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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.


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wgs84EllipsoidReference ellipsoid for World Geodetic System of 1984
egm96geoidGeoid height from Earth Gravitational Model 1996 (EGM96)
earthRadiusMean radius of planet Earth
geocrsGeographic coordinate reference system object (Since R2020b)
geocentricLatitudeConvert geodetic to geocentric latitude
parametricLatitudeConvert geodetic to parametric latitude
geodeticLatitudeFromGeocentricConvert geocentric to geodetic latitude
geodeticLatitudeFromParametricConvert parametric to geodetic latitude
rcurveEllipsoidal radii of curvature
rsphereRadii of auxiliary spheres
axes2eccEccentricity of ellipse from axes lengths
majaxisSemimajor axis of ellipse
minaxisSemiminor axis of ellipse
ecc2flatFlattening of ellipse from eccentricity
flat2eccEccentricity of ellipse from flattening
ecc2nThird flattening of ellipse from eccentricity
n2eccEccentricity of ellipse from third flattening


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referenceEllipsoidReference ellipsoid
referenceSphereReference sphere
oblateSpheroidOblate ellipsoid of revolution
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


  • 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.