Hierarchical triangular mesh

Diagram of Hierarchical Triangular Mesh (HTM). The spherical polygons are the projection of the edges of the octahedron onto the circumscribing sphere.

Hierarchical Triangular Mesh (HTM) is a kind of quad tree based on subdivision of a distorted octahedron, used for mesh generation in 3-D computer graphics and geometric data structures.^[1]

Functions

• It provides a systematic indexing method for objects localized on a sphere.^[2]
• It is an efficient method for searching different resolutions like arc seconds or hemispheres.^[1]
• It can be used as a method to subdivide the spherical surface into triangles of nearly equal shape and size.^[2]

See also

• HEALPix
• Quadrilateralized spherical cube
• Geodesic grid

References

1. Szalay, Alexander S.; Gray, Jim; Fekete, George; Kunszt, Peter Z.; Kukol, Peter; Thakar, Ani (2007). "Indexing the Sphere with the Hierarchical Triangular Mesh". arXiv:cs/0701164.
2. Kunszt, Peter Z.; Szalay, Alexander S.; Thakar, Aniruddha R. (2001). "The Hierarchical Triangular Mesh". In Banday, Anthony J.; Zaroubi, Saleem; Bartelmann, Matthias (eds.). Mining the Sky. ESO Astrophysics Symposia. Berlin, Heidelberg: Springer. pp. 631–637. Bibcode:2001misk.conf..631K. doi:10.1007/10849171_83. ISBN 3-540-42468-7.