Indexing the Sphere with the Hierarchical Triangular Mesh

TL;DR

The paper introduces the Hierarchical Triangular Mesh (HTM), a spherical surface subdivision method that enables efficient, multi-resolution geospatial indexing and querying, outperforming traditional coordinate-based methods especially near poles.

Contribution

It presents a universal subdivision scheme for the sphere, algorithms for region specification, and demonstrates HTM's advantages for geospatial indexing in databases.

Findings

HTM supports searches from arc seconds to hemispheres.

HTM provides efficient region representation and querying.

HTM outperforms coordinate-based methods near poles.

Abstract

We describe a method to subdivide the surface of a sphere into spherical triangles of similar, but not identical, shapes and sizes. The Hierarchical Triangular Mesh (HTM) is a quad-tree that is particularly good at supporting searches at different resolutions, from arc seconds to hemispheres. The subdivision scheme is universal, providing the basis for addressing and for fast lookups. The HTM provides the basis for an efficient geospatial indexing scheme in relational databases where the data have an inherent location on either the celestial sphere or the Earth. The HTM index is superior to cartographical methods using coordinates with singularities at the poles. We also describe a way to specify surface regions that efficiently represent spherical query areas. This article presents the algorithms used to identify the HTM triangles covering such regions.