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https://github.com/lggomez/go-geodesy
geodesics utils, including ellipsoid data and ellipsoidal distance
https://github.com/lggomez/go-geodesy
ellipsoid geodesics geodesy haversine vincenty
Last synced: 27 days ago
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geodesics utils, including ellipsoid data and ellipsoidal distance
- Host: GitHub
- URL: https://github.com/lggomez/go-geodesy
- Owner: lggomez
- License: mit
- Created: 2021-09-19T19:10:55.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2021-10-12T21:15:19.000Z (about 3 years ago)
- Last Synced: 2024-10-14T17:19:09.814Z (2 months ago)
- Topics: ellipsoid, geodesics, geodesy, haversine, vincenty
- Language: Go
- Homepage:
- Size: 73.2 KB
- Stars: 3
- Watchers: 3
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# geodesy
go-geodesy is a package of geodesy-related utilities made in golang, including ellipsoid constants for development of geographic and geospatial implementations
```
import "github.com/lggomez/go-geodesy"
```
- [geodesy](#geodesy)
- [Usage](#usage)
- [Point definitions](#point-definitions)
- [type Point](#type-point)
- [func (Point) Antipode](#func-point-antipode)
- [func (Point) Equals](#func-point-equals)
- [func (Point) IsAntipode](#func-point-isantipode)
- [func (Point) Lat](#func-point-lat)
- [func (Point) LatRadians](#func-point-latradians)
- [func (Point) Lon](#func-point-lon)
- [func (Point) LonRadians](#func-point-lonradians)
- [Calculating distances](#calculating-distances)
- [func Haversine](#func--haversine)
- [func VincentyInverse](#func--Vincentyinverse)
- [Ellipsoids](#ellipsoids)
- [GRS-80](#grs-80)
- [WGS-84](#wgs-84)
## Usage
### Point definitions
#### type Point
```go
type Point [2]float64
```
Point represents a latitude-longitude pair in decimal degrees
Constants
```go
const (
LatLowerBound = float64(-90)
LatUpperBound = float64(90)
LonLowerBound = float64(-180)
LonUpperBound = float64(180)
)
```
#### func (Point) Antipode
```go
func (p Point) Antipode() Point
```
Antipode returns a new point representing the geographical antipode of p
#### func (Point) Equals
```go
func (p Point) Equals(p2 Point) bool
```
Equals returns whether p is equal in latitude and longitude to p2
#### func (Point) IsAntipodeOf
```go
func (p Point) IsAntipodeOf(p2 Point) bool
```
IsAntipodeOf returns whether p is the exact antipode of p2 or not
#### func (Point) Lat
```go
func (p Point) Lat() float64
```
Lat returns point p's latitude
#### func (Point) LatRadians
```go
func (p Point) LatRadians() float64
```
LatRadians returns point p's latitude in radians
#### func (Point) Lon
```go
func (p Point) Lon() float64
```
Lon returns point p's longitude
#### func (Point) LonRadians
```go
func (p Point) LonRadians() float64
```
LonRadians returns point p's longitude in radians
### Calculating distances
```
import "github.com/lggomez/go-geodesy/distance"
```
#### func Haversine
```go
func Haversine(p1, p2 geodesy.Point) float64
```
Haversine calculates the ellipsoidal distance in meters between 2 points
using the Haversine formula and the WGS-84 ellipsoid constants.
If any of the points does not constitute a valid geographic coordinate,
the returned distance will be math.NaN().
#### func VincentyInverse
```go
func VincentyInverse(p1, p2 geodesy.Point, accuracy float64, calculateAzimuth bool) (float64, float64, float64)
```
VincentyInverse calculates the ellipsoidal distance in meters and azimuth in degrees between 2 points using the
inverse Vincenty formulae and the WGS-84 ellipsoid constants. As it is an iterative operation it will converge to
the defined accuracy, if accuracy < 0 it will use the default accuracy of 1e-12 (approximately 0.06 mm, magnitude should be no bigger than 1e-6).
If calculateAzimuth is set to true, it will compute the forward and reverse azimuths (otherwise, these default to math.NaN()).
If any of the points does not constitute a valid geographic coordinate, the returned distance will be math.NaN().
The following notations are used in the implementation:
* a length of semi-major axis of the ellipsoid (radius at equator)
* ƒ flattening of the ellipsoid
* b = (1 − ƒ) a length of semi-minor axis of the ellipsoid (radius at the poles)
* u1 = arctan( (1 − ƒ) tan lat1 ) reduced latitude for p1 (latitude on the auxiliary sphere);
* u2 = arctan( (1 − ƒ) tan lat2 ) reduced latitude for p2 (latitude on the auxiliary sphere);
* L1, L2 longitude of the points;
* L = L2 − L1 difference in longitude of two points;
* λ Difference in longitude of the points on the auxiliary sphere;
* α1, α2 forward azimuths at the points;
* α forward azimuth of the geodesic at the equator, if it were extended that far;
* s ellipsoidal distance between the two points;
* σ angular separation between points;
* σ1 angular separation between the point and the equator;
* σm angular separation between the midpoint of the line and the equator;
### Ellipsoids
```
import "github.com/lggomez/go-geodesy/ellipsoids"
```
#### GRS-80
```go
const (
// Geocentric gravitational constant GM, defined in (m^3)/(s^2)
GRS80_GEOCENTRIC_GRAVITATIONAL_CONSTANT float64 = 3_986_005_000_000_000
// Dynamical form factor J2; adimensional
GRS80_DYNAMICAL_FORM_FACTOR float64 = 0.0108263
// Dynamical form factor ω; defined in s^-1
GRS80_ANGULAR_VELOCITY float64 = 0.0007292115
)
```
Defining physical constants
```go
const (
// Semi minor axis b, defined in meters (m)
GRS80_SEMI_MINOR_AXIS float64 = 6_356_752.314140
// Aspect ratio (b/a); adimensional
GRS80_ASPECT_RATIO float64 = 0.996647189318816362
// Mean radius R1 = (2a+b)/3, defined in meters (m)
GRS80_MEAN_RADIUS = 6_371_008.7714
// Mean radius R2, defined in meters (m)
GRS80_AUTHALIC_MEAN_RADIUS = 6_371_007.1810
// Radius of a sphere of the same volume R3 = ((a^2)*b)^(1/3); defined in meters (m)
GRS80_SPHERE_RADIUS = 6_371_000.7900
// Polar radius of curvature = (a^2)/b; defined in meters (m)
GRS80_POLAR_CURVATURE_RADIUS = 6_399_593.6259
// Equatorial radius of curvature for a meridian = (b^2)/a; defined in meters (m)
GRS80_MERIDIAN_CURVATURE_EQUATORIAL_RADIUS = 6_335_439.3271
// Meridian quadrant (meridian quarter); defined in meters (m)
// See https://en.wikipedia.org/wiki/Meridian_arc#Quarter_meridian
GRS80_MERIDIAN_QUADRANT = 10_001_965.7293
// Linear eccentricity c = sqrt((a^2)-(b^2)); defined in meters (m)
GRS80_LINEAR_ECCENTRICITY = 521_854.0097
// Eccentricity of elliptical section through poles e = sqrt((a^2)-(b^2))/a; adimensional
GRS80_LINEAR_ECCENTRICITY_POLES = 0.0818191910435
// Flattening f; adimensional
GRS80_FLATTENING float64 = 0.003352810681183637418
// Flattening inverse (1/f); adimensional
GRS80_FLATTENING_INVERSE float64 = 1 / 0.003352810681183637418
)
```
Derived geometrical constants (all rounded)
```go
const (
// Period of rotation (sidereal day) = 2π/ω; defined in seconds (s)
GRS80_ROTATION_PERIOD float64 = 8_616.4100637
)
```
Derived physical constants (all rounded)
```go
const (
// Semi major axis a, defined in meters (m)
GRS80_SEMI_MAJOR_AXIS float64 = 6_378_137
)
```
Derived geometrical constants (all rounded)
#### WGS-84
```go
const (
// WGS84_GEOCENTRIC_GRAVITATIONAL_CONSTANT Geocentric gravitational constant GM, defined in (m^3)/(s^2)
WGS84_GEOCENTRIC_GRAVITATIONAL_CONSTANT float64 = 3_986_005_000_000_000
// WGS84_DYNAMICAL_FORM_FACTOR Dynamical form factor J2; adimensional
// See https://ahrs.readthedocs.io/en/latest/wgs84.html#ahrs.utils.wgs84.WGS.dynamical_form_factor
WGS84_DYNAMICAL_FORM_FACTOR float64 = 0.0010826298213129219
// WGS84_ANGULAR_VELOCITY Dynamical form factor ω; defined in s^-1
WGS84_ANGULAR_VELOCITY float64 = 0.0007292115
)
```
Defining physical constants
```go
const (
// WGS84_SEMI_MINOR_AXIS Semi minor axis b, defined in meters (m)
WGS84_SEMI_MINOR_AXIS float64 = 6_356_752.31424518
// WGS84_ASPECT_RATIO Aspect ratio (b/a); adimensional
WGS84_ASPECT_RATIO float64 = 0.9966471893352525
// WGS84_MEAN_RADIUS Mean radius R1 = (2a+b)/3, defined in meters (m)
WGS84_MEAN_RADIUS = 6_371_008.771415059
// WGS84_AUTHALIC_MEAN_RADIUS Mean radius R2, defined in meters (m)
WGS84_AUTHALIC_MEAN_RADIUS = 6_371_007.1809182055
// WGS84_SPHERE_RADIUS Radius of a sphere of the same volume R3 = ((a^2)*b)^(1/3); defined in meters (m)
WGS84_SPHERE_RADIUS = 6_371_000.79000916
// WGS84_POLAR_CURVATURE_RADIUS Polar radius of curvature = (a^2)/b; defined in meters (m)
WGS84_POLAR_CURVATURE_RADIUS = 6_399_593.625758493
// WGS84_MERIDIAN_CURVATURE_EQUATORIAL_RADIUS Equatorial radius of curvature for a meridian = (b^2)/a; defined in meters (m)
WGS84_MERIDIAN_CURVATURE_EQUATORIAL_RADIUS = 6_335_439.327292821
// WGS84_MERIDIAN_QUADRANT Meridian quadrant (meridian quarter); defined in meters (m)
// See https://en.wikipedia.org/wiki/Meridian_arc#Quarter_meridian
WGS84_MERIDIAN_QUADRANT = 10_001_965.729
// WGS84_LINEAR_ECCENTRICITY Linear eccentricity c = sqrt((a^2)-(b^2)); defined in meters (m)
WGS84_LINEAR_ECCENTRICITY = 521_854.0084234
// WGS84_LINEAR_ECCENTRICITY_POLES Eccentricity of elliptical section through poles e = sqrt((a^2)-(b^2))/a; adimensional
WGS84_LINEAR_ECCENTRICITY_POLES = 0.0818191918426205
// WGS84_FLATTENING Flattening f; adimensional
WGS84_FLATTENING float64 = 1 / 298.257223563
// WGS84_FLATTENING_INVERSE Flattening inverse (1/f); adimensional
WGS84_FLATTENING_INVERSE float64 = 298.257223563
)
```
Defining geometrical constants
```go
const (
// WGS84_ROTATION_PERIOD Period of rotation (sidereal day) = 2π/ω; defined in seconds (s)
WGS84_ROTATION_PERIOD float64 = 8_616.4100637
)
```
Derived physical constants (all rounded)
```go
const (
// WGS84_SEMI_MAJOR_AXIS Semi major axis a, defined in meters (m)
WGS84_SEMI_MAJOR_AXIS float64 = 6_378_137
)
```
Defining geometrical constants