Unfolding Orthogonal Terrains
Computational Geometry
2007-07-12 v4
Abstract
It is shown that every orthogonal terrain, i.e., an orthogonal (right-angled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single non-overlapping piece by cutting along grid edges defined by coordinate planes through every vertex.
Cite
@article{arxiv.0707.0610,
title = {Unfolding Orthogonal Terrains},
author = {Joseph O'Rourke},
journal= {arXiv preprint arXiv:0707.0610},
year = {2007}
}
Comments
7 pages, 7 figures, 5 references. First revision adds Figure 7, and improves Figure 6. Second revision further improves Figure 7, and adds one clarifying sentence. Third corrects label in Figure 7. Fourth revision corrects a sentence in the conclusion about the class of shapes now known to be grid-unfoldable