[](https://dggal.org/docs/html/dggal/Classes/DGGRS.html)<br>
# DGGAL, the Discrete Global Grid Abstraction Library
https://dggal.org
DGGAL provides a common interface to perform various operations on Discrete Global Grid Reference Systems (DGGRS), facilitating the implementation of Discrete Global Grid Systems (DGGS),
including implementing Web APIs based on the [OGC API - DGGS Standard](https://docs.ogc.org/DRAFTS/21-038r1.html).
Copyright (c) 2014-2025, Ecere Corporation
Licensed under the [BSD 3-Clause License](https://opensource.org/license/bsd-3-clause)
Source: https://github.com/ecere/dggal
Python packaging: https://github.com/ecere/pydggal
## Supported Discrete Global Grid Reference Systems
DGGAL currently supports all nine DGGRSs described in [OGC API - DGGS Annex B](https://docs.ogc.org/DRAFTS/21-038r1.html#annex-dggrs-def), as well as additional DGGRSs:
### Axis-aligned DGGRS in WGS84 latitude and longitude (simple bounding boxes)
* [GNOSIS Global Grid](https://docs.ogc.org/DRAFTS/21-038r1.html#ggg-dggrs): An axis-aligned quad-tree defined in WGS84 latitude and longitude, with special handling of polar regions achieving an approximate maximum of ~48% variance from median zone area, corresponding to the [OGC 2D Tile Matrix Set of the same name](https://docs.ogc.org/is/17-083r4/17-083r4.html#toc58)
### Equal-Area DGGRSs based on Icosahedral Projections (aperture 3 and 7 Hexagonal, aperture 4 and 9 Axis-Aligned Rhombic)
All of these Icosahedral DGGRSs achieve equal-area on the WGS84 ellipsoid, and are oriented with a first vertex of the icosahedron positioned at
authalic latitude of _atan(φ)_ (where φ is the golden ratio), and longitude 11.20°E, with second vertex due North, resulting in only one
vertex / pentagon on land. Each of the 12 pentagons occupies 5/6th the area of a hexagon at the same refinement level.
_WARNING: The aperture 7 hexagonal grids are still experimental; sub-zones are not yet implemented for them._
#### Icosahedral Snyder Equal Area (ISEA) projection
([An Equal-Area Map Projection for Polyhedral Globes (1992)](https://doi.org/10.3138%2F27H7-8K88-4882-1752), or dodecahedron configuration (DVEA) of [Slice & Dice (2006)](https://www.tandfonline.com/doi/abs/10.1559/152304006779500687))
* **ISEA4R**: An equal area rhombic grid with a refinement ratio of 4 defined in the transformed into a 5x6 Cartesian space resulting in axis-aligned square zones
* [ISEA9R](https://docs.ogc.org/DRAFTS/21-038r1.html#isea9r-dggrs): An equal area rhombic grid with a refinement ratio of 9 defined in the ISEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones
* [ISEA3H](https://docs.ogc.org/DRAFTS/21-038r1.html#isea3h-dggrs): An equal area hexagonal grid with a refinement ratio of 3 defined in the ISEA projection
* [ISEA7H](https://docs.ogc.org/DRAFTS/21-038r1.html#isea7h-dggrs): An equal area hexagonal grid with a refinement ratio of 7 defined in the ISEA projection
#### Icosahedral Vertex-oriented great circle Equal Area (IVEA) projection
([Slice & Dice (2006)](https://www.tandfonline.com/doi/abs/10.1559/152304006779500687), or applying [Snyder 1992](https://doi.org/10.3138%2F27H7-8K88-4882-1752) to the dodecahedron (DSEA))
* **IVEA4R**: An equal area rhombic grid with a refinement ratio of 4 defined in the IVEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones, using the same global indexing and sub-zone ordering as for ISEA4R
* [IVEA9R](https://docs.ogc.org/DRAFTS/21-038r1.html#ivea9r-dggrs): An equal area rhombic grid with a refinement ratio of 9 defined in the IVEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones, using the same global indexing and sub-zone ordering as for ISEA9R
* [IVEA3H](https://docs.ogc.org/DRAFTS/21-038r1.html#ivea3h-dggrs): An equal area hexagonal grid with a refinement ratio of 3 defined in the IVEA projection, using the same global indexing and sub-zone ordering as for ISEA3H
* [IVEA7H](https://docs.ogc.org/DRAFTS/21-038r1.html#ivea7h-dggrs): An equal area hexagonal grid with a refinement ratio of 7 defined in the IVEA projection, using the same global indexing and sub-zone ordering as for ISEA7H
**NOTE:** This projection is superior to ISEA and RT(S)EA at avoiding perceptible cusps, resulting in more compact/regular zones.
#### Rhombic Triacontahedron (Snyder) Equal-Area (RT(S)EA) projection
(applying [Snyder 1992](https://doi.org/10.3138%2F27H7-8K88-4882-1752) to the Rhombic Triacontahedron,
alternate configuration of [Slice & Dice (2006)](https://www.tandfonline.com/doi/abs/10.1559/152304006779500687),
[Disdyakis Triacontahedron Discrete Global Grid System](http://hdl.handle.net/1880/114595), or
[Construction of rhombic triacontahedron discrete global grid systems](https://doi.org/10.1080/17538947.2022.2130459))
* **RTEA4R**: An equal area rhombic grid with a refinement ratio of 4 defined in the RTEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones, using the same global indexing and sub-zone ordering as for ISEA4R
* **RTEA9R**: An equal area rhombic grid with a refinement ratio of 9 defined in the RTEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones, using the same global indexing and sub-zone ordering as for ISEA9R
* **RTEA3H**: An equal area hexagonal grid with a refinement ratio of 3 defined in the RTEA projection using the same global indexing and sub-zone ordering as for ISEA3H
* **RTEA7H**: An equal area hexagonal grid with a refinement ratio of 7 defined in the RTEA projection using the same global indexing and sub-zone ordering as for ISEA7H
### Axis-aligned and Equal-Area DGGRSs based on HEALPix Projection
([HEALPix projection](https://arxiv.org/pdf/astro-ph/0409513))
* [HEALPix](https://docs.ogc.org/DRAFTS/21-038r1.html#HEALPix-dggrs): An equal area and axis-aligned grid with square zones topology and a refinement ratio of 4 defined in the HEALPix projection, using configuration Nφ/H = 4, Nθ/K = 3 (same as default [PROJ implementation](https://proj.org/en/stable/operations/projections/healpix.html)), the new indexing described in OGC API - DGGS Annex B, and scanline-based sub-zone ordering
* [rHEALPix](https://docs.ogc.org/DRAFTS/21-038r1.html#rHEALPix-dggrs): An equal area and axis-aligned grid with square zones topology and a refinement ratio of 9 defined in the rHEALPix projection using 50° E prime meridian (equivalent to [PROJ implementation](https://proj.org/en/stable/operations/projections/rhealpix.html) with parameters `+proj=rhealpix +lon_0=50 +ellps=WGS84`), the [original hierarchical indexing](https://iopscience.iop.org/article/10.1088/1755-1315/34/1/012012), and scanline-based sub-zone ordering
## libDGGAL API Documentation
The API documentation can be [found here](https://dggal.org/docs/html/dggal/Classes/DGGRS.html).
The `DGGRS` class provides most of the functionality of the library, allowing to resolve DGGRS zones by textual ID to a unique 64-bit zone integer identifier (`DGGRSZone`).
The geometry and sub-zones of a particular zone can also be queried.
The concept of [sub-zones](https://docs.ogc.org/DRAFTS/21-038r1.html#term-sub-zone) is key to encoding both vector and raster geospatial data quantized to a DGGRS.
The DGGAL library also allows to resolve a sub-zone index at a particular depth from a parent zone, allowing to read DGGS-optimized data such as
[DGGS-JSON](http://dggs-json.org) and [DGGS-JSON-FG](https://docs.ogc.org/DRAFTS/21-038r1.html#rc_data-dggs-jsonfg).
## Language bindings
While the library is written in the [eC programming language](https://ec-lang.org), object-oriented bindings for C, C++ and Python generated using the
Ecere SDK's [`bgen` tool](https://github.com/ecere/bgen) are provided. Bindings for Rust are available as well.
Support for additional languages may be added in the future.
## `dgg` tool
### Syntax
```
dgg <dggrs> <command> [options] <arguments>
```
### Supported DGGRSs
* `gnosis` (Global Grid)
* `isea4r`, `isea9r`, `isea3h`, `isea7h`
* `ivea4r`, `ivea9r`, `ivea3h`, `ivea7h`
* `rtea4r`, `rtea9r`, `rtea3h`, `rtea7h`
* `rhealpix` (aperture 9, 50° E)
* `healpix` (aperture 4, Nφ/H = 4, Nθ/K = 3)
### Commands
[**info**](#info) [_zone_]
- Display information about a DGGRS or about a zone of a DGGRS
[**zone**](#zone) <_coord1,coord2_> [_level_]
- Return DGGRS zone at position -- specified in EPSG:4326 (lat,lon)
[**level**](#level) [_level_]
- Display information about a DGGRS refinement level
[**grid**](#grid) [_level_]
- Generate DGGRS grid at specified refinement level (default: 0)
[**geom**](#geom) <_zone_>
- Generate geometry for a particular zone
[**list**](#list) [_level_]
- List DGGRS zones (as JSON string array)
[**rel**](#rel) <_zone 1_> <_zone 2_>
- Display information about the relationships between two zones of a DGGRS
[**sub**](#sub) <_zone_> [_index_]
- List subzones of a DGGRS zone or resolve a sub-zone by index
[**index**](#index) <_parent zone_> <_sub-zone_>
- Display index of sub-zone within parent
**compact** <_JSON input zone file (zone ID strings array)_>
- Compact input zone list
**decompact** <_JSON input zone file (zone ID strings array)_> [_level_]
- Decompact zone list
[**togeo**](#togeo) <_DGGS-(UB)JSON(-FG) input file_>
- Convert DGGS-JSON (DGGS-quantized raster data) or DGGS-JSON-FG (DGGS-quantized vector data) to GeoJSON
### Options
**-o** <_filename_>
- Output to file instead of standard output
**-crs** <_crs_>
- Select an output coordinate reference system, one of:
EPSG:4326, OGC:CRS84, 5x6, ico (icosahedron net), rhp (rHEALPix), hpx (HEALPix)
**-depth** <_relative depth_>
- For sub, specify relative depth
Also to change depth considered for calculating optional [level] from -scale, -mpp and -pixels
default: depth corresponding to ~64K sub-zones (IS/VEA9R: 5, IS/VEA3H: 10, GNOSIS: 8)
**-bbox** <_llLat,llLon,urLat,urLon_>
- Specify extent for which to list zones, generate grid, or reference extent for -pixels
example: -bbox 60,-120,62,-118 -- specified in EPSG:4326 (lat,lon)
**-centroids**
- For sub, list centroids instead of sub-zone identifiers
For togeo, use centroid points for geometry instead of polygons
**-compact**
- For list and grid, return compact list of zones
**-mpp** <_physical meters per sub-zone_>
- Specify physical meters per sub-zone as substitute for optional [level] arguments
**-scale-denom** <_scale denominator_>
- Specify scale-denominator as substitute for optional [level] arguments (based on -depth)
**-pixels** <_with,height_>
- Specify display pixels as a substitute for optional [level] argument (in combination with -bbox)
**-display-res** <_mm-per-pixels_>
- Specify display resolution in millimeters/pixel in combination with -scale and -pixels (default: 0.28)
### Example Usage
#### `info`
##### Information about a particular DGGRS
```
> dgg isea3h info
DGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H
Refinement Ratio: 3
Maximum level for 64-bit global identifiers (DGGAL DGGRSZone): 33
Default ~64K sub-zones relative depth: 10
```
##### Information about a particular zone
```
> dgg isea3h info A4-0-A
DGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H
Textual Zone ID: A4-0-A
64-bit integer ID: 36028797018963968 (0x80000000000000)
Level 0 zone (5 edges, centroid child)
42505468477007.4 m² (42505468.4770074 km²)
49411 sub-zones at depth 10
WGS84 Centroid (lat, lon): 0, -20.517474730219
WGS84 Extent (lat, lon): { -35.385452137707, -57.8948427221833 }, { 35.385452137707, 11.2 }
No parent
Children (6):
A4-0-B (centroid)
A4-0-C
A4-0-D
A3-0-C
A2-0-D
A2-0-C
Neighbors (5):
(direction 2): A2-0-A
(direction 3): A6-0-A
(direction 0): AA-0-A
(direction 6): A3-0-A
(direction 7): A5-0-A
[EPSG:4326] Vertices (5):
20.9908527620464, 11.2
-20.9908527620465, 11.2
-35.385452137707, -33.8
0, -57.8948427221833
35.385452137707, -33.8
```
#### `zone`
Identify zone at a particular geodetic position.
```
> dgg isea3h zone 34,-70
DGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H
Textual Zone ID: A2-0-A
64-bit integer ID: 18014398509481984 (0x40000000000000)
Level 0 zone (5 edges, centroid child)
42505468477007.4 m² (42505468.4770074 km²)
49411 sub-zones at depth 10
WGS84 Centroid (lat, lon): 31.832357532016, -78.8
WGS84 Extent (lat, lon): { 0, -123.8 }, { 69.1802093248182, -33.8 }
No parent
Children (6):
A2-0-B (centroid)
A2-0-C
A2-0-D
A1-0-C
A0-0-D
A0-0-C
Neighbors (5):
(direction 2): A0-0-A
(direction 3): A4-0-A
(direction 0): AA-0-A
(direction 6): A1-0-A
(direction 7): A3-0-A
[EPSG:4326] Vertices (5):
35.385452137707, -33.8
0, -57.8948427221833
0, -99.7051575819393
35.3854519371908, -123.8
69.1802093248182, -78.8
```
#### `level`
##### Information about levels of a particular DGGRS
```
> dgg isea3h level
DGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H
Assuming sub-zone depth of 10 and display resolution of 0.28 mm/pixel:
Level Reference Area Sub-zones count Sub-zone area Scale Meters/Sub-zone
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
0: 42505468477007.39843750 m² (42505468.47700740 km²) 49411 860243032.46255684 m² ( 8602430324625.56933594 cm²) 1: 104965840 29390.43523832 m ( 2939043.52383217 cm)
1: 15939550678877.77343750 m² (15939550.67887777 km²) 59293 268826854.41582942 m² ( 2688268544158.29394531 cm²) 1: 60602124 16968.59485403 m ( 1696859.48540341 cm)
2: 5544191540479.22558594 m² ( 5544191.54047923 km²) 59293 93504992.84028849 m² ( 935049928402.88488770 cm²) 1: 34988666 9796.82649363 m ( 979682.64936343 cm)
3: 1875241256338.56152344 m² ( 1875241.25633856 km²) 59293 31626688.75480346 m² ( 316266887548.03460693 cm²) 1: 20200718 5656.20112285 m ( 565620.11228463 cm)
4: 628159632665.13391113 m² ( 628159.63266513 km²) 59293 10594161.75037751 m² ( 105941617503.77513123 cm²) 1: 11662891 3265.60937742 m ( 326560.93774175 cm)
5: 209730929985.23385620 m² ( 209730.92998523 km²) 59293 3537195.45283986 m² ( 35371954528.39860535 cm²) 1: 6733573 1885.40047940 m ( 188540.04793995 cm)
6: 69948659040.60459900 m² ( 69948.65904060 km²) 59293 1179711.92283414 m² ( 11797119228.34138870 cm²) 1: 3887630 1088.53647937 m ( 108853.64793690 cm)
7: 23320483802.30837250 m² ( 23320.48380231 km²) 59293 393309.22372470 m² ( 3933092237.24695539 cm²) 1: 2244524 628.46683036 m ( 62846.68303597 cm)
8: 7773968507.65239239 m² ( 7773.96850765 km²) 59293 131111.06720275 m² ( 1311110672.02745557 cm²) 1: 1295877 362.84549387 m ( 36284.54938723 cm)
9: 2591375496.48476219 m² ( 2591.37549648 km²) 59293 43704.57720953 m² ( 437045772.09531683 cm²) 1: 748175 209.48894360 m ( 20948.89435974 cm)
10: 863797683.49797928 m² ( 863.79768350 km²) 59293 14568.29108829 m² ( 145682910.88290006 cm²) 1: 431959 120.94849799 m ( 12094.84979852 cm)
11: 287933211.32035321 m² ( 287.93321132 km²) 59293 4856.10799454 m² ( 48561079.94541568 cm²) 1: 249392 69.82964787 m ( 6982.96478712 cm)
12: 95977809.34637524 m² ( 95.97780935 km²) 59293 1618.70388320 m² ( 16187038.83196587 cm²) 1: 143986 40.31616600 m ( 4031.61659961 cm)
13: 31992611.14208768 m² ( 31.99261114 km²) 59293 539.56809644 m² ( 5395680.96437820 cm²) 1: 83131 23.27654929 m ( 2327.65492906 cm)
14: 10664204.60587722 m² ( 10.66420461 km²) 59293 179.85604719 m² ( 1798560.47187311 cm²) 1: 47995 13.43872200 m ( 1343.87219987 cm)
15: 3554734.96771997 m² ( 3.55473497 km²) 59293 59.95201740 m² ( 599520.17400367 cm²) 1: 27710 7.75884976 m ( 775.88497635 cm)
16: 1184911.66691713 m² ( 1.18491167 km²) 59293 19.98400599 m² ( 199840.05985818 cm²) 1: 15998 4.47957400 m ( 447.95739996 cm)
17: 394970.55686243 m² ( 0.39497056 km²) 59293 6.66133535 m² ( 66613.35349239 cm²) 1: 9237 2.58628325 m ( 258.62832545 cm)
18: 131656.85242341 m² ( 0.13165685 km²) 59293 2.22044512 m² ( 22204.45118706 cm²) 1: 5333 1.49319133 m ( 149.31913332 cm)
19: 43885.61748957 m² ( 0.04388562 km²) 59293 0.74014837 m² ( 7401.48373157 cm²) 1: 3079 0.86209442 m ( 86.20944182 cm)
20: 14628.53916487 m² ( 0.01462854 km²) 59293 0.24671612 m² ( 2467.16124414 cm²) 1: 1778 0.49773044 m ( 49.77304444 cm)
21: 4876.17972181 m² ( 0.00487618 km²) 59293 0.08223871 m² ( 822.38708141 cm²) 1: 1026 0.28736481 m ( 28.73648061 cm)
22: 1625.39324062 m² ( 0.00162539 km²) 59293 0.02741290 m² ( 274.12902714 cm²) 1: 593 0.16591015 m ( 16.59101481 cm)
23: 541.79774688 m² ( 0.00054180 km²) 59293 0.00913763 m² ( 91.37634238 cm²) 1: 342 0.09578827 m ( 9.57882687 cm)
24: 180.59924896 m² ( 0.00018060 km²) 59293 0.00304588 m² ( 30.45878079 cm²) 1: 129 0.03620456 m ( 3.62045625 cm)
25: 60.19974965 m² ( 0.00006020 km²) 59293 0.00101529 m² ( 10.15292693 cm²) 1: 95 0.02656689 m ( 2.65668857 cm)
26: 20.06658322 m² ( 0.00002007 km²) 59293 0.00033843 m² ( 3.38430898 cm²) 1: 56 0.01574749 m ( 1.57474944 cm)
27: 6.68886107 m² ( 0.00000669 km²) 59293 0.00011281 m² ( 1.12810299 cm²) 1: 36 0.01004134 m ( 1.00413390 cm)
28: 2.22962036 m² ( 0.00000223 km²) 59293 0.00003760 m² ( 0.37603433 cm²) 1: 21 0.00581872 m ( 0.58187229 cm)
29: 0.74320679 m² ( 0.00000074 km²) 59293 0.00001253 m² ( 0.12534478 cm²) 1: 12 0.00348148 m ( 0.34814838 cm)
30: 0.24773560 m² ( 0.00000025 km²) 59293 0.00000418 m² ( 0.04178159 cm²) 1: 7 0.00201092 m ( 0.20109213 cm)
31: 0.08257853 m² ( 0.00000008 km²) 59293 0.00000139 m² ( 0.01392720 cm²) 1: 4 0.00117525 m ( 0.11752498 cm)
32: 0.02752618 m² ( 0.00000003 km²) 59293 0.00000046 m² ( 0.00464240 cm²) 1: 2 0.00067856 m ( 0.06785649 cm)
33: 0.00917539 m² ( 0.00000001 km²) 59293 0.00000015 m² ( 0.00154747 cm²) 1: 1 0.00039338 m ( 0.03933785 cm)
```
##### Information about a particular DGGRS level
```
> dgg isea3h level 15
DGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H
Refinement Level: 15
Reference area: 3554734.96771997 m² (3.55473496771997 km²)
Assuming sub-zone depth of 10 (59293 sub-zones) and display resolution of 0.28 mm/pixel:
Sub-zones area: 59.9520174003672 m² (599520.174003672 cm²)
Cartographic scale: 1:27710
Physical meters/sub-zone: 7.75884976353492 (775.884976353492 cm/sub-zone)
```
#### `grid`
##### Generate grid geometry for a particular refinement level
Output is [GeoJSON](https://geojson.org/):
```
> dgg isea3h -crs ico grid 3 > isea3h-level3-isea.geojson
```
```
> dgg isea3h grid 3 > isea3h-level3-crs84.geojson
```
##### Generate grid geometry for a given bounding box using compacted zones
```
> dgg isea3h grid 15 -compact -bbox 44,-76,46,-74
```
#### `geom`
Generate geometry of a specific zone
```
> dgg isea3h geom A4-0-A
```
```geojson
{
"type" : "Feature",
"id" : "A4-0-A",
"geometry" : {
"type" : "Polygon",
"coordinates" : [
[ [11.2, 20.9908533396875], [11.2, 18.9046368254835], [11.2, 16.817317021754], [11.2, 14.7282441160477], [11.2, 12.6367658994772], [11.2, 10.5422256002322], [11.2, 8.44395966388283], [11.2, 6.3412954618102], [11.2, 4.2335489079295], [11.2, 2.12002196235325], [11.2, -0.00000000000000958], [11.2, -2.12002196235327], [11.2, -4.2335489079295], [11.2, -6.34129546181022], [11.2, -8.44395966388284], [11.2, -10.5422256002322], [11.2, -12.6367658994773], [11.2, -14.7282441160477], [11.2, -16.817317021754], [11.2, -18.9046368254835], [11.2, -20.9908533396875], [9.25904611568614, -22.022704447347], [7.2894978850024, -23.0315860032884], [5.2895073521231, -24.0162595826945], [3.2572732870332, -24.9754140020123], [1.19105174674043, -25.907662551343], [-0.910831437312103, -26.8115406666264], [-3.04996620024865, -27.6855041419538], [-5.22784181139874, -28.5279279934546], [-7.44582852527487, -29.3371060956138], [-9.70515744760715, -30.111251717508], [-11.9990182364648, -30.8460627665615], [-14.3199274459944, -31.5377272377057], [-16.6678118661126, -32.1851262644314], [-19.0423550054196, -32.7871381036537], [-21.4429904142008, -33.3426478478608], [-23.868897601607, -33.8505577351568], [-26.319001132268, -34.3097979200868], [-28.791973441741, -34.7193375329077], [-31.2862418322802, -35.0781958218138], [-33.7999999994894, -35.385453143805], [-35.328584064796, -33.7294909375037], [-36.7997931901407, -32.0544538235723], [-38.2190895198383, -30.3615150627895], [-39.591520816704, -28.651669714028], [-40.9217621171856, -26.9257555850354], [-42.2141557503646, -25.184471421695], [-43.4727493595782, -23.4283926793226], [-44.7013318005733, -21.6579851878463], [-45.9034669523704, -19.8736169902905], [-47.0825255880168, -18.075568603016], [-48.2378134716698, -16.2702095110336], [-49.3687568644497, -14.463940351611], [-50.4786064975358, -12.656986739445], [-51.5704092970534, -10.8495265877445], [-52.647041014988, -9.04169850753405], [-53.7112358369818, -7.23360915100237], [-54.765613515085, -5.42533970970474], [-55.8127045186767, -3.61695174870332], [-56.8549736519885, -1.80849253470827], [-57.894842551487, 0.0000000010850795], [-56.8549736519113, 1.80849253683432], [-55.8127045185966, 3.61695175082982], [-54.7656135150002, 5.425339711832], [-53.7112358368904, 7.2336091531306], [-52.6470410148878, 9.04169850966353], [-51.5704092969423, 10.8495265898755], [-50.4786064974117, 12.6569867415778], [-49.36875686431, 14.4639403537457], [-48.237813471512, 16.2702095131705], [-47.082525588539, 18.0755686040723], [-45.9034669536086, 19.873616990275], [-44.7013318018277, 21.6579851878424], [-43.47274936085, 23.428392679331], [-42.214155751655, 25.1844714217162], [-40.9217621184958, 26.9257555850703], [-39.5915208180354, 28.651669714077], [-38.219089521192, 30.3615150628536], [-36.799793191518, 32.0544538236523], [-35.328584066198, 33.7294909376005], [-33.8000000009355, 35.3854531438384], [-31.2862418337828, 35.0781958220137], [-28.7919734432313, 34.7193375331383], [-26.3190011337452, 34.3097979203474], [-23.86889760307, 33.850557735447], [-21.442990415649, 33.34264784818], [-19.0423550068522, 32.787138104001], [-16.6678118675294, 32.1851262648063], [-14.319927447395, 31.5377272381076], [-11.9990182378492, 30.8460627669896], [-9.70515744897538, 30.1112517179616], [-9.7051574476072, 30.1112517175078], [-7.44582852527492, 29.3371060956137], [-5.2278418113988, 28.5279279934545], [-3.0499662002487, 27.6855041419537], [-0.91083143731212, 26.8115406666263], [1.1910517467404, 25.907662551343], [3.2572732870332, 24.9754140020123], [5.289507352124, 24.0162595826945], [7.28949788500238, 23.0315860032884], [9.259046115687, 22.022704447347], [11.2, 20.9908533396875] ]
]
},
"properties" : {
"zoneID" : "A4-0-A"
}
}
```
```
> dgg -crs ico isea3h geom A4-0-A
```
#### `list`
##### List zones of a given refinement level
```
> dgg isea3h list 0
```
```json
[ "A0-0-A", "A1-0-A", "A2-0-A", "A3-0-A", "A4-0-A", "A5-0-A",
"A6-0-A", "A7-0-A", "A8-0-A", "A9-0-A", "AA-0-A", "AB-0-A" ]
```
##### List compacted zones of a given refinement level for a particular bounding box
```
> dgg isea3h list 10 -compact -bbox 44,-76,46,-74
```
```json
[ "E0-1397-A", "F0-AAC7-A", "F0-ABB7-A", "F0-ABB8-A", "F0-ABB9-A", "F0-ABBA-A",
"F0-ABBB-A", "F0-ACA9-A", "F0-ACAA-A", "F0-ACAB-A", "F0-ACAC-A", "F0-ACAD-A",
"F0-ACAE-A", "F0-AD9D-A", "F0-AD9E-A", "F0-ADA1-A", "F0-ADA2-A", "F0-AE91-A",
"F0-AE95-A", "F0-AF84-A", "F0-AF85-A", "F0-AF88-A", "F0-AF89-A", "F0-B078-A",
"F0-B079-A", "F0-B07A-A", "F0-B07B-A", "F0-B07C-A", "F0-B16B-A", "F0-B16C-A",
"F0-B16D-A", "F0-B16E-A", "F0-B16F-A", "F0-B170-A", "F0-B25F-A", "F0-B260-A",
"F0-B261-A", "F0-B262-A", "F0-B263-A", "F0-B352-A", "F0-B353-A", "F0-B354-A",
"F0-B355-A", "F0-B356-A", "F0-B357-A", "F0-B446-A", "F0-B447-A", "F0-B448-A" ]
```
#### `rel`
Show relationships between two zones
```
> dgg isea3h rel A4-0-A D4-20-D
DGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H
Relationships between zones A4-0-A (A) and D4-20-D (B):
Zone A is coarser than zone B by 7 refinement levels
The area of zone A is greater than the area of zone B (area of B is 0.054869684499314 % of zone A)
Zone A is NOT an immediate child of zone B
Zone A is NOT an immediate parent of zone B
Zone A is NOT a descendant of zone B
Zone A is an ancestor of zone B
Zone A is NOT a sub-zone of zone B
Zone A has B as a sub-zone (at depth 7, index 1034)
These zones are NOT neighbors
These zones are NOT siblings
Zone A is NOT contained in zone B
Zone A contains zone B
Zone A and B overlap
```
#### `sub`
##### Query sub-zones of parent zone at a particular relative depth
```
> dgg isea3h sub A4-0-A -depth 3
```
```json
[ "B2-7-B", "B2-4-D", "B2-4-C", "B2-5-B", "B2-7-D", "B2-7-C", "B2-8-B",
"B2-5-D", "B2-5-C", "B3-1-C", "B3-2-B", "B2-8-D", "B2-8-C", "B4-1-B",
"B4-1-C", "B3-5-B", "B3-2-D", "B3-2-C", "B4-0-B", "B4-0-C", "B4-1-D",
"B4-5-B", "B3-5-C", "B4-3-B", "B4-0-D", "B4-4-B", "B4-4-C", "B4-3-D",
"B4-3-C", "B4-4-D", "B4-7-B" ]
```
##### Identify sub-zone of parent zone at a particular relative depth and index
```
> dgg isea3h sub A4-0-A 8 -depth 3
```
```json
"B2-5-C"
```
#### `index`
##### Query index of sub-zone
```
> dgg isea3h index A4-0-A B2-5-C
DGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H
B2-5-C is at index 8 of A4-0-A at depth 3
```
```
> dgg isea3h index A4-0-A B6-5-C
DGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H
sub-zone B6-5-C not found within parent A4-0-A
```
#### `togeo`
Converts [DGGS-JSON](http://dggs-json.org) (and eventually [DGGS-JSON-FG](https://docs.ogc.org/DRAFTS/21-038r1.html#rc_data-dggs-jsonfg) and [UBJSON](https://ubjson.org/) variants) to GeoJSON
to facilitate interoperability with traditional GIS software / software not aware of the DGGRS.
https://maps.gnosis.earth/ogcapi/collections/sentinel2-l2a/dggs/ISEA3H/zones/G7-67252-B/data.json?zone-depth=8&datetime=2022-10-28&properties=B08
```
> dgg isea3h togeo -crs ico G7-67252-B-B08.json
```
_B08 (near-infrared) band retrieved as DGGS-JSON data from [Copernicus/ESA sentinel-2](https://sentinel.esa.int/web/sentinel/missions/sentinel-2) converted to GeoJSON and visualized in QGIS_
Raw data
{
"_id": null,
"home_page": "https://dggal.org",
"name": "dggal",
"maintainer": null,
"docs_url": null,
"requires_python": null,
"maintainer_email": null,
"keywords": "dggs hexagonal-grid global-grid ogc ogc-api gnosis dggrs isea ivea rtea isea3h isea9r ivea3h ivea9r slice-and-dice polyhedral-globe icosahedral rhealpix",
"author": "J\u00e9r\u00f4me Jacovella-St-Louis, Ecere Corporation",
"author_email": "jerome@ecere.com",
"download_url": "https://files.pythonhosted.org/packages/31/22/63cd3d583d5d7c60eba314dd42402fb53e767d6db9e3842324ad40208500/dggal-0.0.4.tar.gz",
"platform": null,
"description": "[](https://dggal.org/docs/html/dggal/Classes/DGGRS.html)<br>\n\n# DGGAL, the Discrete Global Grid Abstraction Library\n\nhttps://dggal.org\n\nDGGAL provides a common interface to perform various operations on Discrete Global Grid Reference Systems (DGGRS), facilitating the implementation of Discrete Global Grid Systems (DGGS),\nincluding implementing Web APIs based on the [OGC API - DGGS Standard](https://docs.ogc.org/DRAFTS/21-038r1.html).\n\nCopyright (c) 2014-2025, Ecere Corporation\n\nLicensed under the [BSD 3-Clause License](https://opensource.org/license/bsd-3-clause)\n\nSource: https://github.com/ecere/dggal\n\nPython packaging: https://github.com/ecere/pydggal\n\n## Supported Discrete Global Grid Reference Systems\n\nDGGAL currently supports all nine DGGRSs described in [OGC API - DGGS Annex B](https://docs.ogc.org/DRAFTS/21-038r1.html#annex-dggrs-def), as well as additional DGGRSs:\n\n### Axis-aligned DGGRS in WGS84 latitude and longitude (simple bounding boxes)\n\n* [GNOSIS Global Grid](https://docs.ogc.org/DRAFTS/21-038r1.html#ggg-dggrs): An axis-aligned quad-tree defined in WGS84 latitude and longitude, with special handling of polar regions achieving an approximate maximum of ~48% variance from median zone area, corresponding to the [OGC 2D Tile Matrix Set of the same name](https://docs.ogc.org/is/17-083r4/17-083r4.html#toc58)\n\n### Equal-Area DGGRSs based on Icosahedral Projections (aperture 3 and 7 Hexagonal, aperture 4 and 9 Axis-Aligned Rhombic)\n\nAll of these Icosahedral DGGRSs achieve equal-area on the WGS84 ellipsoid, and are oriented with a first vertex of the icosahedron positioned at\nauthalic latitude of _atan(\u03c6)_ (where \u03c6 is the golden ratio), and longitude 11.20\u00b0E, with second vertex due North, resulting in only one\nvertex / pentagon on land. Each of the 12 pentagons occupies 5/6th the area of a hexagon at the same refinement level.\n\n_WARNING: The aperture 7 hexagonal grids are still experimental; sub-zones are not yet implemented for them._\n\n#### Icosahedral Snyder Equal Area (ISEA) projection\n\n([An Equal-Area Map Projection for Polyhedral Globes (1992)](https://doi.org/10.3138%2F27H7-8K88-4882-1752), or dodecahedron configuration (DVEA) of [Slice & Dice (2006)](https://www.tandfonline.com/doi/abs/10.1559/152304006779500687))\n\n* **ISEA4R**: An equal area rhombic grid with a refinement ratio of 4 defined in the transformed into a 5x6 Cartesian space resulting in axis-aligned square zones\n* [ISEA9R](https://docs.ogc.org/DRAFTS/21-038r1.html#isea9r-dggrs): An equal area rhombic grid with a refinement ratio of 9 defined in the ISEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones\n* [ISEA3H](https://docs.ogc.org/DRAFTS/21-038r1.html#isea3h-dggrs): An equal area hexagonal grid with a refinement ratio of 3 defined in the ISEA projection\n* [ISEA7H](https://docs.ogc.org/DRAFTS/21-038r1.html#isea7h-dggrs): An equal area hexagonal grid with a refinement ratio of 7 defined in the ISEA projection\n\n#### Icosahedral Vertex-oriented great circle Equal Area (IVEA) projection\n\n([Slice & Dice (2006)](https://www.tandfonline.com/doi/abs/10.1559/152304006779500687), or applying [Snyder 1992](https://doi.org/10.3138%2F27H7-8K88-4882-1752) to the dodecahedron (DSEA))\n\n* **IVEA4R**: An equal area rhombic grid with a refinement ratio of 4 defined in the IVEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones, using the same global indexing and sub-zone ordering as for ISEA4R\n* [IVEA9R](https://docs.ogc.org/DRAFTS/21-038r1.html#ivea9r-dggrs): An equal area rhombic grid with a refinement ratio of 9 defined in the IVEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones, using the same global indexing and sub-zone ordering as for ISEA9R\n* [IVEA3H](https://docs.ogc.org/DRAFTS/21-038r1.html#ivea3h-dggrs): An equal area hexagonal grid with a refinement ratio of 3 defined in the IVEA projection, using the same global indexing and sub-zone ordering as for ISEA3H\n* [IVEA7H](https://docs.ogc.org/DRAFTS/21-038r1.html#ivea7h-dggrs): An equal area hexagonal grid with a refinement ratio of 7 defined in the IVEA projection, using the same global indexing and sub-zone ordering as for ISEA7H\n\n**NOTE:** This projection is superior to ISEA and RT(S)EA at avoiding perceptible cusps, resulting in more compact/regular zones.\n\n#### Rhombic Triacontahedron (Snyder) Equal-Area (RT(S)EA) projection\n\n(applying [Snyder 1992](https://doi.org/10.3138%2F27H7-8K88-4882-1752) to the Rhombic Triacontahedron,\n alternate configuration of [Slice & Dice (2006)](https://www.tandfonline.com/doi/abs/10.1559/152304006779500687),\n[Disdyakis Triacontahedron Discrete Global Grid System](http://hdl.handle.net/1880/114595), or\n[Construction of rhombic triacontahedron discrete global grid systems](https://doi.org/10.1080/17538947.2022.2130459))\n\n* **RTEA4R**: An equal area rhombic grid with a refinement ratio of 4 defined in the RTEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones, using the same global indexing and sub-zone ordering as for ISEA4R\n* **RTEA9R**: An equal area rhombic grid with a refinement ratio of 9 defined in the RTEA projection transformed into a 5x6 Cartesian space resulting in axis-aligned square zones, using the same global indexing and sub-zone ordering as for ISEA9R\n* **RTEA3H**: An equal area hexagonal grid with a refinement ratio of 3 defined in the RTEA projection using the same global indexing and sub-zone ordering as for ISEA3H\n* **RTEA7H**: An equal area hexagonal grid with a refinement ratio of 7 defined in the RTEA projection using the same global indexing and sub-zone ordering as for ISEA7H\n\n### Axis-aligned and Equal-Area DGGRSs based on HEALPix Projection\n\n([HEALPix projection](https://arxiv.org/pdf/astro-ph/0409513))\n\n* [HEALPix](https://docs.ogc.org/DRAFTS/21-038r1.html#HEALPix-dggrs): An equal area and axis-aligned grid with square zones topology and a refinement ratio of 4 defined in the HEALPix projection, using configuration N\u03c6/H = 4, N\u03b8/K = 3 (same as default [PROJ implementation](https://proj.org/en/stable/operations/projections/healpix.html)), the new indexing described in OGC API - DGGS Annex B, and scanline-based sub-zone ordering\n* [rHEALPix](https://docs.ogc.org/DRAFTS/21-038r1.html#rHEALPix-dggrs): An equal area and axis-aligned grid with square zones topology and a refinement ratio of 9 defined in the rHEALPix projection using 50\u00b0 E prime meridian (equivalent to [PROJ implementation](https://proj.org/en/stable/operations/projections/rhealpix.html) with parameters `+proj=rhealpix +lon_0=50 +ellps=WGS84`), the [original hierarchical indexing](https://iopscience.iop.org/article/10.1088/1755-1315/34/1/012012), and scanline-based sub-zone ordering\n\n## libDGGAL API Documentation\n\nThe API documentation can be [found here](https://dggal.org/docs/html/dggal/Classes/DGGRS.html).\n\nThe `DGGRS` class provides most of the functionality of the library, allowing to resolve DGGRS zones by textual ID to a unique 64-bit zone integer identifier (`DGGRSZone`).\nThe geometry and sub-zones of a particular zone can also be queried.\nThe concept of [sub-zones](https://docs.ogc.org/DRAFTS/21-038r1.html#term-sub-zone) is key to encoding both vector and raster geospatial data quantized to a DGGRS.\nThe DGGAL library also allows to resolve a sub-zone index at a particular depth from a parent zone, allowing to read DGGS-optimized data such as\n[DGGS-JSON](http://dggs-json.org) and [DGGS-JSON-FG](https://docs.ogc.org/DRAFTS/21-038r1.html#rc_data-dggs-jsonfg).\n\n## Language bindings\n\nWhile the library is written in the [eC programming language](https://ec-lang.org), object-oriented bindings for C, C++ and Python generated using the\nEcere SDK's [`bgen` tool](https://github.com/ecere/bgen) are provided. Bindings for Rust are available as well.\nSupport for additional languages may be added in the future.\n\n## `dgg` tool\n\n### Syntax\n```\n dgg <dggrs> <command> [options] <arguments>\n```\n\n### Supported DGGRSs\n* `gnosis` (Global Grid)\n* `isea4r`, `isea9r`, `isea3h`, `isea7h`\n* `ivea4r`, `ivea9r`, `ivea3h`, `ivea7h`\n* `rtea4r`, `rtea9r`, `rtea3h`, `rtea7h`\n* `rhealpix` (aperture 9, 50\u00b0 E)\n* `healpix` (aperture 4, N\u03c6/H = 4, N\u03b8/K = 3)\n\n### Commands\n\n[**info**](#info) [_zone_]\n\n- Display information about a DGGRS or about a zone of a DGGRS\n\n[**zone**](#zone) <_coord1,coord2_> [_level_]\n\n- Return DGGRS zone at position -- specified in EPSG:4326 (lat,lon)\n\n[**level**](#level) [_level_]\n\n- Display information about a DGGRS refinement level\n\n[**grid**](#grid) [_level_]\n- Generate DGGRS grid at specified refinement level (default: 0)\n\n[**geom**](#geom) <_zone_>\n- Generate geometry for a particular zone\n\n[**list**](#list) [_level_]\n- List DGGRS zones (as JSON string array)\n\n[**rel**](#rel) <_zone 1_> <_zone 2_>\n- Display information about the relationships between two zones of a DGGRS\n\n[**sub**](#sub) <_zone_> [_index_]\n- List subzones of a DGGRS zone or resolve a sub-zone by index\n\n[**index**](#index) <_parent zone_> <_sub-zone_>\n- Display index of sub-zone within parent\n\n**compact** <_JSON input zone file (zone ID strings array)_>\n- Compact input zone list\n\n**decompact** <_JSON input zone file (zone ID strings array)_> [_level_]\n- Decompact zone list\n\n[**togeo**](#togeo) <_DGGS-(UB)JSON(-FG) input file_>\n- Convert DGGS-JSON (DGGS-quantized raster data) or DGGS-JSON-FG (DGGS-quantized vector data) to GeoJSON\n\n### Options\n\n**-o** <_filename_>\n- Output to file instead of standard output\n\n**-crs** <_crs_>\n- Select an output coordinate reference system, one of:\nEPSG:4326, OGC:CRS84, 5x6, ico (icosahedron net), rhp (rHEALPix), hpx (HEALPix)\n\n**-depth** <_relative depth_>\n- For sub, specify relative depth\nAlso to change depth considered for calculating optional [level] from -scale, -mpp and -pixels\ndefault: depth corresponding to ~64K sub-zones (IS/VEA9R: 5, IS/VEA3H: 10, GNOSIS: 8)\n\n**-bbox** <_llLat,llLon,urLat,urLon_>\n- Specify extent for which to list zones, generate grid, or reference extent for -pixels\nexample: -bbox 60,-120,62,-118 -- specified in EPSG:4326 (lat,lon)\n\n**-centroids**\n- For sub, list centroids instead of sub-zone identifiers\nFor togeo, use centroid points for geometry instead of polygons\n\n**-compact**\n- For list and grid, return compact list of zones\n\n**-mpp** <_physical meters per sub-zone_>\n- Specify physical meters per sub-zone as substitute for optional [level] arguments\n\n**-scale-denom** <_scale denominator_>\n- Specify scale-denominator as substitute for optional [level] arguments (based on -depth)\n\n**-pixels** <_with,height_>\n- Specify display pixels as a substitute for optional [level] argument (in combination with -bbox)\n\n**-display-res** <_mm-per-pixels_>\n- Specify display resolution in millimeters/pixel in combination with -scale and -pixels (default: 0.28)\n\n### Example Usage\n\n#### `info`\n\n##### Information about a particular DGGRS\n\n```\n> dgg isea3h info\nDGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H\nRefinement Ratio: 3\nMaximum level for 64-bit global identifiers (DGGAL DGGRSZone): 33\nDefault ~64K sub-zones relative depth: 10\n```\n\n##### Information about a particular zone\n\n```\n> dgg isea3h info A4-0-A\nDGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H\nTextual Zone ID: A4-0-A\n64-bit integer ID: 36028797018963968 (0x80000000000000)\n\nLevel 0 zone (5 edges, centroid child)\n42505468477007.4 m\u00b2 (42505468.4770074 km\u00b2)\n49411 sub-zones at depth 10\nWGS84 Centroid (lat, lon): 0, -20.517474730219\nWGS84 Extent (lat, lon): { -35.385452137707, -57.8948427221833 }, { 35.385452137707, 11.2 }\n\nNo parent\n\nChildren (6):\n A4-0-B (centroid)\n A4-0-C\n A4-0-D\n A3-0-C\n A2-0-D\n A2-0-C\n\nNeighbors (5):\n (direction 2): A2-0-A\n (direction 3): A6-0-A\n (direction 0): AA-0-A\n (direction 6): A3-0-A\n (direction 7): A5-0-A\n\n[EPSG:4326] Vertices (5):\n 20.9908527620464, 11.2\n -20.9908527620465, 11.2\n -35.385452137707, -33.8\n 0, -57.8948427221833\n 35.385452137707, -33.8\n```\n\n#### `zone`\n\nIdentify zone at a particular geodetic position.\n\n```\n> dgg isea3h zone 34,-70\nDGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H\nTextual Zone ID: A2-0-A\n64-bit integer ID: 18014398509481984 (0x40000000000000)\n\nLevel 0 zone (5 edges, centroid child)\n42505468477007.4 m\u00b2 (42505468.4770074 km\u00b2)\n49411 sub-zones at depth 10\nWGS84 Centroid (lat, lon): 31.832357532016, -78.8\nWGS84 Extent (lat, lon): { 0, -123.8 }, { 69.1802093248182, -33.8 }\n\nNo parent\n\nChildren (6):\n A2-0-B (centroid)\n A2-0-C\n A2-0-D\n A1-0-C\n A0-0-D\n A0-0-C\n\nNeighbors (5):\n (direction 2): A0-0-A\n (direction 3): A4-0-A\n (direction 0): AA-0-A\n (direction 6): A1-0-A\n (direction 7): A3-0-A\n\n[EPSG:4326] Vertices (5):\n 35.385452137707, -33.8\n 0, -57.8948427221833\n 0, -99.7051575819393\n 35.3854519371908, -123.8\n 69.1802093248182, -78.8\n```\n\n#### `level`\n\n##### Information about levels of a particular DGGRS\n\n```\n> dgg isea3h level\nDGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H\nAssuming sub-zone depth of 10 and display resolution of 0.28 mm/pixel:\nLevel Reference Area Sub-zones count Sub-zone area Scale Meters/Sub-zone\n-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n 0: 42505468477007.39843750 m\u00b2 (42505468.47700740 km\u00b2) 49411 860243032.46255684 m\u00b2 ( 8602430324625.56933594 cm\u00b2) 1: 104965840 29390.43523832 m ( 2939043.52383217 cm)\n 1: 15939550678877.77343750 m\u00b2 (15939550.67887777 km\u00b2) 59293 268826854.41582942 m\u00b2 ( 2688268544158.29394531 cm\u00b2) 1: 60602124 16968.59485403 m ( 1696859.48540341 cm)\n 2: 5544191540479.22558594 m\u00b2 ( 5544191.54047923 km\u00b2) 59293 93504992.84028849 m\u00b2 ( 935049928402.88488770 cm\u00b2) 1: 34988666 9796.82649363 m ( 979682.64936343 cm)\n 3: 1875241256338.56152344 m\u00b2 ( 1875241.25633856 km\u00b2) 59293 31626688.75480346 m\u00b2 ( 316266887548.03460693 cm\u00b2) 1: 20200718 5656.20112285 m ( 565620.11228463 cm)\n 4: 628159632665.13391113 m\u00b2 ( 628159.63266513 km\u00b2) 59293 10594161.75037751 m\u00b2 ( 105941617503.77513123 cm\u00b2) 1: 11662891 3265.60937742 m ( 326560.93774175 cm)\n 5: 209730929985.23385620 m\u00b2 ( 209730.92998523 km\u00b2) 59293 3537195.45283986 m\u00b2 ( 35371954528.39860535 cm\u00b2) 1: 6733573 1885.40047940 m ( 188540.04793995 cm)\n 6: 69948659040.60459900 m\u00b2 ( 69948.65904060 km\u00b2) 59293 1179711.92283414 m\u00b2 ( 11797119228.34138870 cm\u00b2) 1: 3887630 1088.53647937 m ( 108853.64793690 cm)\n 7: 23320483802.30837250 m\u00b2 ( 23320.48380231 km\u00b2) 59293 393309.22372470 m\u00b2 ( 3933092237.24695539 cm\u00b2) 1: 2244524 628.46683036 m ( 62846.68303597 cm)\n 8: 7773968507.65239239 m\u00b2 ( 7773.96850765 km\u00b2) 59293 131111.06720275 m\u00b2 ( 1311110672.02745557 cm\u00b2) 1: 1295877 362.84549387 m ( 36284.54938723 cm)\n 9: 2591375496.48476219 m\u00b2 ( 2591.37549648 km\u00b2) 59293 43704.57720953 m\u00b2 ( 437045772.09531683 cm\u00b2) 1: 748175 209.48894360 m ( 20948.89435974 cm)\n10: 863797683.49797928 m\u00b2 ( 863.79768350 km\u00b2) 59293 14568.29108829 m\u00b2 ( 145682910.88290006 cm\u00b2) 1: 431959 120.94849799 m ( 12094.84979852 cm)\n11: 287933211.32035321 m\u00b2 ( 287.93321132 km\u00b2) 59293 4856.10799454 m\u00b2 ( 48561079.94541568 cm\u00b2) 1: 249392 69.82964787 m ( 6982.96478712 cm)\n12: 95977809.34637524 m\u00b2 ( 95.97780935 km\u00b2) 59293 1618.70388320 m\u00b2 ( 16187038.83196587 cm\u00b2) 1: 143986 40.31616600 m ( 4031.61659961 cm)\n13: 31992611.14208768 m\u00b2 ( 31.99261114 km\u00b2) 59293 539.56809644 m\u00b2 ( 5395680.96437820 cm\u00b2) 1: 83131 23.27654929 m ( 2327.65492906 cm)\n14: 10664204.60587722 m\u00b2 ( 10.66420461 km\u00b2) 59293 179.85604719 m\u00b2 ( 1798560.47187311 cm\u00b2) 1: 47995 13.43872200 m ( 1343.87219987 cm)\n15: 3554734.96771997 m\u00b2 ( 3.55473497 km\u00b2) 59293 59.95201740 m\u00b2 ( 599520.17400367 cm\u00b2) 1: 27710 7.75884976 m ( 775.88497635 cm)\n16: 1184911.66691713 m\u00b2 ( 1.18491167 km\u00b2) 59293 19.98400599 m\u00b2 ( 199840.05985818 cm\u00b2) 1: 15998 4.47957400 m ( 447.95739996 cm)\n17: 394970.55686243 m\u00b2 ( 0.39497056 km\u00b2) 59293 6.66133535 m\u00b2 ( 66613.35349239 cm\u00b2) 1: 9237 2.58628325 m ( 258.62832545 cm)\n18: 131656.85242341 m\u00b2 ( 0.13165685 km\u00b2) 59293 2.22044512 m\u00b2 ( 22204.45118706 cm\u00b2) 1: 5333 1.49319133 m ( 149.31913332 cm)\n19: 43885.61748957 m\u00b2 ( 0.04388562 km\u00b2) 59293 0.74014837 m\u00b2 ( 7401.48373157 cm\u00b2) 1: 3079 0.86209442 m ( 86.20944182 cm)\n20: 14628.53916487 m\u00b2 ( 0.01462854 km\u00b2) 59293 0.24671612 m\u00b2 ( 2467.16124414 cm\u00b2) 1: 1778 0.49773044 m ( 49.77304444 cm)\n21: 4876.17972181 m\u00b2 ( 0.00487618 km\u00b2) 59293 0.08223871 m\u00b2 ( 822.38708141 cm\u00b2) 1: 1026 0.28736481 m ( 28.73648061 cm)\n22: 1625.39324062 m\u00b2 ( 0.00162539 km\u00b2) 59293 0.02741290 m\u00b2 ( 274.12902714 cm\u00b2) 1: 593 0.16591015 m ( 16.59101481 cm)\n23: 541.79774688 m\u00b2 ( 0.00054180 km\u00b2) 59293 0.00913763 m\u00b2 ( 91.37634238 cm\u00b2) 1: 342 0.09578827 m ( 9.57882687 cm)\n24: 180.59924896 m\u00b2 ( 0.00018060 km\u00b2) 59293 0.00304588 m\u00b2 ( 30.45878079 cm\u00b2) 1: 129 0.03620456 m ( 3.62045625 cm)\n25: 60.19974965 m\u00b2 ( 0.00006020 km\u00b2) 59293 0.00101529 m\u00b2 ( 10.15292693 cm\u00b2) 1: 95 0.02656689 m ( 2.65668857 cm)\n26: 20.06658322 m\u00b2 ( 0.00002007 km\u00b2) 59293 0.00033843 m\u00b2 ( 3.38430898 cm\u00b2) 1: 56 0.01574749 m ( 1.57474944 cm)\n27: 6.68886107 m\u00b2 ( 0.00000669 km\u00b2) 59293 0.00011281 m\u00b2 ( 1.12810299 cm\u00b2) 1: 36 0.01004134 m ( 1.00413390 cm)\n28: 2.22962036 m\u00b2 ( 0.00000223 km\u00b2) 59293 0.00003760 m\u00b2 ( 0.37603433 cm\u00b2) 1: 21 0.00581872 m ( 0.58187229 cm)\n29: 0.74320679 m\u00b2 ( 0.00000074 km\u00b2) 59293 0.00001253 m\u00b2 ( 0.12534478 cm\u00b2) 1: 12 0.00348148 m ( 0.34814838 cm)\n30: 0.24773560 m\u00b2 ( 0.00000025 km\u00b2) 59293 0.00000418 m\u00b2 ( 0.04178159 cm\u00b2) 1: 7 0.00201092 m ( 0.20109213 cm)\n31: 0.08257853 m\u00b2 ( 0.00000008 km\u00b2) 59293 0.00000139 m\u00b2 ( 0.01392720 cm\u00b2) 1: 4 0.00117525 m ( 0.11752498 cm)\n32: 0.02752618 m\u00b2 ( 0.00000003 km\u00b2) 59293 0.00000046 m\u00b2 ( 0.00464240 cm\u00b2) 1: 2 0.00067856 m ( 0.06785649 cm)\n33: 0.00917539 m\u00b2 ( 0.00000001 km\u00b2) 59293 0.00000015 m\u00b2 ( 0.00154747 cm\u00b2) 1: 1 0.00039338 m ( 0.03933785 cm)\n```\n\n##### Information about a particular DGGRS level\n```\n> dgg isea3h level 15\nDGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H\nRefinement Level: 15\nReference area: 3554734.96771997 m\u00b2 (3.55473496771997 km\u00b2)\n\nAssuming sub-zone depth of 10 (59293 sub-zones) and display resolution of 0.28 mm/pixel:\n Sub-zones area: 59.9520174003672 m\u00b2 (599520.174003672 cm\u00b2)\n Cartographic scale: 1:27710\n Physical meters/sub-zone: 7.75884976353492 (775.884976353492 cm/sub-zone)\n```\n\n#### `grid`\n\n##### Generate grid geometry for a particular refinement level\n\nOutput is [GeoJSON](https://geojson.org/):\n\n```\n> dgg isea3h -crs ico grid 3 > isea3h-level3-isea.geojson\n```\n\n\n\n```\n> dgg isea3h grid 3 > isea3h-level3-crs84.geojson\n```\n\n\n\n##### Generate grid geometry for a given bounding box using compacted zones\n\n```\n> dgg isea3h grid 15 -compact -bbox 44,-76,46,-74\n```\n\n\n\n\n#### `geom`\n\nGenerate geometry of a specific zone\n\n```\n> dgg isea3h geom A4-0-A\n```\n\n```geojson\n{\n \"type\" : \"Feature\",\n \"id\" : \"A4-0-A\",\n \"geometry\" : {\n \"type\" : \"Polygon\",\n \"coordinates\" : [\n [ [11.2, 20.9908533396875], [11.2, 18.9046368254835], [11.2, 16.817317021754], [11.2, 14.7282441160477], [11.2, 12.6367658994772], [11.2, 10.5422256002322], [11.2, 8.44395966388283], [11.2, 6.3412954618102], [11.2, 4.2335489079295], [11.2, 2.12002196235325], [11.2, -0.00000000000000958], [11.2, -2.12002196235327], [11.2, -4.2335489079295], [11.2, -6.34129546181022], [11.2, -8.44395966388284], [11.2, -10.5422256002322], [11.2, -12.6367658994773], [11.2, -14.7282441160477], [11.2, -16.817317021754], [11.2, -18.9046368254835], [11.2, -20.9908533396875], [9.25904611568614, -22.022704447347], [7.2894978850024, -23.0315860032884], [5.2895073521231, -24.0162595826945], [3.2572732870332, -24.9754140020123], [1.19105174674043, -25.907662551343], [-0.910831437312103, -26.8115406666264], [-3.04996620024865, -27.6855041419538], [-5.22784181139874, -28.5279279934546], [-7.44582852527487, -29.3371060956138], [-9.70515744760715, -30.111251717508], [-11.9990182364648, -30.8460627665615], [-14.3199274459944, -31.5377272377057], [-16.6678118661126, -32.1851262644314], [-19.0423550054196, -32.7871381036537], [-21.4429904142008, -33.3426478478608], [-23.868897601607, -33.8505577351568], [-26.319001132268, -34.3097979200868], [-28.791973441741, -34.7193375329077], [-31.2862418322802, -35.0781958218138], [-33.7999999994894, -35.385453143805], [-35.328584064796, -33.7294909375037], [-36.7997931901407, -32.0544538235723], [-38.2190895198383, -30.3615150627895], [-39.591520816704, -28.651669714028], [-40.9217621171856, -26.9257555850354], [-42.2141557503646, -25.184471421695], [-43.4727493595782, -23.4283926793226], [-44.7013318005733, -21.6579851878463], [-45.9034669523704, -19.8736169902905], [-47.0825255880168, -18.075568603016], [-48.2378134716698, -16.2702095110336], [-49.3687568644497, -14.463940351611], [-50.4786064975358, -12.656986739445], [-51.5704092970534, -10.8495265877445], [-52.647041014988, -9.04169850753405], [-53.7112358369818, -7.23360915100237], [-54.765613515085, -5.42533970970474], [-55.8127045186767, -3.61695174870332], [-56.8549736519885, -1.80849253470827], [-57.894842551487, 0.0000000010850795], [-56.8549736519113, 1.80849253683432], [-55.8127045185966, 3.61695175082982], [-54.7656135150002, 5.425339711832], [-53.7112358368904, 7.2336091531306], [-52.6470410148878, 9.04169850966353], [-51.5704092969423, 10.8495265898755], [-50.4786064974117, 12.6569867415778], [-49.36875686431, 14.4639403537457], [-48.237813471512, 16.2702095131705], [-47.082525588539, 18.0755686040723], [-45.9034669536086, 19.873616990275], [-44.7013318018277, 21.6579851878424], [-43.47274936085, 23.428392679331], [-42.214155751655, 25.1844714217162], [-40.9217621184958, 26.9257555850703], [-39.5915208180354, 28.651669714077], [-38.219089521192, 30.3615150628536], [-36.799793191518, 32.0544538236523], [-35.328584066198, 33.7294909376005], [-33.8000000009355, 35.3854531438384], [-31.2862418337828, 35.0781958220137], [-28.7919734432313, 34.7193375331383], [-26.3190011337452, 34.3097979203474], [-23.86889760307, 33.850557735447], [-21.442990415649, 33.34264784818], [-19.0423550068522, 32.787138104001], [-16.6678118675294, 32.1851262648063], [-14.319927447395, 31.5377272381076], [-11.9990182378492, 30.8460627669896], [-9.70515744897538, 30.1112517179616], [-9.7051574476072, 30.1112517175078], [-7.44582852527492, 29.3371060956137], [-5.2278418113988, 28.5279279934545], [-3.0499662002487, 27.6855041419537], [-0.91083143731212, 26.8115406666263], [1.1910517467404, 25.907662551343], [3.2572732870332, 24.9754140020123], [5.289507352124, 24.0162595826945], [7.28949788500238, 23.0315860032884], [9.259046115687, 22.022704447347], [11.2, 20.9908533396875] ]\n ]\n },\n \"properties\" : {\n \"zoneID\" : \"A4-0-A\"\n }\n}\n```\n\n```\n> dgg -crs ico isea3h geom A4-0-A\n```\n\n\n\n#### `list`\n\n##### List zones of a given refinement level\n\n```\n> dgg isea3h list 0\n```\n\n```json\n[ \"A0-0-A\", \"A1-0-A\", \"A2-0-A\", \"A3-0-A\", \"A4-0-A\", \"A5-0-A\",\n\"A6-0-A\", \"A7-0-A\", \"A8-0-A\", \"A9-0-A\", \"AA-0-A\", \"AB-0-A\" ]\n```\n\n##### List compacted zones of a given refinement level for a particular bounding box\n\n```\n> dgg isea3h list 10 -compact -bbox 44,-76,46,-74\n```\n\n```json\n[ \"E0-1397-A\", \"F0-AAC7-A\", \"F0-ABB7-A\", \"F0-ABB8-A\", \"F0-ABB9-A\", \"F0-ABBA-A\",\n\"F0-ABBB-A\", \"F0-ACA9-A\", \"F0-ACAA-A\", \"F0-ACAB-A\", \"F0-ACAC-A\", \"F0-ACAD-A\",\n\"F0-ACAE-A\", \"F0-AD9D-A\", \"F0-AD9E-A\", \"F0-ADA1-A\", \"F0-ADA2-A\", \"F0-AE91-A\",\n\"F0-AE95-A\", \"F0-AF84-A\", \"F0-AF85-A\", \"F0-AF88-A\", \"F0-AF89-A\", \"F0-B078-A\",\n\"F0-B079-A\", \"F0-B07A-A\", \"F0-B07B-A\", \"F0-B07C-A\", \"F0-B16B-A\", \"F0-B16C-A\",\n\"F0-B16D-A\", \"F0-B16E-A\", \"F0-B16F-A\", \"F0-B170-A\", \"F0-B25F-A\", \"F0-B260-A\",\n\"F0-B261-A\", \"F0-B262-A\", \"F0-B263-A\", \"F0-B352-A\", \"F0-B353-A\", \"F0-B354-A\",\n\"F0-B355-A\", \"F0-B356-A\", \"F0-B357-A\", \"F0-B446-A\", \"F0-B447-A\", \"F0-B448-A\" ]\n```\n\n#### `rel`\n\nShow relationships between two zones\n\n```\n> dgg isea3h rel A4-0-A D4-20-D\nDGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H\nRelationships between zones A4-0-A (A) and D4-20-D (B):\n\nZone A is coarser than zone B by 7 refinement levels\nThe area of zone A is greater than the area of zone B (area of B is 0.054869684499314 % of zone A)\nZone A is NOT an immediate child of zone B\nZone A is NOT an immediate parent of zone B\nZone A is NOT a descendant of zone B\nZone A is an ancestor of zone B\nZone A is NOT a sub-zone of zone B\nZone A has B as a sub-zone (at depth 7, index 1034)\nThese zones are NOT neighbors\nThese zones are NOT siblings\nZone A is NOT contained in zone B\nZone A contains zone B\nZone A and B overlap\n```\n\n#### `sub`\n\n##### Query sub-zones of parent zone at a particular relative depth\n\n```\n> dgg isea3h sub A4-0-A -depth 3\n```\n\n```json\n[ \"B2-7-B\", \"B2-4-D\", \"B2-4-C\", \"B2-5-B\", \"B2-7-D\", \"B2-7-C\", \"B2-8-B\",\n\"B2-5-D\", \"B2-5-C\", \"B3-1-C\", \"B3-2-B\", \"B2-8-D\", \"B2-8-C\", \"B4-1-B\",\n\"B4-1-C\", \"B3-5-B\", \"B3-2-D\", \"B3-2-C\", \"B4-0-B\", \"B4-0-C\", \"B4-1-D\",\n\"B4-5-B\", \"B3-5-C\", \"B4-3-B\", \"B4-0-D\", \"B4-4-B\", \"B4-4-C\", \"B4-3-D\",\n\"B4-3-C\", \"B4-4-D\", \"B4-7-B\" ]\n```\n\n##### Identify sub-zone of parent zone at a particular relative depth and index\n\n```\n> dgg isea3h sub A4-0-A 8 -depth 3\n```\n\n```json\n\"B2-5-C\"\n```\n\n#### `index`\n\n##### Query index of sub-zone\n\n```\n> dgg isea3h index A4-0-A B2-5-C\nDGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H\nB2-5-C is at index 8 of A4-0-A at depth 3\n```\n\n```\n> dgg isea3h index A4-0-A B6-5-C\nDGGRS: https://maps.gnosis.earth/ogcapi/dggrs/ISEA3H\nsub-zone B6-5-C not found within parent A4-0-A\n```\n\n#### `togeo`\n\nConverts [DGGS-JSON](http://dggs-json.org) (and eventually [DGGS-JSON-FG](https://docs.ogc.org/DRAFTS/21-038r1.html#rc_data-dggs-jsonfg) and [UBJSON](https://ubjson.org/) variants) to GeoJSON\nto facilitate interoperability with traditional GIS software / software not aware of the DGGRS.\n\nhttps://maps.gnosis.earth/ogcapi/collections/sentinel2-l2a/dggs/ISEA3H/zones/G7-67252-B/data.json?zone-depth=8&datetime=2022-10-28&properties=B08\n\n```\n> dgg isea3h togeo -crs ico G7-67252-B-B08.json\n```\n\n\n\n_B08 (near-infrared) band retrieved as DGGS-JSON data from [Copernicus/ESA sentinel-2](https://sentinel.esa.int/web/sentinel/missions/sentinel-2) converted to GeoJSON and visualized in QGIS_\n",
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