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# -*- coding: utf-8 -*- 

 

u'''(INTERNAL) Spherical base classes C{CartesianSphericalBase} and 

C{LatLonSphericalBase}. 

 

Pure Python implementation of geodetic (lat-/longitude) functions, 

transcribed in part from JavaScript originals by I{(C) Chris Veness 2011-2016} 

and published under the same MIT Licence**, see 

U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>}. 

 

@newfield example: Example, Examples 

''' 

 

from pygeodesy.cartesianBase import CartesianBase 

from pygeodesy.datum import R_M, R_MA, Datum, Datums 

from pygeodesy.dms import parse3llh 

from pygeodesy.ecef import EcefKarney 

from pygeodesy.fmath import EPS, acos1, favg, fsum_, _IsNotError 

from pygeodesy.latlonBase import LatLonBase 

from pygeodesy.lazily import _ALL_DOCS 

from pygeodesy.named import Bearing2Tuple 

from pygeodesy.utily import PI, PI2, PI_2, degrees90, degrees180, \ 

degrees360, property_RO, sincos2d, \ 

tanPI_2_2, _TypeError, wrapPI 

 

from math import atan2, cos, hypot, log, radians, sin 

 

# XXX the following classes are listed only to get 

# Epydoc to include class and method documentation 

__all__ = _ALL_DOCS('CartesianSphericalBase', 'LatLonSphericalBase') 

__version__ = '19.10.21' 

 

 

class CartesianSphericalBase(CartesianBase): 

'''(INTERNAL) Base class for spherical C{Cartesian}s. 

''' 

_datum = Datums.Sphere #: (INTERNAL) L{Datum}. 

_Ecef = EcefKarney #: (INTERNAL) Preferred C{Ecef...} class. 

 

 

class LatLonSphericalBase(LatLonBase): 

'''(INTERNAL) Base class for spherical C{LatLon}s. 

''' 

_datum = Datums.Sphere #: (INTERNAL) Spherical L{Datum}. 

_Ecef = EcefKarney #: (INTERNAL) Preferred C{Ecef...} class. 

 

def __init__(self, lat, lon, height=0, datum=None, name=''): 

'''Create a spherical C{LatLon} point frome the given 

lat-, longitude and height on the given datum. 

 

@param lat: Latitude (C{degrees} or DMS C{[N|S]}). 

@param lon: Longitude (C{degrees} or DMS C{str[E|W]}). 

@keyword height: Optional elevation (C{meter}, the same units 

as the datum's half-axes). 

@keyword datum: Optional, shperical datum to use (L{Datum}). 

@keyword name: Optional name (string). 

 

@raise TypeError: B{C{datum}} is not a L{datum} or 

not spherical. 

 

@example: 

 

>>> p = LatLon(51.4778, -0.0016) # height=0, datum=Datums.WGS84 

''' 

LatLonBase.__init__(self, lat, lon, height=height, name=name) 

if datum: 

self.datum = datum 

 

def bearingTo2(self, other, wrap=False, raiser=False): 

'''Return the initial and final bearing (forward and reverse 

azimuth) from this to an other point. 

 

@param other: The other point (C{LatLon}). 

@keyword wrap: Wrap and unroll longitudes (C{bool}). 

@keyword raiser: Optionally, raise L{CrossError} (C{bool}). 

 

@return: A L{Bearing2Tuple}C{(initial, final)}. 

 

@raise TypeError: The I{other} point is not spherical. 

 

@see: Methods C{initialBearingTo} and C{finalBearingTo}. 

''' 

# .initialBearingTo is inside .-Nvector and .-Trigonometry 

r = Bearing2Tuple(self.initialBearingTo(other, wrap=wrap, raiser=raiser), # PYCHOK .initialBearingTo 

self.finalBearingTo( other, wrap=wrap, raiser=raiser)) 

return self._xnamed(r) 

 

@property 

def datum(self): 

'''Get this point's datum (L{Datum}). 

''' 

return self._datum 

 

@datum.setter # PYCHOK setter! 

def datum(self, datum): 

'''Set this point's datum I{without conversion}. 

 

@param datum: New datum (L{Datum}). 

 

@raise TypeError: If B{C{datum}} is not a L{Datum} 

or not spherical. 

''' 

_TypeError(Datum, datum=datum) 

if not datum.isSpherical: 

raise _IsNotError('spherical', datum=datum) 

self._update(datum != self._datum) 

self._datum = datum 

 

def finalBearingTo(self, other, wrap=False, raiser=False): 

'''Return the final bearing (reverse azimuth) from this to 

an other point. 

 

@param other: The other point (spherical C{LatLon}). 

@keyword wrap: Wrap and unroll longitudes (C{bool}). 

@keyword raiser: Optionally, raise L{CrossError} (C{bool}). 

 

@return: Final bearing (compass C{degrees360}). 

 

@raise TypeError: The I{other} point is not spherical. 

 

@example: 

 

>>> p = LatLon(52.205, 0.119) 

>>> q = LatLon(48.857, 2.351) 

>>> b = p.finalBearingTo(q) # 157.9 

''' 

self.others(other) 

 

# final bearing is the reverse of the other, initial one; 

# .initialBearingTo is inside .-Nvector and .-Trigonometry 

b = other.initialBearingTo(self, wrap=wrap, raiser=raiser) 

return (b + 180) % 360 # == wrap360 since b >= 0 

 

@property_RO 

def isEllipsoidal(self): 

'''Check whether this C{LatLon} is ellipsoidal (C{bool}). 

''' 

return self.datum.isEllipsoidal 

 

@property_RO 

def isSpherical(self): 

'''Check whether this C{LatLon} is spherical (C{bool}). 

''' 

return self.datum.isSpherical 

 

def maxLat(self, bearing): 

'''Return the maximum latitude reached when travelling 

on a great circle on given bearing from this point 

based on Clairaut's formula. 

 

The maximum latitude is independent of longitude 

and the same for all points on a given latitude. 

 

Negate the result for the minimum latitude (on the 

Southern hemisphere). 

 

@param bearing: Initial bearing (compass C{degrees360}). 

 

@return: Maximum latitude (C{degrees90}). 

 

@JSname: I{maxLatitude}. 

''' 

a, _ = self.to2ab() 

m = acos1(abs(sin(radians(bearing)) * cos(a))) 

return degrees90(m) 

 

def minLat(self, bearing): 

'''Return the minimum latitude reached when travelling 

on a great circle on given bearing from this point. 

 

@param bearing: Initial bearing (compass C{degrees360}). 

 

@return: Minimum latitude (C{degrees90}). 

 

@see: Method L{maxLat} for more details. 

 

@JSname: I{minLatitude}. 

''' 

return -self.maxLat(bearing) 

 

def parse(self, strll, height=0, sep=','): 

'''Parse a string representing lat-/longitude point and 

return a C{LatLon}. 

 

The lat- and longitude must be separated by a sep[arator] 

character. If height is present it must follow and be 

separated by another sep[arator]. Lat- and longitude 

may be swapped, provided at least one ends with the 

proper compass direction. 

 

For more details, see functions L{parse3llh} and L{parseDMS} 

in module L{dms}. 

 

@param strll: Lat, lon [, height] (C{str}). 

@keyword height: Optional , default height (C{meter}). 

@keyword sep: Optional separator (C{str}). 

 

@return: The point (spherical C{LatLon}). 

 

@raise ValueError: Invalid I{strll}. 

''' 

return self.classof(*parse3llh(strll, height=height, sep=sep)) 

 

def _rhumb3(self, other): 

'''(INTERNAL) Rhumb_ helper function. 

 

@param other: The other point (spherical C{LatLon}). 

''' 

self.others(other) 

 

a1, b1 = self.to2ab() 

a2, b2 = other.to2ab() 

# if |db| > 180 take shorter rhumb 

# line across the anti-meridian 

db = wrapPI(b2 - b1) 

dp = log(tanPI_2_2(a2) / tanPI_2_2(a1)) 

return (a2 - a1), db, dp 

 

def rhumbBearingTo(self, other): 

'''Return the initial bearing (forward azimuth) from this to 

an other point along a rhumb (loxodrome) line. 

 

@param other: The other point (spherical C{LatLon}). 

 

@return: Initial bearing (compass C{degrees360}). 

 

@raise TypeError: The I{other} point is not spherical. 

 

@example: 

 

>>> p = LatLon(51.127, 1.338) 

>>> q = LatLon(50.964, 1.853) 

>>> b = p.rhumbBearingTo(q) # 116.7 

''' 

_, db, dp = self._rhumb3(other) 

return degrees360(atan2(db, dp)) 

 

def rhumbDestination(self, distance, bearing, radius=R_M, height=None): 

'''Return the destination point having travelled along a rhumb 

(loxodrome) line from this point the given distance on the 

given bearing. 

 

@param distance: Distance travelled (C{meter}, same units as 

I{radius}). 

@param bearing: Bearing from this point (compass C{degrees360}). 

@keyword radius: Optional, mean earth radius (C{meter}). 

@keyword height: Optional height, overriding the default 

height (C{meter}, same unit as I{radius}). 

 

@return: The destination point (spherical C{LatLon}). 

 

@example: 

 

>>> p = LatLon(51.127, 1.338) 

>>> q = p.rhumbDestination(40300, 116.7) # 50.9642°N, 001.8530°E 

 

@JSname: I{rhumbDestinationPoint} 

''' 

a1, b1 = self.to2ab() 

 

r = float(distance) / float(radius) # angular distance in radians 

 

sb, cb = sincos2d(bearing) 

 

da = r * cb 

a2 = a1 + da 

# normalize latitude if past pole 

if a2 > PI_2: 

a2 = PI - a2 

elif a2 < -PI_2: 

a2 = -PI - a2 

 

dp = log(tanPI_2_2(a2) / tanPI_2_2(a1)) 

# E-W course becomes ill-conditioned with 0/0 

q = (da / dp) if abs(dp) > EPS else cos(a1) 

b2 = (b1 + r * sb / q) if abs(q) > EPS else b1 

 

h = self.height if height is None else height 

return self.classof(degrees90(a2), degrees180(b2), height=h) 

 

def rhumbDistanceTo(self, other, radius=R_M): 

'''Return the distance from this to an other point along a rhumb 

(loxodrome) line. 

 

@param other: The other point (spherical C{LatLon}). 

@keyword radius: Optional, mean earth radius (C{meter}). 

 

@return: Distance (C{meter}, the same units as I{radius}). 

 

@raise TypeError: The I{other} point is not spherical. 

 

@example: 

 

>>> p = LatLon(51.127, 1.338) 

>>> q = LatLon(50.964, 1.853) 

>>> d = p.rhumbDistanceTo(q) # 403100 

''' 

# see <https://www.EdWilliams.org/avform.htm#Rhumb> 

da, db, dp = self._rhumb3(other) 

 

# on Mercator projection, longitude distances shrink 

# by latitude; the 'stretch factor' q becomes ill- 

# conditioned along E-W line (0/0); use an empirical 

# tolerance to avoid it 

if abs(dp) > EPS: 

q = da / dp 

else: 

a, _ = self.to2ab() 

q = cos(a) 

return float(radius) * hypot(da, q * db) 

 

def rhumbMidpointTo(self, other, height=None): 

'''Return the (loxodromic) midpoint between this and 

an other point. 

 

@param other: The other point (spherical LatLon). 

@keyword height: Optional height, overriding the mean height 

(C{meter}). 

 

@return: The midpoint (spherical C{LatLon}). 

 

@raise TypeError: The I{other} point is not spherical. 

 

@example: 

 

>>> p = LatLon(51.127, 1.338) 

>>> q = LatLon(50.964, 1.853) 

>>> m = p.rhumb_midpointTo(q) 

>>> m.toStr() # '51.0455°N, 001.5957°E' 

''' 

self.others(other) 

 

# see <https://MathForum.org/library/drmath/view/51822.html> 

a1, b1 = self.to2ab() 

a2, b2 = other.to2ab() 

if abs(b2 - b1) > PI: 

b1 += PI2 # crossing anti-meridian 

 

a3 = favg(a1, a2) 

b3 = favg(b1, b2) 

 

f1 = tanPI_2_2(a1) 

if abs(f1) > EPS: 

f2 = tanPI_2_2(a2) 

f = f2 / f1 

if abs(f) > EPS: 

f = log(f) 

if abs(f) > EPS: 

f3 = tanPI_2_2(a3) 

b3 = fsum_(b1 * log(f2), 

-b2 * log(f1), (b2 - b1) * log(f3)) / f 

 

h = self._havg(other) if height is None else height 

return self.classof(degrees90(a3), degrees180(b3), height=h) 

 

def toWm(self, radius=R_MA): 

'''Convert this C{LatLon} point to a I{WM} coordinate. 

 

@keyword radius: Optional earth radius (C{meter}). 

 

@return: The WM coordinate (L{Wm}). 

 

@see: Function L{toWm} in module L{webmercator} for details. 

''' 

from pygeodesy.webmercator import toWm # PYCHOK recursive import 

return toWm(self, radius=radius) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

# Permission is hereby granted, free of charge, to any person obtaining a 

# copy of this software and associated documentation files (the "Software"), 

# to deal in the Software without restriction, including without limitation 

# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

# and/or sell copies of the Software, and to permit persons to whom the 

# Software is furnished to do so, subject to the following conditions: 

# 

# The above copyright notice and this permission notice shall be included 

# in all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, 

# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

# OTHER DEALINGS IN THE SOFTWARE.