Accurate Determination of Qibla Direction: A Comparative Study of Haversine, Vincenty, Spherical Trigonometry, Great Circle Navigation, and Equatorial Oblique Cylindrical Projection Algorithms using Python Programing Language

Authors

  • Ali Abdulghani Abdulhameed Creative advanced technologies/ Iraq
  • Dalia Abdulrahim Mokheef Department of Mathematics, College of Basic Education, University of Babylon, Iraq
  • Mohammed Amer Shanyoor Department of Mathematics, College of Basic Education, University of Babylon, Iraq
  • Sahab Mohsan Abood Department of Mathematics, College of Basic Education, University of Babylon, Iraq
  • Noor R. Obeid Department of Information Security, College of Information Technology, University of Babylon, Iraq

Keywords:

Qibla Direction, Haversine, Vincenty, Spherical Trigonometry, Great Circle Navigation, Equatorial Oblique Cylindrical Projection, Python

Abstract

Determining the direction of the Qibla, which points towards the Kaaba in Mecca, is an essential requirement for Muslims during their daily prayers. With the advent of modern computational techniques, various algorithms have been developed to calculate the Qibla direction accurately. This paper presents a comparative study of five widely used algorithms: the Haversine formula, Vincenty's formula, the Spherical Trigonometry method, the Great Circle Navigation method, and the Equatorial Oblique Cylindrical Projection method. We provide a detailed explanation of all five algorithms, highlighting their underlying principles, mathematical formulations, and implementation details using python programing language. Additionally, we analyze the accuracy and performance trade-offs between these methods, enabling users to make informed decisions based on their specific requirements. Also, to evaluate the performance of the algorithms, 300 random locations were generated on the map using Python.

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Published

2024-07-06

How to Cite

Abdulhameed, A. A., Mokheef, D. A., Shanyoor, M. A., Abood, S. M., & Obeid, N. R. (2024). Accurate Determination of Qibla Direction: A Comparative Study of Haversine, Vincenty, Spherical Trigonometry, Great Circle Navigation, and Equatorial Oblique Cylindrical Projection Algorithms using Python Programing Language. American Journal of Engineering , Mechanics and Architecture (2993-2637), 2(7), 13–23. Retrieved from http://grnjournal.us/index.php/AJEMA/article/view/5448

Issue

Vol. 2 No. 7 (2024): American Journal of Engineering , Mechanics and Architecture

Section

Articles