Modeling the Earth

Represent shape and size of the Earth, create reference ellipsoids, convert between latitudes

The Earth is round, but it is not a perfect sphere. You can model the shape and size of the Earth using reference spheroids, such as the World Geodetic System of 1984 (WGS84), and geoid models, such as the Earth Gravitational Model of 1996 (EGM96).

When creating map projections, you can preserve characteristics of the Earth by using auxiliary latitudes. For example, when creating an equal area map projection from an ellipsoid, you can preserve surface area by using authalic latitudes. Use latitude conversion functions and objects to convert between types of latitude.

Functions

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Modeling the Earth

`wgs84Ellipsoid`	Reference ellipsoid for World Geodetic System of 1984
`egm96geoid`	Geoid height from Earth Gravitational Model 1996 (EGM96)
`earthRadius`	Mean radius of planet Earth
`geocrs`	Geographic coordinate reference system object (Since R2020b)

Latitude Conversions

`geocentricLatitude`	Convert geodetic to geocentric latitude
`parametricLatitude`	Convert geodetic to parametric latitude
`geodeticLatitudeFromGeocentric`	Convert geocentric to geodetic latitude
`geodeticLatitudeFromParametric`	Convert parametric to geodetic latitude

Radii of Reference Spheroids

`rcurve`	Ellipsoidal radii of curvature
`rsphere`	Radii of auxiliary spheres

Ellipse Parameters

`axes2ecc`	Eccentricity of ellipse from axes lengths
`majaxis`	Semimajor axis of ellipse
`minaxis`	Semiminor axis of ellipse
`ecc2flat`	Flattening of ellipse from eccentricity
`flat2ecc`	Eccentricity of ellipse from flattening
`ecc2n`	Third flattening of ellipse from eccentricity
`n2ecc`	Eccentricity of ellipse from third flattening

Objects

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Reference Spheroids

`referenceEllipsoid`	Reference ellipsoid
`referenceSphere`	Reference sphere
`oblateSpheroid`	Oblate ellipsoid of revolution

Latitude Converters

`AuthalicLatitudeConverter`	Convert between geodetic and authalic latitudes
`ConformalLatitudeConverter`	Convert between geodetic and conformal latitudes
`IsometricLatitudeConverter`	Convert between geodetic and isometric latitudes
`RectifyingLatitudeConverter`	Convert between geodetic and rectifying latitudes

Topics

Shape of the Earth
You can model the Earth using a perfect sphere, an ellipsoid, an oblate spheroid, or a geoid.
Comparison of Reference Spheroids
Learn how to create reference spheroids using different functions and objects.
Work with Reference Spheroids
Use reference spheroids to create map projections, to calculate curves and areas on the surface of a spheroid, and to transform 3-D geodetic coordinates.