Folding a 3D Euclidean space
History and Overview
2018-09-18 v2
Abstract
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry of reflections. Next, a set of 3D elementary fold operations is defined, which satisfy specific combinations of constraints with a finite number of solutions. The set consists of 47 valid fold operations, and solutions to some of them are explored to determine their number and conditions of existence.
Keywords
Cite
@article{arxiv.1803.06224,
title = {Folding a 3D Euclidean space},
author = {Jorge C. Lucero},
journal= {arXiv preprint arXiv:1803.06224},
year = {2018}
}
Comments
22 pages, 18 figures. Expanded explanation in Section 4.1 and minor corrections. This is an expanded version of the paper published in Origami7