# Navigating Around Convex Sets

## TL;DR

This paper reviews fundamental convex analysis and geometry concepts to develop a differential equation for tracking the distance between an external observer and a convex set.

## Contribution

It introduces a differential equation framework for measuring the distance to convex sets based on convex analysis principles.

## Key findings

- Derived a differential equation for distance tracking
- Connected convex geometry with dynamic distance measurement
- Provided theoretical foundations for navigation around convex obstacles

## Abstract

We review some basic results of convex analysis and geometry in $\mathbb{R}^n$ in the context of formulating a differential equation to track the distance between an observer flying outside a convex set $K$ and $K$ itself.