A vortex line, shaped by a zigzag of pinning centers, is described here through a three-dimensional unit cell containing two pinning centers positioned symmetrically with respect to its center. The unit cell is a cube of side L = 12xi, the pinning centers are insulating spheres of radius R, taken within the range 0.2xi to 3.0xi, xi being the coherence length. We calculate the free energy density of these systems in the framework of the Ginzburg-Landau theory.