  Spherical polygons used in practice are nice, but the spherical
point-in-polygon problem (SPiP) has long eluded solutions based on the winding
number (wn). That a punctured sphere is simply connected is to blame. As a
workaround, we prove that requiring the boundary of a spherical polygon to
never intersect its antipode is sufficient to reduce its SPiP problem to the
planar, point-in-polygon (PiP) problem, whose state-of-the-art solution uses wn
and does not utilize known interior points (KIP). We refer to such spherical
polygons as boundary antipode-excluding (BAE) and show that all spherical
polygons fully contained within an open hemisphere is BAE. We document two
successful reduction methods, one based on rotation and the other on shearing,
and address a common concern. Both reduction algorithms, when combined with a
wn-PiP algorithm, solve SPiP correctly and efficiently for BAE spherical
polygons. The MATLAB code provided demonstrates scenarios that are problematic
for previous work.
