EGXPhys
Functions
Circumference
EGXMath Library » Geometry » 2D Objects » Ellipse

Functions

template<typename T >
T EGXMath::EllipseCircumference (const T semiMajorAxisInm, const T semiMinorAxisInm)
 Approximates the circumference (perimeter), \(C_{ellipse}\) in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). This approximation is done using the Pade 3/3 approximation.

\[ h=\left( \frac{a-b}{a+b} \right)^2 \]

\[ C_{ellipse}=\pi (a + b) \left( \frac{135168-85760 h-5568 h^2+ 3867 h^3}{135168-119552 h+ 22208 h^2 - 345h^3} \right) \]

. More...

 
template<typename T >
T EGXMath::EllipsePerimeter (const T semiMajorAxisInm, const T semiMinorAxisInm)
 Approximates the perimeter (circumference), \(C_{ellipse}\) in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). This approximation is done using the Pade 3/3 approximation.

\[ h=\left( \frac{a-b}{a+b} \right)^2 \]

\[ C_{ellipse}=\pi (a + b) \left( \frac{135168-85760 h-5568 h^2+ 3867 h^3}{135168-119552 h+ 22208 h^2 - 345h^3} \right) \]

. More...

 
template<typename T >
T EGXMath::EllipseCircumferencePade33approximation (const T semiMajorAxisInm, const T semiMinorAxisInm)
 Approximates the circumference, \(C_{ellipse}\) in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). This approximation is done using the Ramanujan II approximation.

\[ h=\left( \frac{a-b}{a+b} \right)^2 \]

\[ C_{ellipse}=\pi (a + b) \left( \frac{135168-85760 h-5568 h^2+ 3867 h^3}{135168-119552 h+ 22208 h^2 - 345h^3} \right) \]

. More...

 
template<typename T >
T EGXMath::EllipseCircumferenceRamanujanIIapproximation (const T semiMajorAxisInm, const T semiMinorAxisInm)
 Approximates the circumference, \(C_{ellipse}\) in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). This approximation is done using the Ramanujan II approximation.

\[ h=\left( \frac{a-b}{a+b} \right)^2 \]

\[ C_{ellipse}=\pi (a + b) \left( 1+\frac{3h}{10+\sqrt{4-3h}} \right) \]

. More...

 

Detailed Description

Function Documentation

◆ EllipseCircumference()

template<typename T >
T EGXMath::EllipseCircumference ( const T  semiMajorAxisInm,
const T  semiMinorAxisInm 
)

Approximates the circumference (perimeter), \(C_{ellipse}\) in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). This approximation is done using the Pade 3/3 approximation.

\[ h=\left( \frac{a-b}{a+b} \right)^2 \]

\[ C_{ellipse}=\pi (a + b) \left( \frac{135168-85760 h-5568 h^2+ 3867 h^3}{135168-119552 h+ 22208 h^2 - 345h^3} \right) \]

.

See http://dx.doi.org/10.3247/SL1Math05.004 , http://mathworld.wolfram.com/Ellipse.html http://www.chrisrackauckas.com/assets/Papers/ChrisRackauckas-The_Circumference_of_an_Ellipse.pdf and https://www.mathsisfun.com/geometry/ellipse-perimeter.html

Equations taken from http://dx.doi.org/10.3247/SL1Math05.004

Parameters
semiMajorAxisInm\( a\ (m)\) Semi-major axis of the ellipse in meters.
semiMinorAxisInm\( b\ (m)\) Semi-minor axis of the ellipse in meters.
Returns
\( C_{ellipse}\ (m)\) Circumference of the ellipse in meters.
See also
EllipsePerimeter() for alias.
EllipseCircumferencePade33approximation() for Pade 3/3 approximation of circumference.
EllipseCircumferenceRamanujanIIapproximation() for Ramanujan II of circumference.
EllipseSurfaceArea() for area 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.

◆ EllipseCircumferencePade33approximation()

template<typename T >
T EGXMath::EllipseCircumferencePade33approximation ( const T  semiMajorAxisInm,
const T  semiMinorAxisInm 
)

Approximates the circumference, \(C_{ellipse}\) in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). This approximation is done using the Ramanujan II approximation.

\[ h=\left( \frac{a-b}{a+b} \right)^2 \]

\[ C_{ellipse}=\pi (a + b) \left( \frac{135168-85760 h-5568 h^2+ 3867 h^3}{135168-119552 h+ 22208 h^2 - 345h^3} \right) \]

.

See http://dx.doi.org/10.3247/SL1Math05.004 , http://mathworld.wolfram.com/Ellipse.html http://www.chrisrackauckas.com/assets/Papers/ChrisRackauckas-The_Circumference_of_an_Ellipse.pdf and https://www.mathsisfun.com/geometry/ellipse-perimeter.html

Equations taken from http://dx.doi.org/10.3247/SL1Math05.004

Parameters
semiMajorAxisInm\( a\ (m)\) Semi-major axis of the ellipse in meters.
semiMinorAxisInm\( b\ (m)\) Semi-minor axis of the ellipse in meters.
Returns
\( C_{ellipse}\ (m)\) Circumference of the ellipse in meters.
See also
EllipseCircumferenceRamanujanIIapproximation() for Ramanujan II of circumference.
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.

◆ EllipseCircumferenceRamanujanIIapproximation()

template<typename T >
T EGXMath::EllipseCircumferenceRamanujanIIapproximation ( const T  semiMajorAxisInm,
const T  semiMinorAxisInm 
)

Approximates the circumference, \(C_{ellipse}\) in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). This approximation is done using the Ramanujan II approximation.

\[ h=\left( \frac{a-b}{a+b} \right)^2 \]

\[ C_{ellipse}=\pi (a + b) \left( 1+\frac{3h}{10+\sqrt{4-3h}} \right) \]

.

See http://dx.doi.org/10.3247/SL1Math05.004 , http://mathworld.wolfram.com/Ellipse.html http://www.chrisrackauckas.com/assets/Papers/ChrisRackauckas-The_Circumference_of_an_Ellipse.pdf and https://www.mathsisfun.com/geometry/ellipse-perimeter.html

Equations taken from http://dx.doi.org/10.3247/SL1Math05.004

Parameters
semiMajorAxisInm\( a\ (m)\) Semi-major axis of the ellipse in meters.
semiMinorAxisInm\( b\ (m)\) Semi-minor axis of the ellipse in meters.
Returns
\( C_{ellipse}\ (m)\) Circumference of the ellipse in meters.
See also
EllipseCircumferencePade33approximation() for Pade 3/3 approximation of circumference.
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.

◆ EllipsePerimeter()

template<typename T >
T EGXMath::EllipsePerimeter ( const T  semiMajorAxisInm,
const T  semiMinorAxisInm 
)

Approximates the perimeter (circumference), \(C_{ellipse}\) in meters of an ellipse with semi-major axis \(a\), and semi-minor axis \(b\). This approximation is done using the Pade 3/3 approximation.

\[ h=\left( \frac{a-b}{a+b} \right)^2 \]

\[ C_{ellipse}=\pi (a + b) \left( \frac{135168-85760 h-5568 h^2+ 3867 h^3}{135168-119552 h+ 22208 h^2 - 345h^3} \right) \]

.

See http://dx.doi.org/10.3247/SL1Math05.004 , http://mathworld.wolfram.com/Ellipse.html http://www.chrisrackauckas.com/assets/Papers/ChrisRackauckas-The_Circumference_of_an_Ellipse.pdf and https://www.mathsisfun.com/geometry/ellipse-perimeter.html

Equations taken from http://dx.doi.org/10.3247/SL1Math05.004

Parameters
semiMajorAxisInm\( a\ (m)\) Semi-major axis of the ellipse in meters.
semiMinorAxisInm\( b\ (m)\) Semi-minor axis of the ellipse in meters.
Returns
\( C_{ellipse}\ (m)\) Circumference of the ellipse in meters.
See also
EllipseCircumference() for alias.
EllipseCircumferencePade33approximation() for Pade 3/3 approximation of circumference.
EllipseCircumferenceRamanujanIIapproximation() for Ramanujan II of circumference.
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.