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Continuous Blooming of Convex Polyhedra
Published 2011“…We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. …”
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Refold rigidity of convex polyhedra
Published 2015“…If the unfolding is restricted to cut only edges of the polyhedron, we identify several polyhedra that are “edge-refold rigid” in the sense that each of their unfoldings may only fold back to the original. …”
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On packing and covering polyhedra in infinite dimensions
Published 2018“…We consider the natural generalizations of packing and covering polyhedra in infinite dimensions, and study issues related to duality and integrality of extreme points for these sets. …”
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Embedding Formulations and Complexity for Unions of Polyhedra
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A Heterarchical Program for Recognition of Polyhedra
Published 2004“…Recognition of polyhedra by a heterarchical program is presented. …”
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An Approach to Three-Dimensional Decomposition and Description of Polyhedra
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Capacitated Trees, Capacitated Routing, and Associated Polyhedra
Published 2004“…For each of these problems, and for a forest relaxation of the minimal spanning tree problem, we introduce a number of new valid inequalities and specify conditions for ensuring when these inequalities are facets for the associated integer polyhedra. The inequalities are defined by one of several underlying support graphs: (i) a multistar, a "star" with a clique replacing the central vertex; (ii) a clique cluster, a collection of cliques intersecting at a single vertex, or more generally at a central" clique; and (iii) a ladybug, consisting of a multistar as a head and a clique as a body. …”
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A Generalization of the Source Unfolding of Convex Polyhedra
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Continuously Flattening Polyhedra Using Straight Skeletons
Published 2015“…We show that our method solves the fold-and-cut problem for convex polyhedra in any dimension. As an additional application, we show how a limiting form of our algorithm gives a general design technique for flat origami tessellations, for any spiderweb (planar graph with all-positive equilibrium stress).…”
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Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
Published 2018“…This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques.…”
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Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
Published 2018“…This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques. …”
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Rapid detection of shallow penetration between non-convex polyhedra
Published 2014Get full text
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Prism Trees: An Efficient Representation for Manipulating and Displaying Polyhedra with Many Faces
Published 2004“…When dealing with polyhedra with many faces (typically more than one thousand), the first step is by far the most expensive. …”
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