Focal Length

Functions
template<typename T >
T	EGXMath::EllipseFocalLength (const T linearEccentricityInm)
	Finds the focal length, \(f\), in meters of an ellipse with linear eccentricity, \(c\). \[ f = 2c \] . More...
template<typename T >
T	EGXMath::EllipseFocalLength (const T semiMajorAxisInm, const T semiMinorAxisInm)
	Finds the focal length, \(f\), in meters of an ellipse with semi-major axis, \(a\), and semi-minor axis \(b\). \[ f=2\sqrt{a^2-b^2} \] . More...
template<typename T >
T	EGXMath::EllipseFocalLengthFromSemiMajorAndSemiMinorAxes (const T semiMajorAxisInm, const T semiMinorAxisInm)
	Finds the linear eccentricity, \(f\), in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). \[ f=2\sqrt{a^2-b^2} \] . More...
template<typename T >
T	EGXMath::EllipseFocalLengthFromEccentricity (const T semiMajorAxisInm, const T eccentricity)
	Finds the linear eccentricity, \(f\), in meters of an ellipse with semi-major axis \(a\), and eccentricity \(e\). \[ f=2 a e \] . More...

Detailed Description

Function Documentation

EllipseFocalLength() [1/2]

template<typename T >

T EGXMath::EllipseFocalLength

(

const T

linearEccentricityInm

)

Finds the focal length, \(f\), in meters of an ellipse with linear eccentricity, \(c\).

\[ f = 2c \]

.

The focal length is the distance betweem the two foci.

See http://mathworld.wolfram.com/FocalParameter.html and https://en.wikipedia.org/wiki/Conic_section#Conic_parameters

Parameters

linearEccentricityInm

\( c\ (m)\) Linear eccentricity of the ellipse in meters.

Returns

\( f\ (m)\) focal length of the ellipse in meters.

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.

EllipseEccentricity() for eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.

EllipseFocalLength() [2/2]

template<typename T >

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

Finds the focal length, \(f\), in meters of an ellipse with semi-major axis, \(a\), and semi-minor axis \(b\).

\[ f=2\sqrt{a^2-b^2} \]

.

The focal length is the distance betweem the two foci.

See http://mathworld.wolfram.com/FocalParameter.html and https://en.wikipedia.org/wiki/Conic_section#Conic_parameters

Parameters

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

Returns

\( f\ (m)\) focal length of the ellipse in meters.

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.

EllipseEccentricity() for eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.

EllipseFocalLengthFromEccentricity()

template<typename T >

T EGXMath::EllipseFocalLengthFromEccentricity	(	const T	semiMajorAxisInm,
		const T	eccentricity
	)

Finds the linear eccentricity, \(f\), in meters of an ellipse with semi-major axis \(a\), and eccentricity \(e\).

\[ f=2 a e \]

.

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

Parameters

semiMajorAxisInm	\( a\ (m)\) Semi-major axis of the ellipse in meters.
eccentricity	\( e\ ()\) Eccentricity of the ellipse in meters.

Returns

\( f\ (m)\) focal length of the ellipse in meters.

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.

EllipseEccentricity() for eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.

EllipseFocalLengthFromSemiMajorAndSemiMinorAxes()

template<typename T >

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

Finds the linear eccentricity, \(f\), in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\).

\[ f=2\sqrt{a^2-b^2} \]

.

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

\( f\ (m)\) focal length of the ellipse in meters.

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.

EllipseEccentricity() for eccentricity of an ellipse.

EllipseInertia() for inertial tensor of an ellipse.