2D Matrix Transformations Lecture Slides

Translations again
We could do this:
p ' = B(
Ap + t)
= BAp + Bt = Cp + u
Ugly and awkward
Some systems do it anyhow.
Every transformation would be a matrix and a
vector…
Homogeneous coordinates
Take a vector that represents a point and
append a 1 at the end
p
p =
p
x
y
p
p~
=
p
1
x
y
Homogeneous translation
1
p
~ ' =
0
0
0
1
0
p
~ ~
' = Ap
~
tx
p
t
y
p
1
1
x
y
The tildes are for clarity. If only using homogeneous coordinates,
we would omit them.
Other transformations
~ A
A =
0
0
Now everything looks the same…
0
0
1
Composing matrices
Example
When we rotate, we rotate about the origin
Same for scale
How could we do it about another point
versus
4