The Geopy method for distance calculation between any two points on the globe.

Introduction.

Geopy is essentially a Python library that makes the calculation of geographic distances unchalleging. It becomes considerably easier for developers using Geopy to retrieve the coordinates of various sites by leveraging third-party geocoders and other data sources.

In this article, we'll look at a few alternative ways for calculating the distance between any two points on the globe. We shall dig deep to explain how this is possible using Python package geopy which is the primary Python package for distance calculation.

The user needs first to execute the following command to install geopy.

Before executing the command below, there is a series of steps that are followed so that the command is finally arrived at.

1. Open your cmd and make sure it is running as an administrator.
2. Make sure that you are operating from the root by performing the following. cd..
3. cd.. This shows that you are already at the root.
4. After that now you can perform the command below and geopy will be installed in your machine.

pip install geopy

We are therefore set to calculate the distances of any two points following a successful installation of the geopy module.

Using the Geopy, we can calculate or find the distance between two strategic positions using the various methods that are listed below.

1. Distance Measure using the Geodesic Measure.
2. Distance Measure using The greate circle distance.
3. Distance Measure using The Herversine formula. ### The Geodesic Measure for distance calculation. The geodesic measure or distance is used to define the shortest path between any two given points on the globe.

As in the situation of two diametrically opposing points on a sphere, it is feasible that numerous alternative arcs between two points reduce the distance. In this case, any of these curves is a geodesic. Geodesics are not exactly the same as " the shortest curves" between any two given locations, despite their likeness.

It is rather defined in a better way as the shortest distance between two points at a given position that is parameterized with "constant speed." A geodesic is the "long way around" on a great circle between two points on an earth's surface, even if it is not the shortest path between the two points.

An important point to note when working with geodesic or when calculating any distance between any two points on the sphere is that it does not ignore any curved part. In contrast to this, a distance calculation known as Euclidean distance completely ignores the shape of the path that is involved such that it assumes a straight path from the start of a point to its end.

We'll illustrate how to compute or how to calculate the Geodesic Distance using latitude and longitude data in the following example.

Example 1.1

# To begin, open the geopy library and import the geodesic module. 
from geopy.distance import geodesic as GD
 # Then, for the specified locations, load their latitude and longitude data.
Abuja =(9.072264 , 7.491302)
Dakar =(14.716677 , -17.467686)
#Finally, print the distance between two sites in kilometers.
print("The distance between Abuja  and Dakar is:", GD(Abuja, Dakar).km)

See terminal output below:

The distance between Abuja  and Dakar is: 2787.8012928541466

Example 1.2

# Geopy distance module is first imported for the purpose of computations.

from geopy.distance import geodesic as GD
# Next, input the latitude and longitude data for Nairobi and Cairo.  

Nairobi=(36.817223,-1.286389 )
Cairo=( 31.233334,30.033333, )
# Finally, print the distance between two sites in kilometers. 

print("The distance between Nairobi and Cairo is :",GD(Nairobi,Cairo).km)

See terminal output below:

The distance between Nairobi and Cairo is : 2944.261368793268

NB

The outputs from the two examples above are obtained by loading the latitude data first then the longitude data. If we try to exchange the order in which the two are loaded i.e we load the longitude data first then the latitude data last, the distance obtained will not be equal with the original distance. Let us have a proof on that by using the data in example 1.1 above.

# To begin, open the geopy library and import the geodesic module. 
from geopy.distance import geodesic as GD
# Then, for the specified locations, load their longitude and latitude data
Abuja=(7.491302, 9.072264 )
Dakar=(-17.467686, 14.716677)
#Finally, print the distance between two sites in kilometers.
print("The distance between Abuja and Dakar is:", GD(
Abuja, Dakar).km)

See terminal output below:

The distance between Abuja and Dakar is: 2829.4255581410116

The comparison is as follows:

The distance between Abuja  and Dakar is(Latitude data first followed by longitude data): 2787.8012928541466

The distance between Abuja and Dakar is (Longitude data first followed by the latitude data): 2829.4255581410116

It is very clear that the two distances are not the same. And this will apply to all other methods and it is, therefore, a good practice to begin with the latitude data followed by the longitude data

The great circle distance formula for distance calculation.

This may be defined as the shortest path between any two places or points on the sphere or on the earth's surface. In this example, it is assumed that the globe is a perfect sphere. The following example shows how to compute great circle distance using longitude and latitude data from two locations.

The problem of great-circle navigation includes the computation of azimuths at end points and intermediate waypoints, as well as the calculation of the great-circle distance.

A great circle is formed by any two points on a sphere that are not directly opposite with each other. The great circle is divided into two arcs by these two locations. The shorter arc that is between any two locations equals to the great-circle distance.

Example 1.3

 # First, import the geopy library's great circle module.
from geopy.distance import great_circle as GRC
# Abuja and Dakar latitude and longitude data.
Abuja=(9.072264 , 7.491302)
Dakar=(14.716677 , -17.467686)
# ## Finally print the distance between the two points calculated in km
print("The distance between Abuja  and Dakar is:", GRC(Abuja,Dakar).km) 

See terminal output below:

The distance between Abuja  and Dakar is: 2785.186971064666

The Heversine formula for distance calculation.

The heversine formula executes the great-circle distance between any two points on a sphere using their longitudes and latitudes.

One specific example is the rule of haversines, a more general formula in the field of spherical trigonometry that connects the sides and angles of spherical triangles.

The haversine method therefore gives a very correct way of finding the distance between any two given longitude and latitude.

The haversine formula is a realignment of the spherical law of cosines, although it is more useful for tiny angles and distances since it is written in haversines.

The "Ha" in "Haversine" represents "half versed sine," and haversin(θ) = versin(θ)/2 is the formula.
The orthodromic distance is used to calculate the shortest distance between two sites on the globe separated by latitude and longitude.

If the user want to utilize this method, then they must have the coordinates of two points (X and Y).
They must convert degrees of latitude and longitude to radians before dividing the data by (180/π) and the value of π to be used is 22/7.

"57.29577" will be the value of (180/π).

The user may wish to find the distance in miles where the radius of the Earth can be set to "3,963." The user can also use the value "6,378.80" to compute the distance in Kilometres.

Formulas

Longitude in radians is calculated as follows: In radians, the value of latitude is: Latitude (LaA) = LaA / (180/π )

OR

Latitude (LaA) = LaA / 57.29577
How to compute longitude in radians:
Longitude (LoA) = LoA / (180/π )

OR

Longitude (LoA) = LoA / 57.29577

The longitude and latitude coordinates of P and Q locations, as well as the aforementioned method to convert them to radians, will be required by the user.

By utilizing the following method, distance between any two points can be found.

Hundreds of miles

Distance (D) = 3963.0 * arccos[(sin(LaA) * sin(LaB)) + cos(LaA) * cos(LaB) * cos(LoB - LoA)]

For the kilometer

Distance (D) = 3963.0 * arccos[(sin(LaA) * sin(LaB)) + cos(LaA) * cos(LaB) * cos(LoB - LoA)]

For the kilometer: The shortest distance between two specified points on Earth can be calculated using the Haversine Formula.

Example 1.4

from math import radians, cos, sin, asin, sqrt

# Implement the formula below

def distance_d(LaA, LaB, LoA, LoB):
# The function "radians" is found in the math module, It's also used to convert radians to degrees.  
LoA = radians(LoA)  
LoB = radians(LoB)  
LaA= radians(LaA)  
LaB = radians(LaB) 
# The "Haversine formula" is used.
D_Lo = LoB - LoA 
D_La = LaB - LaA 
P = sin(D_La / 2)**2 + cos(LaA) * cos(LaB) * sin(D_Lo / 2)**2  

Q = 2 * asin(sqrt(P))   
    # The earth's radius in kilometers.
R_km = 6371  
# Then we'll compute the outcome.
return(Q * R km).


LaA=9.072264
LaB=14.716677
LoA=7.491302
LoB=-17.467686

print ("The distance between Abuja and Dakar is: ", distance_d(LaA, LaB, LoA, LoB), "K.M")  

See terminal output below:

The distance between Abuja and Dakar is:  2785.183036572855 K.M

Conclusion

Using the geopy package, we've gone over numerous ways for determining the distance between two points on the earth's surface in this tutorial. Each approach has been demonstrated using examples.
Happy Coding