  Minimal surfaces with planar curvature lines are classical geometric objects,
having been studied since the late 19th century. In this paper, we revisit the
subject from a different point of view. After calculating their metric
functions using an analytical method, we recover the Weierstrass data, and give
clean parametrizations for these surfaces. Then, using these parametrizations,
we show that there exists a single continuous deformation between all minimal
surfaces with planar curvature lines. In the process, we establish the
existence of axial directions for these surfaces.
