Zero-Parity Stabbing Information

Details Zero-Parity Stabbing Information Zero-Parity Stabbing Information

1999-06-22

arxiv.org/abs/cs/9906022v1

Proc. Japan Conf. Discrete Comput. Geom. '98, Dec. 1998, 93--97

Computer Science

Computational Geometry

Scientific paper

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.

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