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Improved Algorithms for Grid-Unfolding Orthogonal Polyhedra.
- Source :
-
International Journal of Computational Geometry & Applications . Mar-Jun2017, Vol. 27 Issue 1/2, p33-56. 24p. - Publication Year :
- 2017
-
Abstract
- An unfolding of a polyhedron is a single connected planar piece without overlap resulting from cutting and flattening the surface of the polyhedron. Even for orthogonal polyhedra, it is known that edge-unfolding, i.e., cuts are performed only along the edges of a polyhedron, is not sufficient to guarantee a successful unfolding in general. However, if additional cuts parallel to polyhedron edges are allowed, it has been shown that every orthogonal polyhedron of genus zero admits a grid-unfolding with quadratic refinement. Using a new unfolding technique developed in this paper, we improve upon the previous result by showing that linear refinement suffices. For 1-layer orthogonal polyhedra of genus , we show a grid-unfolding algorithm using only additional cuts, affirmatively answering an open problem raised in a recent literature. Our approach not only requires fewer cuts but yields much simpler algorithms. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ORTHOGONAL surfaces
*POLYHEDRA
*ALGORITHMS
*PROBLEM solving
*COMPUTATIONAL geometry
Subjects
Details
- Language :
- English
- ISSN :
- 02181959
- Volume :
- 27
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- International Journal of Computational Geometry & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 125144972
- Full Text :
- https://doi.org/10.1142/S0218195917600032