Discrete knot energies

TL;DR

This paper reviews discrete knot energies, emphasizing their computational advantages and geometric consistency, focusing on M"obius energy, integral Menger curvature, and thickness.

Contribution

It provides an overview of discrete knot energies that facilitate numerical computation and maintain geometric properties similar to continuous models.

Findings

Discrete energies enable efficient numerical computations.

Discrete models preserve key geometric features.

Focus on M"obius energy, integral Menger curvature, and thickness.

Abstract

The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an independent, geometrically pleasing and consistent discrete model that behaves similarly to the original model. We will focus on M\"obius energy, integral Menger curvature and thickness.