Calculation

Determination of geodesic distances between two points on a spherical or spheroidal reference surface.

Airline distance calculation

Calculating accurate distances between two points on the Earth's surface is essential for applications like routing and mapping. Common methods include the Haversine formula and Great-circle distance for fast spherical approximations, and Vincenty's formulae and Karney's algorithm for precise geodesic distances on an ellipsoidal Earth model.

Spherical Earth Model

The Spherical Earth Model is a simplified way of representing the Earth as a perfect sphere with a constant radius (usually around 6371 km).

Haversine Formula

• Simplicity: The Haversine formula is simpler and computationally less intensive than Vincenty's formulae, making it easier to implement.

• Accuracy: While accurate for short distances, the Haversine formula may exhibit limitations for long distances, as it assumes a spherical Earth model and does not account for the Earth's ellipsoidal shape.

• Popular Use: The Haversine formula is commonly used in applications where simplicity and speed are prioritized over extreme precision, such as in web and mobile applications.

Haversine formulaWikipedia

Great-circle Distance Method

• Concept: The Great-circle distance method calculates the shortest distance between two points on the surface of a sphere, traveling along the surface of the sphere.

• Accuracy: It provides good accuracy for most practical purposes, especially for shorter distances.

• Applicability: The Great-circle distance method assumes a spherical Earth model, which simplifies calculations. It is suitable for applications where a balance between accuracy and computational efficiency is required.

Great-circle distanceWikipedia

Ellipsoidal Earth Model

The Ellipsoidal Earth Model represents the Earth as an oblate spheroid — slightly flattened at the poles and bulging at the equator. It is more accurate than the spherical model.

Vincenty's Formulae

• Accuracy: Vincenty's formulae are known for their higher accuracy compared to the Haversine formula, especially for long distances and over ellipsoidal surfaces.

• Applicability: Vincenty's formulae are suitable for calculating distances on an ellipsoidal Earth model, making them more precise for geodetic calculations.

• Complexity: These formulae are more complex mathematically than the Haversine formula.

Vincenty's formulaeWikipedia

Karney’s Algorithm

• Accuracy: Karney’s algorithm offers even higher accuracy than Vincenty's formulae, achieving sub-millimeter precision by using exact solutions on the ellipsoidal Earth model. It is highly reliable even for edge cases like antipodal points.

• Applicability: This algorithm is ideal for precise geodetic calculations, particularly in global navigation, GIS, and surveying, where robustness and accuracy are critical.

• Complexity: Karney’s method involves advanced series expansions and geodesic integrals, making it more mathematically sophisticated, but it is implemented efficiently in libraries like GeographicLib.

https://link.springer.com/article/10.1007/s00190-012-0578-zlink.springer.com