// Make a rotation Quat which will rotate vec1 to vec2
// Generally take adot product to get the angle between these
// and then use a cross product to get the rotation axis
// Watch out for the two special cases of when the vectors
// are co-incident or opposite in direction.
void Quat::makeRotate_original( const Vec3d& from, const Vec3d& to )
{
const value_type epsilon = 0.0000001;
value_type length1 = from.length();
value_type length2 = to.length();
// dot product vec1*vec2
value_type cosangle = from*to/(length1*length2);
if ( fabs(cosangle - 1) < epsilon )
{
//OSG_INFO<<"*** Quat::makeRotate(from,to) with near co-linear vectors, epsilon= "<<fabs(cosangle-1)<<std::endl;
// cosangle is close to 1, so the vectors are close to being coincident
// Need to generate an angle of zero with any vector we like
// We'll choose (1,0,0)
makeRotate( 0.0, 0.0, 0.0, 1.0 );
}
else
if ( fabs(cosangle + 1.0) < epsilon )
{
// vectors are close to being opposite, so will need to find a
// vector orthogonal to from to rotate about.
Vec3d tmp;
if (fabs(from.x())<fabs(from.y()))
if (fabs(from.x())<fabs(from.z())) tmp.set(1.0,0.0,0.0); // use x axis.
else tmp.set(0.0,0.0,1.0);
else if (fabs(from.y())<fabs(from.z())) tmp.set(0.0,1.0,0.0);
else tmp.set(0.0,0.0,1.0);
Vec3d fromd(from.x(),from.y(),from.z());
// find orthogonal axis.
Vec3d axis(fromd^tmp);
axis.normalize();
_v[0] = axis[0]; // sin of half angle of PI is 1.0.
_v[1] = axis[1]; // sin of half angle of PI is 1.0.
_v[2] = axis[2]; // sin of half angle of PI is 1.0.
_v[3] = 0; // cos of half angle of PI is zero.
}
else
{
// This is the usual situation - take a cross-product of vec1 and vec2
// and that is the axis around which to rotate.
Vec3d axis(from^to);
value_type angle = acos( cosangle );
makeRotate( angle, axis );
}
}
// Make a rotation Quat which will rotate vec1 to vec2
// Generally take adot product to get the angle between these
// and then use a cross product to get the rotation axis
// Watch out for the two special cases of when the vectors
// are co-incident or opposite in direction.
void t3Quaternion::makeRotate_original(const t3Vector3f& from, const t3Vector3f& to)
{
const float epsilon = 0.0000001f;
float length1 = from.length();
float length2 = to.length();
// dot product vec1*vec2
float cosangle = from.dot(to) / (length1 * length2);
if(fabs(cosangle - 1) < epsilon)
{
//osg::notify(osg::INFO)<<"*** Quat::makeRotate(from,to) with near co-linear vectors, epsilon= "<<fabs(cosangle-1)<<std::endl;
// cosangle is close to 1, so the vectors are close to being coincident
// Need to generate an angle of zero with any vector we like
// We'll choose (1,0,0)
makeRotate(0.0, 0.0, 0.0, 1.0);
}
else
if(fabs(cosangle + 1.0) < epsilon)
{
// vectors are close to being opposite, so will need to find a
// vector orthongonal to from to rotate about.
t3Vector3f tmp;
if(fabs(from.x) < fabs(from.y))
if(fabs(from.x) < fabs(from.z)) tmp.set(1.0, 0.0, 0.0); // use x axis.
else tmp.set(0.0, 0.0, 1.0);
else if(fabs(from.y) < fabs(from.z)) tmp.set(0.0, 1.0, 0.0);
else tmp.set(0.0, 0.0, 1.0);
t3Vector3f fromd(from.x, from.y, from.z);
// find orthogonal axis.
t3Vector3f axis(fromd.getCrossed(tmp));
axis.normalize();
_v.x = axis[0]; // sin of half angle of PI is 1.0.
_v.y = axis[1]; // sin of half angle of PI is 1.0.
_v.z = axis[2]; // sin of half angle of PI is 1.0.
_v.w = 0; // cos of half angle of PI is zero.
}
else
{
// This is the usual situation - take a cross-product of vec1 and vec2
// and that is the axis around which to rotate.
t3Vector3f axis(from.getCrossed(to));
float angle = acos(cosangle);
makeRotate(angle, axis);
}
}