Focal Parameter

Functions
template<typename T >
T	EGXMath::EllipseFocalParameter (const T semiMajorAxisInm, const T semiMinorAxisInm)
	Finds the focal parameter, \(p\), in meters of an ellipse with semi-major axis, \(a\), and semi-minor axis \(b\). \[ p=\frac{b^2}{\sqrt{a^2-b^2}} \] . More...
template<typename T >
T	EGXMath::EllipseFocalParameterFromSemiMajorAndSemiMinorAxes (const T semiMajorAxisInm, const T semiMinorAxisInm)
	Finds the focal parameter, \(p\), in meters of an ellipse with semi-major axis, \(a\), and semi-minor axis \(b\). \[ p=\frac{b^2}{\sqrt{a^2-b^2}} \] . More...
template<typename T >
T	EGXMath::EllipseFocalParameterFromLinearEccentricity (const T semiMajorAxisInm, const T linearEccentricityInm)
	Finds the focal parameter, \(p\), in meters of an ellipse with semi-major axis, \(a\), and linear eccentricity \(c\). \[ p=\frac{a^2-c^2}{c} \] . More...
template<typename T >
T	EGXMath::EllipseFocalParameterFromEccentricity (const T semiMajorAxisInm, const T eccentricity)
	Finds the focal parameter, \(p\), in meters of an ellipse with semi-major axis, \(a\), and eccentricity \(e\). \[ p=\frac{a(1-e^2)}{e} \] . More...
template<typename T >
T	EGXMath::EllipseFocalParameterFromSemiLatusRectum (const T semiLatusRectumInm, const T eccentricity)
	Finds the focal parameter, \(p\), in meters of an ellipse with semi-Latus rectum, \(\ell\), and eccentricity \(e\). \[ p=\frac{\ell}{e} \] . More...

Detailed Description

Function Documentation

EllipseFocalParameter()

template<typename T >

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

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

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

.

The focal parameter is the distance from the focus (or one of the two foci) to the directrix.

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

\( p\ (m)\) Focal Parameter 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.

EllipseFocalParameterFromEccentricity()

template<typename T >

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

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

\[ p=\frac{a(1-e^2)}{e} \]

.

The focal parameter is the distance from the focus (or one of the two foci) to the directrix.

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

Returns

\( p\ (m)\) Focal Parameter 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.

EllipseFocalParameterFromLinearEccentricity()

template<typename T >

T EGXMath::EllipseFocalParameterFromLinearEccentricity	(	const T	semiMajorAxisInm,
		const T	linearEccentricityInm
	)

Finds the focal parameter, \(p\), in meters of an ellipse with semi-major axis, \(a\), and linear eccentricity \(c\).

\[ p=\frac{a^2-c^2}{c} \]

.

The focal parameter is the distance from the focus (or one of the two foci) to the directrix.

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

Returns

\( p\ (m)\) Focal Parameter 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.

EllipseFocalParameterFromSemiLatusRectum()

template<typename T >

T EGXMath::EllipseFocalParameterFromSemiLatusRectum	(	const T	semiLatusRectumInm,
		const T	eccentricity
	)

Finds the focal parameter, \(p\), in meters of an ellipse with semi-Latus rectum, \(\ell\), and eccentricity \(e\).

\[ p=\frac{\ell}{e} \]

.

The focal parameter is the distance from the focus (or one of the two foci) to the directrix.

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

Parameters

semiLatusRectumInm	\( \ell\ (m)\) Semi-latus rectum of the ellipse in meters.
eccentricity	\( e\ (dimensionless)\) Eccentricity of the ellipse.

Returns

\( p\ (m)\) Focal Parameter 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.

EllipseFocalParameterFromSemiMajorAndSemiMinorAxes()

template<typename T >

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

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

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

.

The focal parameter is the distance from the focus (or one of the two foci) to the directrix.

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

\( p\ (m)\) Focal Parameter 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.