Dataset Open Access

Test set for geodesics

Karney, Charles F. F.

This is a set of 500000 geodesics for the WGS84 ellipsoid; this is an ellipsoid of revolution with equatorial radius a = 6378137 m and flattening f = 1/298.257223563.

Each line of the test set gives 10 space delimited numbers

  • latitude at point 1, φ1 (degrees, exact)
  • longitude at point 1, λ1 (degrees, always 0)
  • azimuth at point 1, α1 (clockwise from north in degrees, exact)
  • latitude at point 2, φ2 (degrees, accurate to 10−18 deg)
  • longitude at point 2, λ2 (degrees, accurate to 10−18 deg)
  • azimuth at point 2, α2 (degrees, accurate to 10−18 deg)
  • geodesic distance from point 1 to point 2, s12 (meters, exact)
  • arc distance on the auxiliary sphere, σ12 (degrees, accurate to 10−18 deg)
  • reduced length of the geodesic, m12 (meters, accurate to 0.1 pm)
  • the area between the geodesic and the equator, S12 (m2, accurate to 1 mm2)

These are computed using high-precision direct geodesic calculations with the given φ1, λ1, α1, and s12. The distance s12 always corresponds to an arc length σ12 ≤ 180°, so the given geodesics give the shortest paths from point 1 to point 2. For simplicity and without loss of generality, φ1 is chosen in [0°, 90°], λ1 is taken to be zero, α1 is chosen in [0°, 180°]. Furthermore, φ1 and α1 are taken to be multiples of 10−12 deg and s12 is a multiple of 0.1 μm in [0 m, 20003931.4586254 m]. This results in λ2 in [0°, 180°] and α2 in [0°, 180°].

The contents of the file are as follows:

  • 100000 entries randomly distributed
  • 50000 entries which are nearly antipodal
  • 50000 entries with short distances
  • 50000 entries with one end near a pole
  • 50000 entries with both ends near opposite poles
  • 50000 entries which are nearly meridional
  • 50000 entries which are nearly equatorial
  • 50000 entries running between vertices (α1 = α2 = 90°)
  • 50000 entries ending close to vertices

The values for s12 for the geodesics running between vertices are truncated to a multiple of 0.1 pm and this is used to determine point 2.

Files (86.6 MB)
Name Size
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  • C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87(1), 43-55 (2013).
  • C. F. F. Karney, Geodesics on an ellipsoid of revolution (2011).
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