Which Geo Proximity Formula is Best: Haversine, Great-Circle Distance, or Vicenty?

Navigating the Quandary of Geo Proximity Formulas: Haversine, Great-Circle Distance, and Beyond

The question posed seeks clarity in understanding the principles governing the calculation of geo proximity. Initially, the author expresses confusion over the perceived synonymous nature of the Haversine and Great-Circle Distance formulas. However, a deeper exploration reveals the nuanced differences between them.

Unraveling the Equations

A closer examination indicates that the Spherical Law of Cosines and the Haversine Formula yield identical results under the assumption of infinite precision. However, the practical implementation reveals that the Haversine formula exhibits greater resilience against floating-point errors, a common occurrence in digital computations.

A Matter of Speed and Precision

To answer the question of efficiency, the following ranking emerges:

1. Law of Cosines (fastest, involving 5 trigonometric calculations)
2. Haversine (slightly slower, employing a square root operation)
3. Vicenty (most precise but slowest, requiring iterative solution via a loop)

For the highest accuracy, Vicenty's formula reigns supreme. However, it comes at the cost of computational speed.

Striking a Balance: Speed vs. Accuracy

The optimal choice for practical applications depends on the specific requirements. For scenarios where the earth's curvature can be approximated as negligible, a simplified formula based on longitude and latitude differences might suffice. This approach offers lightning speed, especially when distance squared is sufficient rather than absolute distance.

Conclusion

The choice among these formulas hinges on the balance between speed and accuracy. For projects where speed is paramount, the Law of Cosines or the simplified approach might be suitable. However, if accuracy is crucial, Vicenty's formula remains the gold standard.

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