Geo Proximity Calculation: Formula Comparisons

In developing a geo proximity search, understanding the nuances between formula options is crucial. While the Great-Circle Distance Formula and the Haversine Formula were once considered synonymous, there are subtle distinctions that impact speed, accuracy, and efficiency.

Formula Comparison

The three primary formulas used for geo proximity calculations are:

1. Haversine Formula:

d = 2r * arcsin(sqrt(sin((lat2 - lat1) / 2) ^ 2   cos(lat1) * cos(lat2) * sin((lon2 - lon1) / 2) ^ 2))

2. Spherical Law of Cosines (Great-Circle Distance Formula):

d = r * acos(cos(lat1) * cos(lat2)   sin(lat1) * sin(lat2) * cos(lon2 - lon1))

3. Vicenty's Formulae (Most Accurate):

While this formula is not directly addressed in the provided answer, it is acknowledged to be the most accurate, albeit slower.

Performance Considerations

Speed:

• Law of Cosines (fastest)
• Haversine Formula
• Vicenty's Formula (slowest)

Accuracy:

• Vicenty's Formula (most accurate)
• Haversine Formula
• Spherical Law of Cosines (least accurate)

Practical Recommendations

For fast and accurate results:

• Spherical Law of Cosines is a reasonable choice for most applications.

For extreme precision:

• Vicenty's Formula is recommended, but its slower speed must be considered.

For a simplified and speedy solution (at the cost of accuracy):

• A simplified distance formula can be used if the problem domain is relatively flat.

Conclusion

The appropriate formula for geo proximity calculations depends on the specific requirements of the application. For practical purposes, the Haversine Formula or the Spherical Law of Cosines offer a balance of speed and accuracy. However, if precision is of utmost importance, Vicenty's Formula is the preferred choice.