Next: Summary of Geometric
Up: Geometries
Previous: Euclidean Space
 Cartesian Space:

An Euclidean space with an standard orthonormal frame
.
 Orthogonal:

.
 Normal:
 .
 Notation:
 Specify the Standard Frame as
.
 As defined previously, points and vectors are
 Different objects.
 Have different operations.
 Behave differently under transformation.
 Coordinates:
 Use an ``an extra coordinate'':
 0 for vectors: means
 1 for points: means
 Later we'll see other ways to view the fourth coordinate.

Coordinates have no meaning without an associated frame!
 Sometimes we'll omit the extra coordinate ...
point or vector by context.
 Sometimes we may not state the frame ...
the Standard Frame is assumed.
CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab
cs488@cgl.uwaterloo.ca