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context.drawImage(shipImage,ship.x,ship.y);

You can see this example by executing CH5EX19.html from the code distribution, or by

typing in the code listing shown in Example 5-19.

Example 5-19. Easing in (taking off)

<!doctype html>

<head>

<title>CH5EX19: Taking Off (Fake Ease In)</title>

window.addEventListener('load', eventWindowLoaded, false);

var shipImage;

function eventWindowLoaded() {

shipImage = new Image();

shipImage.src = "ship.png"

shipImage.onload = eventAssetsLoaded;

}

function eventAssetsLoaded() {

canvasApp();

}

function canvasSupport () {

return Modernizr.canvas;

}

function canvasApp() {

if (!canvasSupport()) {

return;

}

var pointImage = new Image();

pointImage.src = "pointwhite.png";

function drawScreen () {

context.fillStyle = '#000000';

context.fillRect(0, 0, theCanvas.width, theCanvas.height);

//Box

context.strokeStyle = '#ffffff';

context.strokeRect(1, 1, theCanvas.width-2, theCanvas.height-2);

ship.velocityx = ship.velocityx + ( ship.velocityx*easeValue);

ship.velocityy = ship.velocityy + ( ship.velocityy*easeValue);

ship.x += ship.velocityx;

Easing | 279

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ship.y += ship.velocityy;

//Draw points to illustrate path

points.push({x:ship.x,y:ship.y});

for (var i = 0; i< points.length; i++) {

context.drawImage(pointImage, points[i].x+shipImage.width/2,

points[i].y,1,1);

}

context.drawImage(shipImage,ship.x,ship.y);

}

var easeValue = .05;

var p1 = {x:240,y:470};

var tempX;

var tempY;

var tempSpeed = .5;

var tempAngle = 270 ;

var tempRadians = tempAngle * Math.PI/ 180;

var tempvelocityx = Math.cos(tempRadians) * tempSpeed;

var tempvelocityy = Math.sin(tempRadians) * tempSpeed;

var ship = {x:p1.x, y:p1.y, velocityx:tempvelocityx, velocityy:tempvelocityy};

var points = new Array();

theCanvas = document.getElementById("canvasOne");

context = theCanvas.getContext("2d");

function gameLoop() {

window.setTimeout(gameLoop, 20);

drawScreen()

}

gameLoop();

}

</script>

</head>

<body>

Your browser does not support HTML5 Canvas.

</canvas>

</div>

</body>

</html>

280 | Chapter 5: Math, Physics, and Animation

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For more information about easing, check out Robert Penner’s easing

equations. These equations have been implemented in jQuery for Java‐

Script.

Box2D and the Canvas

Now that we have discussed how to use math and physics to create animations on the

Canvas, it’s time to take this discussion to the next level and implement a popular Java‐

Script library named Box2D. Box2D is a physics modeling library for 2D graphics. We

will use it to replace some of the complex code we developed manually for some of the

earlier examples in this chapter.

Box2D was originally developed for C++ by Erin Catto and gained popularity as a library

named Box2DFlashAS3 for making Flash games in ActionScript 3. There are two Box2D

implementations for JavaScript. The first is Box2Djs, and the other is Box2dWeb.

Box2dWeb is the latest and greatest and had has been updated to Box2D 2.1, so that is

the version we will use in our examples. Box2dWeb was ported directly from Action‐

Script 3 for use on the HTML5 Canvas.

Downloading Box2dWeb

To start, we need to download the latest version of Box2dWeb. At the time of this writing,

the latest version was Box2dWeb-2.1a.3.

How Does Box2dWeb Work?

Box2dWeb is a physics modeling engine. It allows a developer to create a world with

physics properties and add objects to that world that react to the properties of that world

and to each other. However, the world is not displayed (not formally anyway, as you’ll

see in a bit). The job of the Canvas developer when using Box2dWeb is to define a physics

model and then apply it to the Canvas.

Before we get started, here are some definitions in Box2dWeb related to the examples

we are going to cover. (The World modeled with Box2D is more complicated than just

this, but these are the things we will cover in the examples.)

Shape

A geometrical object that exists 2D space. These are circles, squares, rectangles, and

so on.

Fixture

A logical object that binds a shape to body and give it properties like density, friction,

and restitution.

Box2D and the Canvas | 281

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Rigid Body

A physical manifestation of an object in the 2D world, with a fixture and a shape

applied.

World

A 2D physics world that contains bodies that react to one another

In the examples that follow, we will show how these things relate to one another in

Box2D.

Box2D Hello World

For our first example, we will create a box that contains balls that fall and bounce on

the screen. See Figure 5-24 to see an example.

Figure 5-24. Box2D balls demo

Including the Library

The first thing we need to do is include the Box2dWeb library in JavaScript.

Creating a Box2dWeb World

Next we add the code to initialize the world. The variables created in the following code

are shortcuts to the objects in Box2dWeb. They have shorter names make it much easier

to define new objects in code. Not all the objects in Box2dWeb are represented here, so

282 | Chapter 5: Math, Physics, and Animation

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if you need a different one (such as a joint with b2JointDef), you will need to define a

new shortcut (or just use the full object path name).

var b2Vec2 = Box2D.Common.Math.b2Vec2

, b2BodyDef = Box2D.Dynamics.b2BodyDef

, b2Body = Box2D.Dynamics.b2Body

, b2FixtureDef = Box2D.Dynamics.b2FixtureDef

, b2World = Box2D.Dynamics.b2World

, b2PolygonShape = Box2D.Collision.Shapes.b2PolygonShape

, b2CircleShape = Box2D.Collision.Shapes.b2CircleShape

, b2DebugDraw = Box2D.Dynamics.b2DebugDraw;

Now you create your world object. This will define your physics world. b2Vec() is a

Box2D object that accepts two parameters: x-axis gravity and y-axis gravity. The second

parameter is doSleep, which improves performance by not simulating inactive bodies

if set to true.

var world = new b2World(new b2Vec2(0,10), true);

Units in Box2dWeb

The first Box2D objects we will create are the four walls that define the area that holds

our balls (a 500×400 Canvas). These walls are similar to the boundaries we defined in

code for the earlier bouncing balls demos. We will define the walls as dynamic objects

in an array, each with four properties:

{x:, x position, y: y position, w:width, h: height }

var wallDefs = new Array(

{x:8.3,y:.03,w:8.3 ,h:.03}, //top wall

{x:8.3,y:13.33,w:8.3 ,h:.03}, //bottom wall

{x:0,y:6.67,w:.03 ,h:6.67}, //left wall

{x:16.7,y:6.67,w:.03 ,h:6.67} ); //right wall

Notice that the values defined above do not look like anything we have used before. The

values are in MTS units. As we stated earlier, MTS units refer to “meters-tonne-second”

and are used represent large objects and spaces. However, because we draw everything

in pixels on the Canvas, we need a way to think of MTS units in terms of the Canvas

and vice versa.

To get these values, we need to choose a “scale” value to scale the Canvas pixels to MTS

units. For this example (and all the examples in the rest of this chapter), we have chosen

the value 30 as the scale value to translate pixels to MTS units.

At the same time, objects displayed in Box2D have their origin at the center (not the

upper-left corner), so we need to compensate for that as well. Figure 5-25 shows how

the units translate and the relative origins of the walls.

Box2D and the Canvas | 283

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Figure 5-25. MTS conversion to pixels in Box2D

To get the sizes of the walls (width and height) we need to divide all the relative Canvas

pixel values by 30. To get the location, we need to do the same but also make sure that

we provide origins in the center, not the upper-left side of the object.

To top this off, the width and height passed to the Box2D setAsBox() method (width

and height) are given in ½ width and ½ height. (We will discuss setAsBox()a little later

in this chapter.)

So, for the top wall that we want to extend all the way across the Canvas with a height

of 1 pixel, the code would be as follows:

{x:250/30, y:1/30, w:500/2/30, h:1/30}

Or, alternatively:

{x:8.3,y:.03,w:8.33 ,h:.03}, //top wall

The rest of the wall values use the same type of calculations to convert pixel values to

MTS units for Box2D. Now let’s use those units to make something.

What is interesting about this scale value is that when you use it uniformly (to convert

to MTS units from pixels and from pixels to MTS units), the value can be anything. It

just needs to be consistent. However, the value does have an effect on your physics world.

The size of the value models the world in a different way. The smaller the scale value,

the bigger the objects are in your world and vice versa. You will need to manipulate this

scale value to tweak the physics for the world you are simulating.

Defining the Walls in Box2D

We now have our walls defined with locations and sizes based on MTS units. We can

start defining the walls based on Box2D objects. We start by creating an array to hold

284 | Chapter 5: Math, Physics, and Animation

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our walls, and then we loop through the wallDefs array to create the four walls that

bound the screen.

var walls = new Array();

for (var i = 0; i <wallDefs.length; i++) {

Next we start to define a wall by creating an instance b2BodyDef. A b2BodyDef object

will hold the definitions we need to define a rigid body. Recall that a rigid body will have

a shape and fixture applied to create a Box2D object that we can manipulate. We set the

type to be b2_staticBody, which means that this object will never move and has infinite

mass: perfect for the walls that bound our Canvas. We then set the position of wall

Def to the position for this wall as set in the array of dynamic objects. Finally, we call

world.createBody(wallDef) to create a rigid body in Box2D, based on the definitions

set in the b2BodyDef object:

var wallDef = new b2BodyDef;

wallDef.type = b2Body.b2_staticBody;

wallDef.position.Set(wallDefs[i].x, wallDefs[i].y);

var newWall = world.CreateBody(wallDef)

Now it is time to create the fixture definition for the wall. Recall that a fixture binds a

shape to the rigid body, and it contains properties for our Box2D object. First, we create

a new b2FixtureDef, and then we set the density (mass per unit volume), friction

(resistance, usually between 0 and 1), and the restitution (elasticity, usually between

0 and 1):

var wallFixture = new b2FixtureDef;

wallFixture.density = 10.0;

wallFixture.friction = 0.5;

wallFixture.restitution = 1;

Now that we have the fixture, we need to create the shape. We set the shape property of

the fixture as b2PolygonShape, and then we call the shape’s setAsBox() method (pass

the width and height of the wall) to finish defining the shape. Next we close the loop

by calling the createFixture() method of our rigid body, passing wallFixture as the

parameter. This sets the fixture and shape to the rigid body. Finally, we add the rigid

body to our walls array.

wallFixture.shape = new b2PolygonShape;

wallFixture.shape.SetAsBox(wallDefs[i].w, wallDefs[i].h);

newWall.CreateFixture(wallFixture);

walls.push(newWall);

}

Creating Balls

Creating the balls that will fall and bounce around in our demo is very similar to creating

walls in Box2D. For this exercise, we will create 50 balls with random locations and sizes.

The locations and sizes are (again) in MTS units. The only real difference from creating

Box2D and the Canvas | 285

the walls is that we set the fixture shape property to b2CircleShape(size), where size

is a random size in MTS units.

var numBalls = 50;

var balls = new Array();

for (var i=0; i < numBalls; i++) {

var ballDef = new b2BodyDef;

ballDef.type = b2Body.b2_dynamicBody;

var ypos = (Math.random() * 8)+ 1;

var xpos = (Math.random() * 14)+ 1;

var size = (Math.random() * .4)+ 0.2;

ballDef.position.Set(xpos, ypos);

var ballFixture = new b2FixtureDef;

ballFixture.density = 10.0;

ballFixture.friction = 0.5;

ballFixture.restitution = 1;

ballFixture.shape = new b2CircleShape(size);

var newBall = world.CreateBody(ballDef)

newBall.CreateFixture(ballFixture);

balls.push(newBall);

}

Rendering b2debugDraw vs. Canvas Rendering

The b2debugDraw functionality of Box2D is just a way to test your physics world and

see it working in a web browser. It is not an implementation of the physics for your

application. We will use debugDraw to illustrate the objects we have created so that we

can see them in action. In example CH5EX22.html, we will show you how to apply

Box2D to the Canvas. For now, we just want to see the physics model we have created.

The following code is fairly boilerplate for getting b2debugDraw to work. The Set

Sprite() method takes the Canvas context as a parameter. This means that the Canvas

will be completely overwritten by the output from b2debugDraw. This is why it’s just for

testing. SetScaleFactor() takes the value we used to convert from pixels to MTS units

(30). SetFillAlpha() sets the transparency of the lines of the objects when displayed,

and likewise, SetLineThickness() sets the thickness of those lines. The SetFlags()

method accepts a single bit-wise parameter of options for display: e_shapeBit draws

the shapes, and e_jointBit draws joints (but because we have not created any, you will

not see them):

var debugDraw = new b2DebugDraw();

debugDraw.SetSprite (context2);

debugDraw.SetDrawScale(30);

debugDraw.SetFillAlpha(0.3);

debugDraw.SetLineThickness(1.0);

debugDraw.SetFlags(b2DebugDraw.e_shapeBit | b2DebugDraw.e_jointBit);

world.SetDebugDraw(debugDraw);

286 | Chapter 5: Math, Physics, and Animation

drawScreen()

Finally, we are ready to draw our Box2D physics models to the HTML5 Canvas. To make

that work, we replace all of the code we have previously created in our drawScreen()

function with following three lines:

world.Step(1 / 60, 10, 10);

world.DrawDebugData();

world.ClearForces();

world.Step() takes three parameters: time step, velocity iterations, and position iter‐

ations. The time step is how much time in the simulation to simulate on every call. For

our application, we are simulating 1/60 of a second. The other two parameters set the

precision of the iterations and should be left alone for now. world.DrawDebugData()

draws the b2DebugDraw to the Canvas. world.clearForces() is called after every step

to reset the physics model for the next step.

Example 5-20 provides the full code listing for CH1EX20.html. When you test this ex‐

ample, you will see 50 randomly created balls fall down and bounce off the bottom of

the canvas. Some will bounce around for a long time, others will stop bouncing much

sooner. Notice that balls appear to act the way you would expect balls to act. However,

if you look back at the code we wrote, we did not create any functions for hit detection,

angle of reflection, or linear movement. All of that was handled by Box2D.

Example 5-20. Box2dWeb balls demo

<!doctype html>

<head>

<title>CH5EX20: Box2dWeb Balls Demo</title>

window.addEventListener('load', eventWindowLoaded, false);

function eventWindowLoaded() {

canvasApp();

}

function canvasSupport () {

return Modernizr.canvas;

}

function canvasApp() {

if (!canvasSupport()) {

return;

}

Box2D and the Canvas | 287

function drawScreen () {

world.Step(1 / 60, 10, 10);

world.DrawDebugData();

world.ClearForces();

}

theCanvas = document.getElementById('canvasOne');

context = theCanvas.getContext('2d');

var b2Vec2 = Box2D.Common.Math.b2Vec2

, b2BodyDef = Box2D.Dynamics.b2BodyDef

, b2Body = Box2D.Dynamics.b2Body

, b2FixtureDef = Box2D.Dynamics.b2FixtureDef

, b2World = Box2D.Dynamics.b2World

, b2PolygonShape = Box2D.Collision.Shapes.b2PolygonShape

, b2CircleShape = Box2D.Collision.Shapes.b2CircleShape

, b2DebugDraw = Box2D.Dynamics.b2DebugDraw;

var world = new b2World(new b2Vec2(0,10), true);

var numBalls = 50;

var balls = new Array();

for (var i=0; i < numBalls; i++) {

var ballDef = new b2BodyDef;

ballDef.type = b2Body.b2_dynamicBody;

var ypos = (Math.random() * 8)+1;

var xpos = (Math.random() * 14)+1;

var size = (Math.random() * .4)+.2;

ballDef.position.Set(xpos, ypos);

var ballFixture = new b2FixtureDef;

ballFixture.density = 10.0;

ballFixture.friction = 0.5;

ballFixture.restitution = 1;

ballFixture.shape = new b2CircleShape(size);

var newBall = world.CreateBody(ballDef)

newBall.CreateFixture(ballFixture);

balls.push(newBall);

}

var wallDefs = new Array({x:8.3,y:.03,w:8.3 ,h:.03}, //top

{x:8.3,y:13.33,w:8.3 ,h:.03}, //bottom

{x:0,y:6.67,w:.03 ,h:6.67}, //left

{x:16.7,y:6.67,w:.03 ,h:6.67} ); //right

var walls = new Array();

for (var i = 0; i <wallDefs.length; i++) {

var wallDef = new b2BodyDef;

wallDef.type = b2Body.b2_staticBody;

wallDef.position.Set(wallDefs[i].x, wallDefs[i].y);

var newWall = world.CreateBody(wallDef)

var wallFixture = new b2FixtureDef;

wallFixture.density = 10.0;

wallFixture.friction = 0.5;

wallFixture.restitution = 1;

wallFixture.shape = new b2PolygonShape;

wallFixture.shape.SetAsBox(wallDefs[i].w, wallDefs[i].h);

newWall.CreateFixture(wallFixture);

288 | Chapter 5: Math, Physics, and Animation

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