On-Line Computer Graphics Notes
TRANSFORMATION

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 $4 \times 4$ 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

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Computer Science Department
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