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.