
774 Chapter 17 Rotations
17.2.9 Interpolation
Quaternions are quite amenable to interpolation. Once again, the standard operation
that is used is spherical linear interpolation (slerp). Given quaternions p and q with
acute angle θ between them, slerp is defined as
slerp(t; p, q) = p(p
∗
q)
t
for t ∈ [0, 1]. Note that slerp(0; p, q) = p and slerp(1; p, q) = q. It is not immedi-
ately clear how to compute slerp in the form specified by the definition. An equivalent
definition is
slerp(t; p, q) =
sin((1 − t)θ)p + sin (t θ )q
sin(θ)
If p and q are thought of as points on a unit circle, this formula is a parameterization
of the shortest arc between them. If a particle ...