Ellipsoids and datums

A latitude/longitude pair means nothing on its own — it is always measured on a chosen reference ellipsoid: an ellipse of revolution that approximates the figure of the Earth. Two numbers pin the shape down: the semi-major axis a and the flattening f = (a − b) / a (usually given as 1/f). Everything else — semi-minor axis b, first/second eccentricity e², e′², and the radii of curvature N (prime vertical) and M (meridian) — follows from them.

Ellipsoid<TLinear, TAngular>

Ellipsoid.cs is a generic struct (typed by linear unit, e.g. Meter, and angular unit, e.g. Degree) implementing IEllipsoid. It exposes:

• Geometry — SemiMajorAxis, SemiMinorAxis, Flattening, InverseFlattening, FirstEccentricity, SecondEccentricity
• Curvature — CalculateN(latitude) (prime vertical) and CalculateM(latitude) (meridian) — see below
• Datum definition — DatumTranslation (a Cartesian3DPoint shift of the ellipsoid center) and DatumMisalignment (an OrientationParameter: rotations ω, φ, κ), which position a regional datum relative to the geocentric frame
• Identity — Name, EsriName, Srid (EPSG code)

Radii of curvature — M and N

Unlike a sphere, an ellipsoid curves by a different amount in every direction at a given point. Two normal sections bound the range, and together they carry almost all of the geodetic math:

	Section	Formula	At the equator	At the pole
M	along the meridian — the minimum radius	M(φ) = a(1 − e²) / (1 − e² sin²φ)^{3/2}	b²/a	a²/b
N	along the prime vertical (east–west) — the maximum radius	N(φ) = a / (1 − e² sin²φ)^{1/2}	a	a²/b

M ≤ N everywhere, and the two become equal at the poles. Geometrically, N is the length of the surface normal from the point down to the spin axis — it reaches the axis exactly — while M's centre of curvature stops short of it. N is also the quantity that appears in the geodetic→Cartesian conversion and in the Transverse Mercator / UTM series.

var wgs84 = Ellipsoids.WGS84;

LinearUnit n = wgs84.CalculateN(new Degree(35.689));  // prime vertical radius
LinearUnit m = wgs84.CalculateM(new Degree(35.689));  // meridian radius
double meters = n.Value;                              // ≈ 6 385 415 m

// CalculateN also has a plain-double overload (latitude in degrees)
double nAtLat = wgs84.CalculateN(35.689);

Predefined ellipsoids: Ellipsoids

Ellipsoids.cs provides ready-made instances (Ellipsoid<Meter, Degree>). Notable ones:

Property	a (m)	1/f	EPSG
Ellipsoids.WGS84	6 378 137.0	298.257223563	4326
Ellipsoids.GRS80	6 378 137.0	298.257222101	4019
Ellipsoids.WGS72	6 378 135.0	298.26	4322
Ellipsoids.International1924 (Hayford)	6 378 388.0	297	7022
Ellipsoids.Clarke1866	6 378 206.4	294.9786982	7008
Ellipsoids.Clarke1880Rgs	6 378 249.145	293.465	7012
Ellipsoids.Bessel1841	6 377 397.155	299.1528128	7004
Ellipsoids.Airy1830	6 377 563.396	299.3249646	7001
Ellipsoids.Sphere	6 378 137.0	∞ (no flattening)	—

…plus regional datums carrying a translation toward WGS84, e.g. Ellipsoids.FD58 (Final Datum 1958, used in Iran's oil industry) and Ellipsoids.NahrawanIraq.

Ellipsoids.WGS84 is a cached singleton; treat it as the default datum throughout the library.

Custom ellipsoid

using IRI.Maptor.Core.Common.Metrics;
using IRI.Maptor.Core.SpatialReferenceSystem;
using IRI.Maptor.Core.SpatialReferenceSystem.Models;

// simple: name, semi-major axis, 1/f, srid
var hayford = new Ellipsoid<Meter, Degree>("International 1924", new Meter(6378388.0), 297, 7022);

// full datum definition: with translation + orientation relative to the geocentric frame
var fd58 = new Ellipsoid<Meter, Degree>("D_FD_1958", new Meter(6378249.145), 293.465,
    new Cartesian3DPoint<Meter>(new Meter(-241.54), new Meter(-163.64), new Meter(396.06)),
    new OrientationParameter(new Degree(), new Degree(), new Degree()),
    4132);

To transform geodetic coordinates between two datums (G1 ↔ G2), use Transformations.ChangeDatum(...) from Transformations.cs.

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Back to IRI.Maptor.Core.SpatialReferenceSystem · projections that consume these datums are documented in MapProjections.