9.4.2. Mapping global coordinates to local coordinates#
We get global coordinates using:
\[
^\text{global}p
~~~ =
~~~ ^\text{global}_\text{local}T
~~~ ^\text{local}p
\]
The reverse transform is literally the inverse of the homogeneous matrix:
\[
^\text{global}_\text{local}T^{-1}
~~~ ^\text{global}p
~~~ =
~~~ ^\text{global}_\text{local}T^{-1}
~~~ ^\text{global}_\text{local}T
~~~ ^\text{local}p
\]
\[
^\text{global}_\text{local}T^{-1}
~~~ ^\text{global}p
~~~
=
~~~ ^\text{local}p
\]