Abstract
A convex surface that is flat everywhere but on finitely many smooth curves (or seams) and points is a seam form. We show that the only creases through the flat components of a seam form are either between vertices or tangent to the seams. As corollaries we resolve open problems about certain special seam forms: the flat components of a D-form have no creases at all, and the flat component of a pita-form has at most one crease, between the seam’s endpoints.
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E.D. Demaine partially supported by NSF CAREER award CCF-0347776, DOE grant DE-FG02-04ER25647, and AFOSR grant FA9550-07-1-0538.
G.N. Price partially supported by an NSF Graduate Fellowship.
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Demaine, E.D., Price, G.N. Generalized D-Forms Have No Spurious Creases. Discrete Comput Geom 43, 179–186 (2010). https://doi.org/10.1007/s00454-009-9218-7
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DOI: https://doi.org/10.1007/s00454-009-9218-7