**Metric Space:**- Any space
with a
**distance metric***d*(*P*,*Q*) defined on its elements. **Distance Metric:**-
- Metric
*d*(*P*,*Q*) must satisfy the following axioms:-
*d*(*P*,*Q*) = 0 iff*P*=*Q*. -
*d*(*P*,*Q*) =*d*(*Q*,*P*). - .

- Distance is intrinsic to the space, and
*not*a property of the frame.

- Metric
**Euclidean Space:**- Metric is based on a dot (inner) product:
**Note:**-
- Dot product is defined on
*vectors*. - Distance metric is defined on
*points*.

- Dot product is defined on
**Dot product:**-
**Norm:**-
**Angles:**-
**Perpendicularity:**-
Perpendicularity is

*not*an affine concept!

CS488/688: Introduction to Interactive Computer Graphics

University of Waterloo

Computer Graphics Lab