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Modeling the Earth

Represent the shape and size of the Earth; represent ellipsoids; convert between parameters


geocrsGeographic coordinate reference system object
wgs84EllipsoidReference ellipsoid for World Geodetic System of 1984
egm96geoidGeoid height from Earth Gravitational Model 1996 (EGM96)
earthRadiusMean radius of planet Earth
rcurveEllipsoidal radii of curvature
rsphereRadii of auxiliary spheres
geocentricLatitudeConvert geodetic to geocentric latitude
parametricLatitudeConvert geodetic to parametric latitude
geodeticLatitudeFromGeocentricConvert geocentric to geodetic latitude
geodeticLatitudeFromParametricConvert parametric to geodetic latitude
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


expand all

oblateSpheroidOblate ellipsoid of revolution
referenceEllipsoidReference ellipsoid
referenceSphereReference sphere
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


  • The Shape of the Earth

    The Earth can be modeled with increasing precision as a perfect sphere, an oblate spheroid, an ellipsoid, or a geoid.

  • Reference Spheroids

    A reference spheroid is a model of a roughly-spherical astronomical body with a simplified geometry, such as a sphere with uniform radius or a standard ellipsoid.

  • 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.