Package pygeodesy :: Module ellipses :: Class Ellipse

Class Ellipse

  object --+    
           |    
named._Named --+
               |
              Ellipse

Class to compute attributes of a 2-D ellipse, like perimeter, area and arcs.

Instance Methods

__init__(self, a, b, **name)
New Ellipse with semi-axes a and b.

arc(self, deg2, deg1=0)
Compute the length of elliptic arc (deg2 - deg1), both counter-clockwise from semi-axis a to b of the ellipse.

arc_(self, rad2, rad1=0)
Compute the length of elliptic arc (rad2 - rad1), both counter-clockwise from semi-axis a to b of the ellipse.

Roc_(self, rad_x, *y)
Compute the radius of curvature at angle rad radians or at point (x, y) on this ellipse.

sideOf(self, x, y, eps=2.220446049250313e-16)
Return a positive, negative or 0 scalar if point (x, y) is outside, inside respectively on this ellipse.

toEllipsoid(self)
Return an Ellipsoid from this ellipse's a and b semi-axes.

toTriaxial_(self, c=2.220446049250313e-16)
Return a Triaxial_ from this ellipse's a and b semi-axes with c as minor semi-axis.

Inherited from named._Named: __format__, __imatmul__, __matmul__, __repr__, __rmatmul__, __str__, attrs, classof, copy, dup, methodname, rename, renamed, toRepr, toStr, toStr2

Inherited from object: __delattr__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __setattr__, __sizeof__, __subclasshook__

Properties
	a Return semi-axis `a` of this ellipse (`meter`, conventionally).
	area Return the area of this ellipse (`meter**2`, conventionally).
	b Return semi-axis `b` of this ellipse (`meter`, conventionally).
	foci Get the foci lengths (`meter`, conventionally), `positive` if the ellipse is oblate with foci on semi-axis `a`, `negative` if prolate with foci on semi-axis `b` or `0` if circular with coincident foci in the ellipse' center.
	isCircular Is this ellipse circular? (`bool`)
	isFlat Is this ellipse "flat", too pro-/oblate? (`bool`)
	isOblate Is this ellipse oblate? (`bool`)
	isProlate Is this ellipse prolate? (`bool`)
	perimeterAGM Compute the perimeter of this ellipse using the Arithmetic-Geometric Mean formula (`meter`, same units as semi-axes `a` and `b`).
	perimeter4Arc3 Compute the perimeter (and arcs) of this ellipse using the 4-Arc approximation as a 3-Tuple `(P, Ra, Rb)` with perimeter `P`, arc radii `Ra` and `Rb` at the respective semi-axes (all in `meter`, same units as semi-axes `a` and `b`).
	perimeterGK Compute the perimeter of this ellipse using the Gauss-Kummer series, `b / a > 0.75` (`meter`, same units as semi-axes `a` and `b`).
	perimeter2k Compute the perimeter of this ellipse using the complete integral of the 2nd kind, `Elliptic.cE` (`meter`, same units as semi-axes `a` and `b`).
	perimeter2k_ Compute the perimeter of this ellipse using SciPy's ellipe function if available, otherwise use property `perimeter2k` (`meter`, same units as semi-axes `a` and `b`).
	perimeterHGK Compute the perimeter of this ellipse using the Hypergeometric Gauss-Kummer series (`meter`, same units as semi-axes `a` and `b`).
	perimeter2R Compute the perimeter of this ellipse using Ramanujan's 2nd approximation, `b / a > 0.9` (`meter`, same units as semi-axes `a` and `b`).
	R2 Compute the authalic radius of this ellipse, `sqrt(a * b)` (`meter`, same units as semi-axes `a` and `b`).
Inherited from `named._Named`: `classname`, `classnaming`, `iteration`, `name`, `named`, `named2`, `named3`, `named4`, `sizeof`, `typename` Inherited from `object`: `__class__`

Method Details

init (self, a, b, **name)
(Constructor)

New Ellipse with semi-axes a and b.

The ellipse is oblate if a > b, prolate if a < b circular if a == b and "flat" if min(a, b) near 0.

Arguments:

a - X semi-axis length (meter, conventionally).
b - Y semi-axis length (meter, conventionally).

Raises:

ValueError - Invalid a or b.

Overrides: object.__init__

arc (self, deg2, deg1=0)

Compute the length of elliptic arc (deg2 - deg1), both counter-clockwise from semi-axis a to b of the ellipse.

Arguments:

deg2 - End angle of the elliptic arc (degrees).
deg1 - Start angle of the elliptic arc (degrees).

Returns:

Arc length, signed (meter, same units as semi-axes a and b).

arc_ (self, rad2, rad1=0)

Compute the length of elliptic arc (rad2 - rad1), both counter-clockwise from semi-axis a to b of the ellipse.

Arguments:

rad2 - End angle of the elliptic arc (radians).
rad1 - Start angle of the elliptic arc (radians).

Returns:

Arc length, signed (meter, same units as semi-axes a and b).

Roc_ (self, rad_x, *y)

Compute the radius of curvature at angle rad radians or at point (x, y) on this ellipse.

Returns:

Curvature (meter, same units as semi-axes a and b).

Raises:

ValueError - (x, y) not located on the ellipse.

Property Details

a

Return semi-axis a of this ellipse (meter, conventionally).

Get method:: a(self) - Return semi-axis a of this ellipse (meter, conventionally).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

area

Return the area of this ellipse (meter**2, conventionally).

Get method:: area(self) - Return the area of this ellipse (meter**2, conventionally).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

b

Return semi-axis b of this ellipse (meter, conventionally).

Get method:: b(self) - Return semi-axis b of this ellipse (meter, conventionally).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

foci

Get the foci lengths (meter, conventionally), positive if the ellipse is oblate with foci on semi-axis a, negative if prolate with foci on semi-axis b or 0 if circular with coincident foci in the ellipse' center.

Get method:: foci(self) - Get the foci lengths (meter, conventionally), positive if the ellipse is oblate with foci on semi-axis a, negative if prolate with foci on semi-axis b or 0 if circular with coincident foci in the ellipse' center.
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isCircular

Is this ellipse circular? (bool)

Get method:: isCircular(self) - Is this ellipse circular? (bool)
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isFlat

Is this ellipse "flat", too pro-/oblate? (bool)

Get method:: isFlat(self) - Is this ellipse "flat", too pro-/oblate? (bool)
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isOblate

Is this ellipse oblate? (bool)

Get method:: isOblate(self) - Is this ellipse oblate? (bool)
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

isProlate

Is this ellipse prolate? (bool)

Get method:: isProlate(self) - Is this ellipse prolate? (bool)
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

perimeterAGM

Compute the perimeter of this ellipse using the Arithmetic-Geometric Mean formula (meter, same units as semi-axes a and b).

Get method:: perimeterAGM(self) - Compute the perimeter of this ellipse using the Arithmetic-Geometric Mean formula (meter, same units as semi-axes a and b).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

perimeter4Arc3

Compute the perimeter (and arcs) of this ellipse using the 4-Arc approximation as a 3-Tuple (P, Ra, Rb) with perimeter P, arc radii Ra and Rb at the respective semi-axes (all in meter, same units as semi-axes a and b).

Get method:: perimeter4Arc3(self) - Compute the perimeter (and arcs) of this ellipse using the 4-Arc approximation as a 3-Tuple (P, Ra, Rb) with perimeter P, arc radii Ra and Rb at the respective semi-axes (all in meter, same units as semi-axes a and b).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

perimeterGK

Compute the perimeter of this ellipse using the Gauss-Kummer series, b / a > 0.75 (meter, same units as semi-axes a and b).

Get method:: perimeterGK(self) - Compute the perimeter of this ellipse using the Gauss-Kummer series, b / a > 0.75 (meter, same units as semi-axes a and b).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

perimeter2k

Compute the perimeter of this ellipse using the complete integral of the 2nd kind, Elliptic.cE (meter, same units as semi-axes a and b).

Get method:: perimeter2k(self) - Compute the perimeter of this ellipse using the complete integral of the 2nd kind, Elliptic.cE (meter, same units as semi-axes a and b).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

perimeter2k_

Compute the perimeter of this ellipse using SciPy's ellipe function if available, otherwise use property perimeter2k (meter, same units as semi-axes a and b).

Get method:: perimeter2k_(self) - Compute the perimeter of this ellipse using SciPy's ellipe function if available, otherwise use property perimeter2k (meter, same units as semi-axes a and b).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

perimeterHGK

Compute the perimeter of this ellipse using the Hypergeometric Gauss-Kummer series (meter, same units as semi-axes a and b).

Get method:: perimeterHGK(self) - Compute the perimeter of this ellipse using the Hypergeometric Gauss-Kummer series (meter, same units as semi-axes a and b).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

perimeter2R

Compute the perimeter of this ellipse using Ramanujan's 2nd approximation, b / a > 0.9 (meter, same units as semi-axes a and b).

Get method:: perimeter2R(self) - Compute the perimeter of this ellipse using Ramanujan's 2nd approximation, b / a > 0.9 (meter, same units as semi-axes a and b).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

R2

Compute the authalic radius of this ellipse, sqrt(a * b) (meter, same units as semi-axes a and b).

Get method:: R2(self) - Compute the authalic radius of this ellipse, sqrt(a * b) (meter, same units as semi-axes a and b).
Set method:: _fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:: _fdel(inst) - Zap the cached/memoized property value.

Class Ellipse

__init__ (self, a, b, **name) (Constructor)

arc (self, deg2, deg1=0)

arc_ (self, rad2, rad1=0)

Roc_ (self, rad_x, *y)

a

area

b

foci

isCircular

isFlat

isOblate

isProlate

perimeterAGM

perimeter4Arc3

perimeterGK

perimeter2k

perimeter2k_

perimeterHGK

perimeter2R

R2

init (self, a, b, **name)
(Constructor)