Module gplately.spatial

This sub-module contains spatial tools for calculating distances on the Earth.

Functions

def cartesian_distance(lon1, lon2, lat1, lat2, degrees=True, k=1, return_neighbours=False)

def geocentric_radius(lat, degrees=True)

Calculates the latitude-dependent radius of an ellipsoid Earth.

Parameters

lat : float

The geodetic latitude at which to calculate the Earth's radius

degrees : bool, default=True

Specify whether the given latitude is in degrees.

Returns

earth_radius : float

The Earth's geocentric radius (in metres) at the given geodetic latitude.

def great_circle_distance(lon1, lon2, lat1, lat2, degrees=True, k=1, return_neighbours=False)

def haversine_distance(lon1, lon2, lat1, lat2, degrees=True)

Computes the Haversine distance (the shortest distance on the surface of an ideal spherical Earth) between two points given their latitudes and longitudes.

Sources

https://en.wikipedia.org/wiki/Haversine_formula https://stackoverflow.com/questions/639695/how-to-convert-latitude-or-longitude-to-meters

Parameters

lon1, lon2 : float

Longitudes of both points

lat1, lat2 : float

Latitudes of both points

Returns

d : float

The Haversine distance in metres.

Notes

Default behaviour assumes values in degrees; for radians specify degrees=False

def lonlat2xyz(lon, lat, degrees=True)

Convert lon / lat (radians) for spherical triangulation into Cartesian (x,y,z) coordinates on the unit sphere.

Parameters

lon, lat : lists

Longitudes and latitudes of feature points in radians.

Returns

xs, ys, zs : lists

Cartesian coordinates of each feature point in all 3 dimensions.

def xyz2lonlat(x, y, z, validate=False, degrees=True)

Converts Cartesian (x,y,z) representation of points (on the unit sphere) for spherical triangulation into lon / lat (radians).

Note: No check is made here that (x,y,z) are unit vectors - it is assumed.

Parameters

x, y, z : lists

Cartesian coordinates of each feature point in all 3 dimensions.

Returns

lon, lat : lists

Longitudes and latitudes of feature points in radians.

Notes

No check is made here that (x,y,z) are unit vectors, unless validate=True is specified