Table of Contents
Transformations
Uses of Transformations
Linear Combinations of Vectors
Bases
Vectors Represented in a Basis
Linear and Affine Maps
Transforming a Vector
Matrices to the Rescue
Basic 2D Transformations
Compound Transformations
Postscript (Interlude)
2D Transformations in Postscript, 1
2D Transformations in Postscript, 2
2D Transformations in Postscript, 3
Homogeneous Coordinates
W!? Where did that come from?
Homogeneous 2D Transformations
Postscript and OpenGL Transformations
Sequences of Transformations
Collapsing a Chain of Matrices.
Implementing Transformation Sequences
Column Vector Convention
Beware: Row Vector Convention
Rigid Body Transformations
Viewport Transformations
3D Transformations
3-D Coordinate Systems
Aside: The Dual Matrix
Euler Angles for 3-D Rotations
Axis-angle rotation
Quaternions
Transforming Normals
Normals Do Not Transform Like Points
Normals Transform Like Planes
Transforming Normals - Cases
Spatial Deformations
Bendy Twisties
Example: Z-Taper
Example: Z-twist
Extensions
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