Spherical vs Euclidean Coordinates

When we choose to enter a point by either using the GPS device or manually entering the longitude/ latitude in the Settings screen, at the bottom of the screen we see two more options:

  • Euclidean coordinates
  • Altitude

The Altitude is enabled only when the Euclidean Coordinates are enabled.

Euclidean Coordinates

As we read in the description, when the Euclidean coordinates are enabled, the distances and angles are computed according to Euclidean geometry. This, means, that we silently make the assumption that the area of interest is a flat area, without any curvature. The Euclidean geometry is applicable only in flat surfaces.

In most cases, it is valid to make the aforementioned assumption, but, when we are interested in large areas (e.g., the surface of an island or a country), using the Euclidean coordinates will result in some erroneous calculations. In such cases we need to use the Spherical coordinates.

Spherical Coordinates

The Spherical coordinates are used to describe events that take place on the surface of a sphere. The distance between two points is no longer a straight line, but a curved one. Thus, the curvature of the surface greatly affects the calculations of distances and angles between points.

Since the planet Earth is not a perfect sphere, its curvature varies from point to point. iTopography uses mathematical equations that correctly calculate the distance between two points by taking under consideration the local curvature of the planet Earth. Similar mathematical equations are used to compute the angle between three points.

Summary

In most cases it suffices to use the Euclidean coordinates to compute the distance between two points. But, for large areas, especially when the distance between two points is more than 10 km, we will get more accurate results when we use Spherical coordinates. iTopography allows us to pick either coordinate, enabling us to check the accuracy of the Euclidean coordinates.

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