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pygeodesy
Package pygeodesy :: Module angles :: Class Ang
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Class Ang

  object --+    
           |    
named._Named --+
               |
              Ang

An accurate representation of angles, as 3-tuple (s, c, n).

This class represents an angle via its sine s, cosine c and the number of full turns n. The angle is then atan2(s, c) + n * PI2. This representation offers several advantages:

Note: n is a float, this allows it to be NAN, INF or NINF.

Instance Methods
 
__init__(self, s_ang=0, c=None, n=0, normal=True, **unit_name)
New Ang.
 
__abs__(self)
 
__add__(self, other)
 
__bool__(self)
 
__ceil__(self)
 
__cmp__(self, other)
 
__divmod__(self, other)
 
__eq__(self, other)
 
__float__(self)
 
__floor__(self)
 
__floordiv__(self, other)
 
__ge__(self, other)
 
__gt__(self, other)
 
__hash__(self)
hash(x)
 
__iadd__(self, other)
 
__ifloordiv__(self, other)
 
__imatmul__(self, other)
Not implemented.
 
__imod__(self, other)
 
__imul__(self, other)
 
__int__(self)
 
__invert__(self)
 
__ipow__(self, other, *mod)
 
__isub__(self, other)
 
__itruediv__(self, other)
 
__le__(self, other)
 
__lt__(self, other)
 
__matmul__(self, other)
Not implemented.
 
__mod__(self, other)
 
__mul__(self, other)
 
__ne__(self, other)
 
__neg__(self)
 
__pos__(self)
 
__pow__(self, other, *mod)
 
__radd__(self, other)
 
__rdivmod__(self, other)
 
__repr__(self)
Default repr(self).
 
__rfloordiv__(self, other)
 
__rmatmul__(self, other)
Not implemented.
 
__rmod__(self, other)
 
__rmul__(self, other)
 
__round__(self, *ndigits)
 
__rpow__(self, other, *mod)
 
__rsub__(self, other)
 
__rtruediv__(self, other)
 
__str__(self)
Default str(self).
 
__sub__(self, other)
 
__truediv__(self, other)
 
__trunc__(self)
 
__div__(self, other)
 
__idiv__(self, other)
 
__long__(self)
 
__nonzero__(self)
 
__rdiv__(self, other)
 
base(self, *center)
Return this Angle's base, optionally centered.
 
copy(self, **unit_name)
Return a copy of this Ang.
 
divmod(self, other)
 
flipsign(self, mul=-1, **name)
Copy this Ang with sign flipped.
 
is_integer(self, *n)
Is this Ang's degrees integer? (bool).
 
isnear0(self, eps0=staticmethod(pygeodesy.angles.Ang.EPS0))
Is this Ang near 0 within a tolerance?
 
mod(self, mul=1.0, **unit_name)
Return the reduced latitude atan(mul * tan(this)) as an Ang.
 
nearest(self, ind=0, **name)
Return the closest cardinal direction (Ang).
 
normalize(self, *n)
Re-normalize this Ang, optionally replacing turns.
 
pow(self, other, *mod)
 
reflect(self, flips=False, flipc=False, swapsc=False)
Reflect this Ang in various ways.
 
round(self, *ndigits, **name)
Return this Ang, optionally rounded to ndigits (Ang).
 
shift(self, q=0, **unit_name)
Shift this Ang by q quarter turns (scalar).
 
signOf(self, *n)
Determine this Ang's sign, optionally replacing the turns.
 
toDegrees(self, *n)
Return this Ang as Degrees, optionally replacing the turns.
 
toLambertian(self, **name)
Return this Ang as Lambertian.
 
toRadians(self, *n)
Return this Ang as Radians, optionally replacing the turns.
 
toRepr(self, *n, **prec_fmt)
Return this Ang as "<name>(<value>)" with/out turns (str).
 
toStr(self, *n, **prec_fmt)
Return this Ang as "<value>" with/out turns (str).
 
toTuple(self, **prec_fmt_sep)
Return string "(s, c, n)" or tuple ('s', 'c', 'n') if sep is None.
 
toUnit(self, *n)
Return this Ang as self.units, optionally replacing the turns.

Inherited from named._Named: __format__, attrs, classof, dup, methodname, rename, renamed, toStr2

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

Static Methods
 
cardinal(q=0, **unit_name)
A cardinal direction.
 
EPS0(**unit_name)
Get a tiny Ang.
 
fromDegrees(deg, **unit_name)
Get an Ang from degrees.
 
fromLambertian(psi, **unit_name)
Get an Ang from lamberterian radians.
 
fromRadians(rad, **unit_name)
Get an Ang from radians.
 
fromScalar(ang, **unit_name)
Get an Ang from Degrees, Radians or another Ang.
 
N(**unit_name)
Get North Ang.
 
NAN(**unit_name)
Get an invalid Ang.
Properties
  c
Get the cosine of this Angle (float).
  degrees
Get this Ang in degrees.
  degrees0
Get this Ang in degrees ignoring the turns.
  lambertian
Get this Ang's Lambertian, asinh(tan(radians)).
  n
Return the number of turns (float) or 0.0.
  n0
Return the number of turns, treating -180 as 180 - 1 turn (float).
  ncardinal
Get the nearest cardinal direction (float_int).
  quadrant
Class property with a .name attribute.
  radians
Get this Ang in radians.
  radians0
Get this Ang in radians ignoring the turns.
  s
Get the sine of this Ang (float).
  sc2
Get the 2-tuple (s, c).
  scn3
Get the 3-tuple (s, c, n).
  scnu4
Get the 4-tuple (s, c, n, unit).
  t
Get the tangent of this Ang (float).
  unit
Class property with a .name attribute.

Inherited from named._Named: classname, classnaming, iteration, name, named, named2, named3, named4, sizeof, typename

Inherited from object: __class__

Method Details

__init__ (self, s_ang=0, c=None, n=0, normal=True, **unit_name)
(Constructor)

 

New Ang.

Arguments:
  • s_ang - A previous Ang, Degrees, Radians if c is None, otherwise the sine component (float).
  • c - The cosine component (float) iff not None.
  • n - The number of PI2 turns (float).
  • normal - If True, s and c are normalized, i.e. on the unit circle (boo).
  • unit_name - Type unit=Radians or Degrees of scalar scalar values (Degrees or Radians).
Overrides: object.__init__
Notes:
  • Either s or c can be INF or NINF, but not both.
  • By default, the point (s, c) is scaled to lie on the unit circle.

__hash__ (self)
(Hashing function)

 

hash(x)

Overrides: object.__hash__
(inherited documentation)

__imatmul__ (self, other)

 

Not implemented.

Overrides: named._Named.__imatmul__
(inherited documentation)

__matmul__ (self, other)

 

Not implemented.

Overrides: named._Named.__matmul__
(inherited documentation)

__repr__ (self)
(Representation operator)

 

Default repr(self).

Overrides: object.__repr__
(inherited documentation)

__rmatmul__ (self, other)

 

Not implemented.

Overrides: named._Named.__rmatmul__
(inherited documentation)

__str__ (self)
(Informal representation operator)

 

Default str(self).

Overrides: object.__str__
(inherited documentation)

cardinal (q=0, **unit_name)
Static Method

 

A cardinal direction.

Arguments:
  • q - The number of quarter turns (scalar).
Returns:
An Ang equivalent to q quarter turns.

Note: q is truncated to an integer and signed 0 is distinguished. Ang.NAN is returned if q is not finite.

copy (self, **unit_name)

 

Return a copy of this Ang.

Arguments:
  • deep - If True, make a deep, otherwise a shallow copy (bool).
  • name - Optional, non-empty name=NN (str).
Returns:
The copy (This class).
Overrides: named._Named.copy

EPS0 (**unit_name)
Static Method

 

Get a tiny Ang.

Note: This allows angles extremely close to the cardinal directions to be generated. The .round method will flush this angle to 0.

mod (self, mul=1.0, **unit_name)

 

Return the reduced latitude atan(mul * tan(this)) as an Ang.

Arguments:
  • mul - Factor (scalar, positive).

Note: The quadrant of the result tracks that of this Ang through multiples turns.

nearest (self, ind=0, **name)

 

Return the closest cardinal direction (Ang).

Arguments:
  • ind - An indicator, if ind=0 the closest cardinal direction, otherwise, if ind is even, the closest even (N/S) cardinal direction or if ind is odd, the closest odd (E/W) cardinal direction.

reflect (self, flips=False, flipc=False, swapsc=False)

 

Reflect this Ang in various ways.

Arguments:
  • flips - Flip the sign of s.
  • flipc - Flip the sign of c.
  • swapsc - Swap s and c.

Note: The operations are carried out in the order of the arguments.

signOf (self, *n)

 

Determine this Ang's sign, optionally replacing the turns.

Returns:
The sign (int, -1, 0 or +1).

toRepr (self, *n, **prec_fmt)

 

Return this Ang as "<name>(<value>)" with/out turns (str).

Overrides: named._Named.toRepr

toStr (self, *n, **prec_fmt)

 

Return this Ang as "<value>" with/out turns (str).

Overrides: named._Named.toStr

Property Details

c

Get the cosine of this Angle (float).

Get method:
c(self) - Get the cosine of this Angle (float).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

degrees

Get this Ang in degrees.

Get method:
degrees(self) - Get this Ang in degrees.
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

degrees0

Get this Ang in degrees ignoring the turns.

Get method:
degrees0(self) - Get this Ang in degrees ignoring the turns.
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

lambertian

Get this Ang's Lambertian, asinh(tan(radians)).

Get method:
lambertian(self) - Get this Ang's Lambertian, asinh(tan(radians)).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

n

Return the number of turns (float) or 0.0.

Get method:
n(self) - Return the number of turns (float) or 0.0.
Set method:
n(self, n)

n0

Return the number of turns, treating -180 as 180 - 1 turn (float).

Get method:
n0(self) - Return the number of turns, treating -180 as 180 - 1 turn (float).
Set method:
n0(self, n)

ncardinal

Get the nearest cardinal direction (float_int).

Get method:
ncardinal(self) - Get the nearest cardinal direction (float_int).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

Note: This is the reverse of cardinal.

quadrant

Class property with a .name attribute.

Get method:
quadrant(self)
Set method:
quadrant(self, quadrant)

radians

Get this Ang in radians.

Get method:
radians(self) - Get this Ang in radians.
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

radians0

Get this Ang in radians ignoring the turns.

Get method:
radians0(self) - Get this Ang in radians ignoring the turns.
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

s

Get the sine of this Ang (float).

Get method:
s(self) - Get the sine of this Ang (float).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

sc2

Get the 2-tuple (s, c).

Get method:
sc2(self) - Get the 2-tuple (s, c).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

scn3

Get the 3-tuple (s, c, n).

Get method:
scn3(self) - Get the 3-tuple (s, c, n).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

scnu4

Get the 4-tuple (s, c, n, unit).

Get method:
scnu4(self) - Get the 4-tuple (s, c, n, unit).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

t

Get the tangent of this Ang (float).

Get method:
t(self) - Get the tangent of this Ang (float).
Set method:
_fset_error(inst, val) - Throws an AttributeError, always.
Delete Method:
_fdel(inst) - Zap the cached/memoized property value.

unit

Class property with a .name attribute.

Get method:
unit(self)
Set method:
unit(self, unit)

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