CoreGraphics 学习摘记之 Transforms

The Quartz 2D drawing model defines two completely separate coordinate spaces: user space, which represents the document page, and device space, which represents the native resolution of a device. User space coordinates are floating-point numbers that are unrelated to the resolution of pixels in device space. When you want to print or display your document, Quartz maps user space coordinates to device space coordinates.

You can modify the default user space by operating on the current transformation matrix, or CTM. 

Modifying the Current Transformation Matrix

Before you transform the CTM, you need to save the graphics state so that you can restore it after drawing.

Translation moves the origin of the coordinate space by the amount you specify for the x and y axes. You call the function CGContextTranslateCTM to modify the x and y coordinates of each point by a specified amount. Figure 5-3 shows an image translated by 100 units in the x-axis and 50 units in the y-axis, using the following line of code:

CGContextTranslateCTM (myContext, 100, 50);

Figure 5-3  A translated image

Rotation moves the coordinate space by the angle you specify. You call the function CGContextRotateCTM to specify the rotation angle, in radians. Figure 5-4 shows an image rotated by –45 degrees about the origin, which is the lower left of the window, using the following line of code:

CGContextRotateCTM (myContext, radians(–45.));

The image is clipped because the rotation moved part of the image to a location outside the context. You need to specify the rotation angle in radians.

It’s useful to write a radians routine if you plan to perform many rotations.

#include <math.h>

static inline double radians (double degrees) {return degrees * M_PI/180;}

Figure 5-4  A rotated image

Scaling changes the scale of the coordinate space by the x and y factors you specify, effectively stretching or shrinking the image. The magnitude of the x and y factors governs whether the new coordinates are larger or smaller than the original. In addition, by making the x factor negative, you can flip the coordinates along the x-axis; similarly, you can flip coordinates horizontally, along the y-axis, by making the y factor negative. You call the function CGContextScaleCTM to specify the x and y scaling factors. Figure 5-5 shows an image whose x values are scaled by .5 and whose y values are scaled by .75, using the following line of code:

CGContextScaleCTM (myContext, .5, .75);

Figure 5-5  A scaled image

Concatenation combines two matrices by multiplying them together. You can concatenate several matrices to form a single matrix that contains the cumulative effects of the matrices. You call the function CGContextConcatCTM to combine the CTM with an affine transform. Affine transforms, and the functions that create them, are discussed in “Creating Affine Transforms.”

Another way to achieve a cumulative effect is to perform two or more transformations without restoring the graphics state between transformation calls. Figure 5-6 shows an image that results from translating an image and then rotating it, using the following lines of code:

CGContextTranslateCTM (myContext, w,h);

CGContextRotateCTM (myContext, radians(-180.));

Figure 5-6  An image that is translated and rotated

Creating Affine Transforms

The affine transform functions available in Quartz operate on matrices, not on the CTM. You can use these functions to construct a matrix that you later apply to the CTM by calling the function CGContextConcatCTM. 

Table 5-1  Affine transform functions for translation, rotation, and scaling

Function

Use

CGAffineTransformMakeTranslation

To construct a new translation matrix from x and y values that specify how much to move the origin.

CGAffineTransformTranslate

To apply a translation operation to an existing affine transform.

CGAffineTransformMakeRotation

To construct a new rotation matrix from a value that specifies in radians how much to rotate the coordinate system.

CGAffineTransformRotate

To apply a rotation operation to an existing affine transform.

CGAffineTransformMakeScale

To construct a new scaling matrix from x and y values that specify how much to stretch or shrink coordinates.

CGAffineTransformScale

To apply a scaling operation to an existing affine transform.

Quartz also provides an affine transform function that inverts a matrix, CGAffineTransformInvert. Inversion is generally used to provide reverse transformation of points within transformed objects. Inversion can be useful when you need to recover a value that has been transformed by a matrix: Invert the matrix, and multiply the value by the inverted matrix, and the result is the original value. You usually don’t need to invert transforms because you can reverse the effects of transforming the CTM by saving and restoring the graphics state.

In some situations you might not want to transform the entire space, but just a point or a size. You operate on a CGPoint structure by calling the function CGPointApplyAffineTransform. You operate on a CGSize structure by calling the function CGSizeApplyAffineTransform. You can operate on a CGRect structure by calling the function CGRectApplyAffineTransform. 

Evaluating Affine Transforms

You can determine whether one affine transform is equal to another by calling the function CGAffineTransformEqualToTransform.  The function CGAffineTransformIsIdentity is a useful function for checking whether a transform is the identity transform. The identity transform performs no translation, scaling, or rotation. 

Getting the User to Device Space Transform

Quartz provides a number of convenience functions to transform the following geometries between user space and device space. You might find these functions easier to use than applying the affine transform returned from the function CGContextGetUserSpaceToDeviceSpaceTransform.

• Points. The functions CGContextConvertPointToDeviceSpace and CGContextConvertPointToUserSpace transform a CGPoint data type from one space to the other.

• Sizes. The functions CGContextConvertSizeToDeviceSpace and CGContextConvertSizeToUserSpace transform a CGSize data type from one space to the other.

• Rectangles. The functions CGContextConvertRectToDeviceSpace and CGContextConvertRectToUserSpace transform a CGRect data type from one space to the other.