Dataset Open Access

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, φ
_{1}(degrees, exact) - longitude at point 1, λ
_{1}(degrees, always 0) - azimuth at point 1, α
_{1}(clockwise from north in degrees, exact) - latitude at point 2, φ
_{2}(degrees, accurate to 10^{−18}deg) - longitude at point 2, λ
_{2}(degrees, accurate to 10^{−18}deg) - azimuth at point 2, α
_{2}(degrees, accurate to 10^{−18}deg) - geodesic distance from point 1 to point 2,
*s*_{12}(meters, exact) - arc distance on the auxiliary sphere, σ
_{12}(degrees, accurate to 10^{−18}deg) - reduced length of the geodesic,
*m*_{12}(meters, accurate to 0.1 pm) - the area between the geodesic and the equator,
*S*_{12}(m^{2}, accurate to 1 mm^{2})

These are computed using high-precision direct geodesic calculations with the given φ_{1}, λ_{1}, α_{1}, and *s*_{12}. The distance *s*_{12} always corresponds to an arc length σ_{12} ≤ 180°, so the given geodesics give the shortest paths from point 1 to point 2. For simplicity and without loss of generality, φ_{1} is chosen in [0°, 90°], λ_{1} is taken to be zero, α_{1} is chosen in [0°, 180°]. Furthermore, φ_{1} and α_{1} are taken to be multiples of 10^{−12} deg and *s*_{12} is a multiple of 0.1 μm in [0 m, 20003931.4586254 m]. This results in λ_{2} in [0°, 180°] and α_{2} 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 (α
_{1}= α_{2}= 90°) - 50000 entries ending close to vertices

The values for *s*_{12} for the geodesics running between vertices are truncated to a multiple of 0.1 pm and this is used to determine point 2.

Name | Size | |
---|---|---|

GeodTest.dat md5:3461c4dc2500a8bad9394cd530b13dbe |
86.6 MB | Download |

- 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). http://arxiv.org/abs/1102.1215