2007/07/04 by Joseph O’Rourke, Joseph O'Rourke, O'Rourke, Joseph
Computer Science · Engineering · #Advanced Materials and Mechanics #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Architecture and Computational Design #Computational Geometry (cs.CG) #F.2.2 #FOS: Computer and information sciences #cs.CG
paper · pdf · doi:10.48550/arxiv.0707.0610
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
openalex publication_date 2007/07/04 · arxiv created 2007/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.