Eccentricity

Functions
template<typename T >
T	EGXMath::SpheroidEccentricity (const T flattening)
	Finds the eccentricity, \(e\), of a spheroid from flattening, \(f\): \[ e = \sqrt{f (2 - f)} \] . More...
template<typename T >
T	EGXMath::SpheroidEccentricity (const T equatorialRadiusInm, const T polarRadiusInm)
	Finds the eccentricity, \(e\), of a spheroid with equatorial radius \(a\) and polar radius, \(c\): \[ f =\begin{cases} \sqrt{\frac{a^2-c^2}{a^2}} & oblate \\ \sqrt{\frac{c^2-a^2}{a^2}} & prolate \end{cases} \] . More...

Detailed Description

Function Documentation

SpheroidEccentricity() [1/2]

template<typename T >

T EGXMath::SpheroidEccentricity

(

const T

flattening

)

Finds the eccentricity, \(e\), of a spheroid from flattening, \(f\):

\[ e = \sqrt{f (2 - f)} \]

.

Equation taken from "Map Projections-A Working Manual" (Snyder, 1987), p. 13

See https://en.wikipedia.org/wiki/Eccentricity_(mathematics) , http://mathworld.wolfram.com/Eccentricity.html, http://mathworld.wolfram.com/Flattening.html

Parameters

flattening

\( f\ (dimensionless)\) Flattening of spheroid.

Returns

\( e\ (dimensionless)\) Flatness of spheroid.

See also

SpheroidEquatorialRadius() for equatorial radius of a spheroid.

SpheroidFlattening() for flattening of a spheroid.

SpheroidInertia() for inertia tensor of a spheroid.

SpheroidPolarRadius() for polar radius of a spheroid.

SpheroidSurfaceArea() for surface area of a spheroid.

SpheroidVolume() for volume of a spheroid.

SpheroidEccentricity() [2/2]

template<typename T >

T EGXMath::SpheroidEccentricity	(	const T	equatorialRadiusInm,
		const T	polarRadiusInm
	)

Finds the eccentricity, \(e\), of a spheroid with equatorial radius \(a\) and polar radius, \(c\):

\[ f =\begin{cases} \sqrt{\frac{a^2-c^2}{a^2}} & oblate \\ \sqrt{\frac{c^2-a^2}{a^2}} & prolate \end{cases} \]

.

Spheroid is oblate if the equatorial radius is larger than the polar radius. It is prolate if the polar radius is larger than the equatorial radius.

Equation taken from "Map Projections-A Working Manual" (Snyder, 1987), p. 13

See https://en.wikipedia.org/wiki/Eccentricity_(mathematics) , http://mathworld.wolfram.com/Eccentricity.html, http://mathworld.wolfram.com/Flattening.html

Parameters

equatorialRadiusInm	\( a\ (m)\) Equatorial radius in meters. The degenerate semi-principle axis of the spheroid.
polarRadiusInm	\( c\ (m)\) Polar radius in meters. The unique semi-principle axis of the spheroid.

Returns

\( e\ (dimensionless)\) Eccentricity of spheroid.

See also

SpheroidEquatorialRadius() for equatorial radius of a spheroid.

SpheroidFlattening() for flattening of a spheroid.

SpheroidInertia() for inertia tensor of a spheroid.

SpheroidPolarRadius() for polar radius of a spheroid.

SpheroidSurfaceArea() for surface area of a spheroid.

SpheroidVolume() for volume of a spheroid.