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- Represent
-
points and vectors as
matrices. In 2D,
- This is a Shorthand:
- Coordinates are
specified relative to a frame
:
- Technically,
-
- Should write the
as
.
- The frame F should note what space it's in.
- Usually,
- we're lazy and let '
' denote both
- The point
- Its matrix representation relative to an understood frame.
- Transformations:
-
-
is the frame of the domain,
-
is the frame of the range.
Then ...
-
transforms to
.
- Can also read this as
.
-
is said to be the matrix representation of T
relative to
and
.
- First column of
is
representation of
in
.
- Second column of
is
representation of
in
.
- Third column of
is
representation of
in
.
CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab
cs488@cgl.uwaterloo.ca