HEALPix#

HEALPix (Hierarchical Equal-Area isoLatitude Pixelisation) was originally defined for use in astronomy by Gorski et al., 2005. It has several important properties:

  • equal-area: all cells of the same refinement level have exactly the same area

  • iso-latitude: all cells of the same refinement level are arranged around rings of the same latitude

  • hierarchical: cells are created by recursively and evenly subdividing, which forms a hierarchy of cells

HEALPix nested indexing scheme

The nested indexing scheme of HEALPix#

The latter two properties allow defining the two main indexing schemes:

  • ring, which assigns identifiers along the iso-latitude rings. Thus, cells on the same latitude ring have identifiers that are “close” numerically (and thus in memory for sorted data).

  • nested, which assigns identifiers such that sibling cells are close to each other.

To know what cell a identifier refers to, we need two additional parameters: the refinement level (the depth in the hierarchy) and the indexing scheme.

Based on nested, there are two more schemes that also encode the refinement level in the cell id:

  • nuniq, which represents all cells in the hierarchy breadth-first, i.e. cells of a refinement level are close numerically.

  • zuniq, which represents all cells in the hierarchy depth-first, i.e. descendant cells of a given cell are close numerically.

Extensions#