Terminology#

General terms#

HEALPix#: Hierarchical Equal Area isoLatitude Pixelization. A spherical tiling system that divides a sphere into cells of equal area, organized hierarchically.
Cell#: An individual region of the HEALPix tiling. Each cell is a spherical quadrilateral with 4 vertices.
Depth#: The resolution level in the HEALPix hierarchy. Depth 0 = 12 cells, depth N = 12 × 4^N cells. Range: [0, 29].
Index, ipix#: The unique numeric identifier of a HEALPix cell at a given level. Type: 64-bit unsigned integer (uint64).

Nested#: Hierarchical indexing scheme where child cells have consecutive indices. Optimized for hierarchical operations. Recommended by default.
Ring#: Latitude ring indexing scheme. Cells on the same latitude ring have similar indices. Used primarily for compatibility.
Zuniq#: An indexing scheme that encodes both the depth and the index into a single 64-bit integer. Used for Multi-Order Coverage (MOC).
Nuniq#: A variant of zuniq with breadth-first ordering (by level). Less used than zuniq.

Longitude#: Range: [-180°, +180°]. 0° = Greenwich meridian. Positive towards the East.
Latitude#: Range: [-90°, +90°]. 0° = ecuador. Positive towards the North.
Geodetic latitude, Geographic latitude#: The standard latitude used in cartography, measured perpendicular to the ellipsoid. This is the latitude returned by GPS devices. Symbol: φ (phi).
Geocentric latitude#: Latitude measured from the center of the ellipsoid. Symbol: θ (theta).
Parametric latitude, Reduced latitude#: Auxiliary latitude obtained by “stretching” the ellipsoid into a sphere. Symbol: β (beta)
Authalic latitude#: Latitude on a sphere with the same area as the ellipsoid. Used by HEALPix for ellipsoids. Symbol: ξ (xi).
Vertices#: The coins of an HEALPix cell.
Center of a cell#: The geometric center of a HEALPix cell. Coordinates returned by healpix_to_lonlat.

Ellipsoid#

Mathematical model of the Earth’s shape, described by two radius (equatorial and polar). More accurate than a sphere.

Sphere#

Simplified model where the Earth has a constant radius. Less precise than an ellipsoid but faster calculations.

Flattening#

Measure of the difference between the ellipsoid and a sphere. Symbol: f.

Eccentricity#

Another measure of flatness. Symbol: e. Related to f by: e² = 2f - f².

ellipsoid-like#

An ellipsoid specification. Can be either:

The name of the ellipsoid as a str. For a complete list of known ellipsoids, see the geodesy create.
A dict, with either a "radius" item for spheres or "semimajor_axis" and "inverse_flattening" for ellipsoids. All items need to be floats.
A class with a "radius" attribute for spheres or "semimajor_axis" and "inverse_flattening" attributes for ellipsoids. All attributes need to be floats.

If an object or dict could be interpreted as both a sphere and an ellipsoid, the ellipsoid will be preferred.

Parent#

At depth N, the parent of a cell is the cell of level N-1 which contains it.

Children#

At depth N, a cell has 4 children at depth N+1 which subdivide it.

Siblings#

The 4 children cells of a same parent.

Neighbourhood#

The set of adjacent cells. A neighborhood of order k includes cells at a distance of k.

k-th neighborhood, Neighborhood of order k#

Zoom#

Navigation between resolution levels. zoom_to(ipix, depth_from, depth_to) converts cells from one level to another.