we map onto
as follows:
or if we ignore the frames,
transforms from modeling coordinates to viewing coordinates.
Note: M is performing both modeling transformation and Model to World change of basis.
\
Get this by transforming World Frame elements represented in old View Frame by .
and we translate one unit relative to the first Model Frame basis vector, then we want to translate by (x,y,z,0) relative to the World Frame.
yields that transformation.
Modeling transformations embodied in matrix M
World-to-View change of basis in matrix V
VM transforms from modeling coordinates to viewing coordinates
If we further transform the View Frame by T relative to the View Frame, then the new change-of-basis matrix V' is given by
If we further transform the model by T relative to the modeling frame, the new modeling transformation M' is given by
Readings: Hearn and Baker, Section 6-2, first part of Section 12-3; Red book, 6.7; White book, 6.6