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DIMACS
2001
15 years 1 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
15 years 1 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
14 years 12 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»
14 years 11 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
14 years 11 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...