Affine Space

Definition:

Set of Vectors and a Set of Points

• Vectors form a vector space.
• Points can be combined with vectors to make new points:
  with and .

Frame:

An affine extension of a basis:
Requires a vector basis plus a point (the origin):

Dimension:

The dimension of an affine space is the same as that of .

Note:

• All other point operations are just variations on the operation.
• No distinguished origin
• No notion of distances or angles.
• Most of what we do in graphics is affine.