A bug's eye view: the Riemannian exponential map on polyhedral surfaces
Differential Geometry
2017-06-21 v1 Geometric Topology
History and Overview
Metric Geometry
Abstract
We explore the perspective of a bug living on the two-dimensional surface of a polyhedron. Images of various kinds of effects like lensing and cloaking are shown via color pictures of three viewpoints: the first person perspective of the bug, a map of the bug's viewpoint, and a look at the bug on the embedded polyhedron from a three-dimensional exterior viewer. The pictures were constructed by computing the exponential map of a polyhedron by cutting and rotating faces into the tangent plane of the bug.
Cite
@article{arxiv.1706.06131,
title = {A bug's eye view: the Riemannian exponential map on polyhedral surfaces},
author = {David Glickenstein},
journal= {arXiv preprint arXiv:1706.06131},
year = {2017}
}
Comments
5 pages, 21 figures