Surface Area

Functions
template<typename T >
T	EGXMath::SpheroidSurfaceArea (const T equatorialRadiusInm, const T polarRadiusInm)
	Finds the surface area, \(S_{spheroid}\), in meter squared of a spheroid with equatorial radius \(a\) and polar radius, \(c\). If \(a < c\), the spheroid is prolate, if \(a = c\) it is a sphere and if \(a>c\) the sphere is oblate. \[ S_{spheroid}=\begin{cases} 2\pi a^2 + 2\pi\dfrac{a c^2}{\sqrt{c^2-a^2}}\arcsin \left ( \dfrac{\sqrt{c^2-a^2}}{c} \right ) & a<c\ prolate \\ 2\pi a^2 +\pi \dfrac{a c^2}{\sqrt{a^2-c^2}}\ln \left(\dfrac{1+\dfrac{\sqrt{a^2-c^2}}{a}}{1-\dfrac{\sqrt{a^2-c^2}}{a}}\right )& a>c\ oblate \end{cases} \] . More...

Detailed Description

Function Documentation

SpheroidSurfaceArea()

template<typename T >

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

Finds the surface area, \(S_{spheroid}\), in meter squared of a spheroid with equatorial radius \(a\) and polar radius, \(c\). If \(a < c\), the spheroid is prolate, if \(a = c\) it is a sphere and if \(a>c\) the sphere is oblate.

\[ S_{spheroid}=\begin{cases} 2\pi a^2 + 2\pi\dfrac{a c^2}{\sqrt{c^2-a^2}}\arcsin \left ( \dfrac{\sqrt{c^2-a^2}}{c} \right ) & a<c\ prolate \\ 2\pi a^2 +\pi \dfrac{a c^2}{\sqrt{a^2-c^2}}\ln \left(\dfrac{1+\dfrac{\sqrt{a^2-c^2}}{a}}{1-\dfrac{\sqrt{a^2-c^2}}{a}}\right )& a>c\ oblate \end{cases} \]

.

See http://mathworld.wolfram.com/Ellipse.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

\( S_{spheroid}\ (m^2)\) Surface area of spheroid in meter squared.

See also

SpheroidEccentricity() for eccentricity of a spheroid.

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.

SpheroidVolume() for volume of a spheroid.