Zero-Parity Stabbing Information
<|reference_start|>Zero-Parity Stabbing Information: 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.<|reference_end|>
@article{o'rourke1999zero-parity,
    title={Zero-Parity Stabbing Information},
    author={Joseph O'Rourke and Irena Pashchenko},
    journal={Proc. Japan Conf. Discrete Comput. Geom. '98, Dec. 1998, 93--97},
    year={1999},
    archivePrefix={arXiv},
    eprint={cs/9906022},
    primaryClass={cs.CG cs.DM}
}