Coordinate Systems Overview¶
The Geodetic gem supports 18 coordinate systems organized into six categories. All coordinate classes live under Geodetic::Coordinate.
Global Systems¶
| System | Class | Description |
|---|---|---|
| LLA | Geodetic::Coordinate::LLA |
Latitude, Longitude, Altitude. The most common geographic coordinate system, expressing positions in decimal degrees with altitude in meters. Negative longitude is the Western hemisphere; negative latitude is the Southern hemisphere. |
| ECEF | Geodetic::Coordinate::ECEF |
Earth-Centered, Earth-Fixed. A Cartesian coordinate system with the origin at the Earth's center of mass. Positions are expressed as X, Y, Z in meters. Commonly used in satellite navigation and aerospace applications. |
| UTM | Geodetic::Coordinate::UTM |
Universal Transverse Mercator. Divides the Earth into 60 zones (each 6 degrees of longitude), projecting positions as easting/northing in meters within a zone and hemisphere. Covers latitudes 80S to 84N. |
Local Tangent Plane Systems¶
| System | Class | Description |
|---|---|---|
| ENU | Geodetic::Coordinate::ENU |
East, North, Up. A local tangent plane coordinate system centered on a reference point. Axes point East, North, and Up relative to the reference. Distances are in meters. Used in robotics, surveying, and local navigation. |
| NED | Geodetic::Coordinate::NED |
North, East, Down. A local tangent plane coordinate system centered on a reference point. Axes point North, East, and Down. Used extensively in aerospace and aviation applications. Mathematically related to ENU by axis reordering and sign inversion. |
Military and Grid Systems¶
| System | Class | Description |
|---|---|---|
| MGRS | Geodetic::Coordinate::MGRS |
Military Grid Reference System. An alphanumeric system based on UTM that identifies positions using grid zone designator, 100km square identifier, and numeric easting/northing. Variable precision from 10km down to 1m. |
| USNG | Geodetic::Coordinate::USNG |
United States National Grid. Based on MGRS but formatted with spaces for readability. Used primarily within the United States for emergency services and land management. |
Web Mapping¶
| System | Class | Description |
|---|---|---|
| WebMercator | Geodetic::Coordinate::WebMercator |
Web Mercator (EPSG:3857). Also known as Pseudo-Mercator or Spherical Mercator. The projection used by Google Maps, OpenStreetMap, and Bing Maps. Positions are X/Y in meters. Latitude is clamped to approximately ±85.05 degrees. Includes tile and pixel coordinate methods for web mapping applications. |
Polar¶
| System | Class | Description |
|---|---|---|
| UPS | Geodetic::Coordinate::UPS |
Universal Polar Stereographic. Covers the polar regions not handled by UTM (north of 84N and south of 80S). Uses a stereographic projection centered on each pole with zones Y/Z (north) and A/B (south). |
Spatial Hashing¶
| System | Class | Description |
|---|---|---|
| GH36 | Geodetic::Coordinate::GH36 |
Geohash-36. A hierarchical spatial hashing algorithm that encodes latitude/longitude into a compact, URL-friendly string using a case-sensitive 36-character alphabet (radix-36). Each hash represents a rectangular cell; the coordinate value is the cell midpoint. Supports neighbor lookup, area extraction via to_area, and configurable precision (default 10 characters for sub-meter resolution). |
| GH | Geodetic::Coordinate::GH |
Geohash (base-32). The standard geohash algorithm by Gustavo Niemeyer using a 32-character alphabet (0-9, b-z excluding a, i, l, o). The de facto standard for spatial hashing, natively supported by Elasticsearch, Redis, PostGIS, and many geocoding services. Supports neighbor lookup, area extraction, and configurable precision (default 12 characters for sub-centimeter resolution). |
| HAM | Geodetic::Coordinate::HAM |
Maidenhead Locator System. A hierarchical grid system used worldwide in amateur radio that encodes positions using alternating letter/digit pairs (e.g., FN31pr). Four levels of precision: Field (18x18), Square (10x10), Subsquare (24x24), Extended (10x10). Supports neighbor lookup, area extraction, and configurable precision (default 6 characters for ~5 km resolution). |
| OLC | Geodetic::Coordinate::OLC |
Open Location Code (Plus Codes). Google's open system for encoding locations into short codes like 849VCWC8+R9. Uses a 20-character alphabet with 5 paired levels of base-20 encoding plus optional grid refinement. Includes a + separator at position 8. Supports neighbor lookup, area extraction, and configurable precision (default 10 characters for ~14 m resolution). |
| GEOREF | Geodetic::Coordinate::GEOREF |
World Geographic Reference System. A geocode system used in aviation and military applications that encodes positions using letter tiles (15° grid), letter degree subdivisions, and numeric minute pairs. Uses a 24-letter alphabet (A-Z excluding I and O). Supports variable precision from 15° tiles (2 chars) down to 0.01-minute resolution (12 chars). Default precision is 8 characters (1-minute resolution). |
| GARS | Geodetic::Coordinate::GARS |
Global Area Reference System. An NGA standard that divides the world into 30-minute cells identified by a 3-digit longitude band (001-720) and 2-letter latitude band. Cells are subdivided into 15-minute quadrants (1-4) and 5-minute keypads (1-9, telephone layout). Variable precision: 5 chars (30'), 6 chars (15'), 7 chars (5'). Default precision is 7 characters. |
| H3 | Geodetic::Coordinate::H3 |
H3 Hexagonal Hierarchical Index. Uber's spatial indexing system that divides the globe into hexagonal cells (and 12 pentagons) at 16 resolution levels (0-15). Each cell is a 64-bit integer displayed as a hex string. Unlike the rectangular spatial hashes, to_area returns an Areas::Polygon with 6 vertices (5 for pentagons) and neighbors returns an Array of 6 cells. Requires libh3 installed (brew install h3 on macOS). |
Regional Systems¶
| System | Class | Description |
|---|---|---|
| StatePlane | Geodetic::Coordinate::StatePlane |
State Plane Coordinate System. US state-based coordinate systems using Lambert Conformal Conic or Transverse Mercator projections. Each state has one or more zones with specific parameters. Coordinates are typically in US Survey Feet. |
| BNG | Geodetic::Coordinate::BNG |
British National Grid. The official coordinate system for Great Britain, based on the OSGB36 datum with the Airy 1830 ellipsoid. Uses a Transverse Mercator projection and an alphanumeric grid reference system (e.g., "TQ 30 80"). |
Conversion Matrix¶
Every coordinate system can convert to every other coordinate system. The table below confirms full interoperability:
| From To | LLA | ECEF | UTM | ENU | NED | MGRS | USNG | WebMercator | UPS | StatePlane | BNG | GH36 | GH | HAM | OLC | GEOREF | GARS | H3 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| LLA | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| ECEF | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| UTM | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| ENU | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| NED | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| MGRS | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| USNG | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| WebMercator | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| UPS | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y | Y |
| StatePlane | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y | Y |
| BNG | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y | Y |
| GH36 | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y | Y |
| GH | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y | Y |
| HAM | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y | Y |
| OLC | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y | Y |
| GEOREF | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y | Y |
| GARS | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- | Y |
| H3 | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | Y | -- |
Universal Distance and Bearing Calculations¶
All coordinate systems support universal distance calculations via distance_to (Vincenty great-circle) and straight_line_distance_to (ECEF Euclidean). These methods work across different coordinate types -- for example, computing the distance from a UTM coordinate to an MGRS coordinate. Class-level methods Geodetic::Coordinate.distance_between and Geodetic::Coordinate.straight_line_distance_between compute consecutive chain distances across a sequence of coordinates.
All coordinate systems also support universal bearing calculations via bearing_to (great-circle forward azimuth) and elevation_to (vertical look angle). These return Bearing and Float objects respectively. The class-level method Geodetic::Coordinate.bearing_between computes consecutive chain bearings.
See the Conversions Reference for details on distances and Bearing Calculations for bearings.
Note: ENU and NED are relative systems and must be converted to an absolute system (e.g., LLA) before using universal distance and bearing methods. They retain
local_bearing_toandhorizontal_distance_tofor tangent-plane operations. NED additionally provideslocal_elevation_angle_to.
Conversion Paths¶
Conversions typically route through LLA or ECEF as intermediate steps:
- LLA serves as the universal hub. Most systems convert to LLA first, then from LLA to the target system.
- ECEF is the intermediate for local tangent plane systems (ENU, NED), since the rotation from global Cartesian to local frames is straightforward in ECEF.
- ENU and NED convert between each other directly by reordering axes and inverting the vertical component.
- MGRS and USNG route through UTM, which in turn routes through LLA.
- WebMercator, UPS, BNG, StatePlane, GH36, GH, HAM, OLC, GEOREF, GARS, and H3 all convert through LLA.
For example, converting from BNG to NED follows the chain: BNG -> LLA -> ECEF -> ENU -> NED. The gem handles this automatically when you call a conversion method.