Continuous Flattening of Orthogonal Polyhedra

被引：4

作者：

Demaine, Erik D. ^{[1
]}

Demaine, Martin L. ^{[1
]}

Itoh, Jin-ichi ^{[2
]}

Nara, Chie ^{[3
]}

机构：

[1] MIT, Comp Sci & Artificial Intelligence Lab, 32 Vassar St, Cambridge, MA 02139 USA

[2] Kumamoto Univ, Fac Educ, Kumamoto 8608555, Japan

[3] Meiji Univ Nakano, Meiji Inst Adv Study Math Sci, Tokyo 1648525, Japan

来源：

DISCRETE AND COMPUTATIONAL GEOMETRY AND GRAPHS, JCDCGG 2015 | 2016年 / 9943卷

关键词：

Folding; Continuous flattening; Orthogonal polyhedra;

D O I：

10.1007/978-3-319-48532-4_8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Can we flatten the surface of any 3-dimensional polyhedron P without cutting or stretching? Such continuous flat folding motions are known when P is convex, but the question remains open for nonconvex polyhedra. In this paper, we give a continuous flat folding motion when the polyhedron P is an orthogonal polyhedron, i.e., when every face is orthogonal to a coordinate axis (x, y, or z). More generally, we demonstrate a continuous flat folding motion for any polyhedron whose faces are orthogonal to the z axis or the xy plane.

引用

页码：85 / 93

页数：9

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