Package pygeodesy :: Module formy :: Class Elliperim

Class Elliperim

object --+
         |
        Elliperim

Singleton with various methods to compute the perimeter of an ellipse.

Instance Methods

AGM(self, a, b, maxit=53)
Return the perimeter of an ellipse with semi-axes a and b using the AGM (Arithmetic-Geometric Mean) method.

Arc43(self, a, b)
Return the perimeter (and arcs) of an ellipse with semi-axes a and b with the 4-Arc approximation.

E2k(self, a, b)
Return the perimeter of an ellipse with semi-axes a and b from the complete elliptic integral of the 2nd kind E(k).

GK(self, a, b)
Return the perimeter of an ellipse with semi-axes a and b using the Gauss-Kummer series, and here, b / a > 0.75.

HG(self, a, b, maxit=53)
Return the perimeter of an ellipse with semi-axes a and b using the HG (HyperGeometric Gauss-Kummer) series.

R2(self, a, b)
Return the perimeter of an ellipse with semi-axes a and b using Ramanujan's 2nd approximation, b / a > 0.9.

e2k(self, a, b, E_alt=None)
Return the perimeter of an ellipse with semi-axes a and b using SciPy's ellipe function or method E_alt, otherwise None.

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __init__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Properties
Inherited from `object`: `__class__`

Method Details

AGM (self, a, b, maxit=53)

Return the perimeter of an ellipse with semi-axes a and b using the AGM (Arithmetic-Geometric Mean) method.

Arguments:

maxit - Number of iterations (int).

Raises:

ValueError - No convergence for maxit iterations.

Arc43 (self, a, b)

Return the perimeter (and arcs) of an ellipse with semi-axes a and b with the 4-Arc approximation.

Returns:: 3-Tuple (p, Ra, Rb) with perimeter p, arc radius Ra at the major and arc radius Rb at the minor semi-axis.

HG (self, a, b, maxit=53)

Return the perimeter of an ellipse with semi-axes a and b using the HG (HyperGeometric Gauss-Kummer) series.

Arguments:

maxit - Number of iterations (int), sufficient for b / a > 0.125.

Raises:

ValueError - No convergence for maxit iterations.

e2k (self, a, b, E_alt=None)

Return the perimeter of an ellipse with semi-axes a and b using SciPy's ellipe function or method E_alt, otherwise None.

Arguments:

E_alt - An other Elliperim(a, b) method to use in case SciPy's ellipe is not available.