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Geometric Transformations

Construct
matrices for simple geometric transformations.
Combine
simple transformations into more complex ones.

Translation:
Specified by the vector :

Matrix representation of translation

Scale about the origin:
 
Specified by factors .

Rotation:
Counterclockwise about the origin, by angle .

Shear:
Intermixes coordinates according to :

Reflection:
Through a line.

Note:
Vectors map through all these transformations as we want them to.

Readings: Hearn and Baker, 5-1, 5-2, and 5-4; Red book, 5.2, 5.3; White book, 5.1, 5.2


next up previous
Next: Change of Basis Up: Affine Geometry and Previous: Matrix Representation of

CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab

cs488@cgl.uwaterloo.ca