# Coverage for pygeodesy/sphericalBase.py : 94%

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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.basics import map1, property_doc_ from pygeodesy.cartesianBase import CartesianBase from pygeodesy.datums import Datums, _spherical_datum from pygeodesy.ellipsoids import R_M, R_MA from pygeodesy.errors import IntersectionError from pygeodesy.fmath import favg, fdot from pygeodesy.interns import EPS, NN, PI, PI2, PI_2, _COMMA_, \ _too_, _distant_, _exceed_PI_radians_, \ _near_concentric_, _1_0, _180_0, _360_0 from pygeodesy.latlonBase import LatLonBase, _trilaterate5 # PYCHOK passed from pygeodesy.lazily import _ALL_DOCS from pygeodesy.named import _xnamed from pygeodesy.namedTuples import Bearing2Tuple from pygeodesy.nvectorBase import NvectorBase from pygeodesy.units import Bearing_, Distance, Height, Radius, Radius_ from pygeodesy.utily import acos1, atan2b, degrees90, degrees180, \ sincos2, tanPI_2_2, wrapPI from math import cos, hypot, log, sin, sqrt __all__ = () __version__ = '20.12.18' def _angular(distance, radius): # PYCHOK for export '''(INTERNAL) Return the angular distance in radians. @raise ValueError: Invalid B{C{distance}} or B{C{radius}}. ''' return Distance(distance) / Radius_(radius) def _rads3(rad1, rad2, radius): # in .sphericalTrigonometry '''(INTERNAL) Convert radii to radians. ''' r1 = Radius_(rad1=rad1) r2 = Radius_(rad2=rad2) if radius is not None: # convert radii to radians r = _1_0 / Radius_(radius=radius) r1 *= r r2 *= r x = r1 < r2 if x: r1, r2 = r2, r1 if r1 > PI: raise IntersectionError(rad1=rad1, rad2=rad2, txt=_exceed_PI_radians_) return r1, r2, x class CartesianSphericalBase(CartesianBase): '''(INTERNAL) Base class for spherical C{Cartesian}s. ''' _datum = Datums.Sphere # L{Datum} def intersections2(self, rad1, other, rad2, radius=R_M): '''Compute the intersection points of two circles each defined by a center point and a radius. @arg rad1: Radius of the this circle (C{meter} or C{radians}, see B{C{radius}}). @arg other: Center of the other circle (C{Cartesian}). @arg rad2: Radius of the other circle (C{meter} or C{radians}, see B{C{radius}}). @kwarg radius: Mean earth radius (C{meter} or C{None} if both B{C{rad1}} and B{C{rad2}} are given in C{radians}). @return: 2-Tuple of the intersection points, each C{Cartesian}. The intersection points are the same C{Cartesian} instance for abutting circles. @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting circles. @raise TypeError: If B{C{other}} is not C{Cartesian}. @raise ValueError: Invalid B{C{rad1}}, B{C{rad2}} or B{C{radius}}. @see: U{Calculating intersection of two Circles <https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>} and method or function C{trilaterate3d2}. ''' x1, x2 = self, self.others(other) r1, r2, x = _rads3(rad1, rad2, radius) if x: x1, x2 = x2, x1 n, q = x1.cross(x2), x1.dot(x2) n2, q21 = n.length2, _1_0 - q**2 if min(abs(q21), n2) < EPS: raise IntersectionError(center=self, other=other, txt=_near_concentric_) try: cr1, cr2 = cos(r1), cos(r2) a = (cr1 - q * cr2) / q21 b = (cr2 - q * cr1) / q21 x0 = x1.times(a).plus(x2.times(b)) except ValueError: raise IntersectionError(center=self, rad1=rad1, other=other, rad2=rad2) x = _1_0 - x0.length2 # XXX x0.dot(x0) if x < EPS: raise IntersectionError(center=self, rad1=rad1, other=other, rad2=rad2, txt=_too_(_distant_)) n = n.times(sqrt(x / n2)) if n.length > EPS: x1, x2 = x0.plus(n), x0.minus(n) else: # abutting circles x1 = x2 = x0 for x in (x1, x2): x.datum = self.datum x.name = self.intersections2.__name__ return x1, x2 class LatLonSphericalBase(LatLonBase): '''(INTERNAL) Base class for spherical C{LatLon}s. ''' _datum = Datums.Sphere # spherical L{Datum} def __init__(self, lat, lon, height=0, datum=None, name=NN): '''Create a spherical C{LatLon} point frome the given lat-, longitude and height on the given datum. @arg lat: Latitude (C{degrees} or DMS C{[N|S]}). @arg lon: Longitude (C{degrees} or DMS C{str[E|W]}). @kwarg height: Optional elevation (C{meter}, the same units as the datum's half-axes). @kwarg datum: Optional, spherical datum to use (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}) or C{scalar} earth radius). @kwarg name: Optional name (string). @raise TypeError: If B{C{datum}} invalid or not 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 not in (None, self.datum): self._datum = _spherical_datum(datum, name=self.name, raiser=True) def bearingTo2(self, other, wrap=False, raiser=False): '''Return the initial and final bearing (forward and reverse azimuth) from this to an other point. @arg other: The other point (C{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg 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 i = self.initialBearingTo(other, wrap=wrap, raiser=raiser) # PYCHOK .initialBearingTo f = self.finalBearingTo( other, wrap=wrap, raiser=raiser) return self._xnamed(Bearing2Tuple(i, f)) @property_doc_(''' this point's datum (L{Datum}).''') 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}. @arg datum: New spherical datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple}) or C{scalar} earth radius). @raise TypeError: If B{C{datum}} invalid or not not spherical. ''' d = _spherical_datum(datum, name=self.name, raiser=True) self._update(d != self._datum) self._datum = d def finalBearingTo(self, other, wrap=False, raiser=False): '''Return the final bearing (reverse azimuth) from this to an other point. @arg other: The other point (spherical C{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg 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_0) % _360_0 # == wrap360 since b >= 0 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). @arg bearing: Initial bearing (compass C{degrees360}). @return: Maximum latitude (C{degrees90}). @raise ValueError: Invalid B{C{bearing}}. @JSname: I{maxLatitude}. ''' m = acos1(abs(sin(Bearing_(bearing)) * cos(self.phi))) return degrees90(m) def minLat(self, bearing): '''Return the minimum latitude reached when travelling on a great circle on given bearing from this point. @arg bearing: Initial bearing (compass C{degrees360}). @return: Minimum latitude (C{degrees90}). @see: Method L{maxLat} for more details. @raise ValueError: Invalid B{C{bearing}}. @JSname: I{minLatitude}. ''' return -self.maxLat(bearing) def parse(self, strllh, height=0, sep=_COMMA_, name=NN): '''Parse a string representing a similar, spherical C{LatLon} point, consisting of C{"lat, lon[, height]"}. @arg strllh: Lat, lon and optional height (C{str}), see function L{parse3llh}. @kwarg height: Optional, default height (C{meter}). @kwarg sep: Optional separator (C{str}). @kwarg name: Optional instance name (C{str}), overriding this name. @return: The similar point (spherical C{LatLon}). @raise ParseError: Invalid B{C{strllh}}. ''' from pygeodesy.dms import parse3llh r = self.classof(*parse3llh(strllh, height=height, sep=sep)) return _xnamed(r, name or self.name, force=True) def _rhumb3(self, other): '''(INTERNAL) Rhumb_ helper function. @arg other: The other point (spherical C{LatLon}). ''' self.others(other) a1, b1 = self.philam a2, b2 = other.philam # 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. @arg 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 atan2b(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. @arg distance: Distance travelled (C{meter}, same units as I{radius}). @arg bearing: Bearing from this point (compass C{degrees360}). @kwarg radius: Mean earth radius (C{meter}). @kwarg height: Optional height, overriding the default height (C{meter}, same unit as I{radius}). @return: The destination point (spherical C{LatLon}). @raise ValueError: Invalid B{C{distance}}, B{C{bearing}}, B{C{radius}} or B{C{height}}. @example: >>> p = LatLon(51.127, 1.338) >>> q = p.rhumbDestination(40300, 116.7) # 50.9642°N, 001.8530°E @JSname: I{rhumbDestinationPoint} ''' r = _angular(distance, radius) a1, b1 = self.philam sb, cb = sincos2(Bearing_(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(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. @arg other: The other point (spherical C{LatLon}). @kwarg radius: Mean earth radius (C{meter}). @return: Distance (C{meter}, the same units as I{radius}). @raise TypeError: The B{C{other}} point is not spherical. @raise ValueError: Invalid B{C{radius}}. @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 q = (da / dp) if abs(dp) > EPS else cos(self.phi) return hypot(da, q * db) * Radius(radius) def rhumbMidpointTo(self, other, height=None): '''Return the (loxodromic) midpoint between this and an other point. @arg other: The other point (spherical LatLon). @kwarg height: Optional height, overriding the mean height (C{meter}). @return: The midpoint (spherical C{LatLon}). @raise TypeError: The I{other} point is not spherical. @raise ValueError: Invalid B{C{height}}. @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.philam a2, b2 = other.philam 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 = fdot(map1(log, f1, f2, f3), -b2, b1, b2 - b1) / f h = self._havg(other) if height is None else Height(height) return self.classof(degrees90(a3), degrees180(b3), height=h) def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature '''Convert this point to C{Nvector} components, I{including height}. @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if B{C{Nvector=None}}. @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. ''' return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds) def toWm(self, radius=R_MA): '''Convert this point to a I{WM} coordinate. @kwarg 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) __all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase) # **) MIT License # # Copyright (C) 2016-2021 -- 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.