VOID Quaternion::slerp( F32 t, const Quaternion& from, const Quaternion& to)
{
const F32 epsilon = 0.00001f;
F32 omega, cosomega, sinomega, scale_from, scale_to ;
Quaternion quatTo(to);
// this is a dot product
cosomega = from._v[0]*to._v[0] + from._v[1]*to._v[1] + from._v[2]*to._v[2] + from._v[3]*to._v[3];
if ( cosomega < 0.0f )
{
cosomega = -cosomega;
quatTo = -to;
}
if( (1.0f - cosomega) > epsilon )
{
omega= ::acos(cosomega) ; // 0 <= omega <= Pi (see man acos)
sinomega = ::sin(omega) ; // this sinomega should always be +ve so
// could try sinomega=sqrtf(1-cosomega*cosomega) to avoid a sin()?
scale_from = ::sin((1.0f-t)*omega)/sinomega ;
scale_to = ::sin(t*omega)/sinomega ;
}
else
{
// The ends of the vectors are very close
// we can use simple linear interpolation - no need
// to worry about the "spherical" interpolation
scale_from = 1.0f - t ;
scale_to = t ;
}
*this = (from*scale_from) + (quatTo*scale_to);
}
/// Spherical Linear Interpolation
/// As t goes from 0 to 1, the Quat object goes from "from" to "to"
/// Reference: Shoemake at SIGGRAPH 89
/// See also
/// http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
void ofQuaternion::slerp( float t, const ofQuaternion& from, const ofQuaternion& to ) {
const double epsilon = 0.00001;
double omega, cosomega, sinomega, scale_from, scale_to ;
ofQuaternion quatTo(to);
// this is a dot product
cosomega = from.asVec4().dot(to.asVec4());
if ( cosomega < 0.0 ) {
cosomega = -cosomega;
quatTo = -to;
}
if ( (1.0 - cosomega) > epsilon ) {
omega = acos(cosomega) ; // 0 <= omega <= Pi (see man acos)
sinomega = sin(omega) ; // this sinomega should always be +ve so
// could try sinomega=sqrt(1-cosomega*cosomega) to avoid a sin()?
scale_from = sin((1.0 - t) * omega) / sinomega ;
scale_to = sin(t * omega) / sinomega ;
} else {
/* --------------------------------------------------
The ends of the vectors are very close
we can use simple linear interpolation - no need
to worry about the "spherical" interpolation
-------------------------------------------------- */
scale_from = 1.0 - t ;
scale_to = t ;
}
*this = (from * scale_from) + (quatTo * scale_to);
// so that we get a Vec4
}
