HEALPix

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https://healpix.jpl.nasa.gov/

the Hierarchical Equal Area iso-Latitude Pixelization -- is a versatile data structure with an associated library of computational algorithms and visualization software that supports fast scientific applications executable directly on very large volumes of astronomical data and large area surveys in the form of discretized spherical maps... A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere.

aw:Projection#HEALPix

base cells[edit | edit source]

12 cells for k0

publications[edit | edit source]

RING[edit | edit source]

HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere ... The Astrophysical Journal · September 2004 Orthographic-view-of-the-HEALPix.png

Tessellations comparison.png HEALPix levels.png

NESTED[edit | edit source]

MRH[edit | edit source]

HEALPix), was introduced in 32... is a novel hybrid combination of the Lambert cylindrical equal area projection (introduced in 1772) and the Collignon pseudocylindrical equal areaprojection (introduced in 1865).... HEALPix uses two different indexing schemes: #RING and #NESTED. In the RING scheme, the cell index winds down from North to South Pole through theconsecutive iso-latitude rings. In the NESTED cell scheme, the cell index grows with consecutive hierarchical subdivisions on a tree structure seeded by the twelve... Both the RING and the NESTED indexing schemes map the two dimensional distribution of discrete cells on a sphere into a one dimensional array (also known as a map)... The #MRH data structure also includes a map of user-defined data records. However, the map is a list of variable length and each element... The map index of a data point is what is eventually stored inside a proper spatially correlated MortonNode within one of the twelve Morton Linear Quadtrees (MLQs) associated with the #base cells. When a range query returns a list of Morton addresses, these addresses are searched in the proper MLQ and the leaf nodes found contain map indexes that indicate where in the MRH map to find the information for the data points within the query’s range. The data type of the MRH map is user-defined and can be either simple data types or more complex structures or classes... Compared to HEALPix, MRH used two to four orders of magnitude less memory for the same data, and on average its queries executed 72% faster.

rotation[edit | edit source]

may be rotated via a 45◦ to get square grid HEALPix 45rotation.png (picture from "Mapping on the HEALPix grid": File:10.1111-j.1365-2966.2007.12297.x.pdf)

codes[edit | edit source]

#RING[edit | edit source]

HEALPix k0and1 tests.png
HEALPix k2 k3 tests.png

for DEM[edit | edit source]

generating json by looking on HEALpix sphere[edit | edit source]

 1
3 0
 2
where these figures define order to loop recursively through basins

orientation inside of json[edit | edit source]

v - row from NE to SW, u - column from SE to NW

therefore directions to neighbors are: down NE is 1, up SW is 2, left SE is 3, right NW is 0 if looking on square of dem array

 2
3 0
 1

or if looking on sphere of Earth

external[edit | edit source]