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# Simple Canvas Transformations

Transformations on the canvas refer to the mathematical adjustment of physical properties of drawn shapes. The two most commonly used shape transformations are scale and rotate, which we will focus on in this section.

Under the hood, a mathematical matrix operation applies to all transformations. Luckily, you do not need to understand this to use simple Canvas transformations. We will discuss how to apply rotation, translation, and scale transformations by changing simple Canvas properties.

## Rotation and Translation Transformations

An object on the canvas is said to be at the 0 angle rotation when it is facing to the left (this is important if an object has a facing; otherwise, we will use this as a guide). Consequently, if we draw an equilateral box (all four sides are the same length), it doesn’t have an initial facing other than one of the flat sides facing to the left. Let’s draw that box for reference:

```//now draw a red square
context.fillStyle = "red";
context.fillRect(100,100,50,50);```

Now, if we want to rotate the entire canvas 45 degrees, we need to do a couple simple steps. First, we always set the current Canvas transformation to the “identity” (or “reset”) matrix:

`context.setTransform(1,0,0,1,0,0);`

Because Canvas uses radians, not degrees, to specify its transformations, we need to convert our 45-degree angle into radians:

```var angleInRadians = 45 * Math.PI / 180;

### Lesson 1: Transformations are applied to shapes and paths drawn after the setTransform() or other transformation function is called

If you use this code verbatim, you will see a funny result…nothing! This is because the `setTransform()` function call only affects shapes drawn to the canvas after it is applied. We drew our square first, then set the transformation properties. This resulted in no change (or transform) to the drawn square. Example 2-7 gives the code in the correct order to produce the expected result, as illustrated in Figure 2-12.

Example 2-7. Simple rotation transformation

```function drawScreen() {

//now draw a red square
context.setTransform(1,0,0,1,0,0);
var angleInRadians = 45 * Math.PI / 180;
context.fillStyle = "red";
context.fillRect(100,100,50,50);

}```

We get a result this time, but it will probably differ from what you expect. The red box is rotated, but it looks like the canvas was rotated with it. The entire canvas did not rotate, only the portion drawn after the `context.rotate()` function was called. So, why did our square both rotate and move off to the left of the screen? The origin of the rotation was set at the “nontranslated” `0,0` position, resulting in the square rotating from the top left of the entire canvas.

Example 2-8 offers a slightly different scenario: draw a black box first, then set the rotation transform, and finally draw the red box again. See the results in Figure 2-13.

Example 2-8. Rotation and the Canvas state

```function drawScreen() {

//draw black square
context.fillStyle = "black";
context.fillRect(20,20,25,25);

//now draw a red square
context.setTransform(1,0,0,1,0,0);
var angleInRadians = 45 * Math.PI / 180;
context.fillStyle = "red";
context.fillRect(100,100,50,50);

}```

The small black square was unaffected by the rotation, so you can see that only the shapes drawn after the `context.rotate()` function was called were affected.

Again, the red box was moved far off to the left. To reiterate, this occurred because the canvas did not know what origin to use for the rotation. In the absence of an actual translated origin, the `0,0` position setting is applied, resulting in the `context.rotate()` function rotating “around” the `0,0` point, which brings us to our next lesson.

### Lesson 2: We must “translate” the point of origin to the center of our shape to rotate it around its own center

Let’s change Example 2-8 to rotate the red square 45 degrees while keeping it in its current location.

First, we take the numbers we applied to the `fillRect()` function call to create a few variables to hold the red square’s attributes. This is not necessary, but it will make the code much easier to read and change later:

```var x = 100;
var y = 100;
var width = 50;
var height = 50;```

Next, using the `context.translate()` function call, we must change the origin of the canvas to be the center of the red square we want to rotate and draw. This function moves the origin of the canvas to the accepted `x` and `y` locations. The center of our red square will now be the desired top-left corner `x` location for our object (`100`), plus half the width of our object. Using the variables we created to hold attributes of the red square, this would look like:

`x+0.5*width`

Next, we must find the `y` location for the origin translation. This time, we use the `y` value of the top-left corner of our shape and the height of the shape:

`y+.05*height`

The `translate()` function call looks like this:

`context.translate(x+.05*width, y+.05*height)`

Now that we have translated the canvas to the correct point, we can do our rotation. The code has not changed:

`context.rotate(angleInRadians);`

Finally, we need to draw our shape. We cannot simply reuse the same values from Example 2-8 because the canvas origin point has moved to the center of the location where we want to draw our object. You can now consider 125,125 as the starting point for all draw operations. We get `125` for `x` by taking the upper-left corner of the square (`100`) and adding half its width (`25`). We do the same for the `y` origin position. The `translate()` method call accomplishes this.

We will need to draw the object starting with the correct upper-left coordinates for `x` and `y`. We do this by subtracting half the width of our object from the origin `x`, and half the height of our object from the origin `y`:

`context.fillRect(-0.5*width,-0.5*height, width, height);`

Why do we do this? Figure 2-14 illustrates the situation.

Consider that we want to draw our square starting at the top-left corner. If our origin point is at 125,125, the top left is actually 100,100. However, we have translated our origin so the canvas now considers 125,125 to be 0,0. To start our box drawing at the nontranslated canvas, we have to start at –25,–25 on the “translated” canvas.

This forces us to draw our box as though the origin is at 0,0, not 125,125. Therefore, when we do the actual drawing of the box, we must use these coordinates, as shown in Figure 2-15.

In summary, we needed to change the point of origin to the center of our square so it would rotate around that point. But when we draw the square, we need our code to act as though the (125,125) point is actually (0,0). If we had not translated the origin, we could have used the (125,125) point as the center of our square (as in Figure 2-14). Example 2-9 demonstrates how this works, creating the result shown in Figure 2-16.

Example 2-9. Rotation around the center point

```function drawScreen() {

//draw black square
context.fillStyle = "black";
context.fillRect(20,20 ,25,25);

//now draw a red square
context.setTransform(1,0,0,1,0,0);
var angleInRadians = 45 * Math.PI / 180;
var x = 100;
var y = 100;
var width = 50;
var height = 50;
context.translate(x+.5*width, y+.5*height);
context.fillStyle = "red";
context.fillRect(-.5*width,-.5*height , width, height);

}```

Let’s look at one final rotation example. Example 2-10 takes Example 2-9 and simply adds four separate 40×40 squares to the canvas, rotating each one slightly. The result is shown in Figure 2-17.

Example 2-10. Multiple rotated squares

```function drawScreen() {

//now draw a red square
context.setTransform(1,0,0,1,0,0);
var angleInRadians = 45 * Math.PI / 180;
var x = 50;
var y = 100;
var width = 40;
var height = 40;
context.translate(x+.5*width, y+.5*height);
context.fillStyle = "red";
context.fillRect(-.5*width,-.5*height , width, height);

context.setTransform(1,0,0,1,0,0);
var angleInRadians = 75 * Math.PI / 180;
var x = 100;
var y = 100;
var width = 40;
var height = 40;
context.translate(x+.5*width, y+.5*height);
context.fillStyle = "red";
context.fillRect(-.5*width,-.5*height , width, height);

context.setTransform(1,0,0,1,0,0);
var angleInRadians = 90 * Math.PI / 180;
var x = 150;
var y = 100;
var width = 40;
var height = 40;
context.translate(x+.5*width, y+.5*height);
context.fillStyle = "red";
context.fillRect(-.5*width,-.5*height , width, height);
context.setTransform(1,0,0,1,0,0);
var angleInRadians = 120 * Math.PI / 180;
var x = 200;
var y = 100;
var width = 40;
var height = 40;
context.translate(x+.5*width, y+.5*height);
context.fillStyle = "red";
context.fillRect(-.5*width,-.5*height , width, height);

}```

Next, we will examine scale transformations.

## Scale Transformations

The `context.scale()` function takes in two parameters: the first is the scale attribute for the x-axis, and the second is the scale attribute for the y-axis. The value `1` is the normal scale for an object. Therefore, if we want to double an object’s size, we can set both values to `2`. Using the code below in `drawScreen()` produces the red square shown in Figure 2-18:

```context.setTransform(1,0,0,1,0,0);
context.scale(2,2);
context.fillStyle = "red";
context.fillRect(100,100 ,50,50);```

If you test this code, you will find that scale works in a similar manner as rotation. We did not translate the origin of the scale point to double the size of the square; rather, we used the top-left corner of the canvas as the origin point. The result is that the red square appears to move farther down and to the left. What we would like is for the red square to remain in place and to scale from its center. We do this by translating to the center of the square before we scale, and by drawing the square around this center point (just as we did in Example 2-9). Example 2-11 produces the result shown in Figure 2-19.

Example 2-11. Scale from the center point

```function drawScreen() {

//now draw a red square
context.setTransform(1,0,0,1,0,0);
var x = 100;
var y = 100;
var width = 50;
var height = 50;
context.translate(x+.5*width, y+.5*height);
context.scale(2,2);
context.fillStyle = "red";
context.fillRect(-.5*width,-.5*height , width, height);

}```

## Combining Scale and Rotation Transformations

If we want to both scale and rotate an object, Canvas transformations can easily be combined to achieve the desired results (as shown in Figure 2-20). Let’s look in Example 2-12 at how we might combine them by using `scale(2,2)` and `rotate(angleInRadians)` from our previous examples.

Example 2-12. Scale and rotation combined

```function drawScreen() {
context.setTransform(1,0,0,1,0,0);
var angleInRadians = 45 * Math.PI / 180;
var x = 100;
var y = 100;
var width = 50;
var height = 50;
context.translate(x+.5*width, y+.5*height);
context.scale(2,2);
context.fillStyle = "red";
context.fillRect(-.5*width,-.5*height , width, height);

}```

Example 2-13 also combines rotation and scale, this time using a rectangle. Figure 2-21 reveals what it creates.

Example 2-13. Scale and rotate a nonsquare object

```function drawScreen() {

//now draw a red rectangle
context.setTransform(1,0,0,1,0,0);
var angleInRadians = 90 * Math.PI / 180;
var x = 100;
var y = 100;
var width = 100;
var height = 50;
context.translate(x+.5*width, y+.5*height);