Frames
In our basis definition, we will accommodate this
difference between the spaces that points live in and
the spaces that vectors live in. We will call the
spaces that points live in Affine
spaces, and explain why shortly. We will also call
affine-basis-sets frames.
In order to use this new basis, we will need to adjust
our coordinates. Noting that the origin component of
our basis is a point, and remembering from our
previous discussion that it makes no sense to multiply
points by arbitrary scalar values, we arrive at the
following convention for giving points (and vectors)
coordinates:
Graphically, we will distinguish between vector bases
and affine bases (frames) using the convention shown
on the left.
|
|
