Chirality for crooked curves

TL;DR

This paper introduces a tensorial measure of chirality for rigid curves and filaments, applicable to various geometrical structures, based on hydrodynamic principles, capturing the handedness and twist orientation.

Contribution

It proposes a novel, minimal-smoothness tensorial chirality measure that quantifies the handedness of curves and filaments in a general and versatile manner.

Findings

The measure effectively captures the right- and left-handed twists.

It applies to biomolecules, polymers, and polygonal curves.

The tensor is trace-free, indicating orthogonal twist directions.

Abstract

Chiral objects rotate when placed in a collimated flow or wind. We exploit this hydrodynamic intuition to construct a tensorial chirality measure for rigid filaments and curves. This tensor is trace-free, so if a curve has a right-handed twist about some axis, there is a perpendicular axis about which the twist is left-handed. Our measure places minimal requirements on the smoothness of the curve, hence it can be readily used to quantify chirality for biomolecules and polymers, polygonal and rectifiable curves, and other discrete geometrical structures.