
242 Chapter 4 Scene Graphs
and translation −S
−1
R
T
T,allstoredbyrkInverse. If you were to use rkInverse to
transform a point Y, the result would be
X = R
T
S
−1
Y − S
−1
R
T
T
which is not correct. The storage that
rkInverse provides is for convenience only.
Call the
Inverse function, access the individual components of rkInverse, and then
discard
rkInverse.
The transformation of a plane from model space to world space is also sometimes
necessary. Let the model-space plane be
N
0
.
X = c
0
where N
0
is a unit-length normal vector, c
0
is a constant, and X is any point on
the plane and is specified in model-space coordinates. The inverse transformation
of the point is X = S