---

Transforms

Using Quartz 2D you never have to rewrite your application or write additional code to adjust the output from your application for optimum display on different devices. This is because 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. After you create a graphics context, the CTM is the identity matrix. You can use Quartz transformation functions to modify the CTM and, as a result, modify drawing in user space.

This chapter:

• Provides an overview of the functions you can use to perform transformations

• Shows how to modify the CTM

• Describes how to create an affine transform

• Show how to determine if two transforms are equivalent

• Describes how to obtain the user-to-device-space transform

• Discusses the math behind affine transforms

Contents:

About Quartz Transformation Functions
Modifying the Current Transformation Matrix
Creating Affine Transforms
Evaluating Affine Transforms
Getting the User to Device Space Transform
The Math Behind the Matrices

---