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Full-Text Articles in Geometry and Topology

Zero-Parity Stabbing Information, Joseph O'Rourke, Irena Pashchenko Jun 1999

Zero-Parity Stabbing Information, Joseph O'Rourke, Irena Pashchenko

Computer Science: Faculty Publications

Everett et al. [EHN96, EHN97] 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 …


Locked And Unlocked Polygonal Chains In 3d, Therese Biedl, Erik D. Demaine, Martin L. Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Mark Overmars, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides Jan 1999

Locked And Unlocked Polygonal Chains In 3d, Therese Biedl, Erik D. Demaine, Martin L. Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Mark Overmars, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides

Computer Science: Faculty Publications

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a …


Computational Geometry Column 35, Joseph O'Rourke Jan 1999

Computational Geometry Column 35, Joseph O'Rourke

Computer Science: Faculty Publications

The subquadratic algorithm of Kapoor for finding shortest paths on a polyhedron is described.


Computational Geometry Column 33, Joseph O'Rourke Jun 1998

Computational Geometry Column 33, Joseph O'Rourke

Computer Science: Faculty Publications

Several recent SIGGRAPH papers on surface simplification are described.


Computational Geometry Column 34, Pankaj K. Agarwal, Joseph O'Rourke Jan 1998

Computational Geometry Column 34, Pankaj K. Agarwal, Joseph O'Rourke

Computer Science: Faculty Publications

Problems presented at the open-problem session of the 14th Annual ACM Symposium on Computational Geometry are listed.


Computational Geometry Column 32, Joseph O'Rourke Oct 1997

Computational Geometry Column 32, Joseph O'Rourke

Computer Science: Faculty Publications

The proof of Dey's new k-set bound is illustrated.