Test set for geodesics

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.