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Global shortest path: How to calculate the shortest distance from two coordinates?
In this digital age, whether it is online dating or navigation services, the same problem often troubles people: how to quickly and accurately calculate the distance between two geographical coordinates? Many people already measure distance in a habitual way in their daily lives, but few people know the mathematical principles behind it.
Initial understanding of geographical distance
Geographic distance, or geodesic distance, is a distance measured along the surface of the Earth, often expressed as the shortest arc length. When it comes to calculating distances with longitude and latitude coordinates, there are several different abstractions commonly used, such as flat surfaces, spherical surfaces, and elliptical surfaces. These methods all ignore the ups and downs of the earth's surface.
The process of calculating distance is actually a simplification of part of the real surface situation, but this simplification will not be completely accurate.
Basic concepts of distance calculation
The distance calculation from one point to another on the earth's surface is usually simplified by using the latitude and longitude of two points. For example, when we use "longitude" and "latitude" to locate a location, we can calculate the distance between these two points. Such calculations not only apply to points at all latitudes and longitudes, but can also be extended to more complex coordinate systems.
Different classifications of calculation formulas
These distance calculation formulas can be classified according to the approximation they use. The most common ones are as follows:
- Plane approximation formula, suitable for very short distances.
- Spherical approximation formula for longer distance calculations.
- Ellipse surface approximation formula provides higher precision distance calculation.
Choosing the appropriate calculation formula will directly affect the accuracy and practicality of the distance.
Planar approximation and spherical approximation
When studying short-distance operations, plane approximation formulas are usually used. This method assumes that the earth's surface can be regarded as a plane, and then uses simple Cartesian coordinate calculations. Under this assumption, the distance between two points can be calculated by Pythagorean theorem.
High accuracy of elliptical surface approximation
With the development of science and technology, elliptical surface approximation has gradually become a common method for accurate distance measurement. This method takes into account the curvature of the Earth and the inconsistencies in longitude at different locations. Using the elliptical surface formula can improve the calculation accuracy of distance to a whole new level, especially suitable for calculations at mid-to-high latitudes.
Practical applications and future prospects
As data science and big data technology further develop, our distance calculation methods will continue to improve. In the future, more intelligent computing tools may appear. These tools can not only calculate distances, but also consider terrain changes, traffic conditions and other factors to provide more accurate path planning.
Have you ever wondered how modern technology can push the accuracy of ranging to new heights?
