continue;

            c.moveTo(body.position.x, body.position.y);
            c.lineTo(body.position.x + (body.position.x - body.positionPrev.x) * 2, body.position.y + (body.position.y - body.positionPrev.y) * 2);
        }

        c.lineWidth = 3;
        c.strokeStyle = 'cornflowerblue';
        c.stroke();
    };

    /**
     * Draws body ids
     * @private
     * @method bodyIds
     * @param {engine} engine
     * @param {body[]} bodies
     * @param {RenderingContext} context
     */
    Render.bodyIds = function(engine, bodies, context) {
        var c = context;

        for (var i = 0; i < bodies.length; i++) {
            var body = bodies[i];

            if (!body.render.visible)
                continue;

            c.font = "12px Arial";
            c.fillStyle = 'rgba(255,255,255,0.5)';
            c.fillText(body.id, body.position.x + 10, body.position.y - 10);
        }
    };

    /**
     * Description
     * @private
     * @method collisions
     * @param {engine} engine
     * @param {pair[]} pairs
     * @param {RenderingContext} context
     */
    Render.collisions = function(engine, pairs, context) {
        var c = context,
            options = engine.render.options,
            pair,
            collision,
            i,
            j;

        c.beginPath();

        // render collision positions
        for (i = 0; i < pairs.length; i++) {
            pair = pairs[i];
            collision = pair.collision;
            for (j = 0; j < pair.activeContacts.length; j++) {
                var contact = pair.activeContacts[j],
                    vertex = contact.vertex;
                c.rect(vertex.x - 1.5, vertex.y - 1.5, 3.5, 3.5);
            }
        }

        if (options.wireframes) {
            c.fillStyle = 'rgba(255,255,255,0.7)';
        } else {
            c.fillStyle = 'orange';
        }
        c.fill();

        c.beginPath();
            
        // render collision normals
        for (i = 0; i < pairs.length; i++) {
            pair = pairs[i];
            collision = pair.collision;

            if (pair.activeContacts.length > 0) {
                var normalPosX = pair.activeContacts[0].vertex.x,
                    normalPosY = pair.activeContacts[0].vertex.y;

                if (pair.activeContacts.length === 2) {
                    normalPosX = (pair.activeContacts[0].vertex.x + pair.activeContacts[1].vertex.x) / 2;
                    normalPosY = (pair.activeContacts[0].vertex.y + pair.activeContacts[1].vertex.y) / 2;
                }
                
                c.moveTo(normalPosX - collision.normal.x * 8, normalPosY - collision.normal.y * 8);
                c.lineTo(normalPosX, normalPosY);
            }
        }

        if (options.wireframes) {
            c.strokeStyle = 'rgba(255,165,0,0.7)';
        } else {
            c.strokeStyle = 'orange';
        }

        c.lineWidth = 1;
        c.stroke();
    };

    /**
     * Description
     * @private
     * @method grid
     * @param {engine} engine
     * @param {grid} grid
     * @param {RenderingContext} context
     */
    Render.grid = function(engine, grid, context) {
        var c = context,
            options = engine.render.options;

        if (options.wireframes) {
            c.strokeStyle = 'rgba(255,180,0,0.1)';
        } else {
            c.strokeStyle = 'rgba(255,180,0,0.5)';
        }

        c.beginPath();

        var bucketKeys = Common.keys(grid.buckets);

        for (var i = 0; i < bucketKeys.length; i++) {
            var bucketId = bucketKeys[i];

            if (grid.buckets[bucketId].length < 2)
                continue;

            var region = bucketId.split(',');
            c.rect(0.5 + parseInt(region[0], 10) * grid.bucketWidth, 
                    0.5 + parseInt(region[1], 10) * grid.bucketHeight, 
                    grid.bucketWidth, 
                    grid.bucketHeight);
        }

        c.lineWidth = 1;
        c.stroke();
    };

    /**
     * Description
     * @private
     * @method inspector
     * @param {inspector} inspector
     * @param {RenderingContext} context
     */
    Render.inspector = function(inspector, context) {
        var engine = inspector.engine,
            selected = inspector.selected,
            render = engine.render,
            options = render.options,
            bounds;

        if (options.hasBounds) {
            var boundsWidth = render.bounds.max.x - render.bounds.min.x,
                boundsHeight = render.bounds.max.y - render.bounds.min.y,
                boundsScaleX = boundsWidth / render.options.width,
                boundsScaleY = boundsHeight / render.options.height;
            
            context.scale(1 / boundsScaleX, 1 / boundsScaleY);
            context.translate(-render.bounds.min.x, -render.bounds.min.y);
        }

        for (var i = 0; i < selected.length; i++) {
            var item = selected[i].data;

            context.translate(0.5, 0.5);
            context.lineWidth = 1;
            context.strokeStyle = 'rgba(255,165,0,0.9)';
            context.setLineDash([1,2]);

            switch (item.type) {

            case 'body':

                // render body selections
                bounds = item.bounds;
                context.beginPath();
                context.rect(Math.floor(bounds.min.x - 3), Math.floor(bounds.min.y - 3), 
                             Math.floor(bounds.max.x - bounds.min.x + 6), Math.floor(bounds.max.y - bounds.min.y + 6));
                context.closePath();
                context.stroke();

                break;

            case 'constraint':

                // render constraint selections
                var point = item.pointA;
                if (item.bodyA)
                    point = item.pointB;
                context.beginPath();
                context.arc(point.x, point.y, 10, 0, 2 * Math.PI);
                context.closePath();
                context.stroke();

                break;

            }

            context.setLineDash([0]);
            context.translate(-0.5, -0.5);
        }

        // render selection region
        if (inspector.selectStart !== null) {
            context.translate(0.5, 0.5);
            context.lineWidth = 1;
            context.strokeStyle = 'rgba(255,165,0,0.6)';
            context.fillStyle = 'rgba(255,165,0,0.1)';
            bounds = inspector.selectBounds;
            context.beginPath();
            context.rect(Math.floor(bounds.min.x), Math.floor(bounds.min.y), 
                         Math.floor(bounds.max.x - bounds.min.x), Math.floor(bounds.max.y - bounds.min.y));
            context.closePath();
            context.stroke();
            context.fill();
            context.translate(-0.5, -0.5);
        }

        if (options.hasBounds)
            context.setTransform(1, 0, 0, 1, 0, 0);
    };

    /**
     * Description
     * @method _createCanvas
     * @private
     * @param {} width
     * @param {} height
     * @return canvas
     */
    var _createCanvas = function(width, height) {
        var canvas = document.createElement('canvas');
        canvas.width = width;
        canvas.height = height;
        canvas.oncontextmenu = function() { return false; };
        canvas.onselectstart = function() { return false; };
        return canvas;
    };

    /**
     * Gets the pixel ratio of the canvas.
     * @method _getPixelRatio
     * @private
     * @param {HTMLElement} canvas
     * @return {Number} pixel ratio
     */
    var _getPixelRatio = function(canvas) {
        var context = canvas.getContext('2d'),
            devicePixelRatio = window.devicePixelRatio || 1,
            backingStorePixelRatio = context.webkitBackingStorePixelRatio || context.mozBackingStorePixelRatio
                                      || context.msBackingStorePixelRatio || context.oBackingStorePixelRatio
                                      || context.backingStorePixelRatio || 1;

        return devicePixelRatio / backingStorePixelRatio;
    };

    /**
     * Gets the requested texture (an Image) via its path
     * @method _getTexture
     * @private
     * @param {render} render
     * @param {string} imagePath
     * @return {Image} texture
     */
    var _getTexture = function(render, imagePath) {
        var image = render.textures[imagePath];

        if (image)
            return image;

        image = render.textures[imagePath] = new Image();
        image.src = imagePath;

        return image;
    };

    /**
     * Applies the background to the canvas using CSS.
     * @method applyBackground
     * @private
     * @param {render} render
     * @param {string} background
     */
    var _applyBackground = function(render, background) {
        var cssBackground = background;

        if (/(jpg|gif|png)$/.test(background))
            cssBackground = 'url(' + background + ')';

        render.canvas.style.background = cssBackground;
        render.canvas.style.backgroundSize = "contain";
        render.currentBackground = background;
    };

    /*
    *
    *  Properties Documentation
    *
    */

    /**
     * A back-reference to the `Matter.Render` module.
     *
     * @property controller
     * @type render
     */

    /**
     * A reference to the element where the canvas is to be inserted (if `render.canvas` has not been specified)
     *
     * @property element
     * @type HTMLElement
     * @default null
     */

    /**
     * The canvas element to render to. If not specified, one will be created if `render.element` has been specified.
     *
     * @property canvas
     * @type HTMLCanvasElement
     * @default null
     */

    /**
     * The configuration options of the renderer.
     *
     * @property options
     * @type {}
     */

    /**
     * The target width in pixels of the `render.canvas` to be created.
     *
     * @property options.width
     * @type number
     * @default 800
     */

    /**
     * The target height in pixels of the `render.canvas` to be created.
     *
     * @property options.height
     * @type number
     * @default 600
     */

    /**
     * A flag that specifies if `render.bounds` should be used when rendering.
     *
     * @property options.hasBounds
     * @type boolean
     * @default false
     */

    /**
     * A `Bounds` object that specifies the drawing view region. 
     * Rendering will be automatically transformed and scaled to fit within the canvas size (`render.options.width` and `render.options.height`).
     * This allows for creating views that can pan or zoom around the scene.
     * You must also set `render.options.hasBounds` to `true` to enable bounded rendering.
     *
     * @property bounds
     * @type bounds
     */

    /**
     * The 2d rendering context from the `render.canvas` element.
     *
     * @property context
     * @type CanvasRenderingContext2D
     */

    /**
     * The sprite texture cache.
     *
     * @property textures
     * @type {}
     */

})();


;   // End src/render/Render.js


// Begin src/render/RenderPixi.js

/**
* See [Demo.js](https://github.com/liabru/matter-js/blob/master/demo/js/Demo.js) 
* and [DemoMobile.js](https://github.com/liabru/matter-js/blob/master/demo/js/DemoMobile.js) for usage examples.
*
* @class RenderPixi
*/

var RenderPixi = {};

(function() {
    
    /**
     * Creates a new Pixi.js WebGL renderer
     * @method create
     * @param {object} options
     * @return {RenderPixi} A new renderer
     */
    RenderPixi.create = function(options) {
        var defaults = {
            controller: RenderPixi,
            element: null,
            canvas: null,
            options: {
                width: 800,
                height: 600,
                background: '#fafafa',
                wireframeBackground: '#222',
                hasBounds: false,
                enabled: true,
                wireframes: true,
                showSleeping: true,
                showDebug: false,
                showBroadphase: false,
                showBounds: false,
                showVelocity: false,
                showCollisions: false,
                showAxes: false,
                showPositions: false,
                showAngleIndicator: false,
                showIds: false,
                showShadows: false
            }
        };

        var render = Common.extend(defaults, options),
            transparent = !render.options.wireframes && render.options.background === 'transparent';

        // init pixi
        render.context = new PIXI.WebGLRenderer(render.options.width, render.options.height, render.canvas, transparent, true);
        render.canvas = render.context.view;
        render.container = new PIXI.DisplayObjectContainer();
        render.stage = new PIXI.Stage();
        render.stage.addChild(render.container);
        render.bounds = render.bounds || { 
            min: { 
                x: 0,
                y: 0
            }, 
            max: { 
                x: render.options.width,
                y: render.options.height
            }
        };

        // caches
        render.textures = {};
        render.sprites = {};
        render.primitives = {};

        // use a sprite batch for performance
        render.spriteBatch = new PIXI.SpriteBatch();
        render.container.addChild(render.spriteBatch);

        // insert canvas
        if (Common.isElement(render.element)) {
            render.element.appendChild(render.canvas);
        } else {
            Common.log('No "render.element" passed, "render.canvas" was not inserted into document.', 'warn');
        }

        // prevent menus on canvas
        render.canvas.oncontextmenu = function() { return false; };
        render.canvas.onselectstart = function() { return false; };

        return render;
    };

    /**
     * Clears the scene graph
     * @method clear
     * @param {RenderPixi} render
     */
    RenderPixi.clear = function(render) {
        var container = render.container,
            spriteBatch = render.spriteBatch;

        // clear stage container
        while (container.children[0]) { 
            container.removeChild(container.children[0]); 
        }

        // clear sprite batch
        while (spriteBatch.children[0]) { 
            spriteBatch.removeChild(spriteBatch.children[0]); 
        }

        var bgSprite = render.sprites['bg-0'];

        // clear caches
        render.textures = {};
        render.sprites = {};
        render.primitives = {};

        // set background sprite
        render.sprites['bg-0'] = bgSprite;
        if (bgSprite)
            spriteBatch.addChildAt(bgSprite, 0);

        // add sprite batch back into container
        render.container.addChild(render.spriteBatch);

        // reset background state
        render.currentBackground = null;

        // reset bounds transforms
        container.scale.set(1, 1);
        container.position.set(0, 0);
    };

    /**
     * Sets the background of the canvas 
     * @method setBackground
     * @param {RenderPixi} render
     * @param {string} background
     */
    RenderPixi.setBackground = function(render, background) {
        if (render.currentBackground !== background) {
            var isColor = background.indexOf && background.indexOf('#') !== -1,
                bgSprite = render.sprites['bg-0'];

            if (isColor) {
                // if solid background color
                var color = Common.colorToNumber(background);
                render.stage.setBackgroundColor(color);

                // remove background sprite if existing
                if (bgSprite)
                    render.spriteBatch.removeChild(bgSprite); 
            } else {
                // initialise background sprite if needed
                if (!bgSprite) {
                    var texture = _getTexture(render, background);

                    bgSprite = render.sprites['bg-0'] = new PIXI.Sprite(texture);
                    bgSprite.position.x = 0;
                    bgSprite.position.y = 0;
                    render.spriteBatch.addChildAt(bgSprite, 0);
                }
            }

            render.currentBackground = background;
        }
    };

    /**
     * Description
     * @method world
     * @param {engine} engine
     */
    RenderPixi.world = function(engine) {
        var render = engine.render,
            world = engine.world,
            context = render.context,
            stage = render.stage,
            container = render.container,
            options = render.options,
            bodies = Composite.allBodies(world),
            allConstraints = Composite.allConstraints(world),
            constraints = [],
            i;

        if (options.wireframes) {
            RenderPixi.setBackground(render, options.wireframeBackground);
        } else {
            RenderPixi.setBackground(render, options.background);
        }

        // handle bounds
        var boundsWidth = render.bounds.max.x - render.bounds.min.x,
            boundsHeight = render.bounds.max.y - render.bounds.min.y,
            boundsScaleX = boundsWidth / render.options.width,
            boundsScaleY = boundsHeight / render.options.height;

        if (options.hasBounds) {
            // Hide bodies that are not in view
            for (i = 0; i < bodies.length; i++) {
                var body = bodies[i];
                body.render.sprite.visible = Bounds.overlaps(body.bounds, render.bounds);
            }

            // filter out constraints that are not in view
            for (i = 0; i < allConstraints.length; i++) {
                var constraint = allConstraints[i],
                    bodyA = constraint.bodyA,
                    bodyB = constraint.bodyB,
                    pointAWorld = constraint.pointA,
                    pointBWorld = constraint.pointB;

                if (bodyA) pointAWorld = Vector.add(bodyA.position, constraint.pointA);
                if (bodyB) pointBWorld = Vector.add(bodyB.position, constraint.pointB);

                if (!pointAWorld || !pointBWorld)
                    continue;

                if (Bounds.contains(render.bounds, pointAWorld) || Bounds.contains(render.bounds, pointBWorld))
                    constraints.push(constraint);
            }

            // transform the view
            container.scale.set(1 / boundsScaleX, 1 / boundsScaleY);
            container.position.set(-render.bounds.min.x * (1 / boundsScaleX), -render.bounds.min.y * (1 / boundsScaleY));
        } else {
            constraints = allConstraints;
        }

        for (i = 0; i < bodies.length; i++)
            RenderPixi.body(engine, bodies[i]);

        for (i = 0; i < constraints.length; i++)
            RenderPixi.constraint(engine, constraints[i]);

        context.render(stage);
    };


    /**
     * Description
     * @method constraint
     * @param {engine} engine
     * @param {constraint} constraint
     */
    RenderPixi.constraint = function(engine, constraint) {
        var render = engine.render,
            bodyA = constraint.bodyA,
            bodyB = constraint.bodyB,
            pointA = constraint.pointA,
            pointB = constraint.pointB,
            container = render.container,
            constraintRender = constraint.render,
            primitiveId = 'c-' + constraint.id,
            primitive = render.primitives[primitiveId];

        // initialise constraint primitive if not existing
        if (!primitive)
            primitive = render.primitives[primitiveId] = new PIXI.Graphics();

        // don't render if constraint does not have two end points
        if (!constraintRender.visible || !constraint.pointA || !constraint.pointB) {
            primitive.clear();
            return;
        }

        // add to scene graph if not already there
        if (Common.indexOf(container.children, primitive) === -1)
            container.addChild(primitive);

        // render the constraint on every update, since they can change dynamically
        primitive.clear();
        primitive.beginFill(0, 0);
        primitive.lineStyle(constraintRender.lineWidth, Common.colorToNumber(constraintRender.strokeStyle), 1);
        
        if (bodyA) {
            primitive.moveTo(bodyA.position.x + pointA.x, bodyA.position.y + pointA.y);
        } else {
            primitive.moveTo(pointA.x, pointA.y);
        }

        if (bodyB) {
            primitive.lineTo(bodyB.position.x + pointB.x, bodyB.position.y + pointB.y);
        } else {
            primitive.lineTo(pointB.x, pointB.y);
        }

        primitive.endFill();
    };
    
    /**
     * Description
     * @method body
     * @param {engine} engine
     * @param {body} body
     */
    RenderPixi.body = function(engine, body) {
        var render = engine.render,
            bodyRender = body.render;

        if (!bodyRender.visible)
            return;

        if (bodyRender.sprite && bodyRender.sprite.texture) {
            var spriteId = 'b-' + body.id,
                sprite = render.sprites[spriteId],
                spriteBatch = render.spriteBatch;

            // initialise body sprite if not existing
            if (!sprite)
                sprite = render.sprites[spriteId] = _createBodySprite(render, body);

            // add to scene graph if not already there
            if (Common.indexOf(spriteBatch.children, sprite) === -1)
                spriteBatch.addChild(sprite);

            // update body sprite
            sprite.position.x = body.position.x;
            sprite.position.y = body.position.y;
            sprite.rotation = body.angle;
            sprite.scale.x = bodyRender.sprite.xScale || 1;
            sprite.scale.y = bodyRender.sprite.yScale || 1;
        } else {
            var primitiveId = 'b-' + body.id,
                primitive = render.primitives[primitiveId],
                container = render.container;

            // initialise body primitive if not existing
            if (!primitive) {
                primitive = render.primitives[primitiveId] = _createBodyPrimitive(render, body);
                primitive.initialAngle = body.angle;
            }

            // add to scene graph if not already there
            if (Common.indexOf(container.children, primitive) === -1)
                container.addChild(primitive);

            // update body primitive
            primitive.position.x = body.position.x;
            primitive.position.y = body.position.y;
            primitive.rotation = body.angle - primitive.initialAngle;
        }
    };

    /**
     * Creates a body sprite
     * @method _createBodySprite
     * @private
     * @param {RenderPixi} render
     * @param {body} body
     * @return {PIXI.Sprite} sprite
     */
    var _createBodySprite = function(render, body) {
        var bodyRender = body.render,
            texturePath = bodyRender.sprite.texture,
            texture = _getTexture(render, texturePath),
            sprite = new PIXI.Sprite(texture);

        sprite.anchor.x = 0.5;
        sprite.anchor.y = 0.5;

        return sprite;
    };

    /**
     * Creates a body primitive
     * @method _createBodyPrimitive
     * @private
     * @param {RenderPixi} render
     * @param {body} body
     * @return {PIXI.Graphics} graphics
     */
    var _createBodyPrimitive = function(render, body) {
        var bodyRender = body.render,
            options = render.options,
            primitive = new PIXI.Graphics();

        primitive.clear();

        if (!options.wireframes) {
            primitive.beginFill(Common.colorToNumber(bodyRender.fillStyle), 1);
            primitive.lineStyle(body.render.lineWidth, Common.colorToNumber(bodyRender.strokeStyle), 1);
        } else {
            primitive.beginFill(0, 0);
            primitive.lineStyle(1, Common.colorToNumber('#bbb'), 1);
        }

        primitive.moveTo(body.vertices[0].x - body.position.x, body.vertices[0].y - body.position.y);

        for (var j = 1; j < body.vertices.length; j++) {
            primitive.lineTo(body.vertices[j].x - body.position.x, body.vertices[j].y - body.position.y);
        }

        primitive.lineTo(body.vertices[0].x - body.position.x, body.vertices[0].y - body.position.y);

        primitive.endFill();

        // angle indicator
        if (options.showAngleIndicator || options.showAxes) {
            primitive.beginFill(0, 0);

            if (options.wireframes) {
                primitive.lineStyle(1, Common.colorToNumber('#CD5C5C'), 1);
            } else {
                primitive.lineStyle(1, Common.colorToNumber(body.render.strokeStyle));
            }

            primitive.moveTo(0, 0);
            primitive.lineTo(((body.vertices[0].x + body.vertices[body.vertices.length-1].x) / 2) - body.position.x, 
                             ((body.vertices[0].y + body.vertices[body.vertices.length-1].y) / 2) - body.position.y);

            primitive.endFill();
        }

        return primitive;
    };

    /**
     * Gets the requested texture (a PIXI.Texture) via its path
     * @method _getTexture
     * @private
     * @param {RenderPixi} render
     * @param {string} imagePath
     * @return {PIXI.Texture} texture
     */
    var _getTexture = function(render, imagePath) {
        var texture = render.textures[imagePath];

        if (!texture)
            texture = render.textures[imagePath] = PIXI.Texture.fromImage(imagePath);

        return texture;
    };

})();


;   // End src/render/RenderPixi.js


// aliases

World.add = Composite.add;
World.remove = Composite.remove;
World.addComposite = Composite.addComposite;
World.addBody = Composite.addBody;
World.addConstraint = Composite.addConstraint;
World.clear = Composite.clear;

Engine.run = Runner.run;

// exports

Matter.Body = Body;
Matter.Composite = Composite;
Matter.World = World;
Matter.Contact = Contact;
Matter.Detector = Detector;
Matter.Grid = Grid;
Matter.Pairs = Pairs;
Matter.Pair = Pair;
Matter.Resolver = Resolver;
Matter.SAT = SAT;
Matter.Constraint = Constraint;
Matter.MouseConstraint = MouseConstraint;
Matter.Common = Common;
Matter.Engine = Engine;
Matter.Metrics = Metrics;
Matter.Mouse = Mouse;
Matter.Sleeping = Sleeping;
Matter.Bodies = Bodies;
Matter.Composites = Composites;
Matter.Axes = Axes;
Matter.Bounds = Bounds;
Matter.Vector = Vector;
Matter.Vertices = Vertices;
Matter.Render = Render;
Matter.RenderPixi = RenderPixi;
Matter.Events = Events;
Matter.Query = Query;
Matter.Runner = Runner;

// CommonJS module
if (typeof exports !== 'undefined') {
    if (typeof module !== 'undefined' && module.exports) {
        exports = module.exports = Matter;
    }
    exports.Matter = Matter;
}

// AMD module
if (typeof define === 'function' && define.amd) {
    define('Matter', [], function () {
        return Matter;
    });
}

// browser
if (typeof window === 'object' && typeof window.document === 'object') {
    window.Matter = Matter;
}

// End Matter namespace closure

})();