Edge-unfolding nested prismatoids
@inproceedings{Radons2021EdgeunfoldingNP, title={Edge-unfolding nested prismatoids}, author={Manuel Radons}, year={2021} }
A 3-Prismatoid is the convex hull of two convex polygons A and B which lie in parallel planes HA, HB ⊂ R . Let A be the orthogonal projection of A onto HB. A prismatoid is called nested if A ′ is properly contained in B, or vice versa. We show that every nested prismatoid has an edge-unfolding to a non-overlapping polygon in the plane. 1
References
SHOWING 1-10 OF 24 REFERENCES
Acutely Triangulated, Stacked, and Very Ununfoldable Polyhedra
- MathematicsCCCG
- 2020
We present new examples of topologically convex edge-ununfoldable polyhedra, i.e., polyhedra that are combinatorially equivalent to convex polyhedra, yet cannot be cut along their edges and unfolded…
Pseudo-Edge Unfoldings of Convex Polyhedra
- MathematicsDiscret. Comput. Geom.
- 2020
This work constructs a convex polyhedron K in Euclidean 3-space with a pseudo-edge graph with respect to which K is not unfoldable, and confirms that Dürer’s conjecture does not hold for pseudo- edge unfoldings.
Edge-Unfolding Nearly Flat Convex Caps
- MathematicsSoCG
- 2018
A proof that a nearly flat, acutely triangulated convex cap C in R^3 has an edge-unfolding to a non-overlapping polygon in the plane, leading to a polynomial-time algorithm for finding the edge-cuts, at worst O(n^2).
Addendum to: Edge-Unfolding Nearly Flat Convex Caps
- MathematicsArXiv
- 2017
This addendum to [O'R17] establishes that a nearly flat acutely triangulated convex cap in the sense of that paper can be edge-unfolded even if closed to a polyhedron by adding the convex polygonal…
Affine unfoldings of convex polyhedra
- Mathematics
- 2014
We show that every convex polyhedron admits a simple edge unfolding after an affine transformation. In particular there exists no combinatorial obstruction to a positive resolution of Durer's…
Geometry and Topology
- MathematicsSpringer Handbook of Geographic Information
- 2012
This chapter introduces the most important geometrical and topological concepts, considering the two dimensional as well as the three dimensional case, particularly the concepts of the standard ISO 19107 Spatial schema.
Unfolding Prismatoids as Convex Patches: Counterexamples and Positive Results
- MathematicsArXiv
- 2012
It is shown that the natural extension to a convex patch consisting of a face of a polyhedron and all its incident faces, does not always have a nonoverlapping petal unfolding, however, a positive result is obtained by excluding the problematical patches.