A parameter-free, solid-angle based, nearest-neighbor algorithm

TL;DR

The paper introduces SANN, a simple, parameter-free solid-angle based algorithm for identifying nearest neighbors in 3D data, with advantages in ease of use and computational efficiency over existing methods.

Contribution

It presents a novel solid-angle based approach for neighbor identification that requires no parameters and is computationally efficient, suitable for experimental and simulation data.

Findings

Accurately identifies neighbors in various 3D systems.

Outperforms fixed-distance cutoff and Voronoi methods in tests.

Efficiently applicable in real-time simulations.

Abstract

We propose a parameter-free algorithm for the identification of nearest neighbors. The algorithm is very easy to use and has a number of advantages over existing algorithms to identify nearest- neighbors. This solid-angle based nearest-neighbor algorithm (SANN) attributes to each possible neighbor a solid angle and determines the cutoff radius by the requirement that the sum of the solid angles is 4{\pi}. The algorithm can be used to analyze 3D images, both from experiments as well as theory, and as the algorithm has a low computational cost, it can also be used "on the fly" in simulations. In this paper, we describe the SANN algorithm, discuss its properties, and compare it to both a fixed-distance cutoff algorithm and to a Voronoi construction by analyzing its behavior in bulk phases of systems of carbon atoms, Lennard-Jones particles and hard spheres as well as in Lennard-Jones systems with liquid-crystal and liquid-vapor interfaces.