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.

Together these types of transformations are known as affine transformations. Affine transformations preserve the straightness of lines while transforming, so that parallel lines stay parallel.

To apply a transformation matrix to a display object, you create a Transform object, set its matrix property to the transformation matrix, and then set the transform property of the display object to the Transform object. Matrix objects are also used as parameters of some methods, such as the following:

  • The draw() method of a BitmapData object
  • The beginBitmapFill() method, beginGradientFill() method, or lineGradientStyle() method of a Graphics object

A transformation matrix object is a 3 x 3 matrix with the following contents:

In traditional transformation matrixes, the u, v, and w properties provide extra capabilities. The Matrix class can only operate in two-dimensional space, so it always assumes that the property values u and v are 0.0, and that the property value w is 1.0. The effective values of the matrix are as follows:

You can get and set the values of all six of the other properties in a Matrix object: a, b, c, d, tx, and ty.

The Matrix class supports the four major types of transformations: translation, scaling, rotation, and skewing. You can set three of these transformations by using specialized methods, as described in the following table:

Each transformation function alters the current matrix properties so that you can effectively combine multiple transformations. To do this, you call more than one transformation function before applying the matrix to its display object target(by using the transform property of that display object).

Use the new Matrix() constructor to create a Matrix object before you can call the methods of the Matrix object.

Constructor

new (a:Float = 1, b:Float = 0, c:Float = 0, d:Float = 1, tx:Float = 0, ty:Float = 0)

Creates a new Matrix object with the specified parameters. In matrix notation, the properties are organized like this:

If you do not provide any parameters to the new Matrix() constructor, it creates an identity matrix with the following values:

In matrix notation, the identity matrix looks like this:

Parameters:

a

The value that affects the positioning of pixels along the x axis when scaling or rotating an image.

b

The value that affects the positioning of pixels along the y axis when rotating or skewing an image.

c

The value that affects the positioning of pixels along the x axis when rotating or skewing an image.

d

The value that affects the positioning of pixels along the y axis when scaling or rotating an image..

tx

The distance by which to translate each point along the x axis.

ty

The distance by which to translate each point along the y axis.

Variables

a:Float

The value that affects the positioning of pixels along the x axis when scaling or rotating an image.

b:Float

The value that affects the positioning of pixels along the y axis when rotating or skewing an image.

c:Float

The value that affects the positioning of pixels along the x axis when rotating or skewing an image.

d:Float

The value that affects the positioning of pixels along the y axis when scaling or rotating an image.

tx:Float

The distance by which to translate each point along the x axis.

ty:Float

The distance by which to translate each point along the y axis.

Methods

clone ():Matrix

Returns a new Matrix object that is a clone of this matrix, with an exact copy of the contained object.

Returns:

A Matrix object.

concat (m:Matrix):Void

Concatenates a matrix with the current matrix, effectively combining the geometric effects of the two. In mathematical terms, concatenating two matrixes is the same as combining them using matrix multiplication.

For example, if matrix m1 scales an object by a factor of four, and matrix m2 rotates an object by 1.5707963267949 radians(Math.PI/2), then m1.concat(m2) transforms m1 into a matrix that scales an object by a factor of four and rotates the object by Math.PI/2 radians.

This method replaces the source matrix with the concatenated matrix. If you want to concatenate two matrixes without altering either of the two source matrixes, first copy the source matrix by using the clone() method, as shown in the Class Examples section.

Parameters:

m

The matrix to be concatenated to the source matrix.

copyColumnFrom (column:Int, vector3D:Vector3D):Void

copyColumnTo (column:Int, vector3D:Vector3D):Void

copyFrom (sourceMatrix:Matrix):Void

copyRowFrom (row:Int, vector3D:Vector3D):Void

copyRowTo (row:Int, vector3D:Vector3D):Void

createBox (scaleX:Float, scaleY:Float, rotation:Float = 0, tx:Float = 0, ty:Float = 0):Void

Includes parameters for scaling, rotation, and translation. When applied to a matrix it sets the matrix's values based on those parameters.

Using the createBox() method lets you obtain the same matrix as you would if you applied the identity(), rotate(), scale(), and translate() methods in succession. For example, mat1.createBox(2,2,Math.PI/4, 100, 100) has the same effect as the following:

Parameters:

scaleX

The factor by which to scale horizontally.

scaleY

The factor by which scale vertically.

rotation

The amount to rotate, in radians.

tx

The number of pixels to translate(move) to the right along the x axis.

ty

The number of pixels to translate(move) down along the y axis.

createGradientBox (width:Float, height:Float, rotation:Float = 0, tx:Float = 0, ty:Float = 0):Void

Creates the specific style of matrix expected by the beginGradientFill() and lineGradientStyle() methods of the Graphics class. Width and height are scaled to a scaleX/scaleY pair and the tx/ty values are offset by half the width and height.

For example, consider a gradient with the following characteristics:

  • GradientType.LINEAR
  • Two colors, green and blue, with the ratios array set to [0, 255]
  • SpreadMethod.PAD
  • InterpolationMethod.LINEAR_RGB

The following illustrations show gradients in which the matrix was defined using the createGradientBox() method with different parameter settings:

Parameters:

width

The width of the gradient box.

height

The height of the gradient box.

rotation

The amount to rotate, in radians.

tx

The distance, in pixels, to translate to the right along the x axis. This value is offset by half of the width parameter.

ty

The distance, in pixels, to translate down along the y axis. This value is offset by half of the height parameter.

deltaTransformPoint (point:Point):Point

Given a point in the pretransform coordinate space, returns the coordinates of that point after the transformation occurs. Unlike the standard transformation applied using the transformPoint() method, the deltaTransformPoint() method's transformation does not consider the translation parameters tx and ty.

Parameters:

point

The point for which you want to get the result of the matrix transformation.

Returns:

The point resulting from applying the matrix transformation.

equals (matrix:Matrix):Bool

identity ():Void

Sets each matrix property to a value that causes a null transformation. An object transformed by applying an identity matrix will be identical to the original.

After calling the identity() method, the resulting matrix has the following properties: a=1, b=0, c=0, d=1, tx=0, ty=0.

In matrix notation, the identity matrix looks like this:

invert ():Matrix

Performs the opposite transformation of the original matrix. You can apply an inverted matrix to an object to undo the transformation performed when applying the original matrix.

rotate (theta:Float):Void

Applies a rotation transformation to the Matrix object.

The rotate() method alters the a, b, c, and d properties of the Matrix object. In matrix notation, this is the same as concatenating the current matrix with the following:

Parameters:

angle

The rotation angle in radians.

scale (sx:Float, sy:Float):Void

Applies a scaling transformation to the matrix. The x axis is multiplied by sx, and the y axis it is multiplied by sy.

The scale() method alters the a and d properties of the Matrix object. In matrix notation, this is the same as concatenating the current matrix with the following matrix:

Parameters:

sx

A multiplier used to scale the object along the x axis.

sy

A multiplier used to scale the object along the y axis.

setTo (a:Float, b:Float, c:Float, d:Float, tx:Float, ty:Float):Void

toString ():String

Returns a text value listing the properties of the Matrix object.

Returns:

A string containing the values of the properties of the Matrix object: a, b, c, d, tx, and ty.

transformPoint (pos:Point):Point

Returns the result of applying the geometric transformation represented by the Matrix object to the specified point.

Parameters:

point

The point for which you want to get the result of the Matrix transformation.

Returns:

The point resulting from applying the Matrix transformation.

translate (dx:Float, dy:Float):Void

Translates the matrix along the x and y axes, as specified by the dx and dy parameters.

Parameters:

dx

The amount of movement along the x axis to the right, in pixels.

dy

The amount of movement down along the y axis, in pixels.