Fitting 3D points to a plane or a line

fitting3D.cpp

template<class Vector3>
std::pair<Vector3, Vector3> best_plane_from_points(const std::vector<Vector3> & c)
{
	// copy coordinates to  matrix in Eigen format
	size_t num_atoms = c.size();
	Eigen::Matrix< Vector3::Scalar, Eigen::Dynamic, Eigen::Dynamic > coord(3, num_atoms);
	for (size_t i = 0; i < num_atoms; ++i) coord.col(i) = c[i];

	// calculate centroid
	Vector3 centroid(coord.row(0).mean(), coord.row(1).mean(), coord.row(2).mean());

	// subtract centroid
	coord.row(0).array() -= centroid(0); coord.row(1).array() -= centroid(1); coord.row(2).array() -= centroid(2);

	// we only need the left-singular matrix here
	//  http://math.stackexchange.com/questions/99299/best-fitting-plane-given-a-set-of-points
	auto svd = coord.jacobiSvd(Eigen::ComputeThinU | Eigen::ComputeThinV);
	Vector3 plane_normal = svd.matrixU().rightCols<1>();
	return std::make_pair(centroid, plane_normal);
}

template<class Vector3>
std::pair < Vector3, Vector3 > best_line_from_points(const std::vector<Vector3> & c)
{
	// copy coordinates to  matrix in Eigen format
	size_t num_atoms = c.size();
	Eigen::Matrix< Vector3::Scalar, Eigen::Dynamic, Eigen::Dynamic > centers(num_atoms, 3);
	for (size_t i = 0; i < num_atoms; ++i) centers.row(i) = c[i];

	Vector3 origin = centers.colwise().mean();
	Eigen::MatrixXd centered = centers.rowwise() - origin.transpose();
	Eigen::MatrixXd cov = centered.adjoint() * centered;
	Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eig(cov);
	Vector3 axis = eig.eigenvectors().col(2).normalized();

	return std::make_pair(origin, axis);
}

For the record: I found a sign error into my code!
The functions work properly.
Thanks

I wonder if using SelfAdjointEigenSolver for fitting line is correct.
That is because the document says:

Computes eigenvalues and eigenvectors of selfadjoint matrices.

and centers cannot be selfadjoint unless num_atoms == 3, I think.

For { {0,0,0}, {0,0,1} } and { {0,0,0}, {0,0,0} } the same line {0,0,1} is fit.
Is there a way to distinguish the former, valid input from the latter, degenerate input?