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authorMattias Andrée <m@maandree.se>2024-10-22 22:22:41 +0200
committerMattias Andrée <m@maandree.se>2024-10-22 22:22:41 +0200
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Signed-off-by: Mattias Andrée <m@maandree.se>
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Finish libtellurian_vincenty_inverse__
+Document the details of NaN returns in libtellurian_distance.3
+Document what happens to the azimuths when the starting point is a pole.
+
+libtellurian_coarse_distance can be simplified to (d/2R)²
+which would be an good alternative for simply sorting distances,
+and it would still be easy to afterwards convert the values for
+a selection of them into approximate distances.
+
+Add inverse function of libtellurian_effective_gravity_radians
+
+Add inverse function of libtellurian_elevated_gravity_radians
+
+And functions for converting between coordinate systems
+ Geodetic (h, φ, λ) : Angle between normal and equatorial plane
+ Inverse of Cartesian (see Cartesian for definition of N)
+ Iteration is required unless φ or h is known
+ λ = atan2(Y, X)
+ h = p / cos φ - N
+ φ = tan⁻¹(Zp⁻¹/(1 - e²N/(N + h)))
+ where p = √(X² + Y²)
+ https://en.wikipedia.org/wiki/Geographic_coordinate_conversion#From_ECEF_to_geodetic_coordinates
+ When h=0
+ λ = atan2(Y, X)
+ φ = tan⁻¹(Zp⁻¹/(1 - e²))
+ where p = √(X² + Y²)
+ wouldn't it easier to convert to geocentric intermittently
+ Geocentric ϕ : Angle from centre of earth
+ ϕ = tan⁻¹((1 - e²) tan φ)
+ Geometric : Arc length = geodetic
+ Parametric/reduced β : spherical angle resulting in same distance from polar axis as
+ β = tan⁻¹((1 - f) tan φ)
+ Ellipsoidal-harmonic
+ TODO
+ Rectifying μ
+ μ = πm(φ) / 2m(½π), where m(u) = a(1 - e²) ∫{0→u} √(1 - e² sin² v)⁻³ dv
+ Authalic ξ
+ ξ = sin⁻¹(q(φ) / q(½π)), where q(u) = ((1 - e²) sin u)/(1 - e² sin u) + (1 - e²) e⁻¹ tanh⁻¹ (e sin u)
+ q(½π) = 1 + (1 - e²) e⁻¹ tanh⁻¹ e
+ Conformal χ
+ χ = tan⁻¹ (sinh [sinh⁻¹ tan φ - e tanh⁻¹ (e sin φ)])
+ Isometric ψ
+ ψ = sinh⁻¹ tan φ - e than⁻¹ (e sin φ)
+ Astronomical Φ : angle between equatorial plane and the true vertical direction
+ the true vertical direction, is the direction of gravity which is affect
+ byu the centrifugal acceleration in addition to the gravitational acceleration.
+ Cartesian (geocentric Cartesian)
+ X = (N + h) cos φ cos λ
+ Y = (N + h) cos φ sin λ
+ Z = (Nb²/a² + h) sin φ
+ where
+ N = a²/√(a² cos² φ + b² sin² φ)