Great Circle Calculator

This is a collection of equations and formulas that I've been using across my many projects to compute various distances using great circle calculations. The formulas here were adapted into python from here and here.

Because I've been using these equations across several projects, I decided to upload this to PyPI for ease of keeping updated and distribution. Feel free to clone, fork, or modify the code as needed. I believe there are more robust packages out there. One example is geodesy.

Any questions, feel free to get in touch.

How to install

Clone/download the package to your project or use pip install great-circle-calculator (PyPI)

How to use

The convention of this package is for the spatial points to be represented as a tuple of length 2 with longitude being the first element and latitude being the second element, i.e. (lon, lat).

Here is an outline of the functions available to you.

Library great_circle_calculator

Depending on my needs, I will either import this library as

import great_circle_calculator.great_circle_calculator as gcc

or

from great_circle_calculator.great_circle_calculator import *

where * can be a specific function (or left as * for all the functions)

The functions are distance_between_points, bearing_at_p1, bearing_at_p2, midpoint, intermediate_point, point_given_start_and_bearing

Function distance_between_points()

Function distance_between_points(p1, p2, unit='meters', haversine=True) computes the distance between two points in the unit given in the unit parameter. It will calculate the distance using the law of cosines unless the user specifies haversine to be true. p1 and p2 are points (i.e. tuples, lists of length 2) in the form of (lon, lat) in decimal degrees (That is, a tuple of float values, the library cannot handle DMS data). unit is a unit of measurement that can be accessed by great_circle_calculator.constants.eligible_units, default is 'meters'. haversine=True uses the haversine formula, which is consideered superior for short distances (which is my often use case). Changing it to haversine=False yeilds the law of cosines which, typically, will have a quicker computational time.

Function bearing_at_p1()

Function bearing_at_p1(p1, p2) computes the bearing (i.e. course) at p1 given a destination of p2. Use in conjunction with midpoint() and intermediate_point() to find the course along the route. Use bearing_at_p2() to find the bearing at the endpoint, p2. p1 and p2 are points (i.e. tuples, lists of length 2) in the form of (lon, lat) in decimal degrees.

Example to find a course enroute:

import great_circle_calculator.great_circle_calculator as gcc
""" This code snippit will find the the course at a point p3 which is 20% the way between points p1 and p2
"""
p1, p2 = (lon1, lat1), (lon2, lat2)
frac_along_route = 0.2
course_enroute = gcc.bearing_at_p1(gcc.intermediate_point(p1, p2, frac_along_route), p2)

Function bearing_at_p2

Function bearing_at_p2(p1, p2) computes the bearing (i.e. course) at p2 given a start of p1. Use in conjunction with midpoint() and intermediate_point() to find the course along the route. Use bearing_at_p1() to find the bearing at the starting point, p1. p1 and p2 are points (i.e. tuples, lists of length 2) in the form of (lon, lat) in decimal degrees.

Function midpoint()

Function midpoint(p1, p2) is the half-way point along a great circle path between the two points. p1 and p2 are points (i.e. tuples, lists of length 2) in the form of (lon, lat) in decimal degrees. For example, say p3 = midpoint(p1, p2), distance_between_points(p1, p3) == distance_between_points(p2, p3)

Function intermediate_point()

Function intermediate_point(p1, p2, fraction=0.5) an intermediate point along the course laid out by p1 to p2 given the fractional distance. fraction is the fraction of the distance between p1 and p2, where 0 is p1, 0.5 is equivalent to midpoint(), and 1 is p2.

Function point_given_start_and_bearing()

Function point_given_start_and_bearing(p1, course, distance, unit='meters') is given a start point p1, initial bearing course, and distance distance, this will calculate the destination point bearing travelling along a (shortest distance) great circle arc. unit is a unit of measurement that can be accessed by great_circle_calculator.constants.eligible_units, default is 'meters'.

Library compass

This libaray was created to let me call, say Compass.east so I can get 90deg. I thought it helped with code readability at first, kept it because it might be useful...

It has two classes called CompassSimple and CompassComplex. CompassComplex is still in the todo list but it contains more information about each compass point.

To see the eligble points, see here. Simply use the terms in "Compass point", use lower case and underscores where there are spaces or dashes. Alternatively you may use the "Abbreviation" with the appropriate case to call the same value.

To use CompassSimple:

import great_circle_calculator.CompassSimple as compass

print(compass.east)  # prints 90
print(compass.north)  # prints 0
print(compass.northwest_by_north)  # prints 326.250
print(compass.SEbE)  # Southeast by east, prints 123.750
print(compass.SWbS == compass.southwest_by_south)  # prints True

Library _constants

This was created for two purposes:

1. To easily store the radius of the earth in various units

2. To simplify the code in the program so I don't have to call math.* each time I want sin, cos, etc.

To see the available units, call _constants.eligible_units and a list of the units that are available will be given.

eligible_units

To see the available units, call _constants.eligible_units and a list of the units that are available will be given.

Libraries __conversion and __error_checking

Private libraries that convert (__conversion.py) values between radians and degrees as the default option for python's math package is radians.

Updated for V1.3.0! The error checking library (__error_checking.py) is used to ensure that the points passed to through the code make sense in the project. That is, it checks two things. First, that the point passed to the function is a tuple of length 2. If this check fails, a TypeError is thrown. The second is that the information contained within the tuple matches the expected range of latitude and longitude. The first element of the tuple should be the longitude in the range of [-180, 180] and the second element is the latitude in the range of [-90, 90]. If this check fails, but it appears that the user has "flipped" the elements of the point (i.e. (lat, lon) is provided), a ValueError is thrown with information indicating the belief you have flipped the elements of the coordinates. If this is not true, ValueError is thrown with a different error message indicating the expected input. Danger Zone The function _error_check_point(point, correct_point=False) takes a second argument that I have intentionally made very inaccessible from the PyPI package. If you would like the program to automatically correct a point it thinks is backwards, clone the package into your program and set this parameter to True.

And finally...

Package last updated Aug 31, 2022. Readme last updated Aug 31, 2022.

Change Log

• 1.3.1 - Put in a line of code when computing the haversine distance to ensure that (due to floating point errors) may be above 1
• 1.3.0 - Updated the code in the __error_checking.py file to, by default, throw errors rather than try to correct points. Also expanded the error messages here to be more clear.
• 1.2.0 - If the user sends a point that is decimal data type, it will convert to a tuple of float types. Updated the readme for clarity
• 1.1.0 - Changed haversine=True as the default for distance_between_points as it more accurately reflects the small distance calculation I am using in my projects.
• 1.0.2 - squished an error in the intermediate function. The number of errors has been embarrassing. I hope you won't judge me too harshly.
• 1.0.1.post1 - includes a domain checker for asin() and acos() because rounding errors can cause the function to be out of range.
• 1.0.post1 - I screwed up the numbering order, still new at this... please ignore.
• 1.0.1 - Fixed an error in the (point_given_start_and_bearing)[#point_given_start_and_bearing]
• 1.0.0 - First Edition, inital commit, etc.