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DIMACS
2001
13 years 8 months ago
Combinatorial Roadmaps in Configuration Spaces of Simple Planar Polygons
Abstract. One-degree-of-freedom mechanisms induced by minimum pseudotriangulations with one convex hull edge removed have been recently introduced by the author to solve a family o...
Ileana Streinu
CCCG
2006
13 years 8 months ago
Polygon Reconstruction from Line Cross-Sections
We study the following geometric probing problem: Reconstruct a planar polygon from its intersections with a collection of arbitrarily-oriented "cutting" lines. We propo...
Gill Barequet, Craig Gotsman, Avishay Sidlesky
COMGEO
2008
ACM
13 years 7 months ago
Unfolding Manhattan Towers
We provide an algorithm for unfolding the surface of any orthogonal polyhedron that falls into a particular shape class we call Manhattan Towers, to a nonoverlapping planar orthog...
Mirela Damian, Robin Y. Flatland, Joseph O'Rourke
CORR
2007
Springer
100views Education» more  CORR 2007»
13 years 7 months ago
Unfolding Convex Polyhedra via Quasigeodesics
We show that cutting shortest paths from every vertex of a convex polyhedron to a simple closed quasigeodesic, and cutting all but a short segment of the quasigeodesic, unfolds th...
Jin-ichi Itoh, Joseph O'Rourke, Costin Vîlcu
GC
2007
Springer
13 years 7 months ago
Decompositions, Partitions, and Coverings with Convex Polygons and Pseudo-Triangles
We propose a novel subdivision of the plane that consists of both convex polygons and pseudotriangles. This pseudo-convex decomposition is significantly sparser than either conve...
Oswin Aichholzer, Clemens Huemer, S. Kappes, Betti...