return Modernizr.canvas;
}
function canvasApp() {
if (!canvasSupport()) {
return;
}
var pointImage = new Image();
pointImage.src = "point.png";
function  drawScreen () {
context.fillStyle = '#EEEEEE';
context.fillRect(00theCanvas.width, theCanvas.height);
//Box
context.strokeStyle = '#000000';
context.strokeRect(1 1theCanvas.width-2, theCanvas.height-2);
var t = ball.t;
var cx = 3 * (p1.x - p0.x)
var bx = 3 * (p2.x - p1.x- cx;
var ax = p3.x - p0.x - cx - bx;
var cy = 3 * (p1.y - p0.y);
var by = 3 * (p2.y - p1.y- cy;
var ay = p3.y - p0.y - cy - by;
var xt = ax*(t*t*t) + bx*(t*t+ cx*t + p0.x;
var yt = ay*(t*t*t) + by*(t*t+ cy*t + p0.y;
ball.t += ball.speed;
if (ball.t > 1) {
ball.t = 1;
     //draw the points
context.font ="10px sans";
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p0.x,p0.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("0",p0.x-2,p0.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p1.x,p1.y,8,0,Math.PI*2,true);
context.closePath();
Curve and Circular Movement  |  249
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context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("1",p1.x-2,p1.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p2.x,p2.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("2",p2.x-2p2.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p3.x,p3.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("3",p3.x-2p3.y+2);
//Draw points to illustrate path
points.push({x:xt,y:yt});
for (var i = 0i< points.lengthi++) {
context.drawImage(pointImagepoints[i].xpoints[i].y,1,1);
}
context.closePath();
//Draw circle moving
context.fillStyle = "#000000";
context.beginPath();
context.arc(xt,yt,5,0,Math.PI*2,true);
context.closePath();
context.fill();
}
var p0 = {x:60y:10};
var p1 = {x:70y:200};
var p2 = {x:125, y:295};
var p3 = {x:350, y:350};
var ball = {x:0y:0, speed:.01t:0};
var points = new Array();
theCanvas = document.getElementById("canvasOne");
context = theCanvas.getContext("2d");
function gameLoop() {
window.setTimeout(gameLoop20);
250  |  Chapter 5: Math, Physics, and Animation
C# PDF Text Extract Library: extract text content from PDF file in
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drawScreen()
}
gameLoop();
}
</script>
</head>
<body>
<div style="position: absolute; top: 50px; left: 50px;">
<canvas id="canvasOne" width="500" height="500">
Your browser does not support HTML5 Canvas.
</canvas>
</div>
</body>
</html>
Moving an Image
Moving an image on a cubic Bezier curve path is just as easy as moving a circular drawing
object, as we’ll demonstrate in the next two examples. Suppose you are making a game
where bull’s-eyes move across the canvas and the player must shoot at them. You could
use cubic Bezier curve paths to create new and interesting patterns for the bull’s-eyes to
move along.
For this example, we first create a global variable named bullseye, which we will use
to hold the bullseye.png image that we will load to display on the canvas:
var bullseye;
function eventWindowLoaded() {
bullseye = new Image();
bullseye.src = "bullseye.png"
bullseye.onload = eventAssetsLoaded;
}
In canvasApp(), we will create a different path for the curve from the one in the first
example by setting new values for p0p1p2, and p3. Using these values, the bullseye
will move on a parabola-like path. (Figure 5-16 shows the path of the curve.)
var p0 = {x:60y:10};
var p1 = {x:150y:350};
var p2 = {x:300y:375};
var p3 = {x:400y:20};
We also need to create a player object that represents the bull’s-eye on the canvas:
var player = {x:0y:0speed:.01t:0};
In drawImage(), after we calculate txt, and yt, we draw the image on the canvas:
Curve and Circular Movement  |  251
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player.x = xt-bullseye.width/2;
player.y = yt-bullseye.height/2;
context.drawImage(bullseye,player.x,player.y);
Figure 5-16. Moving an image on a cubic Bezier curve path
The rest of Example 5-12 works just like Example 5-11.
Example 5-12. Moving an image
<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>CH5EX12: Moving An Image </title>
<script src="modernizr.js"></script>
<script type="text/javascript">
window.addEventListener('load'eventWindowLoadedfalse);
var bullseye;
252  |  Chapter 5: Math, Physics, and Animation
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C# Project: DLLs for PDF Image Extraction. In Document. C# programming sample for extracting all images from PDF. // Open a document.
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function eventWindowLoaded() {
bullseye = new Image();
bullseye.src = "bullseye.png"
bullseye.onload = eventAssetsLoaded;
}
function eventAssetsLoaded() {
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(00theCanvas.width, theCanvas.height);
//Box
context.strokeStyle = '#000000';
context.strokeRect(1 1theCanvas.width-2, theCanvas.height-2);
var t = player.t;
var cx = 3 * (p1.x - p0.x)
var bx = 3 * (p2.x - p1.x- cx;
var ax = p3.x - p0.x - cx - bx;
var cy = 3 * (p1.y - p0.y);
var by = 3 * (p2.y - p1.y- cy;
var ay = p3.y - p0.y - cy - by;
var xt = ax*(t*t*t) + bx*(t*t+ cx*t + p0.x;
var yt = ay*(t*t*t) + by*(t*t+ cy*t + p0.y;
player.t += player.speed;
if (player.t > 1) {
player.t = 1;
     //draw the points
context.font = "10px sans";
Curve and Circular Movement  |  253
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context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p0.x,p0.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("0",p0.x-2,p0.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p1.x,p1.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("1",p1.x-2,p1.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p2.x,p2.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("2",p2.x-2p2.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p3.x,p3.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("3",p3.x-2p3.y+2);
//Draw points to illustrate path
points.push({x:xt,y:yt});
for (var i = 0i< points.lengthi++) {
context.drawImage(pointImagepoints[i].xpoints[i].y,1,1);
}
context.closePath();
player.x = xt-bullseye.width/2;
player.y = yt-bullseye.height/2;
context.drawImage(bullseye,player.x,player.y);
}
var p0 = {x:60y:10};
var p1 = {x:150, y:350};
254  |  Chapter 5: Math, Physics, and Animation
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var p2 = {x:300y:375};
var p3 = {x:400, y:20};
var player = {x:0y:0speed:.01, t:0};
var points = new Array();
theCanvas = document.getElementById("canvasOne");
context = theCanvas.getContext("2d");
function gameLoop() {
window.setTimeout(gameLoop20);
drawScreen()
}
gameLoop();
}
</script>
</head>
<body>
<div style="position: absolute; top: 50px; left: 50px;">
<canvas id="canvasOne" width="500" height="500">
Your browser does not support HTML5 Canvas.
</canvas>
</div>
</body>
</html>
Creating a Cubic Bezier Curve Loop
You can create some very interesting paths using the four points in a cubic Bezier curve.
One such effect is a loop. To create a loop, you need to make sure the points form an X,
with p0 diagonal from p1, and p2 and p3 on an opposite diagonal from the other two
points. p0 and p3 must be closer to the center of the canvas than p1 or p2. The points
we will use to create this effect in Example 5-13 are as follows:
var p0 = {x:150y:440;
var p1 = {x:450y:10};
var p2 = {x:50y:10};
var p3 = {x:325y:450};
Because it is much easier to show than tell when it comes to cubic Bezier curves, look
at Figure 5-17. It shows what the looping curve looks like when Example 5-13 is executed
in a web browser.
Curve and Circular Movement  |  255
This effect can be created only with the four points of a cubic Bezier
curve. There is also a three-point Bezier curve known as a quadratic
Bezier curve. You cannot create loops or S curves with quadratic Bezier
curves because the three points are not as precise as the four points of
a cubic Bezier curve.
Figure 5-17. Moving an object in a loop using a cubic Bezier curve
Because the code for this example is essentially the same as in Example 5-12 (besides
the four points), we have highlighted in bold the changed code in Example 5-13. We
have done this to show you that—with relatively simple changes—you can create dra‐
matic animation effects using cubic Bezier curves.
Example 5-13. Bezier curve loop
<!doctype html>
<html lang="en">
<head>
256  |  Chapter 5: Math, Physics, and Animation
<meta charset="UTF-8">
<title>CH5EX13: Bezier Curve Loop </title>
<script src="modernizr.js"></script>
<script type="text/javascript">
window.addEventListener('load'eventWindowLoadedfalse);
var bullseye;
function eventWindowLoaded() {
bullseye = new Image();
bullseye.src = "bullseye.png"
bullseye.onload = eventAssetsLoaded;
}
function eventAssetsLoaded() {
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(00theCanvas.width, theCanvas.height);
//Box
context.strokeStyle = '#000000';
context.strokeRect(1 1theCanvas.width-2, theCanvas.height-2);
var t = player.t;
var cx = 3 * (p1.x - p0.x)
var bx = 3 * (p2.x - p1.x- cx;
var ax = p3.x - p0.x - cx - bx;
var cy = 3 * (p1.y - p0.y);
var by = 3 * (p2.y - p1.y- cy;
var ay = p3.y - p0.y - cy - by;
var xt = ax*(t*t*t) + bx*(t*t+ cx*t + p0.x;
var yt = ay*(t*t*t) + by*(t*t+ cy*t + p0.y;
Curve and Circular Movement  |  257
player.t += player.speed;
if (player.t > 1) {
player.t = 1;
}
//draw the points
context.font = "10px sans";
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p0.x,p0.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("0",p0.x-2,p0.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p1.x,p1.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("1",p1.x-2,p1.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p2.x,p2.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("2",p2.x-2p2.y+2);
context.fillStyle = "#FF0000";
context.beginPath();
context.arc(p3.x,p3.y,8,0,Math.PI*2,true);
context.closePath();
context.fill();
context.fillStyle = "#FFFFFF";
context.fillText("3",p3.x-2p3.y+2);
points.push({x:xt,y:yt});
for (var i = 0i< points.lengthi++) {
context.drawImage(pointImagepoints[i].xpoints[i].y,1,1);
}
context.closePath();
player.x = xt-bullseye.width/2;
player.y = yt-bullseye.height/2;
258  |  Chapter 5: Math, Physics, and Animation
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