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matter.js
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/**
* matter-js 0.14.2 by @liabru 2018-06-11
* http://brm.io/matter-js/
* License MIT
*/
/**
* The MIT License (MIT)
*
* Copyright (c) Liam Brummitt and contributors.
*
* 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(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}g.Matter = f()}})(function(){var define,module,exports;return (function(){function r(e,n,t){function o(i,f){if(!n[i]){if(!e[i]){var c="function"==typeof require&&require;if(!f&&c)return c(i,!0);if(u)return u(i,!0);var a=new Error("Cannot find module '"+i+"'");throw a.code="MODULE_NOT_FOUND",a}var p=n[i]={exports:{}};e[i][0].call(p.exports,function(r){var n=e[i][1][r];return o(n||r)},p,p.exports,r,e,n,t)}return n[i].exports}for(var u="function"==typeof require&&require,i=0;i<t.length;i++)o(t[i]);return o}return r})()({1:[function(_dereq_,module,exports){
/**
* 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 the included usage [examples](https://github.com/liabru/matter-js/tree/master/examples).
* @class Body
*/
var Body = {};
module.exports = Body;
var Vertices = _dereq_('../geometry/Vertices');
var Vector = _dereq_('../geometry/Vector');
var Sleeping = _dereq_('../core/Sleeping');
var Render = _dereq_('../render/Render');
var Common = _dereq_('../core/Common');
var Bounds = _dereq_('../geometry/Bounds');
var Axes = _dereq_('../geometry/Axes');
(function() {
Body._inertiaScale = 4;
Body._nextCollidingGroupId = 1;
Body._nextNonCollidingGroupId = -1;
Body._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.
* Vertices must be specified in clockwise order.
* See the properties 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',
parts: [],
plugin: {},
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 },
totalContacts: 0,
speed: 0,
angularSpeed: 0,
velocity: { x: 0, y: 0 },
angularVelocity: 0,
isSensor: false,
isStatic: false,
isSleeping: false,
motion: 0,
sleepThreshold: 60,
density: 0.001,
restitution: 0,
friction: 0.1,
frictionStatic: 0.5,
frictionAir: 0.01,
collisionFilter: {
category: 0x0001,
mask: 0xFFFFFFFF,
group: 0
},
slop: 0.05,
timeScale: 1,
render: {
visible: true,
opacity: 1,
sprite: {
xScale: 1,
yScale: 1,
xOffset: 0,
yOffset: 0
},
lineWidth: 0
}
};
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 Body._nextNonCollidingGroupId--;
return Body._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() {
Body._nextCategory = Body._nextCategory << 1;
return Body._nextCategory;
};
/**
* Initialises body properties.
* @method _initProperties
* @private
* @param {body} body
* @param {} [options]
*/
var _initProperties = function(body, options) {
options = options || {};
// init required properties (order is important)
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,
parts: body.parts || [body],
isStatic: body.isStatic,
isSleeping: body.isSleeping,
parent: body.parent || body
});
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 ? '#2e2b44' : Common.choose(['#006BA6', '#0496FF', '#FFBC42', '#D81159', '#8F2D56'])),
defaultStrokeStyle = '#000';
body.render.fillStyle = body.render.fillStyle || defaultFillStyle;
body.render.strokeStyle = body.render.strokeStyle || defaultStrokeStyle;
body.render.sprite.xOffset += -(body.bounds.min.x - body.position.x) / (body.bounds.max.x - body.bounds.min.x);
body.render.sprite.yOffset += -(body.bounds.min.y - body.position.y) / (body.bounds.max.y - body.bounds.min.y);
};
/**
* 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;
case 'parts':
Body.setParts(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) {
for (var i = 0; i < body.parts.length; i++) {
var part = body.parts[i];
part.isStatic = isStatic;
if (isStatic) {
part._original = {
restitution: part.restitution,
friction: part.friction,
mass: part.mass,
inertia: part.inertia,
density: part.density,
inverseMass: part.inverseMass,
inverseInertia: part.inverseInertia
};
part.restitution = 0;
part.friction = 1;
part.mass = part.inertia = part.density = Infinity;
part.inverseMass = part.inverseInertia = 0;
part.positionPrev.x = part.position.x;
part.positionPrev.y = part.position.y;
part.anglePrev = part.angle;
part.angularVelocity = 0;
part.speed = 0;
part.angularSpeed = 0;
part.motion = 0;
} else if (part._original) {
part.restitution = part._original.restitution;
part.friction = part._original.friction;
part.mass = part._original.mass;
part.inertia = part._original.inertia;
part.density = part._original.density;
part.inverseMass = part._original.inverseMass;
part.inverseInertia = part._original.inverseInertia;
delete part._original;
}
}
};
/**
* Sets the mass of the body. Inverse mass, density and inertia are automatically updated to reflect the change.
* @method setMass
* @param {body} body
* @param {number} mass
*/
Body.setMass = function(body, mass) {
var moment = body.inertia / (body.mass / 6);
body.inertia = moment * (mass / 6);
body.inverseInertia = 1 / body.inertia;
body.mass = mass;
body.inverseMass = 1 / body.mass;
body.density = body.mass / body.area;
};
/**
* Sets the density of the body. Mass and inertia are 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 parts of the `body` and updates mass, inertia and centroid.
* Each part will have its parent set to `body`.
* By default the convex hull will be automatically computed and set on `body`, unless `autoHull` is set to `false.`
* Note that this method will ensure that the first part in `body.parts` will always be the `body`.
* @method setParts
* @param {body} body
* @param [body] parts
* @param {bool} [autoHull=true]
*/
Body.setParts = function(body, parts, autoHull) {
var i;
// add all the parts, ensuring that the first part is always the parent body
parts = parts.slice(0);
body.parts.length = 0;
body.parts.push(body);
body.parent = body;
for (i = 0; i < parts.length; i++) {
var part = parts[i];
if (part !== body) {
part.parent = body;
body.parts.push(part);
}
}
if (body.parts.length === 1)
return;
autoHull = typeof autoHull !== 'undefined' ? autoHull : true;
// find the convex hull of all parts to set on the parent body
if (autoHull) {
var vertices = [];
for (i = 0; i < parts.length; i++) {
vertices = vertices.concat(parts[i].vertices);
}
Vertices.clockwiseSort(vertices);
var hull = Vertices.hull(vertices),
hullCentre = Vertices.centre(hull);
Body.setVertices(body, hull);
Vertices.translate(body.vertices, hullCentre);
}
// sum the properties of all compound parts of the parent body
var total = Body._totalProperties(body);
body.area = total.area;
body.parent = body;
body.position.x = total.centre.x;
body.position.y = total.centre.y;
body.positionPrev.x = total.centre.x;
body.positionPrev.y = total.centre.y;
Body.setMass(body, total.mass);
Body.setInertia(body, total.inertia);
Body.setPosition(body, total.centre);
};
/**
* 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.positionPrev.x += delta.x;
body.positionPrev.y += delta.y;
for (var i = 0; i < body.parts.length; i++) {
var part = body.parts[i];
part.position.x += delta.x;
part.position.y += delta.y;
Vertices.translate(part.vertices, delta);
Bounds.update(part.bounds, part.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.anglePrev += delta;
for (var i = 0; i < body.parts.length; i++) {
var part = body.parts[i];
part.angle += delta;
Vertices.rotate(part.vertices, delta, body.position);
Axes.rotate(part.axes, delta);
Bounds.update(part.bounds, part.vertices, body.velocity);
if (i > 0) {
Vector.rotateAbout(part.position, delta, body.position, part.position);
}
}
};
/**
* 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
* @param {vector} [point]
*/
Body.rotate = function(body, rotation, point) {
if (!point) {
Body.setAngle(body, body.angle + rotation);
} else {
var cos = Math.cos(rotation),
sin = Math.sin(rotation),
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.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) {
var totalArea = 0,
totalInertia = 0;
point = point || body.position;
for (var i = 0; i < body.parts.length; i++) {
var part = body.parts[i];
// scale vertices
Vertices.scale(part.vertices, scaleX, scaleY, point);
// update properties
part.axes = Axes.fromVertices(part.vertices);
part.area = Vertices.area(part.vertices);
Body.setMass(part, body.density * part.area);
// update inertia (requires vertices to be at origin)
Vertices.translate(part.vertices, { x: -part.position.x, y: -part.position.y });
Body.setInertia(part, Body._inertiaScale * Vertices.inertia(part.vertices, part.mass));
Vertices.translate(part.vertices, { x: part.position.x, y: part.position.y });
if (i > 0) {
totalArea += part.area;
totalInertia += part.inertia;
}
// scale position
part.position.x = point.x + (part.position.x - point.x) * scaleX;
part.position.y = point.y + (part.position.y - point.y) * scaleY;
// update bounds
Bounds.update(part.bounds, part.vertices, body.velocity);
}
// handle parent body
if (body.parts.length > 1) {
body.area = totalArea;
if (!body.isStatic) {
Body.setMass(body, body.density * totalArea);
Body.setInertia(body, totalInertia);
}
}
// handle circles
if (body.circleRadius) {
if (scaleX === scaleY) {
body.circleRadius *= scaleX;
} else {
// body is no longer a circle
body.circleRadius = null;
}
}
};
/**
* 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
for (var i = 0; i < body.parts.length; i++) {
var part = body.parts[i];
Vertices.translate(part.vertices, body.velocity);
if (i > 0) {
part.position.x += body.velocity.x;
part.position.y += body.velocity.y;
}
if (body.angularVelocity !== 0) {
Vertices.rotate(part.vertices, body.angularVelocity, body.position);
Axes.rotate(part.axes, body.angularVelocity);
if (i > 0) {
Vector.rotateAbout(part.position, body.angularVelocity, body.position, part.position);
}
}
Bounds.update(part.bounds, part.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;
};
/**
* Returns the sums of the properties of all compound parts of the parent body.
* @method _totalProperties
* @private
* @param {body} body
* @return {}
*/
Body._totalProperties = function(body) {
// from equations at:
// https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=st&chap_sec=07.2&page=theory
// http://output.to/sideway/default.asp?qno=121100087
var properties = {
mass: 0,
area: 0,
inertia: 0,
centre: { x: 0, y: 0 }
};
// sum the properties of all compound parts of the parent body
for (var i = body.parts.length === 1 ? 0 : 1; i < body.parts.length; i++) {
var part = body.parts[i],
mass = part.mass !== Infinity ? part.mass : 1;
properties.mass += mass;
properties.area += part.area;
properties.inertia += part.inertia;
properties.centre = Vector.add(properties.centre, Vector.mult(part.position, mass));
}
properties.centre = Vector.div(properties.centre, properties.mass);
return properties;
};
/*
*
* Events Documentation
*
*/
/**
* Fired when a body starts sleeping (where `this` is the body).
*
* @event sleepStart
* @this {body} The body that has started sleeping
* @param {} event An event object
* @param {} event.source The source object of the event
* @param {} event.name The name of the event
*/
/**
* Fired when a body ends sleeping (where `this` is the body).
*
* @event sleepEnd
* @this {body} The body that has ended sleeping
* @param {} event An event object
* @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 `Body.create` by `Common.nextId`.
*
* @property id
* @type number
*/
/**
* A `String` denoting the type of object.
*
* @property type
* @type string
* @default "body"
* @readOnly
*/
/**
* An arbitrary `String` name to help the user identify and manage bodies.
*
* @property label
* @type string
* @default "Body"
*/
/**
* An array of bodies that make up this body.
* The first body in the array must always be a self reference to the current body instance.
* All bodies in the `parts` array together form a single rigid compound body.
* Parts are allowed to overlap, have gaps or holes or even form concave bodies.
* Parts themselves should never be added to a `World`, only the parent body should be.
* Use `Body.setParts` when setting parts to ensure correct updates of all properties.
*
* @property parts
* @type body[]
*/
/**
* An object reserved for storing plugin-specific properties.
*
* @property plugin
* @type {}
*/
/**
* A self reference if the body is _not_ a part of another body.
* Otherwise this is a reference to the body that this is a part of.
* See `body.parts`.
*
* @property parent
* @type 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 vertices 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 a body is a sensor. Sensor triggers collision events, but doesn't react with colliding body physically.
*
* @property isSensor
* @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)