Quaternion to Rotation

template<class Derived>
inline typename QuaternionBase<Derived>::Matrix3
QuaternionBase<Derived>::toRotationMatrix(void) const
{
  // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
  // if not inlined then the cost of the return by value is huge ~ +35%,
  // however, not inlining this function is an order of magnitude slower, so
  // it has to be inlined, and so the return by value is not an issue
  Matrix3 res;

  const Scalar tx  = Scalar(2)*this->x();
  const Scalar ty  = Scalar(2)*this->y();
  const Scalar tz  = Scalar(2)*this->z();
  const Scalar twx = tx*this->w();
  const Scalar twy = ty*this->w();
  const Scalar twz = tz*this->w();
  const Scalar txx = tx*this->x();
  const Scalar txy = ty*this->x();
  const Scalar txz = tz*this->x();
  const Scalar tyy = ty*this->y();
  const Scalar tyz = tz*this->y();
  const Scalar tzz = tz*this->z();

  res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
  res.coeffRef(0,1) = txy-twz;
  res.coeffRef(0,2) = txz+twy;
  res.coeffRef(1,0) = txy+twz;
  res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
  res.coeffRef(1,2) = tyz-twx;
  res.coeffRef(2,0) = txz-twy;
  res.coeffRef(2,1) = tyz+twx;
  res.coeffRef(2,2) = Scalar(1)-(txx+tyy);

  return res;
}