ABSTRACT
In general, a virtual Three-dimensional (3D) scene is composed of many objects. Each object has its own position and orientation in the scene, which is defined by translation and rotation, respectively. It may also be scaled larger or smaller. Such scaling, rotation, and translation are collectively called the transforms. This chapter presents two-dimensional (2D) transforms and their matrix representations. Then it extends them into 3D. In computer graphics, inverse transforms are encountered quite frequently. Recall that translation does not fall into the linear transform class, which encompasses scaling and rotation. The union of the translation and the linear transform is called the affine transform. The coordinate system used for creating an object is named the object space, which is also called the body space or model space. In contrast, the coordinate system for the entire 3D virtual environment is often called the world space.
