...HEADmaster

Signed-off-by: Mattias Andrée <m@maandree.se>

1 files changed, 51 insertions, 0 deletions

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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)