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Subsections

Slerp_prime

Syntax

Quaternion Slerp_prime(const Quaternion & q0, const Quaternion & q1, 
                       const Real t);

Description

Slerp_prime represent the Slerp derivative. Slerp_prime is not a member function of the class Quaternion. The quaternions $q_0$ and $q_1$ needs to be unit quaternions. It does not necessary returns a unit quaternion.

It is customary to choose the sign $G$ on $q_1$ so that $q_0 \cdot
Gq_1 \geq 0$ (the angle between $q_0$ and $Gq_1$ is acute). This choice avoids extra spinning caused by the interpolated rotations [2]. For unit quaternions Slerp is defined as

$\displaystyle q = \Bigg\{
\begin{array}{cc}
Slerp(q_0, q_1, t)Log(q_0^{-1}q_1) ...
... \\
Slerp(q_0, q_1, t)Log(q_0^{-1}(-q_1)) & \textrm{otherwise} \\
\end{array}$     (2.26)

Return Value

Quaternion



Richard Gourdeau 2004-07-06