Converting XYZ coordinates to longitutde/latitude in Python

Question

I've got some XYZ coordinates in Kilometers (gotten using wgs) with the origin at the center of the Earth, is it possible to convert this into latitude and longitude?

In addition: how can I do this quickly inside python?

It's simply a reverse of this question here: Converting from longitude\latitude to Cartesian coordinates

Prateek Dhanuka · Answer 1 · 2019-12-20T11:11:27.383

3

Based on @daphshez answer

You can use this code, Here, x, y and z are in Kms and R is an approximate diameter of Earth.

import numpy as np

R = 6371 
lat = np.degrees(np.arcsin(z/R))
lon = np.degrees(np.arctan2(y, x))

edited Dec 20 '19 at 11:11

answered Jul 09 '19 at 04:54

Prateek Dhanuka

380
2
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thanks, but it still gives me incorrect data. possibly because wgs considers the earth to be an ellipsoid, any ideas? – scarab Jul 09 '19 at 05:06
Surely its `np.acsin` and `np.arctan2` – batFINGER Dec 20 '19 at 06:48
Yes. I've fixed it just now – Prateek Dhanuka Dec 20 '19 at 11:11

score 2 · Accepted Answer · edited Apr 13 '21 at 15:57

This is how you do it. Taking into account both radiuses. Based on: https://gist.github.com/govert/1b373696c9a27ff4c72a and verifyed.

import math

x = float(4333216) #in meters
y = float(3193635) #in meters
z = float(3375365) #in meters

a = 6378137.0 #in meters
b = 6356752.314245 #in meters

f = (a - b) / a
f_inv = 1.0 / f

e_sq = f * (2 - f)                       
eps = e_sq / (1.0 - e_sq)

p = math.sqrt(x * x + y * y)
q = math.atan2((z * a), (p * b))

sin_q = math.sin(q)
cos_q = math.cos(q)

sin_q_3 = sin_q * sin_q * sin_q
cos_q_3 = cos_q * cos_q * cos_q

phi = math.atan2((z + eps * b * sin_q_3), (p - e_sq * a * cos_q_3))
lam = math.atan2(y, x)

v = a / math.sqrt(1.0 - e_sq * math.sin(phi) * math.sin(phi))
h   = (p / math.cos(phi)) - v

lat = math.degrees(phi)
lon = math.degrees(lam)

print(lat,lon,h)

Converting XYZ coordinates to longitutde/latitude in Python

2 Answers2