  Everett et al. introduced several varieties of stabbing information for the
lines determined by pairs of vertices of a simple polygon P, and established
their relationships to vertex visibility and other combinatorial data. In the
same spirit, we define the ``zero-parity (ZP) stabbing information'' to be a
natural weakening of their ``weak stabbing information,'' retaining only the
distinction among {zero, odd, even>0} in the number of polygon edges stabbed.
Whereas the weak stabbing information's relation to visibility remains an open
problem, we completely settle the analogous questions for zero-parity
information, with three results: (1) ZP information is insufficient to
distinguish internal from external visibility graph edges; (2) but it does
suffice for all polygons that avoid a certain complex substructure; and (3) the
natural generalization of ZP information to the continuous case of smooth
curves does distinguish internal from external visibility.
