def _streprs(prec, objs, fmt, ints, force, strepr):
'''(INTERNAL) Helper for C{fstr}, C{pairs}, C{reprs} and C{strs}
'''
# <https://docs.Python.org/3/library/stdtypes.html#printf-style-string-formatting>
if fmt in _FfEeGg:
fGg = fmt in _Gg
fmt = NN(_PERCENT_, _DOT_, abs(prec), fmt)
elif fmt.startswith(_PERCENT_):
fGg = False
try: # to make sure fmt is valid
f = fmt.replace(_DOTSTAR_, Fmt.DOT(abs(prec)))
_ = f % (0.0, )
except (TypeError, ValueError):
raise _ValueError(fmt=fmt, txt=_not_(repr(_DOTSTAR_)))
fmt = f
else:
raise _ValueError(fmt=fmt, txt=_not_(repr(_Fspec_)))
for o in objs:
if force or isinstance(o, float):
t = fmt % (float(o), )
if ints and (isint(o, both=True) or # for ...
# corner case testLcc lon0=-96.0
t.rstrip(_0_).endswith(_DOT_)):
t = t.split(_DOT_)[0]
elif prec > 1:
t = fstrzs(t, ap1z=fGg)
elif strepr:
t = strepr(o)
else:
raise _IsnotError(_scalar_, floats=o)
yield t
def _xtend(self, xTuple, *items):
'''(INTERNAL) Extend this C{Named-Tuple} with C{items} to an other B{C{xTuple}}.
'''
if not (issubclassof(xTuple, _NamedTuple) and
(len(self._Names_) + len(items)) == len(xTuple._Names_)
and self._Names_ == xTuple._Names_[:len(self)]):
c = NN(self.classname, repr(self._Names_))
x = NN(xTuple.__name__, repr(xTuple._Names_))
raise TypeError(_SPACE_(c, _vs_, x))
return self._xnamed(xTuple(*(self + items)))
def clips(bstr, limit=50, white=NN):
'''Clip a string to the given length limit.
@arg bstr: String (C{bytes} or C{str}).
@kwarg limit: Length limit (C{int}).
@kwarg white: Optionally, replace all whitespace (C{str}).
@return: The clipped or unclipped B{C{bstr}}.
'''
if len(bstr) > limit > 8:
h = limit // 2
bstr = NN(bstr[:h], type(bstr)('....'), bstr[-h:])
if white: # replace whitespace
bstr = type(bstr)(white).join(bstr.split())
return bstr
def callername(up=1, dflt=NN, source=False):
'''Get the name of the calling callable.
@kwarg up: Number of call stack frames up (C{int}).
@kwarg dflt: Default return value (C{any}).
@kwarg source: Include source file name and line
number (C{bool}).
@return: Name of the non-internal callable (C{str})
or B{C{dflt}} if none found.
'''
try:
from sys import _getframe
for u in range(up, up + 32):
f = _getframe(u)
n = f.f_code.co_name
if n and (n.startswith(_DUNDER_)
or not n.startswith(_UNDERSCORE_)):
if source:
from os.path import basename
n = NN.join(
(n, _AT_, basename(f.f_code.co_filename), _COLON_,
str(f.f_lineno)))
return n
except (AttributeError, ImportError):
pass
return dflt
def utmupsStr(self, B=False):
'''Get the UTM/UPS zone, band and hemisphere/-pole (C{str}).
'''
b = self.band if B else NN
h = s = self.hemisphere
if h:
s = _SPACE_
return NN(Fmt.zone(self.zone), b, s, h)
def fstrzs(efstr, ap1z=False):
'''Strip trailing zero decimals from a C{float} string.
@arg efstr: Float with or without exponent (C{str}).
@kwarg ap1z: Append the decimal point and one zero decimal
if the B{C{efstr}} is all digits (C{bool}).
@return: Float (C{str}).
'''
s = efstr.find(_DOT_)
if s >= 0:
e = efstr.rfind(Fmt.e)
if e < 0:
e = efstr.rfind(Fmt.E)
if e < 0:
e = len(efstr)
s += 2 # keep 1st _DOT_ + _0_
if s < e and efstr[e - 1] == _0_:
efstr = NN(efstr[:s], efstr[s:e].rstrip(_0_), efstr[e:])
elif ap1z:
# %.G and %.g formats may drop the decimal
# point and all trailing zeros, ...
if efstr.isdigit():
efstr += _DOT_ + _0_ # ... append or ...
else: # ... insert one dot and zero
e = efstr.rfind(Fmt.e)
if e < 0:
e = efstr.rfind(Fmt.E)
if e > 0:
efstr = NN(efstr[:e], _DOT_, _0_, efstr[e:])
return efstr
def hStr(self, prec=-2, m=NN):
'''Return a string for the height B{C{h}}.
@kwarg prec: Optional number of decimals, unstripped (C{int}).
@kwarg m: Optional unit of the height (C{str}).
@see: Function L{hstr}.
'''
return NN(self.H, hstr(self.h, prec=prec, m=m))
def _clipped_(angle, limit, units):
'''(INTERNAL) Helper for C{clipDegrees} and C{clipRadians}.
'''
c = min(limit, max(-limit, angle))
if c != angle and _rangerrors:
t = NN(fstr(angle, prec=6, ints=True), 'beyond',
copysign(limit, angle), units)
raise RangeError(t, txt=None)
return c
def encode(lat, lon, precision=3, height=None, radius=None): # MCCABE 14
'''Encode a lat-/longitude as a C{georef} of the given precision.
@arg lat: Latitude (C{degrees}).
@arg lon: Longitude (C{degrees}).
@kwarg precision: Optional, the desired C{georef} resolution and length
(C{int} 0..11).
@kwarg height: Optional, height in C{meter}, see U{Designation of area
<https://WikiPedia.org/wiki/World_Geographic_Reference_System>}.
@kwarg radius: Optional, radius in C{meter}, see U{Designation of area
<https://WikiPedia.org/wiki/World_Geographic_Reference_System>}.
@return: The C{georef} (C{str}).
@raise RangeError: Invalid B{C{lat}} or B{C{lon}}.
@raise WGRSError: Invalid B{C{precision}}, B{C{height}} or B{C{radius}}.
@note: The B{C{precision}} value differs from U{Georef<https://
GeographicLib.SourceForge.io/html/classGeographicLib_1_1Georef.html>}.
The C{georef} length is M{2 * (precision + 1)} and the
C{georef} resolution is I{15°} for B{C{precision}} 0, I{1°}
for 1, I{1′} for 2, I{0.1′} for 3, I{0.01′} for 4, ...
M{10**(2 - precision)}.
'''
def _option(name, m, m2_, K):
f = Scalar_(m, name=name, Error=WGRSError)
return '%s%d' % (name[0].upper(), int(m2_(f * K) + 0.5))
def _pstr(p, x):
return '%0*d' % (p, x)
p = _2Precision(precision)
lat, lon, _ = _2fllh(lat, lon)
if lat == 90:
lat *= EPS1_2
xt, xd, x = _2divmod3(lon, _LonOrig_M_)
yt, yd, y = _2divmod3(lat, _LatOrig_M_)
g = _LonTile[xt], _LatTile[yt]
if p > 0:
g += _DegChar[xd], _DegChar[yd]
p -= 1
if p > 0:
d = pow(_Base, _MaxPrec - p)
x = _pstr(p, x // d)
y = _pstr(p, y // d)
g += x, y
if radius is not None: # R before H
g += _option(_radius_, radius, m2NM, 1.0),
if height is not None: # H is last
g += _option(_height_, height, m2ft, 1e-3),
return NN.join(g) # XXX Georef(''.join(g))
def _DDDMMSS_(strDDDMMSS, suffix, sep, clip):
S = suffix.upper()
if isstr(strDDDMMSS):
t = strDDDMMSS.strip()
if sep:
t = t.replace(sep, NN).strip()
s = t[:1] # sign or digit
P = t[-1:] # compass point, digit or dot
t = t.lstrip(_PLUSMINUS_).rstrip(S).strip()
f = t.split(_DOT_)
d = len(f[0])
f = NN.join(f)
if 1 < d < 8 and f.isdigit() and (
(P in S and s.isdigit()) or
(P.isdigit() and s in '-0123456789+' # PYCHOK indent
and S in ((_NS_, _EW_) + _WINDS))):
# check [D]DDMMSS form and compass point
X = _EW_ if (d & 1) else _NS_
if not (P in X or (S in X and (P.isdigit() or P == _DOT_))):
t = 'DDDMMSS'[d & 1 ^ 1:d | 1], X[:1], X[1:]
raise ParseError('form %s applies %s-%s' % t)
f = 0 # fraction
else: # try other forms
return _DMS2deg(strDDDMMSS, S, sep, clip)
else: # float or int to [D]DDMMSS[.fff]
f = float(strDDDMMSS)
s = _MINUS_ if f < 0 else NN
P = _0_ # anything except _SW_
f, i = modf(abs(f))
t = Fmt.f(i, prec=0) # str(i) == 'i.0'
d = len(t)
# bump number of digits to match
# the given, valid compass point
if S in (_NS_ if (d & 1) else _EW_):
t = _0_ + t
d += 1
# P = S
# elif d > 1:
# P = (_EW_ if (d & 1) else _NS_)[0]
if d < 4: # [D]DD[.ddd]
if f:
t = float(t) + f
t = t, 0, 0
else:
f += float(t[d - 2:])
if d < 6: # [D]DDMM[.mmm]
t = t[:d - 2], f, 0
else: # [D]DDMMSS[.sss]
t = t[:d - 4], t[d - 4:d - 2], f
d = _dms2deg(s, P, *map2(float, t))
return clipDegrees(d, float(clip)) if clip else d
def _update(self, updated, *attrs):
'''(INTERNAL) Zap cached instance attributes.
'''
if updated and attrs:
for a in attrs: # zap attrs to None
if getattr(self, a, None) is not None:
setattr(self, a, None)
elif not hasattr(self, a):
a = NN(_DOT_, a, _SPACE_, _invalid_)
raise _AssertionError(a, txt=repr(self))
def __init__(self, Class, *Classes, **name):
'''New C{_NamedEnum}.
@arg Class: Initial class or type acceptable as enum
values (C{str}).
@arg Classes: Additional, acceptable classes or types.
'''
self._item_Classes = (Class, ) + Classes
n = name.get(_name_, NN) or NN(Class.__name__, _s_)
if n and _xvalid(n, _OK=True):
_Named.name.fset(self, n) # see _Named.name
def _toStr(self, hemipole, B, cs, prec, sep):
'''(INTERNAL) Return a string for this ETM/UTM/UPS coordinate.
'''
z = NN(Fmt.zone(self.zone), (self.band if B else NN)) # PYCHOK band
t = (z, hemipole) + _fstrENH2(self, prec, None)[0]
if cs:
prec = cs if isint(cs) else 8 # for backward compatibility
t += (_n_a_ if self.convergence is None else degDMS(
self.convergence, prec=prec, pos=_PLUS_),
_n_a_ if self.scale is None else fstr(self.scale, prec=prec))
return t if sep is None else sep.join(t)
def _boolkwds(inst, **name_value_pairs): # in .frechet, .hausdorff, .heights
'''(INTERNAL) Set applicable C{bool} properties/attributes.
'''
for n, v in name_value_pairs.items():
b = getattr(inst, n, None)
if b is None: # invalid bool attr
t = _SPACE_(_EQUAL_(n, repr(v)), 'for',
inst.__class__.__name__) # XXX .classname
raise _AttributeError(t, txt=_not_('applicable'))
if v in (False, True) and v != b:
setattr(inst, NN(_UNDER_, n), v)
def degDMS(deg, prec=6, s_D=S_DEG, s_M=S_MIN, s_S=S_SEC, neg=_MINUS_, pos=NN):
'''Convert degrees to a string in degrees, minutes B{I{or}} seconds.
@arg deg: Value in degrees (C{scalar}).
@kwarg prec: Optional number of decimal digits (0..9 or
C{None} for default). Trailing zero decimals
are stripped for B{C{prec}} values of 1 and
above, but kept for negative B{C{prec}}.
@kwarg s_D: Symbol for degrees (C{str}).
@kwarg s_M: Symbol for minutes (C{str}) or C{""}.
@kwarg s_S: Symbol for seconds (C{str}) or C{""}.
@kwarg neg: Optional sign for negative (C{'-'}).
@kwarg pos: Optional sign for positive (C{''}).
@return: I{Either} degrees, minutes B{I{or}} seconds (C{str}).
'''
try:
deg = float(deg)
except (TypeError, ValueError) as x:
raise _ValueError(deg=deg, txt=str(x))
d, s = abs(deg), s_D
if d < 1:
if s_M:
d *= _60_0
if d < 1 and s_S:
d *= _60_0
s = s_S
else:
s = s_M
elif s_S:
d *= 3600
s = s_S
n = neg if deg < 0 else pos
z = int(prec)
t = NN(n, Fmt.F(d, prec=abs(z)))
if z > 1:
t = fstrzs(t)
return NN(t, s)
def hstr(height, prec=2, fmt=Fmt.h, ints=False, m=NN):
'''Return a string for the height value.
@arg height: Height value (C{float}).
@kwarg prec: The C{float} precision, number of decimal digits (0..9).
Trailing zero decimals are stripped if B{C{prec}} is
positive, but kept for negative B{C{prec}} values.
@kwarg fmt: Optional, C{float} format (C{str}).
@kwarg ints: Optionally, remove the decimal dot for C{int} values (C{bool}).
@kwarg m: Optional unit of the height (C{str}).
'''
h = next(_streprs(prec, (height, ), fmt, ints, True, None))
return NN(h, str(m)) if m else h
def __call__(self, *name_value_, **name_value):
'''Format a C{name=value} pair or C{name, value} pair
or just a single C{value}.
'''
for n, v in name_value.items():
break
else:
if len(name_value_) > 1:
n, v = name_value_[:2]
elif name_value_:
n, v = NN, name_value_[0]
else:
n, v = NN, MISSING
t = str.__mod__(self, v)
return NN(n, t) if n else t
def encode(lat, lon, precision=1): # MCCABE 14
'''Encode a lat-/longitude as a C{garef} of the given precision.
@arg lat: Latitude (C{degrees}).
@arg lon: Longitude (C{degrees}).
@kwarg precision: Optional, the desired C{garef} resolution
and length (C{int} 0..2).
@return: The C{garef} (C{str}).
@raise RangeError: Invalid B{C{lat}} or B{C{lon}}.
@raise GARSError: Invalid B{C{precision}}.
@note: The C{garef} length is M{precision + 5} and the C{garef}
resolution is B{30′} for B{C{precision}} 0, B{15′} for 1
and B{5′} for 2, respectively.
'''
def _digit(x, y, m):
return _Digits[m * (m - y - 1) + x + 1],
def _str(chars, x, n):
s, b = [], len(chars)
for i in range(n):
x, i = divmod(x, b)
s.append(chars[i])
return tuple(reversed(s))
p = _2Precision(precision)
lat, lon = _2fll(lat, lon)
if lat == 90:
lat *= EPS1_2
ix, x = _2divmod2(lon, _LonOrig_M_)
iy, y = _2divmod2(lat, _LatOrig_M_)
g = _str(_Digits, ix + 1, _LonLen) + _str(_Letters, iy, _LatLen)
if p > 0:
ix, x = divmod(x, _M3)
iy, y = divmod(y, _M3)
g += _digit(ix, iy, _M2)
if p > 1:
g += _digit(x, y, _M3)
return NN.join(g)
def _qURL(url, timeout=2, **params):
'''(INTERNAL) Build B{C{url}} query, get and verify response.
'''
if params: # build url query, don't map(quote, params)!
p = '&'.join(Fmt.EQUAL(p, v) for p, v in params.items() if v)
if p:
url = NN(url, '?', p)
u = urlopen(url, timeout=timeout) # secs
s = u.getcode()
if s != 200: # http.HTTPStatus.OK or http.client.OK
raise IOError('code %d: %s' % (s, u.geturl()))
r = u.read()
u.close()
# urlcleanup()
return ub2str(r).strip()
def _error_init(Error,
inst,
name_value,
fmt_name_value='%s (%r)',
txt=_invalid_,
**name_values): # by .lazily
'''(INTERNAL) Format an error text and initialize an C{Error} instance.
@arg Error: The error super-class (C{Exception}).
@arg inst: Sub-class instance to be initialized (C{_Exception}).
@arg name_value: Either just a value or several name, value, ...
positional arguments (C{str}, any C{type}), in
particular for name conflicts with keyword
arguments of C{error_init} or which can't be
used as C{name=value} keyword arguments.
@kwarg name_value_fmt: Format for (name, value) (C{str}).
@kwarg txt: Optional explanation of the error (C{str}).
@kwarg name_values: One or more B{C{name=value}} pairs overriding
any B{C{name_value}} positional arguments.
'''
if name_values:
t = _or(*(fmt_name_value % t
for t in name_values.items())) # XXX sorted
elif len(name_value) > 1:
t = _or(*(fmt_name_value % t
for t in zip(name_value[0::2], name_value[1::2])))
elif name_value:
t = str(name_value[0])
else:
t = '%s %s' % (_Missing, _Missing)
if txt is None:
x = NN
else:
x = str(txt) or _invalid_
c = _COMMA_ if _COLON_ in t else _COLON_
t = NN.join((t, c, _SPACE_, x))
Error.__init__(inst, t)
# inst.__x_txt__ = x # hold explanation
_cause_(inst) # no Python 3+ exception chaining
_ename_(inst)
def callername(up=1, dflt=NN, source=False):
'''Get the name of the calling callable.
@kwarg up: Number of call stack frames up (C{int}).
@kwarg dflt: Default return value (C{any}).
@kwarg source: Include source file name and line
number (C{bool}).
@return: Name of the non-internal callable (C{str})
or B{C{dflt}} if none found.
'''
try: # see .lazily._caller3
for u in range(up, up + 32):
n, f, s = _caller3(u)
if n and (n.startswith(_DUNDER_) or not n.startswith(_UNDER_)):
if source:
n = NN(n, _AT_, f, _COLON_, str(s))
return n
except (AttributeError, ValueError): # PYCHOK no cover
pass
return dflt
def toStr(self, prec=10, sep=_SPACE_): # PYCHOK expected
'''Return a string representation of this MGRS grid reference.
Note that MGRS grid references are truncated, not rounded
(unlike UTM coordinates).
@kwarg prec: Optional number of digits (C{int}), 4:km, 10:m.
@kwarg sep: Optional separator to join (C{str}) or C{None}
to return an unjoined C{tuple} of C{str}s.
@return: This Mgrs as "00B EN easting northing" (C{str}).
@raise ValueError: Invalid B{C{prec}}.
@example:
>>> m = Mgrs(31, 'DQ', 48251, 11932, band='U')
>>> m.toStr() # '31U DQ 48251 11932'
'''
t = NN(Fmt.zone(self._zone), self._band)
t = enstr2(self._easting, self._northing, prec, t, self._en100k)
return t if sep is None else sep.join(t)
def __init__(self):
for n, a in self.__class__.__dict__.items():
if isinstance(a, (Fstr, _Fmt)):
setattr(a, _name_, n)
Fmt = Fmt() # PYCHOK singleton
Fmt.__name__ = Fmt.__class__.__name__
_DOTSTAR_ = Fmt.DOT(_STAR_)
# formats %G and %g drop all trailing zeros and the
# decimal point, making the float appear as an int
_Gg = (Fmt.G, Fmt.g)
_FfEeGg = (Fmt.F, Fmt.f, Fmt.E, Fmt.e) + _Gg # float formats
_Fspec_ = NN('[%[<flags>][<width>]', _DOTSTAR_, ']',
_BAR_.join(_FfEeGg)) # in testStreprs
def _streprs(prec, objs, fmt, ints, force, strepr):
'''(INTERNAL) Helper for C{fstr}, C{pairs}, C{reprs} and C{strs}
'''
# <https://docs.Python.org/3/library/stdtypes.html#printf-style-string-formatting>
if fmt in _FfEeGg:
fGg = fmt in _Gg
fmt = NN(_PERCENT_, _DOT_, abs(prec), fmt)
elif fmt.startswith(_PERCENT_):
fGg = False
try: # to make sure fmt is valid
f = fmt.replace(_DOTSTAR_, Fmt.DOT(abs(prec)))
_ = f % (0.0, )
def _toRepr(self, value):
'''(INTERNAL) Representation "<name> (<value>)" or "<classname>(<value>)".
'''
t = NN(self.name, _SPACE_) if self.name else self.classname
return Fmt.PAREN(t, value)
def _toDMS(deg, form, prec, sep, ddd, suff): # MCCABE 15 by .units.py
'''(INTERNAL) Convert degrees to C{str}, with/-out sign and/or suffix.
'''
try:
deg = float(deg)
except (TypeError, ValueError) as x:
raise _ValueError(deg=deg, txt=str(x))
form = form.lower()
sign = form[:1]
if sign in _PLUSMINUS_:
form = form[1:]
else:
sign = S_NUL
if prec is None:
z = p = _F_prec.get(form, 6)
else:
z = int(prec)
p = abs(z)
w = p + (1 if p else 0)
d = abs(deg)
if form in _F_symb:
s_deg = s_min = s_sec = S_NUL # no symbols
else:
s_deg, s_min, s_sec = S_DEG, S_MIN, S_SEC
F = _F_case.get(form, F_DMS)
if F is F_DMS: # 'deg+min+sec'
d, s = divmod(round(d * _3600_0, p), _3600_0)
m, s = divmod(s, _60_0)
t = NN(_0wpF(ddd, 0, d), s_deg, sep, _0wpF(2, 0, m), s_min, sep,
_0wpF(w + 2, p, s))
s = s_sec
elif F is F_DM: # 'deg+min'
d, m = divmod(round(d * _60_0, p), _60_0)
t = NN(_0wpF(ddd, 0, d), s_deg, sep, _0wpF(w + 2, p, m))
s = s_min
elif F is F_D: # 'deg'
t = _0wpF(ddd + w, p, d)
s = s_deg
elif F is F_RAD:
t = NN(_PERCENTDOTSTAR_, 'F') % (p, radians(d))
s = S_RAD
else: # F in (F__E, F__F, F__G)
t = NN(_PERCENTDOTSTAR_, F) % (p, d)
s = S_NUL
if z > 1:
t = fstrzs(t, ap1z=F is F__G)
if sign:
if deg < 0:
t = _MINUS_ + t
elif deg > 0 and sign == _PLUS_:
t = _PLUS_ + t
elif suff: # and deg: # zero suffix?
s += sep + suff
return t + s
def _option(name, m, m2_, K):
f = Scalar_(m, name=name, Error=WGRSError)
return NN(name[0].upper(), int(m2_(f * K) + _0_5))
def _invokationError(name, *args): # PYCHOK no cover
'''(INTERNAL) Return an L{EllipticError}.
'''
return EllipticError(_SPACE_('invokation', NN(name, repr(args)))) # unstr
def _trilaterate(point1,
distance1,
point2,
distance2,
point3,
distance3,
radius=R_M,
height=None,
useZ=False,
**LatLon_LatLon_kwds):
# (INTERNAL) Locate a point at given distances from
# three other points, see LatLon.triangulate above
def _nd2(p, d, r, _i_, *qs): # .toNvector and angular distance squared
for q in qs:
if p.isequalTo(q, EPS):
raise _ValueError(points=p, txt=_coincident_)
return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2
r = Radius_(radius)
n1, r12 = _nd2(point1, distance1, r, _1_)
n2, r22 = _nd2(point2, distance2, r, _2_, point1)
n3, r32 = _nd2(point3, distance3, r, _3_, point1, point2)
# the following uses x,y coordinate system with origin at n1, x axis n1->n2
y = n3.minus(n1)
x = n2.minus(n1)
z = None
d = x.length # distance n1->n2
if d > EPS_2: # and y.length > EPS_2:
X = x.unit() # unit vector in x direction n1->n2
i = X.dot(y) # signed magnitude of x component of n1->n3
Y = y.minus(X.times(i)).unit() # unit vector in y direction
j = Y.dot(y) # signed magnitude of y component of n1->n3
if abs(j) > EPS_2:
# courtesy Carlos Freitas <https://GitHub.com/mrJean1/PyGeodesy/issues/33>
x = fsum_(r12, -r22, d**2) / (2 * d) # n1->intersection x- and ...
y = fsum_(r12, -r32, i**2, j**2, -2 * x * i) / (
2 * j) # ... y-component
# courtesy AleixDev <https://GitHub.com/mrJean1/PyGeodesy/issues/43>
z = fsum_(max(r12, r22, r32), -(x**2),
-(y**2)) # XXX not just r12!
if z > EPS:
n = n1.plus(X.times(x)).plus(Y.times(y))
if useZ: # include Z component
Z = X.cross(Y) # unit vector perpendicular to plane
n = n.plus(Z.times(sqrt(z)))
if height is None:
h = fidw((point1.height, point2.height, point3.height),
map1(fabs, distance1, distance2, distance3))
else:
h = Height(height)
kwds = _xkwds(LatLon_LatLon_kwds, height=h)
return n.toLatLon(**
kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
# no intersection, d < EPS_2 or abs(j) < EPS_2 or z < EPS
t = NN(_no_, _intersection_, _SPACE_)
raise IntersectionError(point1=point1,
distance1=distance1,
point2=point2,
distance2=distance2,
point3=point3,
distance3=distance3,
txt=unstr(t, z=z, useZ=useZ))
def _inverse(self, other, azis, wrap):
'''(INTERNAL) Inverse Vincenty method.
@raise TypeError: The B{C{other}} point is not L{LatLon}.
@raise ValueError: If this and the B{C{other}} point's L{Datum}
ellipsoids are not compatible.
@raise VincentyError: Vincenty fails to converge for the current
L{LatLon.epsilon} and L{LatLon.iterations}
limit and/or if this and the B{C{other}}
point are coincident or near-antipodal.
'''
E = self.ellipsoids(other)
c1, s1, _ = _r3(self.lat, E.f)
c2, s2, _ = _r3(other.lat, E.f)
c1c2, s1c2 = c1 * c2, s1 * c2
c1s2, s1s2 = c1 * s2, s1 * s2
dl, _ = unroll180(self.lon, other.lon, wrap=wrap)
ll = dl = radians(dl)
for self._iteration in range(1, self._iterations + 1):
ll_ = ll
sll, cll = sincos2(ll)
ss = hypot(c2 * sll, c1s2 - s1c2 * cll)
if ss < EPS: # coincident or antipodal, ...
if self.isantipodeTo(other, eps=self._epsilon):
t = '%r %sto %r' % (self, _antipodal_, other)
raise VincentyError(_ambiguous_, txt=t)
# return zeros like Karney, but unlike Veness
return Distance3Tuple(0.0, 0, 0)
cs = s1s2 + c1c2 * cll
s = atan2(ss, cs)
sa = c1c2 * sll / ss
c2a = 1 - sa**2
if abs(c2a) < EPS:
c2a = 0 # equatorial line
ll = dl + E.f * sa * s
else:
c2sm = cs - 2 * s1s2 / c2a
ll = dl + _dl(E.f, c2a, sa, s, cs, ss, c2sm)
if abs(ll - ll_) < self._epsilon:
break
# # omitted and applied only after failure to converge below, see footnote
# # under Inverse at <https://WikiPedia.org/wiki/Vincenty's_formulae>
# # <https://GitHub.com/ChrisVeness/geodesy/blob/master/latlon-vincenty.js>
# elif abs(ll) > PI and self.isantipodeTo(other, eps=self._epsilon):
# raise VincentyError('%s, %r %sto %r' % ('ambiguous', self,
# _antipodal_, other))
else:
t = _antipodal_ if self.isantipodeTo(other,
eps=self._epsilon) else NN
t = _SPACE_(repr(self), NN(t, _to_), repr(other))
raise VincentyError(_no_(_convergence_), txt=t)
if c2a: # e22 == (a / b)**2 - 1
A, B = _p2(c2a * E.e22)
s = A * (s - _ds(B, cs, ss, c2sm))
b = E.b
# if self.height or other.height:
# b += self._havg(other)
d = b * s
if azis: # forward and reverse azimuth
sll, cll = sincos2(ll)
f = atan2b(c2 * sll, c1s2 - s1c2 * cll)
r = atan2b(c1 * sll, -s1c2 + c1s2 * cll)
else:
f = r = 0
return Distance3Tuple(d, f, r)
def _property(method):
'''(INTERNAL) Return C{method} as documented C{property.getter}.
'''
t = 'get and set' if doc.startswith(_SPACE_) else NN
return property(method, None, None, NN('Property to ', t, doc))
