  The extraction of singular patterns is a fundamental problem in theoretical
and practical domains due to the ability of such patterns to detect the
intrinsic characteristics of vector fields. In this study, we propose an
approach for extracting singular patterns from discrete planar vector fields.
Our method involves converting the planar discrete vector field into a
specialized digraph and computing its one-dimensional persistent path homology.
By analyzing the persistence diagram, we can determine the location of
singularity and segment a region of the singular pattern, which is referred to
as a singular polygon. Moreover, the variations of singular patterns can also
be analyzed. The experimental results demonstrate the effectiveness of our
method in analyzing the centers and impact areas of tropical cyclones,
positioning the dip poles from geomagnetic fields, and measuring variations of
singular patterns between vector fields.
