CGAffineTransform Reference

Discussion

Concatenation combines two affine transformation matrices by multiplying them together. You might perform several concatenations in order to create a single affine transform that contains the cumulative effects of several transformations.

Note that matrix operations are not commutative—the order in which you concatenate matrices is important. That is, the result of multiplying matrix t1 by matrix t2 does not necessarily equal the result of multiplying matrix t2 by matrix t1.

Discussion

Inversion is generally used to provide reverse transformation of points within transformed objects. Given the coordinates (x,y), which have been transformed by a given matrix to new coordinates (x’,y’), transforming the coordinates (x’,y’) by the inverse matrix produces the original coordinates (x,y).

Discussion

This function creates a CGAffineTransform structure that represents a new affine transformation matrix, which you can use (and reuse, if you want) to transform a coordinate system. The matrix takes the following form:

Because the third column is always (0,0,1), the CGAffineTransform data structure returned by this function contains values for only the first two columns.

If you want only to transform an object to be drawn, it is not necessary to construct an affine transform to do so. The most direct way to transform your drawing is by calling the appropriate CGContext function to adjust the current transformation matrix. For a list of functions, see CGContext Reference.

Discussion

This function creates a CGAffineTransform structure, which you can use (and reuse, if you want) to rotate a coordinate system. The matrix takes the following form:

The actual direction of rotation is dependent on the coordinate system orientation of the target platform, which is different in iOS and OS X. Because the third column is always (0,0,1), the CGAffineTransform data structure returned by this function contains values for only the first two columns.

These are the resulting equations that Quartz uses to apply the rotation to a point (x, y):

If you want only to rotate an object to be drawn, it is not necessary to construct an affine transform to do so. The most direct way to rotate your drawing is by calling the function CGContextRotateCTM.

Discussion

This function creates a CGAffineTransform structure, which you can use (and reuse, if you want) to scale a coordinate system. The matrix takes the following form:

Because the third column is always (0,0,1), the CGAffineTransform data structure returned by this function contains values for only the first two columns.

These are the resulting equations that Quartz uses to scale the coordinates of a point (x,y):

If you want only to scale an object to be drawn, it is not necessary to construct an affine transform to do so. The most direct way to scale your drawing is by calling the function CGContextScaleCTM.

Discussion

This function creates a CGAffineTransform structure. which you can use (and reuse, if you want) to move a coordinate system. The matrix takes the following form:

Because the third column is always (0,0,1), the CGAffineTransform data structure returned by this function contains values for only the first two columns.

These are the resulting equations Quartz uses to apply the translation to a point (x,y):

If you want only to move the location where an object is drawn, it is not necessary to construct an affine transform to do so. The most direct way to move your drawing is by calling the function CGContextTranslateCTM.

Discussion

You use this function to create a new affine transformation matrix by adding a rotation value to an existing affine transform. The resulting structure represents a new affine transform, which you can use (and reuse, if you want) to rotate a coordinate system.

The actual direction of rotation is dependent on the coordinate system orientation of the target platform, which is different in iOS and OS X.

Discussion

You use this function to create a new affine transformation matrix by adding scaling values to an existing affine transform. The resulting structure represents a new affine transform, which you can use (and reuse, if you want) to scale a coordinate system.

Discussion

You use this function to create a new affine transform by adding translation values to an existing affine transform. The resulting structure represents a new affine transform, which you can use (and reuse, if you want) to move a coordinate system.

Discussion

Because affine transforms do not preserve rectangles in general, the function CGRectApplyAffineTransform returns the smallest rectangle that contains the transformed corner points of the rect parameter. If the affine transform t consists solely of scaling and translation operations, then the returned rectangle coincides with the rectangle constructed from the four transformed corners.

Discussion

In Quartz 2D, an affine transformation matrix is used to rotate, scale, translate, or skew the objects you draw in a graphics context. The CGAffineTransform type provides functions for creating, concatenating, and applying affine transformations.

In Quartz, affine transforms are represented by a 3 by 3 matrix:

Because the third column is always (0,0,1), the CGAffineTransform data structure contains values for only the first two columns.

Conceptually, a Quartz affine transform multiplies a row vector representing each point (x,y) in your drawing by this matrix, producing a vector that represents the corresponding point (x’,y’):

Given the 3 by 3 matrix, Quartz uses the following equations to transform a point (x, y) in one coordinate system into a resultant point (x’,y’) in another coordinate system.

The matrix thereby “links” two coordinate systems—it specifies how points in one coordinate system map to points in another.

Note that you do not typically need to create affine transforms directly. If you want only to draw an object that is scaled or rotated, for example, it is not necessary to construct an affine transform to do so. The most direct way to manipulate your drawing—whether by movement, scaling, or rotation—is to call the functions CGContextTranslateCTM, CGContextScaleCTM, or CGContextRotateCTM, respectively. You should generally only create an affine transform if you want to reuse it later.