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var bluepixel = ((pixelX-blueObject.x ) + (pixelY-blueObject.y )

*blueObject.width )*4 + 3 ;

var redpixel = ((pixelX-redObject.x) +

(pixelY-redObject.y)*redObject.width)*4 + 3 ;

if (( blueObject.blueImageData.data [ bluepixel ] !== 0 ) &&

( redObject.redImageData.data[ redpixel ] !== 0 )) {

console.log("pixel collision")

blueObject.dx=0;

redObject.dx=0;

break;

}

function boundingBoxCollide(object1, object2) {

var left1 = object1.x;

var left2 = object2.x;

var right1 = object1.x + object1.width;

var right2 = object2.x + object2.width;

var top1 = object1.y;

var top2 = object2.y;

var bottom1 = object1.y + object1.height;

var bottom2 = object2.y + object2.height;

if (bottom1 < top2) return(false);

if (top1 > bottom2) return(false);

if (right1 < left2) return(false);

if (left1 > right2) return(false);

return(true);

};

function startUp(){

gameLoop();

}

function gameLoop() {

window.setTimeout(gameLoop, 100);

drawScreen();

}

startUp();

Using Pixel Data to Detect Object Collisions | 189

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}

</script>

</head>

<body>

<div>

<canvas id="canvas" width="400" height="400" style="position: absolute; top:

50px; left: 50px;">

Your browser does not support the HTML 5 Canvas.

</canvas>

</div>

</body>

</html>

What’s Next?

We covered quite a lot in this chapter, evolving from simply loading images to animating

and rotating them. We looked at using tile sheets and tile maps, and then we built some

useful applications with Canvas image functions and capabilities. In the first four chap‐

ters, we’ve covered most of what Canvas offers as a drawing surface. In the next six

chapters, we will cover more advanced topics, such as applying 2D physics to Canvas

objects, integrating the HTML5 <video> and <audio> tags with the <canvas> tag, cre‐

ating games, and looking at some libraries and features that we can use to extend the

functionality of HTML5 Canvas—even creating applications for mobile devices.

190 | Chapter 4: Images on the Canvas

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CHAPTER 5

Math, Physics, and Animation

Impressing users with animation involves more than knowing how to move objects—

you also need to know how to move them in ways that users expect. That requires

understanding some common algorithms for math-based movement and physics in‐

teractions. Simple movement based on points and vectors provides a foundation, and

then it’s time to create objects that bounce off walls and one another with a bit of friction

added to the mix. After that, we will step back and talk about movement that goes beyond

straight lines: circles, spirals, and complex Bezier curves. We will then cover how adding

gravity can affect movement. Finally, we will finish this chapter by discussing easing

and how it can have a positive effect on math-based animations.

Moving in a Straight Line

The simplest kinds of animations—moving objects in a straight line up and down the

canvas—can take the form of adding a constant value to the x or y position of an object

every time it is drawn.

So, to animate graphics, we will need to create an interval and then call a function that

will display our updated graphics on every frame. Each example in this chapter will be

built in a similar way. The first step is to set up the necessary variables in our canva

sApp() function. For this first, basic example of movement, we will create a variable

named speed. We will apply this value to the y position of our object on every call to

drawScreen(). The x and y variables set up the initial position of the object (a filled

circle) that we will move down the canvas:

var speed = 5;

var y = 10;

var x = 250;

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After we create the variables, we set up an interval to call the drawScreen() function

every 20 milliseconds. This is the loop we need to update our objects and move them

around the canvas:

function gameLoop() {

window.setTimeout(gameLoop, 20);

drawScreen()

}

gameLoop();

In the drawScreen() function, we update the value of y by adding to it the value of the

speed variable:

y += speed;

Finally, we draw our circle on the canvas. We position it using the current values of x

and y. Because y is updated every time the function is called, the circle effectively moves

down the canvas:

context.fillStyle = "#000000";

context.beginPath();

context.arc(x,y,15,0,Math.PI*2,true);

context.closePath();

context.fill();

To move the circle up the screen, we would make speed a negative number. To move it

left or right, we would update the x instead of the y variable. To move the circle diago‐

nally, we would update both x and y at the same time.

Example 5-1 shows the complete code needed to create basic movement in a straight

line.

Example 5-1. Moving in a straight line

<!doctype html>

<head>

<title>CH5EX1: Moving In A Straight Line</title>

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

function eventWindowLoaded() {

canvasApp();

}

function canvasSupport () {

return Modernizr.canvas;

}

function canvasApp() {

192 | Chapter 5: Math, Physics, and Animation

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if (!canvasSupport()) {

return;

}

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);

// Create ball

y += speed;

context.fillStyle = "#000000";

context.beginPath();

context.arc(x,y,15,0,Math.PI*2,true);

context.closePath();

context.fill();

}

theCanvas = document.getElementById("canvasOne");

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

var speed = 5;

var y = 10;

var x = 250;

function gameLoop() {

window.setTimeout(gameLoop, 20);

drawScreen()

}

gameLoop();

}

</script>

</head>

<body>

Your browser does not support HTML5 Canvas.

</canvas>

</div>

Moving in a Straight Line | 193

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</body>

</html>

The basic structure of the HTML for all the examples in this chapter

will follow these rules. In the interest of saving space, we will refrain

from discussing this code further, but it will appear in the examples

provided.

Moving Between Two Points: The Distance of a Line

Movement based on constant changes to the x or y position of an object works well for

some applications, but at other times you will need to be more precise. One such instance

is when you need to move an object from point A to point B at a constant rate of speed.

In mathematics, a common way to find the length of an unknown oline is to use the

Pythagorean theorem:

+ B

= C

In this equation, C is the unknown side of a triangle when A and B are already known.

However, we need to translate this equation into something that we can use with the

points and pixels we have available on the canvas.

This is a good example of using a mathematical equation in your application. In this

case, we want to find the distance of a line, given two points. In English, this equation

reads like this:

The distance equals the square root of the square of the difference between the x value

of the second point minus the x value of the first point, plus the square of the difference

between the y value of the second point minus the y value of the first point.

You can see this in Figure 5-1. It’s much easier to understand in this format.

Figure 5-1. Distance equation

In the second example, we need to create some new variables in the canvasApp()

function. We will still use a speed variable, just like in the first example, but this time

we set it to 5, which means it will move 5 pixels on every call to drawScreen():

var speed = 5;

194 | Chapter 5: Math, Physics, and Animation

We then create a couple of dynamic objects—each with an x and a y property—that will

represent the two points we want to move between. For this example, we will move our

circle from 20,250 to 480,250:

var p1 = {x:20,y:250};

var p2 = {x:480,y:250};

Now it is time to re-create the distance equation in Figure 5-1. The first step is to calculate

the differences between the second and first x and y points:

var dx = p2.x - p1.x;

var dy = p2.y - p1.y;

To determine the distance value, we square both the values we just created, add them,

and then use the Math.sqrt()function to get the square root of the number:

var distance = Math.sqrt(dx*dx + dy*dy);

Next, we need to use that calculated distance value in a way that will allow us to move

an object a uniform number of pixels from p1 to p2. The first thing we do is calculate

how many moves (calls to drawScreen()) it will take the object to move at the given

value of speed. We get this by dividing the distance by the speed:

var moves = distance/speed;

Then we find the distance to move both x and y on each call to drawScreen(). We name

these variables xunits and yunits:

var xunits = (p2.x - p1.x)/moves;

var yunits = (p2.y - p1.y)/moves;

Finally, we create a dynamic object named ball that holds the x and y value of p1:

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

And create the interval to call drawScreen() every 33 milliseconds:

function gameLoop() {

window.setTimeout(gameLoop, 20);

drawScreen()

}

gameLoop();

Drawing the ball

Let’s draw the ball on the screen. In the drawScreen() function, we first check to see

whether the moves variable is greater than zero. If so, we are still supposed to move the

ball across the screen because we have not yet reached p2. We decrement moves

(moves--) and then update the x and y properties of the ball object by adding the xunits

to x and yunits to y:

if (moves > 0 ) {

moves--;

Moving in a Straight Line | 195

ball.x += xunits;

ball.y += yunits;

}

Now that our values have been updated, we simply draw the ball at the x and y coordi‐

nates specified by the x and y properties, and we are done—that is, until drawScreen()

is called 33 milliseconds later:

context.fillStyle = "#000000";

context.beginPath();

context.arc(ball.x,ball.y,15,0,Math.PI*2,true);

context.closePath();

context.fill();

Let’s try the example by executing it in a web browser. You can find it in the code

distribution as CH5EX2.html, or you can type in Example 5-2. Watch the ball move

from one point to another. If you update the x and y values of each point, or change the

speed, watch the results. You can do a lot with this very simple example.

Tracing movement: A path of points

For many of the examples in this chapter, we will create a way to trace an object’s move‐

ment on the canvas by drawing points to show its path. We have done this to help

illustrate how objects move. However, in the real world, you would need to remove this

functionality so that your application will perform to its potential. This is the only place

we will discuss this code, so if you see it listed in any of the later examples in this chapter,

refer back to this section to refresh your memory on its functionality.

First, we create an array in canvasApp() to hold the set of points we will draw on the

canvas:

var points = new Array();

Next, we load a black 4×4 pixel image, point.png, which we will use to display the points

on the canvas:

var pointImage = new Image();

pointImage.src = "point.png";

Whenever we calculate a point for an object we will move, we push that point into the

points array:

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

On each call to drawScreen(), we draw the set of points we have put into the points

array. Remember, we have to redraw every point each time because the canvas is an

immediate-mode display surface that does not retain any information about the images

drawn onto it:

196 | Chapter 5: Math, Physics, and Animation

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

context.drawImage(pointImage, points[i].x, points[i].y,1,1);

}

In Figure 5-2, you can see what the ball looks like when moving on a line from one point

to another and also what the points path looks like when it is drawn.

This is the only time in this chapter where we will discuss the points

path in depth. If you see the points being drawn, you will know how

and why we have added that functionality. You should also have enough

information to remove the code when necessary.

Figure 5-2. A ball moving from one point to another along the line, with the points

drawn for illustration

Example 5-2 is the full code listing for CH5EX2.html.

Example 5-2. Moving on a simple line

<!doctype html>

<head>

Moving in a Straight Line | 197

<title>CH5EX2: Moving On A Simple Line</title>

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

function eventWindowLoaded() {

canvasApp();

}

function canvasSupport () {

return Modernizr.canvas;

}

function canvasApp() {

if (!canvasSupport()) {

return;

}

var pointImage = new Image();

pointImage.src = "point.png";

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);

// Create ball

if (moves > 0 ) {

moves--;

ball.x += xunits;

ball.y += yunits;

}

//Draw points to illustrate path

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

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

context.drawImage(pointImage, points[i].x, points[i].y,1,1);

}

context.fillStyle = "#000000";

context.beginPath();

context.arc(ball.x,ball.y,15,0,Math.PI*2,true);

198 | Chapter 5: Math, Physics, and Animation

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