The Hierarchical Triangular Mesh

Abstract

The Hierarchical Triangular Mesh (HTM) is a method to subdivide the spherical surface into triangles of nearly equal shape and size. The HTM gives us a very efficient indexing method for objects localized on the sphere. We also developed a simple geometrical method to define an arbitrary area on the sphere which can be intersected by the HTM, returning the triangles covered by the area. Thus we have a powerful querying tool to find objects on the sphere by location. In this contribution we define the Hierarchical Triangular Mesh, the geometric querying and we give concrete numbers of the performance of the current implementation.