Geometries

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.

 
• Vector Spaces
• Affine Space
• Euclidean Space
• Cartesian Space
• Summary of Geometric Spaces