Eccentricity

Functions
template<typename T >
T	EGXMath::EllipseEccentricity (const T flattening)
	Finds the eccentricity, \(e\), of an ellipse from flattening, \(f\): \[ e = \sqrt{f (2 - f)} \] . More...
template<typename T >
T	EGXMath::EllipseEccentricity (const T semiMajorAxisInm, const T semiMinorAxisInm)
	Finds the eccentricity, \(e\), of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\): \[ e = \sqrt{1-\frac{b^2}{a^2}}\] . More...

Detailed Description

Function Documentation

EllipseEccentricity() [1/2]

template<typename T >

T EGXMath::EllipseEccentricity

(

const T

flattening

)

Finds the eccentricity, \(e\), of an ellipse 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 the ellipse.

Returns

\( e\ (dimensionless)\) Eccentricity of the ellipse.

See also

EllipseSurfaceArea() for area of an ellipse.

EllipseCircumference() for circumference of an ellipse.

EllipseSemiMajorAxis() for semi-major axis of an ellipse.

EllipseSemiMinorAxis() for semi-minor axis of an ellipse.

EllipseSemiLatusRectum() for semi-latus rectum of an ellipse.

EllipseDirectrix() for directrix of an ellipse.

EllipseFocalParameter() for focal parameter of an ellipse.

EllipseFocalLength() for focal length of an ellipse.

EllipseLinearEccentricity() for linear eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.

EllipseEccentricity() [2/2]

template<typename T >

T EGXMath::EllipseEccentricity	(	const T	semiMajorAxisInm,
		const T	semiMinorAxisInm
	)

Finds the eccentricity, \(e\), of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\):

\[ e = \sqrt{1-\frac{b^2}{a^2}}\]

.

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

semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the ellipse in meters.
semiMinorAxisInm	\( b\ (m)\) Semi-minor axis of the ellipse in meters.

Returns

\( e\ (dimensionless)\) Eccentricity of the ellipse.

See also

EllipseSurfaceArea() for area of an ellipse.

EllipseCircumference() for circumference of an ellipse.

EllipseSemiMajorAxis() for semi-major axis of an ellipse.

EllipseSemiMinorAxis() for semi-minor axis of an ellipse.

EllipseSemiLatusRectum() for semi-latus rectum of an ellipse.

EllipseDirectrix() for directrix of an ellipse.

EllipseFocalParameter() for focal parameter of an ellipse.

EllipseFocalLength() for focal length of an ellipse.

EllipseLinearEccentricity() for linear eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.