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In the case of 100 balls bouncing on the canvas, we will need to create a ball object with

a few more properties. Recall that the ball object we created previously had only x and

y properties and looked like this:

var ball = {x:p1.x, y:p1.y};

All the other variables that represented the ball (speed, angle, xunits, yunits) were

global in scope to the canvasApp(). We used global variables because we could get away

with it. However, because we need to make sure everything works the same way in this

app, we make all those values properties of each ball object.

For the multiple-ball-bounce application, we will create an object that holds all the

pertinent information about each bouncing ball: x, y, speed, angle, xunits, and

yunits. Because we are going to create 100 balls of various sizes, we also add a property

named radius, which represents the size of the ball (well, half the size because it is a

radius):

tempBall = {x:tempX,y:tempY,radius:tempRadius, speed:tempSpeed,

angle:tempAngle, xunits:tempXunits, yunits:tempYunits}

Inside canvasApp(), we define some new variables to help manage the multiple balls

that will bounce around the canvas:

numBalls

The number of balls to randomly create

maxSize

The maximum radius length for any given ball

minSize

The minimum radius length for any given ball

maxSpeed

The maximum speed any ball can travel

balls

An array to hold all of the ball objects we will create

The following code shows the newly defined variables:

var numBalls = 100 ;

var maxSize = 8;

var minSize = 5;

var maxSpeed = maxSize+5;

var balls = new Array();

We also create a set of temporary variables to hold the values for each ball before we

push it into the balls array:

var tempBall;

var tempX;

var tempY;

Bouncing Off Walls | 209

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var tempSpeed;

var tempAngle;

var tempRadius;

var tempRadians;

var tempXunits;

var tempYunits;

Next, in canvasApp(), we iterate through a loop to create all the ball objects. Notice how

tempX and tempY are created below. These values represent the ball’s starting location

on the canvas. We create a random value for each, but we offset it by the size of the ball

(tempRadius*2). If we did not do that, some of the balls would get “stuck” in a wall when

the app starts because their x or y location would be “through” the wall, but their speed

would not be enough so that a “bounce” would get them back on the playfield. They

would be stuck in bouncing limbo forever (which is kind of sad when you think

about it).

When you try this app, you will see that occasionally a ball still gets

stuck in a wall. There is a further optimization we need to make to

prevent this, but it is a bigger subject than this little iteration. We will

talk about it in the section “Multiple Balls Bouncing and Colliding” on

page 219.

The tempSpeed variable is created by subtracting the value of tempRadius from the value

of maxSpeed, which we created earlier. The speed is not random, but it is inversely

proportional to the size (radius) of the ball. A larger ball has a larger radius, so the value

you subtract from tempSpeed will be larger, thus making the ball move more slowly.

When you run CH5EX5.html in your web browser, you will notice that

this little trick makes the ball appear more “real” because your brain

expects larger objects to move more slowly.

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

tempRadius = Math.floor(Math.random()*maxSize)+minSize;

tempX = tempRadius*2 + (Math.floor(Math.random()*theCanvas.width)

-tempRadius*2);

tempY = tempRadius*2 + (Math.floor(Math.random()*theCanvas.height)

-tempRadius*2);

tempSpeed = maxSpeed-tempRadius;

tempAngle = Math.floor(Math.random()*360);

tempRadians = tempAngle * Math.PI/ 180;

tempXunits = Math.cos(tempRadians) * tempSpeed;

tempYunits = Math.sin(tempRadians) * tempSpeed;

tempBall = {x:tempX,y:tempY,radius:tempRadius, speed:tempSpeed,

210 | Chapter 5: Math, Physics, and Animation

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angle:tempAngle,

xunits:tempXunits, yunits:tempYunits}

balls.push(tempBall);

}

Now we need to draw the balls onto the canvas. Inside drawScreen(), the code to draw

the balls should look very familiar because it is essentially the same code we used for

one ball in Example 5-4. We just need to loop through the balls array to render each

ball object:

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

ball = balls[i];

ball.x += ball.xunits;

ball.y += ball.yunits;

context.beginPath();

context.arc(ball.x,ball.y,ball.radius,0,Math.PI*2,true);

context.closePath();

context.fill();

if (ball.x > theCanvas.width || ball.x < 0 ) {

ball.angle = 180 - ball.angle;

updateBall(ball);

} else if (ball.y > theCanvas.height || ball.y < 0) {

ball.angle = 360 - ball.angle;

updateBall(ball);

}

When you load Example 5-5 in your web browser, you will see a bunch of balls all moving

around the screen independently, as shown in Figure 5-7. For the fun of it, why not

change the numBalls variable to 500 or 1,000? What does the canvas look like then?

Bouncing Off Walls | 211

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Figure 5-7. Multiple balls of different sizes bouncing off walls

Example 5-5. Multiple ball bounce

<!doctype html>

<head>

<title>CH5EX5: Multiple Ball Bounce</title>

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

function eventWindowLoaded() {

canvasApp();

}

function canvasSupport () {

return Modernizr.canvas;

}

function canvasApp() { if (!canvasSupport()) {

return;

}

function drawScreen () {

212 | Chapter 5: Math, Physics, and Animation

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context.fillStyle = '#EEEEEE';

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

//Box

context.strokeStyle = '#000000';

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

//Place balls

context.fillStyle = "#000000";

var ball;

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

ball = balls[i];

ball.x += ball.xunits;

ball.y += ball.yunits;

context.beginPath();

context.arc(ball.x,ball.y,ball.radius,0,Math.PI*2,true);

context.closePath();

context.fill();

if (ball.x > theCanvas.width || ball.x < 0 ) {

ball.angle = 180 - ball.angle;

updateBall(ball);

} else if (ball.y > theCanvas.height || ball.y < 0) {

ball.angle = 360 - ball.angle;

updateBall(ball);

}

function updateBall(ball) {

ball.radians = ball.angle * Math.PI/ 180;

ball.xunits = Math.cos(ball.radians) * ball.speed;

ball.yunits = Math.sin(ball.radians) * ball.speed;

}

var numBalls = 100 ;

var maxSize = 8;

var minSize = 5;

var maxSpeed = maxSize+5;

var balls = new Array();

var tempBall;

var tempX;

var tempY;

var tempSpeed;

var tempAngle;

var tempRadius;

var tempRadians;

Bouncing Off Walls | 213

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var tempXunits;

var tempYunits;

theCanvas = document.getElementById("canvasOne");

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

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

tempRadius = Math.floor(Math.random()*maxSize)+minSize;

tempX = tempRadius*2 + (Math.floor(Math.random()*theCanvas.width)-tempRadius*2);

tempY = tempRadius*2 + (Math.floor(Math.random()*theCanvas.height)-tempRadius*2);

tempSpeed = maxSpeed-tempRadius;

tempAngle = Math.floor(Math.random()*360);

tempRadians = tempAngle * Math.PI/ 180;

tempXunits = Math.cos(tempRadians) * tempSpeed;

tempYunits = Math.sin(tempRadians) * tempSpeed;

tempBall = {x:tempX,y:tempY,radius:tempRadius, speed:tempSpeed, angle:tempAngle,

xunits:tempXunits, yunits:tempYunits}

balls.push(tempBall);

}

function gameLoop() {

window.setTimeout(gameLoop, 20);

drawScreen()

}

gameLoop();

}

</script>

</head>

<body>

Your browser does not support HTML5 Canvas.

</canvas>

</div>

</body>

</html>

Multiple Balls Bouncing with a Dynamically Resized Canvas

Before we move on to more complex interaction among balls, let’s try one more thing.

Back in Chapter 3, we resized the canvas with some HTML5 form controls to display

text in the center of the canvas. Well, let’s do the same thing now with the ball example.

This will give you a better idea of how we can make objects interact with a dynamically

resizing canvas.

214 | Chapter 5: Math, Physics, and Animation

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First, in the HTML, we create two HTML5 range controls, one for width and one for

height, and set their maximum values to 1000. We will use these controls to set the

width and height of the canvas at runtime:

<form>

Canvas Width: <input type="range" id="canvasWidth"

min="0"

max="1000"

step="1"

value="500"/>

<br>

Canvas Height: <input type="range" id="canvasHeight"

min="0"

max="1000"

step="1"

value="500"/>

<br>

</form>

In canvasApp(), we create the event listeners for the HTML5 form controls. We listen

for the change event, which means that any time the range control is moved, the event

handlers will be called:

formElement = document.getElementById("canvasWidth")

formElement.addEventListener('change', canvasWidthChanged, false);

formElement = document.getElementById("canvasHeight")

formElement.addEventListener('change', canvasHeightChanged, false);

The event handler functions capture the changes to the range, set theCanvas.width or

theCanvas.height, and then call drawScreen() to render the new size. Without a call

to drawScreen() here, the canvas will blink when the new size is applied in

drawScreen() on the next interval:

function canvasWidthChanged(e) {

var target = e.target;

theCanvas.width = target.value;

drawScreen();

}

function canvasHeightChanged(e) {

var target = e.target;

theCanvas.height = target.value;

drawScreen();

}

Bouncing Off Walls | 215

All of this is explained in gory detail in Chapter 3.

One last thing—let’s increase the number of balls set in canvasApp() to 500:

var numBalls = 500 ;

Now, check out Example 5-6 (CH5EX6.html from the code distribution). When you

run the code in a web browser, you should see 500 balls bounce around the canvas, as

shown in Figure 5-8. When you increase the width or height using the range controls,

they continue moving until they hit the new edge of the canvas. If you make the canvas

smaller, the balls will be contained within the smaller space. If you adjust the size too

rapidly, some balls will be lost off the canvas, but they will reappear when the canvas is

resized. Neat, huh?

Figure 5-8. Multiple balls bouncing while the canvas is resized on the fly

Example 5-6. Multiple ball bounce with dynamically resized canvas

<!doctype html>

<head>

216 | Chapter 5: Math, Physics, and Animation

<title>CH5EX6: Multiple Ball Bounce With Resize</title>

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

function eventWindowLoaded() {

canvasApp();

}function canvasSupport () {

return Modernizr.canvas;

}

function canvasApp() {

if (!canvasSupport()) {

return;

}

formElement = document.getElementById("canvasWidth")

formElement.addEventListener('change', canvasWidthChanged, false);

formElement = document.getElementById("canvasHeight")

formElement.addEventListener('change', canvasHeightChanged, false);

function drawScreen () {

context.fillStyle = '#EEEEEE';

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

//Box

context.strokeStyle = '#000000';

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

//Place balls

context.fillStyle = "#000000";

var ball;

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

ball = balls[i];

ball.x += ball.xunits;

ball.y += ball.yunits;

context.beginPath();

context.arc(ball.x,ball.y,ball.radius,0,Math.PI*2,true);

context.closePath();

context.fill();

if (ball.x > theCanvas.width || ball.x < 0 ) {

ball.angle = 180 - ball.angle;

updateBall(ball);

} else if (ball.y > theCanvas.height || ball.y < 0) {

ball.angle = 360 - ball.angle;

updateBall(ball);

}

Bouncing Off Walls | 217

}

function updateBall(ball) {

ball.radians = ball.angle * Math.PI/ 180;

ball.xunits = Math.cos(ball.radians) * ball.speed;

ball.yunits = Math.sin(ball.radians) * ball.speed;

}

var numBalls = 500 ;

var maxSize = 8;

var minSize = 5;

var maxSpeed = maxSize+5;

var balls = new Array();

var tempBall;

var tempX;

var tempY;

var tempSpeed;

var tempAngle;

var tempRadius;

var tempRadians;

var tempXunits;

var tempYunits;

theCanvas = document.getElementById("canvasOne");

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

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

tempRadius = Math.floor(Math.random()*maxSize)+minSize;

tempX = tempRadius*2 + (Math.floor(Math.random()*theCanvas.width)-tempRadius*2);

tempY = tempRadius*2 + (Math.floor(Math.random()*theCanvas.height)-tempRadius*2);

tempSpeed = maxSpeed-tempRadius;

tempAngle = Math.floor(Math.random()*360);

tempRadians = tempAngle * Math.PI/ 180;

tempXunits = Math.cos(tempRadians) * tempSpeed;

tempYunits = Math.sin(tempRadians) * tempSpeed;

tempBall = {x:tempX,y:tempY,radius:tempRadius, speed:tempSpeed, angle:tempAngle,

xunits:tempXunits, yunits:tempYunits}

balls.push(tempBall);

}

function gameLoop() {

window.setTimeout(gameLoop, 20);

drawScreen()

}

gameLoop();

218 | Chapter 5: Math, Physics, and Animation

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