On-Line Computer Graphics Notes

Transformations

Transformations are one of the primary vehicles used in computer graphics to manipulate objects in three-dimensional space. Their development is motivated by the process of converting coordinates between frames, which results in the generation of a matrix. We can generalize this process and develop matrices that implement various transformations in space.

In these notes, we discuss the basic transformations that are utilized in computer graphics - translation, rotation, scaling - along with several useful complex transformations, including those that work directly with the definition of a camera and the projections to image space.

The reader should read and understand the notes on frames before pursuing these notes.

• How transformations work
• From simple transformations to complex transformations
• Translation
• Scaling
• Basic Rotation
• Shearing
• The frame-to-Cartesian-frame transformation
• The Cartesian-frame-to-frame transformation
• General rotation by frame conversion
• Rotation about an arbitrary axis
• The Camera Transformation
• The Viewing Transformation

This document maintained by Ken Joy Comments to the Author All contents copyright (c) 1996, 1997 Computer Science Department, University of California, Davis All rights reserved.