Formulas to Calculate Geo Proximity

by

The Law of Cosines and the Haversine Formula will give identical results assuming a machine with infinite precision. The Haversine formula is more robust to floating point errors. However, today’s machines have double precision of the order of 15 significant figures, and the law of cosines may work just fine for you. Both these formulas assume spherical earth, whereas Vicenty’s iterative solution (most accurate) assumes ellipsoidal earth (in reality the earth is not even an ellipsoid – it is a geoid). Some references:
http://www.movable-type.co.uk/scripts/gis-faq-5.1.html

It gets better: note the latitude to be used in the law of cosines as well as the Haversine is the geocentric latitude, which is different from geodetic latitude. For a sphere, these two are the same.

Which one is fastest to compute?

In order from fastest to slowest are: law of cosines (5 trig. calls) -> haversine (involves sqrt) -> Vicenty (have to solve this iteratively in a for loop)

Which one is most accurate?

Vicenty.

Which one is best when speed and accuracy are both considered?

If your problem domain is such that for the distances you are trying to calculate, the earth can be considered as flat, then you can work out (I am not going to give details) a formula of the form x = kx * difference in longitude, y = ky * difference in latitude. Then distance = sqrt(dxdx + dydy). If your problem domain is such that it can be solved with distance squared, then you won’t have to take sqrt, and this formula will be as fast as you get possibly get. It has the added advantage that you can calculate the vector distance – x is distance in east direction, and y is distance in the north direction.
Otherwise, experiment with the 3 and choose what works best in your situation.

More Related Contents:

  1. Calculating distance between zip codes in PHP
  2. how to write php code for the key press enter button when fill the form?
  3. How to update multiple MySQL table entries with different id?
  4. Create hyperlink from html table row to open record on a new page
  5. mysql_fetch_array(): supplied argument is not a valid MySQL result resource [duplicate]
  6. I don’t know what’s wrong with my code. I’m a newbie. The prob is – Notice: Undefined variable: result [duplicate]
  7. How to run deprecated php codes on the latest XAMPP [duplicate]
  8. Warning: mysql_connect(): [2002] No such file or directory (trying to connect via unix:///tmp/mysql.sock) in
  9. Is closing the mysql connection important?
  10. selecting unique values from a column
  11. Shortcomings of mysql_real_escape_string?
  12. Alternative to mysql_real_escape_string without connecting to DB
  13. HTML – Change\Update page contents without refreshing\reloading the page
  14. Calculate age based on date of birth
  15. Post and get at the same time in php
  16. Setting up Laravel on a Mac php artisan migrate error: No such file or directory [duplicate]
  17. ini_set, set_time_limit, (max_execution_time) – not working
  18. What is the best way to insert multiple rows in PHP PDO MYSQL?
  19. How do I set the selected item in a drop down box
  20. Fatal error: Call to undefined function mysqli_result()
  21. access denied for user @ ‘localhost’ to database ” [closed]
  22. How can I employ “if exists” for creating or dropping an index in MySQL?
  23. adding 30 minutes to datetime php/mysql
  24. PHP MySQL pagination with random ordering
  25. Create table with PHP and populate from MySQL
  26. Auto Increment skipping numbers?
  27. PDO bindParam into one statement?
  28. Is mysql_real_escape_string enough to Anti SQL Injection?
  29. How to make mysqli connect function?
  30. Using PHP to upload file and add the path to MySQL database

Leave a Comment