Which Geo Proximity Formula Is Best for You?

Formulas for Geo Proximity Calculation

When implementing a geo proximity search, selecting the appropriate formula is essential. Several formulas are available, each with its pros and cons.

Haversine Formula vs. Great-Circle Distance Formula

Contrary to popular belief, the Haversine Formula and the Great-Circle Distance Formula are not synonymous. The latter is a general term for algorithms that calculate the distance along the surface of a sphere, while the Haversine Formula is a specific implementation using trigonometric functions.

The Haversine Formula is较为 robust to floating-point errors due to the use of nested additions and subtractions, while the Great-Circle Distance Formula may lead to inaccuracies in certain cases.

Accuracy Considerations

For distances on a spherical earth, the Haversine Formula and the Law of Cosines (a variant of the Great-Circle Distance Formula) provide virtually identical results on machines with high precision. However, for ellipsoidal approximations of the earth, Vicenty's Formula is more accurate, especially for long distances.

Performance

In terms of computational speed, the Law of Cosines is the fastest to compute, followed by the Haversine Formula and then Vicenty's Formula.

Choosing the Best Formula

The best formula to choose depends on the specific use case. If speed is a priority and the distance range is limited, the Law of Cosines or the Haversine Formula may suffice. However, if accuracy is paramount, especially for long distances, Vicenty's Formula is recommended.

Conclusion

While several formulas exist for calculating geo proximity, the choice depends on the required accuracy and computational efficiency. The Law of Cosines and the Haversine Formula are suitable for most applications, while Vicenty's Formula offers superior accuracy for applications that demand it.

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