The Matrix class represents a transformation
matrix that determines how to map points from one coordinate space
to another. You can perform various graphical transformations on
a display object by setting the properties of a Matrix object, applying
that Matrix object to the `matrix` property of a
Transform object, and then applying that Transform object as the `transform` property
of the display object. These transformation functions include translation
(*x* and *y* repositioning), rotation, scaling, and skewing.

Although you could define a matrix by directly
adjusting the properties (`a`, `b`, `c`, `d`, `tx`, `ty`)
of a Matrix object, it is easier to use the `createBox()` method.
This method includes parameters that let you directly define the
scaling, rotation, and translation effects of the resulting matrix.
For example, the following code creates a Matrix object that scales
an object horizontally by 2.0, scales it vertically by 3.0, rotates
it by 45°, moving (translating) it 10 pixels to the right, and moving it
20 pixels down:

var matrix:Matrix = new Matrix();
var scaleX:Number = 2.0;
var scaleY:Number = 3.0;
var rotation:Number = 2 * Math.PI * (45 / 360);
var tx:Number = 10;
var ty:Number = 20;
matrix.createBox(scaleX, scaleY, rotation, tx, ty);

You can also adjust the scaling, rotation,
and translation effects of a Matrix object by using the `scale()`, `rotate()`,
and `translate() `methods. Note that these methods
combine with the values of the existing Matrix object. For example,
the following code sets a Matrix object that scales an object by
a factor of 4 and rotates it 60°, since the `scale()` and `rotate()` methods
are called twice:

var matrix:Matrix = new Matrix();
var rotation:Number = 2 * Math.PI * (30 / 360); // 30°
var scaleFactor:Number = 2;
matrix.scale(scaleFactor, scaleFactor);
matrix.rotate(rotation);
matrix.scale(scaleX, scaleY);
matrix.rotate(rotation);
myDisplayObject.transform.matrix = matrix;

To apply a skew transformation to a Matrix
object, adjust its `b` or `c` property. Adjusting
the `b` property skews the matrix vertically, and
adjusting the `c` property skews the matrix horizontally.
The following code skews the `myMatrix` Matrix object
vertically by a factor of 2:

var skewMatrix:Matrix = new Matrix();
skewMatrix.b = Math.tan(2);
myMatrix.concat(skewMatrix);

You can apply a Matrix transformation to
the `transform` property of a display object. For
example, the following code applies a matrix transformation to a display
object named `myDisplayObject`:

var matrix:Matrix = myDisplayObject.transform.matrix;
var scaleFactor:Number = 2;
var rotation:Number = 2 * Math.PI * (60 / 360); // 60°
matrix.scale(scaleFactor, scaleFactor);
matrix.rotate(rotation);
myDisplayObject.transform.matrix = matrix;

The first line sets a Matrix object to the existing transformation
matrix used by the `myDisplayObject `display object
(the `matrix` property of the `transformation` property
of the `myDisplayObject `display object). This way,
the Matrix class methods that you call have a cumulative effect
on the display object’s existing position, scale, and rotation.

Note: The ColorTransform class is also included
in the flash.geometry package. This class is used to set the

`colorTransform` property
of a Transform object. Since it does not apply any geometrical transformation,
it is not discussed, in detail, here. For more information, see
the

ColorTransform class in the

ActionScript 3.0 Reference for the Adobe
Flash Platform.