Fast and robust mesh generation on the sphere Application to coastal domains

TL;DR

This paper introduces a fast, robust mesh generation method for the Earth's surface that automatically simplifies coastline data and produces high-quality meshes in seconds, suitable for oceanic and continental applications.

Contribution

The paper presents a novel sphere mesh generation algorithm that handles geospatial data efficiently without parametrization and automatically simplifies coastline features.

Findings

Mesh generation in seconds for large domains

Automatic coastline data simplification

High-performance multi-threaded implementation

Abstract

This paper presents a fast an robust mesh generation procedure that is able to generate meshes of the earth system (ocean and continent) in matters of seconds. Our algorithm takes as input a standard shape-file i.e. geospatial vector data format for geographic information system (GIS) software. The input is initially coarsened in order to automatically remove unwanted channels that are under a desired resolution. A valid non-overlapping 1D mesh is then created on the sphere using the Euclidian coordinates system $x,y,z$. A modified Delaunay kernel is then proposed that enables to generate meshes on the sphere in a straightforward manner without parametrization. One of the main difficulty in dealing with geographical data is the over-sampled nature of coastline representations. We propose here an algorithm that automatically unrefines coastline data. Small features are automatically removed while always keeping a valid (non-overlapping) geometrical representation of the domain. A Delaunay refinement procedure is subsequently applied to the domain. The refinement scheme is also multi-threaded at a fine grain level, allowing to generate about a million points per second on 8 threads. Examples of meshes of the Baltic sea as well as of the global ocean are presented.