Surface Area

Functions
template<typename T >
T	EGXMath::EllipsoidSurfaceArea (const T aSemiPrincipleAxisInm, const T bSemiPrincipleAxisInm, const T cSemiPrincipleAxisInm)
	Finds the surface area, \(S_{ellipsoid}\), in meter squared of an ellipsoid with three distinct semi-principle axes, \(a\), \(b\) and \(c\). \[ S_{ellipsoid} \approx 4 \pi \left ( \dfrac{(ab)^{1.605}+(ac)^{1.605}+(bc)^{1.605}}{3} \right )^{\dfrac{1}{1.605}} \] . More...

Detailed Description

Function Documentation

EllipsoidSurfaceArea()

template<typename T >

T EGXMath::EllipsoidSurfaceArea	(	const T	aSemiPrincipleAxisInm,
		const T	bSemiPrincipleAxisInm,
		const T	cSemiPrincipleAxisInm
	)

Finds the surface area, \(S_{ellipsoid}\), in meter squared of an ellipsoid with three distinct semi-principle axes, \(a\), \(b\) and \(c\).

\[ S_{ellipsoid} \approx 4 \pi \left ( \dfrac{(ab)^{1.605}+(ac)^{1.605}+(bc)^{1.605}}{3} \right )^{\dfrac{1}{1.605}} \]

.

See http://mathworld.wolfram.com/Ellipsoid.html and https://en.wikipedia.org/wiki/Ellipsoid

See http://www.numericana.com/answer/ellipsoid.htm for formula constant derived by Knud Thomsen.

See Klamkin, Murray S. "Elementary approximations to the area of n-dimensional ellipsoids." The American Mathematical Monthly 78.3 (1971): 280-283. for formula derivation.

Parameters

aSemiPrincipleAxisInm	\( a\ (m)\) Semi-principle axis of the ellipsoid that lays along the x-axis in meters.
bSemiPrincipleAxisInm	\( b\ (m)\) Semi-principle axis of the ellipsoid that lays along the y-axis in meters.
cSemiPrincipleAxisInm	\( c\ (m)\) Semi-principle axis of the ellipsoid that lays along the z-axis in meters.

Returns

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

See also

EllipsoidVolume() for volume of an ellipsoid.

EllipsoidInertia() for inertial tensor of an ellipsoid.

SphereSurfaceArea() for surface area of a sphere.

SpheroidSurfaceArea() for surface area of a spheroid.