Set of algorithms and structures related to geodesy and geospatial data
Project description
Set of algorithms and structures related to geodesy.
API
geo.sphere
Functions onto sphere
geo.sphere.approximate_distance
def approximate_distance(point1, point2):
Approximate calculation distance (expanding the trigonometric functions around the midpoint)
geo.sphere.haversine_distance
def _haversine_distance(point1, point2):
Calculating haversine distance between two points (see https://en.wikipedia.org/wiki/Haversine_formula, https://www.math.ksu.edu/~dbski/writings/haversine.pdf)
Is numerically better-conditioned for small distances
geo.sphere.distance
def distance(point1, point2):
Calculating great-circle distance (see https://en.wikipedia.org/wiki/Great-circle_distance)
geo.sphere.bearing
def bearing(point1, point2):
Calculating initial bearing between two points (see http://www.movable-type.co.uk/scripts/latlong.html)
geo.sphere.final_bearing
def final_bearing(point1, point2):
Calculating finatl bearing (initial bering + 180) between two points
geo.sphere.destination
def destination(point, distance, bearing):
Given a start point, initial bearing, and distance, this will calculate the destination point and final bearing travelling along a (shortest distance) great circle arc. (see http://www.movable-type.co.uk/scripts/latlong.htm)
geo.sphere.approximate_destination
def approximate_destination(point, distance, theta):
geo.sphere.from4326_to3857
def from4326_to3857(point):
Reproject point from EPSG:4326 (https://epsg.io/4326) to EPSG:3857 (https://epsg.io/3857) (see http://wiki.openstreetmap.org/wiki/Mercator)
- Spherical Mercator:
E = R*(λ - λo) N = R*ln(tan(π/4+φ/2))
geo.sphere.from3857_to4326
def from4326_to3857(point):
Reproject point from EPSG:3857 (https://epsg.io/3857) to EPSG:4326 (https://epsg.io/4326) (see http://wiki.openstreetmap.org/wiki/Mercator)
- Reverse Spherical Mercator:
λ = E/R + λo φ = π/2 - 2*arctan(exp(-N/R))
geo.ellipsoid
Functions onto ellipsoid
geo.ellipsoid.distance
def distance(point1, point2, ellipsoid=WGS84):
Calculating distance with using vincenty’s formula (see https://en.wikipedia.org/wiki/Vincenty’s_formulae)
geo.ellipsoid.from4326_to3395
def from4326_to3395(point, ellipsoid=WGS84):
Reproject point from EPSG:4326 (https://epsg.io/4326) to EPSG:3395 (https://epsg.io/3395) (see https://en.wikipedia.org/wiki/Mercator_projection#Generalization_to_the_ellipsoid)
- Ellipsoidal Mercator:
E = a*(λ - λo) N = a*ln(tan(π/4+φ/2)*((1-e*sin(φ))/(1+e*sin(φ)))**e/2)
geo.ellipsoid.from3395_to4326
def from3395_to4326(point, ellipsoid=WGS84):
Reproject point from EPSG:3395 (https://epsg.io/3395) to EPSG:4326 (https://epsg.io/4326) (see https://en.wikipedia.org/wiki/Mercator_projection#Generalization_to_the_ellipsoid)
- Reverse Ellipsoidal Mercator:
λ = E/a + λo φ = π/2 + 2*arctan(exp(-N/a)*((1-e*sin(φ))/(1+e*sin(φ))**e/2))
Project details
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.