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02/15/2023
Polar Zonohedra Edge-Unfold to Nets
This note proves that every polar zonohedron has an edge-unfolding to a ...
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12/30/2022
Every Combinatorial Polyhedron Can Unfold with Overlap
Ghomi proved that every convex polyhedron could be stretched via an affi...
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06/10/2022
Hamiltonian Quasigeodesics yield Nets
This note establishes that every polyhedron that has a Hamiltonian quasi...
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03/09/2022
Simple Closed Quasigeodesics on Tetrahedra
Pogorelov proved in 1949 that every every convex polyhedron has at least...
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07/07/2021
Reshaping Convex Polyhedra
Given a convex polyhedral surface P, we define a tailoring as excising f...
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02/22/2021
Cut Locus Realizations on Convex Polyhedra
We prove that every positively-weighted tree T can be realized as the cu...
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08/04/2020
Tailoring for Every Body: Reshaping Convex Polyhedra
Given any two convex polyhedra P and Q, we prove as one of our main resu...
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02/15/2020
A Note on Unbounded Polyhedra Derived from Convex Caps
The construction of an unbounded polyhedron from a "jagged” convex cap i...
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08/13/2019
Unfolding Polyhedra
Starting with the unsolved "Dürer's problem" of edge-unfolding a convex ...
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07/19/2019
Some Polycubes Have No Edge-Unzipping
It is unknown whether or not every polycube has an edge-unfolding. A pol...
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02/05/2018
Un-unzippable Convex Caps
An unzipping of a polyhedron P is a cut-path through its vertices that u...
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01/24/2018
Threadable Curves
We define a plane curve to be threadable if it can rigidly pass through ...
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09/02/2017
Addendum to: Edge-Unfolding Nearly Flat Convex Caps
This addendum to [O'R17] establishes that a nearly flat acutely triangul...
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07/04/2017
Edge-Unfolding Nearly Flat Convex Caps
This paper proves a conjecture from [LO17]: A nearly flat, acutely trian...
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07/01/2017
Angle-monotone Paths in Non-obtuse Triangulations
We reprove a result of Dehkordi, Frati, and Gudmundsson: every two verti...
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05/01/2008
Morphing of Triangular Meshes in Shape Space
We present a novel approach to morph between two isometric poses of the ...
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01/28/2000
Computational Geometry Column 38
Recent results on curve reconstruction are described....
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10/22/1998
Computational Geometry Column 32
The proof of Dey's new k-set bound is illustrated....
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10/22/1998