Topological configurations of the magnetic field play key roles in the
evolution of space plasmas. This paper presents a novel algorithm that
can estimate the quadratic magnetic gradient as well as the complete
geometrical features of magnetic field lines, based on magnetic field
and current density measurements by a multiple spacecraft constellation
at 4 or more points. The explicit estimators for the linear and
quadratic gradients, the apparent velocity of the magnetic structure and
the curvature and torsion of the magnetic field lines can be obtained
with well predicted accuracies. The feasibility and accuracy of the
method have been verified with thorough tests. The algorithm has been
successfully applied to exhibit the geometrical structure of a flux
rope. This algorithm has wide applications for uncovering a variety of
magnetic configurations in space plasmas.