# TURTLE: A C library for an optimistic stepping through a topography

## TL;DR

TURTLE is a C library that enables efficient, constant-time navigation through large digital elevation models using an optimistic ray tracing algorithm, suitable for particle transport and ray tracing in large topographies.

## Contribution

The paper introduces an innovative optimistic ray tracing algorithm that allows traversal of large topographies in constant time without additional memory, enhancing efficiency for particle transport simulations.

## Key findings

- Outperforms traditional algorithms in speed and memory efficiency.
- Enables handling of DEMs with over a billion nodes.
- Validated through performance comparisons and muon transport simulations.

## Abstract

TURTLE is a C library providing utilities allowing to navigate through a topography described by a Digital Elevation Model (DEM). The library has been primarily designed for the Monte Carlo transport of particles scattering over medium to long ranges, e.g. atmospheric muons. But, it can also efficiently handle ray tracing problems with very large DEMs ($10^9$ nodes or more), e.g. for neutrino simulations. The TURTLE library was built on an optimistic ray tracing algorithm, detailed in the present paper. This algorithm proceeds by trials and errors, approximating the topography within the modelling uncertainties of the DEM data. This allows to traverse a topography in constant time, i.e. independently of the number of grid nodes, and with no added memory. Detailed performance studies are provided by comparison to other ray tracing algorithms and as an application to muon transport in a Monte Carlo simulation.