Edge-Unfolding Nearly Flat Convex Caps

07/04/2017
by   Joseph O'Rourke, et al.
0

This paper proves a conjecture from [LO17]: A nearly flat, acutely triangulated convex cap C has an edge-unfolding to a non-overlapping polygon in the plane. "Nearly flat" means that every face normal forms a sufficiently small angle with the z-axis. Although the result is not surprising, the proof relies on some recently developed concepts, angle-monotone and radially monotone curves.

READ FULL TEXT

page 2

page 6

page 9

page 10

page 11

page 12

page 28

page 34

research
09/02/2017

Addendum to: Edge-Unfolding Nearly Flat Convex Caps

This addendum to [O'R17] establishes that a nearly flat acutely triangul...
research
07/01/2017

Angle-monotone Paths in Non-obtuse Triangulations

We reprove a result of Dehkordi, Frati, and Gudmundsson: every two verti...
research
02/05/2018

Un-unzippable Convex Caps

An unzipping of a polyhedron P is a cut-path through its vertices that u...
research
03/23/2020

A Toroidal Maxwell-Cremona-Delaunay Correspondence

We consider three classes of geodesic embeddings of graphs on Euclidean ...
research
02/06/2020

Which convex polyhedra can be made by gluing regular hexagons?

Which convex 3D polyhedra can be obtained by gluing several regular hexa...
research
11/30/2021

Acute Tours in the Plane

We confirm the following conjecture of Fekete and Woeginger from 1997: f...

Please sign up or login with your details

Forgot password? Click here to reset