Flattening/Oblateness

Functions
template<typename T >
T	EGXMath::SpheroidFlattening (const T equatorialRadiusInm, const T polarRadiusInm)
	Finds the flattening (oblateness), \(f\), of a spheroid with equatorial radius, \(a\), and polar radius, \(c\): \[ f =\begin{cases} \frac{a-c}{a}{} & oblate \\ \frac{c-a}{a} & prolate \end{cases} \] . More...
template<typename T >
T	EGXMath::SpheroidFlattening (const T eccentricity)
	Finds the flattening (oblateness), \(f\), of a spheroid with eccentricity \(e\): \[ f = 1 - \sqrt{1-e^2} \] . More...
template<typename T >
T	EGXMath::SpheroidOblateness (const T equatorialRadiusInm, const T polarRadiusInm)
	Finds the oblateness (flattening), \(f\), of a spheroid with equatorial radius, \(a\), and polar radius, \(c\): \[ f =\begin{cases} \frac{a-c}{a}{} & oblate \\ \frac{c-a}{a} & prolate \end{cases} \] . More...
template<typename T >
T	EGXMath::SpheroidOblateness (const T eccentricity)
	Finds the oblateness (flattening), \(f\), of a spheroid with eccentricity \(e\): \[ f = 1 - \sqrt{1-e^2} \] . More...

Detailed Description

Function Documentation

SpheroidFlattening() [1/2]

template<typename T >

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

Finds the flattening (oblateness), \(f\), of a spheroid with equatorial radius, \(a\), and polar radius, \(c\):

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

.

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 http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

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

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

See also

SpheroidOblateness() for alias.

SpheroidEccentricity() for eccentricity of a spheroid.

SpheroidEquatorialRadius() for equatorial radius 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.

SpheroidFlattening() [2/2]

template<typename T >

T EGXMath::SpheroidFlattening

(

const T

eccentricity

)

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

\[ f = 1 - \sqrt{1-e^2} \]

.

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

See http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

Parameters

eccentricity

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

Returns

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

See also

SpheroidOblateness() for alias.

SpheroidEccentricity() for eccentricity of a spheroid.

SpheroidEquatorialRadius() for equatorial radius 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.

SpheroidOblateness() [1/2]

template<typename T >

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

Finds the oblateness (flattening), \(f\), of a spheroid with equatorial radius, \(a\), and polar radius, \(c\):

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

.

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 http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

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

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

See also

SpheroidFlattening() for alias.

SpheroidEccentricity() for eccentricity of a spheroid.

SpheroidEquatorialRadius() for equatorial radius 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.

SpheroidOblateness() [2/2]

template<typename T >

T EGXMath::SpheroidOblateness

(

const T

eccentricity

)

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

\[ f = 1 - \sqrt{1-e^2} \]

.

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

See http://mathworld.wolfram.com/Flattening.html , https://en.wikipedia.org/wiki/Flattening and https://en.wikipedia.org/wiki/Equatorial_bulge

Parameters

eccentricity

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

Returns

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

See also

SpheroidFlattening() for alias.

SpheroidEccentricity() for eccentricity of a spheroid.

SpheroidEquatorialRadius() for equatorial radius 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.