Polygon reconstruction from visibility information

Reconstruction results attempt to rebuild polygons from visibility information. Reconstruction of a general polygon from its visibility graph is still open and only known to be in PSPACE; thus additional information, such as the ordering of the edges around nodes that corresponds to the order of the visibilities around vertices is frequently added. The first section of this thesis extracts, in o(E) time, the Hamiltonian cycle that corresponds to the boundary of the polygon from the polygon's ordered visibility graph. Also, it converts an unordered visibility graph and Hamiltonian cycle to the ordered visibility graph for that polygon in O(E) time. The secod, and major result is an algorithm to reconstruct an arthogonal polygon that is consistent with the Hamiltonian cylce and visibility stabs of the sides of an unknown polygon. The algorithm uses O(nlogn) time, assuming there are no collinear sides, and )(n2) time otherwise.

Authors

• Jackson, LillAnne Elaine
• University of Lethbridge. Faculty of Arts and Science

• Polygons
• Graph theory
• Dissertations, Academic

Identifier

hdl:10133/41

OAI identifier oai:identifier

oai:opus.uleth.ca:10133/41