Graphics Reference
In-Depth Information
1.2
1
0.8
0.6
0.4
0.2
0
−
1
−
0.5
0
0.5
1
1.5
x
1
√
2
1
√
2
]
T
.
Fig. 8.14.
A trace of the interpolated vectors between [1 0]
T
and [
−
1.2
1
0.8
0.6
0.4
0.2
0
−
1.5
−
1
−
0.5
0
0.5
1
1.5
x
Fig. 8.15.
Interpolating between two vectors 179
◦
apart.
The separating angle
θ
=90
◦
, and the result is shown in Figure 8.16. Note
how the initial length of
V
1
reducesfrom2to1over90
◦
. It is left to the reader
to examine other combinations of vectors. But there is one more application
for this interpolant, and that is with quaternions.
8.4 Interpolating Quaternions
It just so happens that the interpolant used for vectors also works with quater-
nions. Which means that, given two quaternions
q
1
and
q
2
, the interpolated
quaternion
q
is given by
q
=
sin((1
t
)
θ
)
sin(
θ
)
−
q
1
+
sin(
tθ
)
sin(
θ
)
q
2
(8.35)
The interpolant is applied individually to the four terms of the quaternion.
