# A bug's eye view: the Riemannian exponential map on polyhedral surfaces

## TL;DR

This paper investigates the geometric properties of polyhedral surfaces by computing the Riemannian exponential map, enabling visual effects like lensing and cloaking from a bug's perspective on the surface.

## Contribution

It introduces a method to compute the exponential map on polyhedral surfaces, facilitating novel visualizations and understanding of surface geometry from a bug's viewpoint.

## Key findings

- Visual effects such as lensing and cloaking demonstrated
- Method for computing exponential map on polyhedra developed
- Multiple viewpoints illustrated through constructed images

## 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.