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File: src/render/Render.js

                                /**
                                * The `Matter.Render` module is a lightweight, optional utility which provides a simple canvas based renderer for visualising instances of `Matter.Engine`.
                                * It is intended for development and debugging purposes, but may also be suitable for simple games.
                                * It includes a number of drawing options including wireframe, vector with support for sprites and viewports.
                                *
                                * @class Render
                                */
                                
                                var Render = {};
                                
                                module.exports = Render;
                                
                                var Body = require('../body/Body');
                                var Common = require('../core/Common');
                                var Composite = require('../body/Composite');
                                var Bounds = require('../geometry/Bounds');
                                var Events = require('../core/Events');
                                var Vector = require('../geometry/Vector');
                                var Mouse = require('../core/Mouse');
                                
                                (function() {
                                
                                    var _requestAnimationFrame,
                                        _cancelAnimationFrame;
                                
                                    if (typeof window !== 'undefined') {
                                        _requestAnimationFrame = window.requestAnimationFrame || window.webkitRequestAnimationFrame
                                                                      || window.mozRequestAnimationFrame || window.msRequestAnimationFrame
                                                                      || function(callback){ window.setTimeout(function() { callback(Common.now()); }, 1000 / 60); };
                                
                                        _cancelAnimationFrame = window.cancelAnimationFrame || window.mozCancelAnimationFrame
                                                                      || window.webkitCancelAnimationFrame || window.msCancelAnimationFrame;
                                    }
                                
                                    Render._goodFps = 30;
                                    Render._goodDelta = 1000 / 60;
                                
                                    /**
                                     * 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 properties 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 = {
                                            engine: null,
                                            element: null,
                                            canvas: null,
                                            mouse: null,
                                            frameRequestId: null,
                                            timing: {
                                                historySize: 60,
                                                delta: 0,
                                                deltaHistory: [],
                                                lastTime: 0,
                                                lastTimestamp: 0,
                                                lastElapsed: 0,
                                                timestampElapsed: 0,
                                                timestampElapsedHistory: [],
                                                engineDeltaHistory: [],
                                                engineElapsedHistory: [],
                                                engineUpdatesHistory: [],
                                                elapsedHistory: []
                                            },
                                            options: {
                                                width: 800,
                                                height: 600,
                                                pixelRatio: 1,
                                                background: '#14151f',
                                                wireframeBackground: '#14151f',
                                                wireframeStrokeStyle: '#bbb',
                                                hasBounds: !!options.bounds,
                                                enabled: true,
                                                wireframes: true,
                                                showSleeping: true,
                                                showDebug: false,
                                                showStats: false,
                                                showPerformance: false,
                                                showBounds: false,
                                                showVelocity: false,
                                                showCollisions: false,
                                                showSeparations: false,
                                                showAxes: false,
                                                showPositions: false,
                                                showAngleIndicator: false,
                                                showIds: false,
                                                showVertexNumbers: false,
                                                showConvexHulls: false,
                                                showInternalEdges: false,
                                                showMousePosition: false
                                            }
                                        };
                                
                                        var render = Common.extend(defaults, options);
                                
                                        if (render.canvas) {
                                            render.canvas.width = render.options.width || render.canvas.width;
                                            render.canvas.height = render.options.height || render.canvas.height;
                                        }
                                
                                        render.mouse = options.mouse;
                                        render.engine = options.engine;
                                        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.canvas.width,
                                                y: render.canvas.height
                                            }
                                        };
                                
                                        // for temporary back compatibility only
                                        render.controller = Render;
                                        render.options.showBroadphase = false;
                                
                                        if (render.options.pixelRatio !== 1) {
                                            Render.setPixelRatio(render, render.options.pixelRatio);
                                        }
                                
                                        if (Common.isElement(render.element)) {
                                            render.element.appendChild(render.canvas);
                                        }
                                
                                        return render;
                                    };
                                
                                    /**
                                     * Continuously updates the render canvas on the `requestAnimationFrame` event.
                                     * @method run
                                     * @param {render} render
                                     */
                                    Render.run = function(render) {
                                        (function loop(time){
                                            render.frameRequestId = _requestAnimationFrame(loop);
                                            
                                            _updateTiming(render, time);
                                
                                            Render.world(render, time);
                                
                                            render.context.setTransform(render.options.pixelRatio, 0, 0, render.options.pixelRatio, 0, 0);
                                
                                            if (render.options.showStats || render.options.showDebug) {
                                                Render.stats(render, render.context, time);
                                            }
                                
                                            if (render.options.showPerformance || render.options.showDebug) {
                                                Render.performance(render, render.context, time);
                                            }
                                
                                            render.context.setTransform(1, 0, 0, 1, 0, 0);
                                        })();
                                    };
                                
                                    /**
                                     * Ends execution of `Render.run` on the given `render`, by canceling the animation frame request event loop.
                                     * @method stop
                                     * @param {render} render
                                     */
                                    Render.stop = function(render) {
                                        _cancelAnimationFrame(render.frameRequestId);
                                    };
                                
                                    /**
                                     * 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';
                                    };
                                
                                    /**
                                     * Sets the render `width` and `height`.
                                     * 
                                     * Updates the canvas accounting for `render.options.pixelRatio`.  
                                     * 
                                     * Updates the bottom right render bound `render.bounds.max` relative to the provided `width` and `height`.
                                     * The top left render bound `render.bounds.min` isn't changed.
                                     * 
                                     * Follow this call with `Render.lookAt` if you need to change the render bounds.
                                     * 
                                     * See also `Render.setPixelRatio`.
                                     * @method setSize
                                     * @param {render} render
                                     * @param {number} width The width (in CSS pixels)
                                     * @param {number} height The height (in CSS pixels)
                                     */
                                    Render.setSize = function(render, width, height) {
                                        render.options.width = width;
                                        render.options.height = height;
                                        render.bounds.max.x = render.bounds.min.x + width;
                                        render.bounds.max.y = render.bounds.min.y + height;
                                
                                        if (render.options.pixelRatio !== 1) {
                                            Render.setPixelRatio(render, render.options.pixelRatio);
                                        } else {
                                            render.canvas.width = width;
                                            render.canvas.height = height;
                                        }
                                    };
                                
                                    /**
                                     * Positions and sizes the viewport around the given object bounds.
                                     * Objects must have at least one of the following properties:
                                     * - `object.bounds`
                                     * - `object.position`
                                     * - `object.min` and `object.max`
                                     * - `object.x` and `object.y`
                                     * @method lookAt
                                     * @param {render} render
                                     * @param {object[]} objects
                                     * @param {vector} [padding]
                                     * @param {bool} [center=true]
                                     */
                                    Render.lookAt = function(render, objects, padding, center) {
                                        center = typeof center !== 'undefined' ? center : true;
                                        objects = Common.isArray(objects) ? objects : [objects];
                                        padding = padding || {
                                            x: 0,
                                            y: 0
                                        };
                                
                                        // find bounds of all objects
                                        var bounds = {
                                            min: { x: Infinity, y: Infinity },
                                            max: { x: -Infinity, y: -Infinity }
                                        };
                                
                                        for (var i = 0; i < objects.length; i += 1) {
                                            var object = objects[i],
                                                min = object.bounds ? object.bounds.min : (object.min || object.position || object),
                                                max = object.bounds ? object.bounds.max : (object.max || object.position || object);
                                
                                            if (min && max) {
                                                if (min.x < bounds.min.x)
                                                    bounds.min.x = min.x;
                                
                                                if (max.x > bounds.max.x)
                                                    bounds.max.x = max.x;
                                
                                                if (min.y < bounds.min.y)
                                                    bounds.min.y = min.y;
                                
                                                if (max.y > bounds.max.y)
                                                    bounds.max.y = max.y;
                                            }
                                        }
                                
                                        // find ratios
                                        var width = (bounds.max.x - bounds.min.x) + 2 * padding.x,
                                            height = (bounds.max.y - bounds.min.y) + 2 * padding.y,
                                            viewHeight = render.canvas.height,
                                            viewWidth = render.canvas.width,
                                            outerRatio = viewWidth / viewHeight,
                                            innerRatio = width / height,
                                            scaleX = 1,
                                            scaleY = 1;
                                
                                        // find scale factor
                                        if (innerRatio > outerRatio) {
                                            scaleY = innerRatio / outerRatio;
                                        } else {
                                            scaleX = outerRatio / innerRatio;
                                        }
                                
                                        // enable bounds
                                        render.options.hasBounds = true;
                                
                                        // position and size
                                        render.bounds.min.x = bounds.min.x;
                                        render.bounds.max.x = bounds.min.x + width * scaleX;
                                        render.bounds.min.y = bounds.min.y;
                                        render.bounds.max.y = bounds.min.y + height * scaleY;
                                
                                        // center
                                        if (center) {
                                            render.bounds.min.x += width * 0.5 - (width * scaleX) * 0.5;
                                            render.bounds.max.x += width * 0.5 - (width * scaleX) * 0.5;
                                            render.bounds.min.y += height * 0.5 - (height * scaleY) * 0.5;
                                            render.bounds.max.y += height * 0.5 - (height * scaleY) * 0.5;
                                        }
                                
                                        // padding
                                        render.bounds.min.x -= padding.x;
                                        render.bounds.max.x -= padding.x;
                                        render.bounds.min.y -= padding.y;
                                        render.bounds.max.y -= padding.y;
                                
                                        // update mouse
                                        if (render.mouse) {
                                            Mouse.setScale(render.mouse, {
                                                x: (render.bounds.max.x - render.bounds.min.x) / render.canvas.width,
                                                y: (render.bounds.max.y - render.bounds.min.y) / render.canvas.height
                                            });
                                
                                            Mouse.setOffset(render.mouse, render.bounds.min);
                                        }
                                    };
                                
                                    /**
                                     * Applies viewport transforms based on `render.bounds` to a render context.
                                     * @method startViewTransform
                                     * @param {render} render
                                     */
                                    Render.startViewTransform = function(render) {
                                        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;
                                
                                        render.context.setTransform(
                                            render.options.pixelRatio / boundsScaleX, 0, 0, 
                                            render.options.pixelRatio / boundsScaleY, 0, 0
                                        );
                                        
                                        render.context.translate(-render.bounds.min.x, -render.bounds.min.y);
                                    };
                                
                                    /**
                                     * Resets all transforms on the render context.
                                     * @method endViewTransform
                                     * @param {render} render
                                     */
                                    Render.endViewTransform = function(render) {
                                        render.context.setTransform(render.options.pixelRatio, 0, 0, render.options.pixelRatio, 0, 0);
                                    };
                                
                                    /**
                                     * 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 {render} render
                                     */
                                    Render.world = function(render, time) {
                                        var startTime = Common.now(),
                                            engine = render.engine,
                                            world = engine.world,
                                            canvas = render.canvas,
                                            context = render.context,
                                            options = render.options,
                                            timing = render.timing;
                                
                                        var allBodies = Composite.allBodies(world),
                                            allConstraints = Composite.allConstraints(world),
                                            background = options.wireframes ? options.wireframeBackground : options.background,
                                            bodies = [],
                                            constraints = [],
                                            i;
                                
                                        var event = {
                                            timestamp: engine.timing.timestamp
                                        };
                                
                                        Events.trigger(render, 'beforeRender', event);
                                
                                        // 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) {
                                            // 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
                                            Render.startViewTransform(render);
                                
                                            // update mouse
                                            if (render.mouse) {
                                                Mouse.setScale(render.mouse, {
                                                    x: (render.bounds.max.x - render.bounds.min.x) / render.options.width,
                                                    y: (render.bounds.max.y - render.bounds.min.y) / render.options.height
                                                });
                                
                                                Mouse.setOffset(render.mouse, render.bounds.min);
                                            }
                                        } else {
                                            constraints = allConstraints;
                                            bodies = allBodies;
                                
                                            if (render.options.pixelRatio !== 1) {
                                                render.context.setTransform(render.options.pixelRatio, 0, 0, render.options.pixelRatio, 0, 0);
                                            }
                                        }
                                
                                        if (!options.wireframes || (engine.enableSleeping && options.showSleeping)) {
                                            // fully featured rendering of bodies
                                            Render.bodies(render, bodies, context);
                                        } else {
                                            if (options.showConvexHulls)
                                                Render.bodyConvexHulls(render, bodies, context);
                                
                                            // optimised method for wireframes only
                                            Render.bodyWireframes(render, bodies, context);
                                        }
                                
                                        if (options.showBounds)
                                            Render.bodyBounds(render, bodies, context);
                                
                                        if (options.showAxes || options.showAngleIndicator)
                                            Render.bodyAxes(render, bodies, context);
                                
                                        if (options.showPositions)
                                            Render.bodyPositions(render, bodies, context);
                                
                                        if (options.showVelocity)
                                            Render.bodyVelocity(render, bodies, context);
                                
                                        if (options.showIds)
                                            Render.bodyIds(render, bodies, context);
                                
                                        if (options.showSeparations)
                                            Render.separations(render, engine.pairs.list, context);
                                
                                        if (options.showCollisions)
                                            Render.collisions(render, engine.pairs.list, context);
                                
                                        if (options.showVertexNumbers)
                                            Render.vertexNumbers(render, bodies, context);
                                
                                        if (options.showMousePosition)
                                            Render.mousePosition(render, render.mouse, context);
                                
                                        Render.constraints(constraints, context);
                                
                                        if (options.hasBounds) {
                                            // revert view transforms
                                            Render.endViewTransform(render);
                                        }
                                
                                        Events.trigger(render, 'afterRender', event);
                                
                                        // log the time elapsed computing this update
                                        timing.lastElapsed = Common.now() - startTime;
                                    };
                                
                                    /**
                                     * Renders statistics about the engine and world useful for debugging.
                                     * @private
                                     * @method stats
                                     * @param {render} render
                                     * @param {RenderingContext} context
                                     * @param {Number} time
                                     */
                                    Render.stats = function(render, context, time) {
                                        var engine = render.engine,
                                            world = engine.world,
                                            bodies = Composite.allBodies(world),
                                            parts = 0,
                                            width = 55,
                                            height = 44,
                                            x = 0,
                                            y = 0;
                                        
                                        // count parts
                                        for (var i = 0; i < bodies.length; i += 1) {
                                            parts += bodies[i].parts.length;
                                        }
                                
                                        // sections
                                        var sections = {
                                            'Part': parts,
                                            'Body': bodies.length,
                                            'Cons': Composite.allConstraints(world).length,
                                            'Comp': Composite.allComposites(world).length,
                                            'Pair': engine.pairs.list.length
                                        };
                                
                                        // background
                                        context.fillStyle = '#0e0f19';
                                        context.fillRect(x, y, width * 5.5, height);
                                
                                        context.font = '12px Arial';
                                        context.textBaseline = 'top';
                                        context.textAlign = 'right';
                                
                                        // sections
                                        for (var key in sections) {
                                            var section = sections[key];
                                            // label
                                            context.fillStyle = '#aaa';
                                            context.fillText(key, x + width, y + 8);
                                
                                            // value
                                            context.fillStyle = '#eee';
                                            context.fillText(section, x + width, y + 26);
                                
                                            x += width;
                                        }
                                    };
                                
                                    /**
                                     * Renders engine and render performance information.
                                     * @private
                                     * @method performance
                                     * @param {render} render
                                     * @param {RenderingContext} context
                                     */
                                    Render.performance = function(render, context) {
                                        var engine = render.engine,
                                            timing = render.timing,
                                            deltaHistory = timing.deltaHistory,
                                            elapsedHistory = timing.elapsedHistory,
                                            timestampElapsedHistory = timing.timestampElapsedHistory,
                                            engineDeltaHistory = timing.engineDeltaHistory,
                                            engineUpdatesHistory = timing.engineUpdatesHistory,
                                            engineElapsedHistory = timing.engineElapsedHistory,
                                            lastEngineUpdatesPerFrame = engine.timing.lastUpdatesPerFrame,
                                            lastEngineDelta = engine.timing.lastDelta;
                                        
                                        var deltaMean = _mean(deltaHistory),
                                            elapsedMean = _mean(elapsedHistory),
                                            engineDeltaMean = _mean(engineDeltaHistory),
                                            engineUpdatesMean = _mean(engineUpdatesHistory),
                                            engineElapsedMean = _mean(engineElapsedHistory),
                                            timestampElapsedMean = _mean(timestampElapsedHistory),
                                            rateMean = (timestampElapsedMean / deltaMean) || 0,
                                            neededUpdatesPerFrame = Math.round(deltaMean / lastEngineDelta),
                                            fps = (1000 / deltaMean) || 0;
                                
                                        var graphHeight = 4,
                                            gap = 12,
                                            width = 60,
                                            height = 34,
                                            x = 10,
                                            y = 69;
                                
                                        // background
                                        context.fillStyle = '#0e0f19';
                                        context.fillRect(0, 50, gap * 5 + width * 6 + 22, height);
                                
                                        // show FPS
                                        Render.status(
                                            context, x, y, width, graphHeight, deltaHistory.length, 
                                            Math.round(fps) + ' fps', 
                                            fps / Render._goodFps,
                                            function(i) { return (deltaHistory[i] / deltaMean) - 1; }
                                        );
                                
                                        // show engine delta
                                        Render.status(
                                            context, x + gap + width, y, width, graphHeight, engineDeltaHistory.length,
                                            lastEngineDelta.toFixed(2) + ' dt', 
                                            Render._goodDelta / lastEngineDelta,
                                            function(i) { return (engineDeltaHistory[i] / engineDeltaMean) - 1; }
                                        );
                                
                                        // show engine updates per frame
                                        Render.status(
                                            context, x + (gap + width) * 2, y, width, graphHeight, engineUpdatesHistory.length,
                                            lastEngineUpdatesPerFrame + ' upf', 
                                            Math.pow(Common.clamp((engineUpdatesMean / neededUpdatesPerFrame) || 1, 0, 1), 4),
                                            function(i) { return (engineUpdatesHistory[i] / engineUpdatesMean) - 1; }
                                        );
                                
                                        // show engine update time
                                        Render.status(
                                            context, x + (gap + width) * 3, y, width, graphHeight, engineElapsedHistory.length,
                                            engineElapsedMean.toFixed(2) + ' ut', 
                                            1 - (lastEngineUpdatesPerFrame * engineElapsedMean / Render._goodFps),
                                            function(i) { return (engineElapsedHistory[i] / engineElapsedMean) - 1; }
                                        );
                                
                                        // show render time
                                        Render.status(
                                            context, x + (gap + width) * 4, y, width, graphHeight, elapsedHistory.length,
                                            elapsedMean.toFixed(2) + ' rt', 
                                            1 - (elapsedMean / Render._goodFps),
                                            function(i) { return (elapsedHistory[i] / elapsedMean) - 1; }
                                        );
                                
                                        // show effective speed
                                        Render.status(
                                            context, x + (gap + width) * 5, y, width, graphHeight, timestampElapsedHistory.length, 
                                            rateMean.toFixed(2) + ' x', 
                                            rateMean * rateMean * rateMean,
                                            function(i) { return (((timestampElapsedHistory[i] / deltaHistory[i]) / rateMean) || 0) - 1; }
                                        );
                                    };
                                
                                    /**
                                     * Renders a label, indicator and a chart.
                                     * @private
                                     * @method status
                                     * @param {RenderingContext} context
                                     * @param {number} x
                                     * @param {number} y
                                     * @param {number} width
                                     * @param {number} height
                                     * @param {number} count
                                     * @param {string} label
                                     * @param {string} indicator
                                     * @param {function} plotY
                                     */
                                    Render.status = function(context, x, y, width, height, count, label, indicator, plotY) {
                                        // background
                                        context.strokeStyle = '#888';
                                        context.fillStyle = '#444';
                                        context.lineWidth = 1;
                                        context.fillRect(x, y + 7, width, 1);
                                
                                        // chart
                                        context.beginPath();
                                        context.moveTo(x, y + 7 - height * Common.clamp(0.4 * plotY(0), -2, 2));
                                        for (var i = 0; i < width; i += 1) {
                                            context.lineTo(x + i, y + 7 - (i < count ? height * Common.clamp(0.4 * plotY(i), -2, 2) : 0));
                                        }
                                        context.stroke();
                                
                                        // indicator
                                        context.fillStyle = 'hsl(' + Common.clamp(25 + 95 * indicator, 0, 120) + ',100%,60%)';
                                        context.fillRect(x, y - 7, 4, 4);
                                
                                        // label
                                        context.font = '12px Arial';
                                        context.textBaseline = 'middle';
                                        context.textAlign = 'right';
                                        context.fillStyle = '#eee';
                                        context.fillText(label, x + width, y - 5);
                                    };
                                
                                    /**
                                     * 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,
                                                start,
                                                end;
                                
                                            if (bodyA) {
                                                start = Vector.add(bodyA.position, constraint.pointA);
                                            } else {
                                                start = constraint.pointA;
                                            }
                                
                                            if (constraint.render.type === 'pin') {
                                                c.beginPath();
                                                c.arc(start.x, start.y, 3, 0, 2 * Math.PI);
                                                c.closePath();
                                            } else {
                                                if (bodyB) {
                                                    end = Vector.add(bodyB.position, constraint.pointB);
                                                } else {
                                                    end = constraint.pointB;
                                                }
                                
                                                c.beginPath();
                                                c.moveTo(start.x, start.y);
                                
                                                if (constraint.render.type === 'spring') {
                                                    var delta = Vector.sub(end, start),
                                                        normal = Vector.perp(Vector.normalise(delta)),
                                                        coils = Math.ceil(Common.clamp(constraint.length / 5, 12, 20)),
                                                        offset;
                                
                                                    for (var j = 1; j < coils; j += 1) {
                                                        offset = j % 2 === 0 ? 1 : -1;
                                
                                                        c.lineTo(
                                                            start.x + delta.x * (j / coils) + normal.x * offset * 4,
                                                            start.y + delta.y * (j / coils) + normal.y * offset * 4
                                                        );
                                                    }
                                                }
                                
                                                c.lineTo(end.x, end.y);
                                            }
                                
                                            if (constraint.render.lineWidth) {
                                                c.lineWidth = constraint.render.lineWidth;
                                                c.strokeStyle = constraint.render.strokeStyle;
                                                c.stroke();
                                            }
                                
                                            if (constraint.render.anchors) {
                                                c.fillStyle = constraint.render.strokeStyle;
                                                c.beginPath();
                                                c.arc(start.x, start.y, 3, 0, 2 * Math.PI);
                                                c.arc(end.x, end.y, 3, 0, 2 * Math.PI);
                                                c.closePath();
                                                c.fill();
                                            }
                                        }
                                    };
                                
                                    /**
                                     * Description
                                     * @private
                                     * @method bodies
                                     * @param {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.bodies = function(render, bodies, context) {
                                        var c = context,
                                            engine = render.engine,
                                            options = render.options,
                                            showInternalEdges = options.showInternalEdges || !options.wireframes,
                                            body,
                                            part,
                                            i,
                                            k;
                                
                                        for (i = 0; i < bodies.length; i++) {
                                            body = bodies[i];
                                
                                            if (!body.render.visible)
                                                continue;
                                
                                            // handle compound parts
                                            for (k = body.parts.length > 1 ? 1 : 0; k < body.parts.length; k++) {
                                                part = body.parts[k];
                                
                                                if (!part.render.visible)
                                                    continue;
                                
                                                if (options.showSleeping && body.isSleeping) {
                                                    c.globalAlpha = 0.5 * part.render.opacity;
                                                } else if (part.render.opacity !== 1) {
                                                    c.globalAlpha = part.render.opacity;
                                                }
                                
                                                if (part.render.sprite && part.render.sprite.texture && !options.wireframes) {
                                                    // part sprite
                                                    var sprite = part.render.sprite,
                                                        texture = _getTexture(render, sprite.texture);
                                
                                                    c.translate(part.position.x, part.position.y);
                                                    c.rotate(part.angle);
                                
                                                    c.drawImage(
                                                        texture,
                                                        texture.width * -sprite.xOffset * sprite.xScale,
                                                        texture.height * -sprite.yOffset * sprite.yScale,
                                                        texture.width * sprite.xScale,
                                                        texture.height * sprite.yScale
                                                    );
                                
                                                    // revert translation, hopefully faster than save / restore
                                                    c.rotate(-part.angle);
                                                    c.translate(-part.position.x, -part.position.y);
                                                } else {
                                                    // part polygon
                                                    if (part.circleRadius) {
                                                        c.beginPath();
                                                        c.arc(part.position.x, part.position.y, part.circleRadius, 0, 2 * Math.PI);
                                                    } else {
                                                        c.beginPath();
                                                        c.moveTo(part.vertices[0].x, part.vertices[0].y);
                                
                                                        for (var j = 1; j < part.vertices.length; j++) {
                                                            if (!part.vertices[j - 1].isInternal || showInternalEdges) {
                                                                c.lineTo(part.vertices[j].x, part.vertices[j].y);
                                                            } else {
                                                                c.moveTo(part.vertices[j].x, part.vertices[j].y);
                                                            }
                                
                                                            if (part.vertices[j].isInternal && !showInternalEdges) {
                                                                c.moveTo(part.vertices[(j + 1) % part.vertices.length].x, part.vertices[(j + 1) % part.vertices.length].y);
                                                            }
                                                        }
                                
                                                        c.lineTo(part.vertices[0].x, part.vertices[0].y);
                                                        c.closePath();
                                                    }
                                
                                                    if (!options.wireframes) {
                                                        c.fillStyle = part.render.fillStyle;
                                
                                                        if (part.render.lineWidth) {
                                                            c.lineWidth = part.render.lineWidth;
                                                            c.strokeStyle = part.render.strokeStyle;
                                                            c.stroke();
                                                        }
                                
                                                        c.fill();
                                                    } else {
                                                        c.lineWidth = 1;
                                                        c.strokeStyle = render.options.wireframeStrokeStyle;
                                                        c.stroke();
                                                    }
                                                }
                                
                                                c.globalAlpha = 1;
                                            }
                                        }
                                    };
                                
                                    /**
                                     * Optimised method for drawing body wireframes in one pass
                                     * @private
                                     * @method bodyWireframes
                                     * @param {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.bodyWireframes = function(render, bodies, context) {
                                        var c = context,
                                            showInternalEdges = render.options.showInternalEdges,
                                            body,
                                            part,
                                            i,
                                            j,
                                            k;
                                
                                        c.beginPath();
                                
                                        // render all bodies
                                        for (i = 0; i < bodies.length; i++) {
                                            body = bodies[i];
                                
                                            if (!body.render.visible)
                                                continue;
                                
                                            // handle compound parts
                                            for (k = body.parts.length > 1 ? 1 : 0; k < body.parts.length; k++) {
                                                part = body.parts[k];
                                
                                                c.moveTo(part.vertices[0].x, part.vertices[0].y);
                                
                                                for (j = 1; j < part.vertices.length; j++) {
                                                    if (!part.vertices[j - 1].isInternal || showInternalEdges) {
                                                        c.lineTo(part.vertices[j].x, part.vertices[j].y);
                                                    } else {
                                                        c.moveTo(part.vertices[j].x, part.vertices[j].y);
                                                    }
                                
                                                    if (part.vertices[j].isInternal && !showInternalEdges) {
                                                        c.moveTo(part.vertices[(j + 1) % part.vertices.length].x, part.vertices[(j + 1) % part.vertices.length].y);
                                                    }
                                                }
                                
                                                c.lineTo(part.vertices[0].x, part.vertices[0].y);
                                            }
                                        }
                                
                                        c.lineWidth = 1;
                                        c.strokeStyle = render.options.wireframeStrokeStyle;
                                        c.stroke();
                                    };
                                
                                    /**
                                     * Optimised method for drawing body convex hull wireframes in one pass
                                     * @private
                                     * @method bodyConvexHulls
                                     * @param {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.bodyConvexHulls = function(render, bodies, context) {
                                        var c = context,
                                            body,
                                            part,
                                            i,
                                            j,
                                            k;
                                
                                        c.beginPath();
                                
                                        // render convex hulls
                                        for (i = 0; i < bodies.length; i++) {
                                            body = bodies[i];
                                
                                            if (!body.render.visible || body.parts.length === 1)
                                                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 = 'rgba(255,255,255,0.2)';
                                        c.stroke();
                                    };
                                
                                    /**
                                     * Renders body vertex numbers.
                                     * @private
                                     * @method vertexNumbers
                                     * @param {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.vertexNumbers = function(render, bodies, context) {
                                        var c = context,
                                            i,
                                            j,
                                            k;
                                
                                        for (i = 0; i < bodies.length; i++) {
                                            var parts = bodies[i].parts;
                                            for (k = parts.length > 1 ? 1 : 0; k < parts.length; k++) {
                                                var part = parts[k];
                                                for (j = 0; j < part.vertices.length; j++) {
                                                    c.fillStyle = 'rgba(255,255,255,0.2)';
                                                    c.fillText(i + '_' + j, part.position.x + (part.vertices[j].x - part.position.x) * 0.8, part.position.y + (part.vertices[j].y - part.position.y) * 0.8);
                                                }
                                            }
                                        }
                                    };
                                
                                    /**
                                     * Renders mouse position.
                                     * @private
                                     * @method mousePosition
                                     * @param {render} render
                                     * @param {mouse} mouse
                                     * @param {RenderingContext} context
                                     */
                                    Render.mousePosition = function(render, mouse, context) {
                                        var c = context;
                                        c.fillStyle = 'rgba(255,255,255,0.8)';
                                        c.fillText(mouse.position.x + '  ' + mouse.position.y, mouse.position.x + 5, mouse.position.y - 5);
                                    };
                                
                                    /**
                                     * Draws body bounds
                                     * @private
                                     * @method bodyBounds
                                     * @param {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.bodyBounds = function(render, bodies, context) {
                                        var c = context,
                                            engine = render.engine,
                                            options = render.options;
                                
                                        c.beginPath();
                                
                                        for (var i = 0; i < bodies.length; i++) {
                                            var body = bodies[i];
                                
                                            if (body.render.visible) {
                                                var parts = bodies[i].parts;
                                                for (var j = parts.length > 1 ? 1 : 0; j < parts.length; j++) {
                                                    var part = parts[j];
                                                    c.rect(part.bounds.min.x, part.bounds.min.y, part.bounds.max.x - part.bounds.min.x, part.bounds.max.y - part.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 {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.bodyAxes = function(render, bodies, context) {
                                        var c = context,
                                            engine = render.engine,
                                            options = render.options,
                                            part,
                                            i,
                                            j,
                                            k;
                                
                                        c.beginPath();
                                
                                        for (i = 0; i < bodies.length; i++) {
                                            var body = bodies[i],
                                                parts = body.parts;
                                
                                            if (!body.render.visible)
                                                continue;
                                
                                            if (options.showAxes) {
                                                // render all axes
                                                for (j = parts.length > 1 ? 1 : 0; j < parts.length; j++) {
                                                    part = parts[j];
                                                    for (k = 0; k < part.axes.length; k++) {
                                                        var axis = part.axes[k];
                                                        c.moveTo(part.position.x, part.position.y);
                                                        c.lineTo(part.position.x + axis.x * 20, part.position.y + axis.y * 20);
                                                    }
                                                }
                                            } else {
                                                for (j = parts.length > 1 ? 1 : 0; j < parts.length; j++) {
                                                    part = parts[j];
                                                    for (k = 0; k < part.axes.length; k++) {
                                                        // render a single axis indicator
                                                        c.moveTo(part.position.x, part.position.y);
                                                        c.lineTo((part.vertices[0].x + part.vertices[part.vertices.length-1].x) / 2,
                                                            (part.vertices[0].y + part.vertices[part.vertices.length-1].y) / 2);
                                                    }
                                                }
                                            }
                                        }
                                
                                        if (options.wireframes) {
                                            c.strokeStyle = 'indianred';
                                            c.lineWidth = 1;
                                        } else {
                                            c.strokeStyle = 'rgba(255, 255, 255, 0.4)';
                                            c.globalCompositeOperation = 'overlay';
                                            c.lineWidth = 2;
                                        }
                                
                                        c.stroke();
                                        c.globalCompositeOperation = 'source-over';
                                    };
                                
                                    /**
                                     * Draws body positions
                                     * @private
                                     * @method bodyPositions
                                     * @param {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.bodyPositions = function(render, bodies, context) {
                                        var c = context,
                                            engine = render.engine,
                                            options = render.options,
                                            body,
                                            part,
                                            i,
                                            k;
                                
                                        c.beginPath();
                                
                                        // render current positions
                                        for (i = 0; i < bodies.length; i++) {
                                            body = bodies[i];
                                
                                            if (!body.render.visible)
                                                continue;
                                
                                            // handle compound parts
                                            for (k = 0; k < body.parts.length; k++) {
                                                part = body.parts[k];
                                                c.arc(part.position.x, part.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 {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.bodyVelocity = function(render, bodies, context) {
                                        var c = context;
                                
                                        c.beginPath();
                                
                                        for (var i = 0; i < bodies.length; i++) {
                                            var body = bodies[i];
                                
                                            if (!body.render.visible)
                                                continue;
                                
                                            var velocity = Body.getVelocity(body);
                                
                                            c.moveTo(body.position.x, body.position.y);
                                            c.lineTo(body.position.x + velocity.x, body.position.y + velocity.y);
                                        }
                                
                                        c.lineWidth = 3;
                                        c.strokeStyle = 'cornflowerblue';
                                        c.stroke();
                                    };
                                
                                    /**
                                     * Draws body ids
                                     * @private
                                     * @method bodyIds
                                     * @param {render} render
                                     * @param {body[]} bodies
                                     * @param {RenderingContext} context
                                     */
                                    Render.bodyIds = function(render, bodies, context) {
                                        var c = context,
                                            i,
                                            j;
                                
                                        for (i = 0; i < bodies.length; i++) {
                                            if (!bodies[i].render.visible)
                                                continue;
                                
                                            var parts = bodies[i].parts;
                                            for (j = parts.length > 1 ? 1 : 0; j < parts.length; j++) {
                                                var part = parts[j];
                                                c.font = "12px Arial";
                                                c.fillStyle = 'rgba(255,255,255,0.5)';
                                                c.fillText(part.id, part.position.x + 10, part.position.y - 10);
                                            }
                                        }
                                    };
                                
                                    /**
                                     * Description
                                     * @private
                                     * @method collisions
                                     * @param {render} render
                                     * @param {pair[]} pairs
                                     * @param {RenderingContext} context
                                     */
                                    Render.collisions = function(render, pairs, context) {
                                        var c = context,
                                            options = render.options,
                                            pair,
                                            collision,
                                            corrected,
                                            bodyA,
                                            bodyB,
                                            i,
                                            j;
                                
                                        c.beginPath();
                                
                                        // render collision positions
                                        for (i = 0; i < pairs.length; i++) {
                                            pair = pairs[i];
                                
                                            if (!pair.isActive)
                                                continue;
                                
                                            collision = pair.collision;
                                            for (j = 0; j < pair.contactCount; j++) {
                                                var contact = pair.contacts[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];
                                
                                            if (!pair.isActive)
                                                continue;
                                
                                            collision = pair.collision;
                                
                                            if (pair.contactCount > 0) {
                                                var normalPosX = pair.contacts[0].vertex.x,
                                                    normalPosY = pair.contacts[0].vertex.y;
                                
                                                if (pair.contactCount === 2) {
                                                    normalPosX = (pair.contacts[0].vertex.x + pair.contacts[1].vertex.x) / 2;
                                                    normalPosY = (pair.contacts[0].vertex.y + pair.contacts[1].vertex.y) / 2;
                                                }
                                
                                                if (collision.bodyB === collision.supports[0].body || collision.bodyA.isStatic === true) {
                                                    c.moveTo(normalPosX - collision.normal.x * 8, normalPosY - collision.normal.y * 8);
                                                } else {
                                                    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 separations
                                     * @param {render} render
                                     * @param {pair[]} pairs
                                     * @param {RenderingContext} context
                                     */
                                    Render.separations = function(render, pairs, context) {
                                        var c = context,
                                            options = render.options,
                                            pair,
                                            collision,
                                            corrected,
                                            bodyA,
                                            bodyB,
                                            i,
                                            j;
                                
                                        c.beginPath();
                                
                                        // render separations
                                        for (i = 0; i < pairs.length; i++) {
                                            pair = pairs[i];
                                
                                            if (!pair.isActive)
                                                continue;
                                
                                            collision = pair.collision;
                                            bodyA = collision.bodyA;
                                            bodyB = collision.bodyB;
                                
                                            var k = 1;
                                
                                            if (!bodyB.isStatic && !bodyA.isStatic) k = 0.5;
                                            if (bodyB.isStatic) k = 0;
                                
                                            c.moveTo(bodyB.position.x, bodyB.position.y);
                                            c.lineTo(bodyB.position.x - collision.penetration.x * k, bodyB.position.y - collision.penetration.y * k);
                                
                                            k = 1;
                                
                                            if (!bodyB.isStatic && !bodyA.isStatic) k = 0.5;
                                            if (bodyA.isStatic) k = 0;
                                
                                            c.moveTo(bodyA.position.x, bodyA.position.y);
                                            c.lineTo(bodyA.position.x + collision.penetration.x * k, bodyA.position.y + collision.penetration.y * k);
                                        }
                                
                                        if (options.wireframes) {
                                            c.strokeStyle = 'rgba(255,165,0,0.5)';
                                        } else {
                                            c.strokeStyle = 'orange';
                                        }
                                        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 = inspector.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([]);
                                            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);
                                    };
                                
                                    /**
                                     * Updates render timing.
                                     * @method _updateTiming
                                     * @private
                                     * @param {render} render
                                     * @param {number} time
                                     */
                                    var _updateTiming = function(render, time) {
                                        var engine = render.engine,
                                            timing = render.timing,
                                            historySize = timing.historySize,
                                            timestamp = engine.timing.timestamp;
                                
                                        timing.delta = time - timing.lastTime || Render._goodDelta;
                                        timing.lastTime = time;
                                
                                        timing.timestampElapsed = timestamp - timing.lastTimestamp || 0;
                                        timing.lastTimestamp = timestamp;
                                
                                        timing.deltaHistory.unshift(timing.delta);
                                        timing.deltaHistory.length = Math.min(timing.deltaHistory.length, historySize);
                                
                                        timing.engineDeltaHistory.unshift(engine.timing.lastDelta);
                                        timing.engineDeltaHistory.length = Math.min(timing.engineDeltaHistory.length, historySize);
                                
                                        timing.timestampElapsedHistory.unshift(timing.timestampElapsed);
                                        timing.timestampElapsedHistory.length = Math.min(timing.timestampElapsedHistory.length, historySize);
                                
                                        timing.engineUpdatesHistory.unshift(engine.timing.lastUpdatesPerFrame);
                                        timing.engineUpdatesHistory.length = Math.min(timing.engineUpdatesHistory.length, historySize);
                                
                                        timing.engineElapsedHistory.unshift(engine.timing.lastElapsed);
                                        timing.engineElapsedHistory.length = Math.min(timing.engineElapsedHistory.length, historySize);
                                
                                        timing.elapsedHistory.unshift(timing.lastElapsed);
                                        timing.elapsedHistory.length = Math.min(timing.elapsedHistory.length, historySize);
                                    };
                                
                                    /**
                                     * Returns the mean value of the given numbers.
                                     * @method _mean
                                     * @private
                                     * @param {Number[]} values
                                     * @return {Number} the mean of given values
                                     */
                                    var _mean = function(values) {
                                        var result = 0;
                                        for (var i = 0; i < values.length; i += 1) {
                                            result += values[i];
                                        }
                                        return (result / values.length) || 0;
                                    };
                                
                                    /**
                                     * @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;
                                    };
                                
                                    /*
                                    *
                                    *  Events Documentation
                                    *
                                    */
                                
                                    /**
                                    * Fired before rendering
                                    *
                                    * @event beforeRender
                                    * @param {} event An event object
                                    * @param {number} event.timestamp The engine.timing.timestamp of the event
                                    * @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 {number} event.timestamp The engine.timing.timestamp of the event
                                    * @param {} event.source The source object of the event
                                    * @param {} event.name The name of the event
                                    */
                                
                                    /*
                                    *
                                    *  Properties Documentation
                                    *
                                    */
                                
                                    /**
                                     * A back-reference to the `Matter.Render` module.
                                     *
                                     * @deprecated
                                     * @property controller
                                     * @type render
                                     */
                                
                                    /**
                                     * A reference to the `Matter.Engine` instance to be used.
                                     *
                                     * @property engine
                                     * @type engine
                                     */
                                
                                    /**
                                     * 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
                                     */
                                
                                    /**
                                     * 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 {}
                                     */
                                
                                    /**
                                     * The mouse to render if `render.options.showMousePosition` is enabled.
                                     *
                                     * @property mouse
                                     * @type mouse
                                     * @default null
                                     */
                                
                                    /**
                                     * The configuration options of the renderer.
                                     *
                                     * @property options
                                     * @type {}
                                     */
                                
                                    /**
                                     * The target width in pixels of the `render.canvas` to be created.
                                     * See also the `options.pixelRatio` property to change render quality.
                                     *
                                     * @property options.width
                                     * @type number
                                     * @default 800
                                     */
                                
                                    /**
                                     * The target height in pixels of the `render.canvas` to be created.
                                     * See also the `options.pixelRatio` property to change render quality.
                                     *
                                     * @property options.height
                                     * @type number
                                     * @default 600
                                     */
                                
                                    /**
                                     * The [pixel ratio](https://developer.mozilla.org/en-US/docs/Web/API/Window/devicePixelRatio) to use when rendering.
                                     *
                                     * @property options.pixelRatio
                                     * @type number
                                     * @default 1
                                     */
                                
                                    /**
                                     * A CSS background color string to use when `render.options.wireframes` is disabled.
                                     * This may be also set to `'transparent'` or equivalent.
                                     *
                                     * @property options.background
                                     * @type string
                                     * @default '#14151f'
                                     */
                                
                                    /**
                                     * A CSS color string to use for background when `render.options.wireframes` is enabled.
                                     * This may be also set to `'transparent'` or equivalent.
                                     *
                                     * @property options.wireframeBackground
                                     * @type string
                                     * @default '#14151f'
                                     */
                                
                                    /**
                                     * A CSS color string to use for stroke when `render.options.wireframes` is enabled.
                                     * This may be also set to `'transparent'` or equivalent.
                                     *
                                     * @property options.wireframeStrokeStyle
                                     * @type string
                                     * @default '#bbb'
                                     */
                                
                                    /**
                                     * A flag that specifies if `render.bounds` should be used when rendering.
                                     *
                                     * @property options.hasBounds
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable all debug information overlays together.  
                                     * This includes and has priority over the values of:
                                     *
                                     * - `render.options.showStats`
                                     * - `render.options.showPerformance`
                                     *
                                     * @property options.showDebug
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the engine stats info overlay.  
                                     * From left to right, the values shown are:
                                     *
                                     * - body parts total
                                     * - body total
                                     * - constraints total
                                     * - composites total
                                     * - collision pairs total
                                     *
                                     * @property options.showStats
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable performance charts.  
                                     * From left to right, the values shown are:
                                     *
                                     * - average render frequency (e.g. 60 fps)
                                     * - exact engine delta time used for last update (e.g. 16.66ms)
                                     * - average updates per frame (e.g. 1)
                                     * - average engine execution duration (e.g. 5.00ms)
                                     * - average render execution duration (e.g. 0.40ms)
                                     * - average effective play speed (e.g. '1.00x' is 'real-time')
                                     *
                                     * Each value is recorded over a fixed sample of past frames (60 frames).
                                     *
                                     * A chart shown below each value indicates the variance from the average over the sample.
                                     * The more stable or fixed the value is the flatter the chart will appear.
                                     *
                                     * @property options.showPerformance
                                     * @type boolean
                                     * @default false
                                     */
                                    
                                    /**
                                     * A flag to enable or disable rendering entirely.
                                     *
                                     * @property options.enabled
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to toggle wireframe rendering otherwise solid fill rendering is used.
                                     *
                                     * @property options.wireframes
                                     * @type boolean
                                     * @default true
                                     */
                                
                                    /**
                                     * A flag to enable or disable sleeping bodies indicators.
                                     *
                                     * @property options.showSleeping
                                     * @type boolean
                                     * @default true
                                     */
                                
                                    /**
                                     * A flag to enable or disable the debug information overlay.
                                     *
                                     * @property options.showDebug
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the collision broadphase debug overlay.
                                     *
                                     * @deprecated no longer implemented
                                     * @property options.showBroadphase
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body bounds debug overlay.
                                     *
                                     * @property options.showBounds
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body velocity debug overlay.
                                     *
                                     * @property options.showVelocity
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body collisions debug overlay.
                                     *
                                     * @property options.showCollisions
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the collision resolver separations debug overlay.
                                     *
                                     * @property options.showSeparations
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body axes debug overlay.
                                     *
                                     * @property options.showAxes
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body positions debug overlay.
                                     *
                                     * @property options.showPositions
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body angle debug overlay.
                                     *
                                     * @property options.showAngleIndicator
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body and part ids debug overlay.
                                     *
                                     * @property options.showIds
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body vertex numbers debug overlay.
                                     *
                                     * @property options.showVertexNumbers
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body convex hulls debug overlay.
                                     *
                                     * @property options.showConvexHulls
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the body internal edges debug overlay.
                                     *
                                     * @property options.showInternalEdges
                                     * @type boolean
                                     * @default false
                                     */
                                
                                    /**
                                     * A flag to enable or disable the mouse position debug overlay.
                                     *
                                     * @property options.showMousePosition
                                     * @type boolean
                                     * @default false
                                     */
                                
                                })();