NSAffineTransform Class Reference
Overview
The NSAffineTransform
class provides methods for creating, concatenating, and applying affine transformations.
A transformation specifies how points in one coordinate system are transformed to points in another coordinate system. An affine transformation is a special type of transformation that preserves parallel lines in a path but does not necessarily preserve lengths or angles. Scaling, rotation, and translation are the most commonly used manipulations supported by affine transforms, but shearing is also possible.
Methods for applying affine transformations to the current graphics context and a method for applying an affine transformation to an NSBezierPath
object are described in NSAffineTransform Additions Reference in the Application Kit.
Adopted Protocols
Tasks
Creating an NSAffineTransform Object
Accumulating Transformations

– rotateByDegrees:

– rotateByRadians:

– scaleBy:

– scaleXBy:yBy:

– translateXBy:yBy:

– appendTransform:

– prependTransform:

– invert
Transforming Data and Objects
Accessing the Transformation Structure
Class Methods
transform
Creates and returns a new NSAffineTransform
object initialized to the identity matrix.
Return Value
A new identity transform object. This matrix transforms any point to the same point.
Availability
 Available in OS X v10.0 and later.
See Also
Declared In
NSAffineTransform.h
Instance Methods
appendTransform:
Appends the specified matrix to the receiver’s matrix.
Parameters
 aTransform
The matrix to append to the receiver.
Discussion
This method multiplies the receiver's matrix by the matrix in aTransform and replaces the receiver's matrix with the results. This type of operation is the same as applying the transformations in the receiver followed by the transformations in aTransform.
Availability
 Available in OS X v10.0 and later.
See Also
Declared In
NSAffineTransform.h
initWithTransform:
Initializes the receiver’s matrix using another transform object and returns the receiver.
Parameters
 aTransform
The transform object whose matrix values should be copied to this object.
Return Value
A new transform object initialized with the matrix values of aTransform.
Availability
 Available in OS X v10.0 and later.
See Also
Declared In
NSAffineTransform.h
invert
Replaces the receiver’s matrix with its inverse matrix.
Discussion
Inverse matrices are useful for undoing the effects of a matrix. If a previous point (x,y) was transformed to (x’,y’), inverting the matrix and applying it to point (x’,y’) yields the point (x,y).
You can also use inverse matrices in conjunction with the concat
method to remove the effects of concatenating the matrix to the current transformation matrix of the current graphic context.
Availability
 Available in OS X v10.0 and later.
Declared In
NSAffineTransform.h
prependTransform:
Prepends the specified matrix to the receiver’s matrix.
Parameters
 aTransform
The matrix to prepend to the receiver.
Discussion
This method multiplies the matrix in aTransform by the receiver’s matrix and replaces the receiver’s matrix with the result. This type of operation is the same as applying the transformations in aTransform followed by the transformations in the receiver.
Availability
 Available in OS X v10.0 and later.
See Also
Declared In
NSAffineTransform.h
rotateByDegrees:
Applies a rotation factor (measured in degrees) to the receiver’s transformation matrix.
Parameters
 angle
The rotation angle, measured in degrees.
Discussion
After invoking this method, applying the receiver’s matrix turns the axes counterclockwise about the current origin by angle degrees, in addition to performing all previous transformations.
Availability
 Available in OS X v10.0 and later.
Declared In
NSAffineTransform.h
rotateByRadians:
Applies a rotation factor (measured in radians) to the receiver’s transformation matrix.
Parameters
 angle
The rotation angle, measured in radians.
Discussion
After invoking this method, applying the receiver’s matrix turns the axes counterclockwise about the current origin by angle radians, in addition to performing all previous transformations.
Availability
 Available in OS X v10.0 and later.
Declared In
NSAffineTransform.h
scaleBy:
Applies the specified scaling factor along both x and y axes to the receiver’s transformation matrix.
Parameters
 scale
The scaling factor to apply to both axes. Specifying a negative value has the effect of inverting the direction of the axes in addition to scaling them. A scaling factor of 1.0 scales the content to exactly the same size.
Discussion
After invoking this method, applying the receiver’s matrix modifies the unit lengths along the current x and y axes by a factor of scale, in addition to performing all previous transformations.
Availability
 Available in OS X v10.0 and later.
Declared In
NSAffineTransform.h
scaleXBy:yBy:
Applies scaling factors to each axis of the receiver’s transformation matrix.
Parameters
 scaleX
The scaling factor to apply to the x axis.
 scaleY
The scaling factor to apply to the y axis.
Discussion
After invoking this method, applying the receiver’s matrix modifies the unit length on the x axis by a factor of scaleX and the y axis by a factor of scaleY, in addition to performing all previous transformations. A value of 1.0 for either axis scales the content on that axis to the same size.
Availability
 Available in OS X v10.0 and later.
Declared In
NSAffineTransform.h
setTransformStruct:
Replaces the receiver’s transformation matrix with the specified values.
Parameters
 aTransformStruct
The structure containing the six transform values you want the receiver to use.
Discussion
The matrix is of the form shown in “Transform Mathematics” in Cocoa Drawing Guide, and the sixelement structure defined by the NSAffineTransformStruct
structure is of the form:
{m11, m12, m21, m22, tX, tY} 
The NSAffineTransformStruct
structure is an alternate representation of a transformation matrix that can be used to specify matrix values directly.
Availability
 Available in OS X v10.0 and later.
See Also
Declared In
NSAffineTransform.h
transformPoint:
Applies the receiver’s transform to the specified NSPoint
data type and returns the results.
Parameters
 aPoint
The point in the current coordinate system to which you want to apply the matrix.
Return Value
The resulting point after applying the receiver's transformations.
Availability
 Available in OS X v10.0 and later.
See Also
Declared In
NSAffineTransform.h
transformSize:
Applies the receiver’s transform to the specified NSSize
data type and returns the results.
Parameters
 aSize
The size data to which you want to apply the matrix.
Return Value
The resulting size after applying the receiver's transformations.
Discussion
This method applies the current rotation and scaling factors to aSize; it does not apply translation factors. You can think of this method as transforming a vector whose origin is (0, 0) and whose end point is specified by the value in aSize. After the rotation and scaling factors are applied, this method effectively returns the end point of the new vector.
This method is useful for transforming delta or distance values when you need to take scaling and rotation factors into account.
Availability
 Available in OS X v10.0 and later.
See Also
Declared In
NSAffineTransform.h
transformStruct
Returns the matrix coefficients stored in the receiver’s matrix.
Return Value
The structure containing the receiver's six matrix values.
Discussion
The matrix is of the form shown in “Transform Mathematics” in Cocoa Drawing Guide, and the sixelement structure defined by the NSAffineTransformStruct
structure is of the form:
{m11, m12, m21, m22, tX, tY} 
The NSAffineTransformStruct
structure is an alternate representation of a transformation matrix that can be used to specify matrix values directly.
Availability
 Available in OS X v10.0 and later.
Declared In
NSAffineTransform.h
translateXBy:yBy:
Applies the specified translation factors to the receiver’s transformation matrix.
Parameters
 deltaX
The number of units to move along the x axis.
 deltaY
The number of units to move along the y axis.
Discussion
Subsequent transformations cause coordinates to be shifted by deltaX units along the x axis and by deltaY units along the y axis. Translation factors do not affect NSSize
values, which specify a differential between points.
Availability
 Available in OS X v10.0 and later.
Declared In
NSAffineTransform.h
Constants
NSAffineTransformStruct
This type defines the threebythree matrix that performs an affine transform between two coordinate systems.
typedef struct _NSAffineTransformStruct { CGFloat m11, m12, m21, m22; CGFloat tX, tY; } NSAffineTransformStruct;
Fields
m11 , m12, m21, m22
Elements of a twobytwo matrix for rotation, scale, and shear transformations.
tX, tY
x and y translation elements
Discussion
For more details, see Cocoa Drawing Guide.
Availability
 Available in OS X v10.0 and later.
Declared In
NSAffineTransform.h
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