Geometry provides a mathematical foundation for much of computer graphics:

- Geometric Spaces: Vector, Affine, Euclidean, Cartesian, Projective
- Affine Geometry
- Affine Transformations
- Perspective
- Projective Transformations
- Matrix Representation of Transformations
- Viewing Transformations
- Quaternions and Orientation

You probably learned geometry relative to coordinate axes,
with points and vectors being given by (*x*,*y*,*z*) triples.

- You ``move that far'' in each coordinate (away from the origin) to find a point.
- Points are fixed while vectors are free to move anywhere.
- This approach glosses over mathematical details...

Formally, there is a hierarchy of geometric spaces, defined by

- Sets of objects.
- Operations on those objects.
- Invariants.

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab