Index: quaternion.h
===================================================================
RCS file: /cvsroot/celestia/celestia/src/celmath/quaternion.h,v
retrieving revision 1.7
diff -r1.7 quaternion.h
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<     static Quaternion<T> slerp(Quaternion<T>, Quaternion<T>, T);
---
>     static Quaternion<T> slerp(const Quaternion<T>&, const Quaternion<T>&, T);
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< //! Spherical interpolation of two unit quaternions
< template<class T> Quaternion<T> Quaternion<T>::slerp(Quaternion<T> q0,
<                                                      Quaternion<T> q1,
---
> /*! Spherical linear interpolation of two unit quaternions. Designed for
>  *  interpolating rotations, so shortest path between rotations will be
>  *  taken.
>  */
> template<class T> Quaternion<T> Quaternion<T>::slerp(const Quaternion<T>& q0,
>                                                      const Quaternion<T>& q1,
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<     T c = dot(q0, q1);
---
>     const double Nlerp_Threshold = 0.99999;
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<     // Because of potential rounding errors, we must clamp c to the domain of acos.
<     if (c > (T) 1.0)
<         c = (T) 1.0;
<     else if (c < (T) -1.0)
<         c = (T) -1.0;
---
>     T cosAngle = dot(q0, q1);
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<     T angle = (T) acos(c);
---
>     // Assuming the quaternions representat rotations, ensure that we interpolate
>     // through the shortest path by inverting one of the quaternions if the
>     // angle between them is negative.
>     Quaternion qstart;
>     if (cosAngle < 0)
>     {
>         qstart = -q0;
>         cosAngle  = -cosAngle;
>     }
>     else
>     {
>         qstart = q0;
>     }
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<     if (abs(angle) < (T) 1.0e-5)
<         return q0;
---
>     // Avoid precision troubles when we're near the limit of acos range and
>     // perform a linear interpolation followed by a normalize when interpolating
>     // very small angles.
>     if (cosAngle > (T) Nlerp_Threshold)
>     {
>         Quaternion<T> q = (1 - t) * qstart + t * q1;
>         q.normalize();
>         return q;
>     }
> 
>     // Below code unnecessary since we've already inverted cosAngle if it's negative.
>     // It will be necessary if we change slerp to not assume that we want the shortest
>     // path between two rotations.
> #if 0
>     // Because of potential rounding errors, we must clamp c to the domain of acos.
>     if (cosAngle < (T) -1.0)
>         cosAngle = (T) -1.0;
> #endif
> 
>     T angle = (T) acos(cosAngle);
>     T interpolatedAngle = t * angle;
> 
>     // qstart and q2 will form an orthonormal basis in the plane of interpolation.
>     Quaternion q2 = q1 - qstart * cosAngle;
>     q2.normalize();
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>     return qstart * (T) cos(interpolatedAngle) + q2 * (T) sin(interpolatedAngle);
> #if 0
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> #endif