def frechet_(points1, points2, distance=None, units=''):
'''Compute the I{discrete} U{Fréchet<https://WikiPedia.org/wiki/Frechet_distance>}
distance between two paths given as sets of points.
@param points1: First set of points (C{LatLon}[], C{Numpy2LatLon}[],
C{Tuple2LatLon}[] or C{other}[]).
@param points2: Second set of points (C{LatLon}[], C{Numpy2LatLon}[],
C{Tuple2LatLon}[] or C{other}[]).
@keyword distance: Callable returning the distance between a B{C{points1}}
and a B{C{points2}} point (signature C{(point1, point2)}).
@keyword units: Optional, name of the distance units (C{str}).
@return: A L{Frechet6Tuple}C{(fd, fi1, fi2, r, n, units)} where C{fi1} and
C{fi2} are type C{int} indices into B{C{points1}} respectively
B{C{points2}}.
@raise FrechetError: Insufficient number of B{C{points1}} or B{C{points2}}.
@raise RecursionError: Recursion depth exceeded, see U{sys.getrecursionlimit()
<https://docs.Python.org/3/library/sys.html#sys.getrecursionlimit>}.
@raise TypeError: If B{C{distance}} is not a callable.
@note: Keyword C{fraction}, intermediate B{C{points1}} and B{C{points2}}
and I{fractional} indices are I{not} supported in this L{frechet_}
function.
'''
if not callable(distance):
raise _IsNotError(callable.__name__, distance=distance)
n1, ps1 = _points2(points1, closed=False, Error=FrechetError)
n2, ps2 = _points2(points2, closed=False, Error=FrechetError)
def dF(i1, i2):
return distance(ps1[i1], ps2[i2])
return _frechet_(n1, 1, n2, 1, dF, units)
def to2ll(self, datum=None):
'''Convert this WM coordinate to a geodetic lat- and longitude.
@keyword datum: Optional datum (C{Datum}).
@return: A L{LatLon2Tuple}C{(lat, lon)}.
@raise TypeError: Non-ellipsoidal B{C{datum}}.
'''
r = self.radius
x = self._x / r
y = 2 * atan(exp(self._y / r)) - PI_2
if datum:
E = datum.ellipsoid
if not E.isEllipsoidal:
raise _IsNotError('ellipsoidal', datum=datum)
# <https://Earth-Info.NGA.mil/GandG/wgs84/web_mercator/
# %28U%29%20NGA_SIG_0011_1.0.0_WEBMERC.pdf>
y = y / r
if E.e:
y -= E.e * atanh(E.e * tanh(y))
y *= E.a
x *= E.a / r
return self._xnamed(LatLon2Tuple(degrees90(y), degrees180(x)))
def __init__(self, knots, datum=None, beta=2, wrap=False, name=''):
'''New L{HeightIDWhaversine} interpolator.
@param knots: The points with known height (C{LatLon}s).
@keyword datum: Optional datum (L{Datum} to use, overriding
the default C{B{knots}[0].datum}
@keyword beta: Inverse distance power (C{int} 1, 2, or 3).
@keyword wrap: Wrap and L{unroll180} longitudes (C{bool}).
@keyword name: Optional height interpolator name (C{str}).
@raise HeightError: Insufficient number of B{C{knots}} or
invalid B{C{knot}}, B{C{datum}} or
B{C{beta}}.
@raise ImportError: Package U{GeographicLib
<https://PyPI.org/project/geographiclib>} missing.
@raise TypeError: Invalid B{C{datum}}.
'''
n, self._lls = len2(knots)
if n < self._kmin:
raise HeightError('insufficient %s: %s, need %s' %
('knots', n, self._kmin))
try:
self._datum = self._lls[0].datum if datum is None else datum
if not isinstance(self.datum, Datum):
raise TypeError
except (AttributeError, TypeError):
raise _IsNotError('valid', datum=self.datum or datum)
self._geodesic = self.datum.ellipsoid.geodesic
self.beta = beta
if wrap:
self._wrap = True
if name:
self.name = name
def toLatLon(self, LatLon=None, height=None):
'''Convert this L{Css} to an (ellipsoidal) geodetic point.
@keyword LatLon: Optional, ellipsoidal (sub-)class to return
the geodetic point (C{LatLon}) or C{None}.
@keyword height: Optional height for the point, overriding
the default height (C{meter}).
@return: The point (B{C{LatLon}}) or a
L{LatLon4Tuple}C{(lat, lon, height, datum)} if
B{C{LatLon}} is C{None}.
@raise TypeError: If B{C{LatLon}} or B{C{datum}} is not ellipsoidal.
'''
if LatLon and not issubclassof(LatLon, _LLEB):
raise _IsNotError(_LLEB.__name__, LatLon=LatLon)
lat, lon = self.latlon
d = self.cs0.datum
h = self.height if height is None else height
r = LatLon4Tuple(lat, lon, h, d) if LatLon is None else \
LatLon(lat, lon, height=h, datum=d)
return self._xnamed(r)
def _2epoch(epoch): # imported by .ellipsoidalBase.py
'''(INTERNAL) Validate an C{epoch}.
'''
if isscalar(epoch) and epoch > 0: # XXX 1970?
return _F(epoch)
raise _IsNotError('scalar', epoch=epoch)