# Coverage for pygeodesy/ellipsoidalKarney.py : 100%

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Here's an example usage of C{ellipsoidalKarney}: >>> from pygeodesy.ellipsoidalKarney import LatLon >>> Newport_RI = LatLon(41.49008, -71.312796) >>> Cleveland_OH = LatLon(41.499498, -81.695391) >>> Newport_RI.distanceTo(Cleveland_OH) 866,455.4329098687 # meter You can change the ellipsoid model used by the I{Karney} formulae as follows: >>> from pygeodesy import Datums >>> from pygeodesy.ellipsoidalKarney import LatLon >>> p = LatLon(0, 0, datum=Datums.OSGB36) or by converting to anothor datum: >>> p = p.toDatum(Datums.OSGB36) @newfield example: Example, Examples ''' from pygeodesy.datums import Datums from pygeodesy.ellipsoidalBase import _intermediateTo, _intersections2, \ CartesianEllipsoidalBase, \ LatLonEllipsoidalBase, _nearestOn from pygeodesy.errors import _ValueError, _xellipsoidal, _xkwds from pygeodesy.formy import points2 from pygeodesy.lazily import _ALL_LAZY, _ALL_OTHER from pygeodesy.namedTuples import Bearing2Tuple, Destination2Tuple from pygeodesy.points import _areaError, ispolar # PYCHOK exported from pygeodesy.props import property_RO from pygeodesy.units import _1mm as _TOL_M from pygeodesy.utily import unroll180, wrap90, wrap180, wrap360 __all__ = _ALL_LAZY.ellipsoidalKarney __version__ = '21.01.07' class Cartesian(CartesianEllipsoidalBase): '''Extended to convert C{Karney}-based L{Cartesian} to C{Karney}-based L{LatLon} points. ''' def toLatLon(self, **LatLon_datum_kwds): # PYCHOK LatLon=LatLon, datum=None '''Convert this cartesian point to a C{Karney}-based geodetic point. @kwarg LatLon_datum_kwds: Optional L{LatLon}, B{C{datum}} and other keyword arguments, ignored if C{B{LatLon}=None}. Use B{C{LatLon=...}} to override this L{LatLon} class or specify C{B{LatLon}=None}. @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} and C{M} if available. @raise TypeError: Invalid B{C{LatLon}}, B{C{datum}} or other B{C{LatLon_datum_kwds}}. ''' kwds = _xkwds(LatLon_datum_kwds, LatLon=LatLon, datum=self.datum) return CartesianEllipsoidalBase.toLatLon(self, **kwds) class LatLon(LatLonEllipsoidalBase): '''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon} but using I{Charles F. F. Karney}'s Python U{geographiclib <https://PyPI.org/project/geographiclib>} to compute the geodesic distance, initial and final bearing (azimuths) between two given points or the destination point given a start point and an (initial) bearing. @note: This L{LatLon} require the U{geographiclib <https://PyPI.org/project/geographiclib>} package. ''' def bearingTo(self, other, wrap=False): # PYCHOK no cover '''DEPRECATED, use method C{initialBearingTo}. ''' return self.initialBearingTo(other, wrap=wrap) def bearingTo2(self, other, wrap=False): '''Compute the initial and final bearing (forward and reverse azimuth) from this to an other point, using I{Karney}'s C{Inverse} method. See methods L{initialBearingTo} and L{finalBearingTo} for more details. @arg other: The other point (L{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: A L{Bearing2Tuple}C{(initial, final)}. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @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. ''' r = self._inverse(other, wrap) return self._xnamed(Bearing2Tuple(r.initial, r.final)) def destination(self, distance, bearing, height=None): '''Compute the destination point after having travelled for the given distance from this point along a geodesic given by an initial bearing, using I{Karney}'s C{Direct} method. See method L{destination2} for more details. @arg distance: Distance (C{meter}). @arg bearing: Initial bearing in (compass C{degrees360}). @kwarg height: Optional height, overriding the default height (C{meter}, same units as C{distance}). @return: The destination point (L{LatLon}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @example: >>> p = LatLon(-37.95103, 144.42487) >>> d = p.destination(54972.271, 306.86816) >>> d LatLon(37°39′10.14″S, 143°55′35.39″E) # 37.652818°S, 143.926498°E ''' r = self._direct(distance, bearing, self.classof, height) return r.destination def destination2(self, distance, bearing, height=None): '''Compute the destination point and the final bearing (reverse azimuth) after having travelled for the given distance from this point along a geodesic given by an initial bearing, using I{Karney}'s C{Direct} method. The distance must be in the same units as this point's datum axes, conventionally C{meter}. The distance is measured on the surface of the ellipsoid, ignoring this point's height. The initial and final bearing (forward and reverse azimuth) are in compass C{degrees360}. The destination point's height and datum are set to this point's height and datum, unless the former is overridden. @arg distance: Distance (C{meter}). @arg bearing: Initial bearing (compass C{degrees360}). @kwarg height: Optional height, overriding the default height (C{meter}, same units as C{distance}). @return: A L{Destination2Tuple}C{(destination, final)}. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @example: >>> p = LatLon(-37.95103, 144.42487) >>> d, f = p.destination2(54972.271, 306.86816) >>> d LatLon(37°39′10.14″S, 143°55′35.39″E) # 37.652818°S, 143.926498°E >>> f 307.1736313846665 ''' r = self._direct(distance, bearing, self.classof, height) return self._xnamed(r) def distanceTo(self, other, wrap=False, **unused): # ignore radius=R_M '''Compute the distance between this and an other point along a geodesic, using I{Karney}'s C{Inverse} method. See method L{distanceTo3} for more details. @arg other: The other point (L{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Distance (C{meter}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @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. @example: >>> p = LatLon(50.06632, -5.71475) >>> q = LatLon(58.64402, -3.07009) >>> d = p.distanceTo(q) # 969,954.1663142084 m ''' return self._inverse(other, wrap).distance def distanceTo3(self, other, wrap=False): '''Compute the distance, the initial and final bearing along a geodesic between this and an other point, using I{Karney}'s C{Inverse} method. The distance is in the same units as this point's datum axes, conventionally meter. The distance is measured on the surface of the ellipsoid, ignoring this point's height. The initial and final bearing (forward and reverse azimuth) are in compass C{degrees360} from North. @arg other: Destination point (L{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: A L{Distance3Tuple}C{(distance, initial, final)}. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @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. ''' return self._xnamed(self._inverse(other, wrap)) def finalBearingOn(self, distance, bearing): '''Compute the final bearing (reverse azimuth) after having travelled for the given distance along a geodesic given by an initial bearing from this point, using I{Karney}'s C{Direct} method. See method L{destination2} for more details. @arg distance: Distance (C{meter}). @arg bearing: Initial bearing (compass C{degrees360}). @return: Final bearing (compass C{degrees360}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @example: >>> p = LatLon(-37.95103, 144.42487) >>> b = 306.86816 >>> f = p.finalBearingOn(54972.271, b) # 307.1736313846665° ''' return self._direct(distance, bearing, None, None).final def finalBearingTo(self, other, wrap=False): '''Compute the final bearing (reverse azimuth) after having travelled along a geodesic from this point to an other point, using I{Karney}'s C{Inverse} method. See method L{distanceTo3} for more details. @arg other: The other point (L{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Final bearing (compass C{degrees360}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @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. @example: >>> p = new LatLon(50.06632, -5.71475) >>> q = new LatLon(58.64402, -3.07009) >>> f = p.finalBearingTo(q) # 11.297220414306684° >>> p = LatLon(52.205, 0.119) >>> q = LatLon(48.857, 2.351) >>> f = p.finalBearingTo(q) # 157.83449958372714° ''' return self._inverse(other, wrap).final @property_RO def geodesic(self): '''Get this C{LatLon}'s I{wrapped} U{Karney Geodesic <https://GeographicLib.SourceForge.io/html/python/code.html>}, provided package U{geographiclib <https://PyPI.org/project/geographiclib>} is installed. ''' return self.datum.ellipsoid.geodesic def initialBearingTo(self, other, wrap=False): '''Compute the initial bearing (forward azimuth) to travel along a geodesic from this point to an other point, using I{Karney}'s C{Inverse} method. See method L{distanceTo3} for more details. @arg other: The other point (L{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Initial bearing (compass C{degrees360}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @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. @example: >>> p = LatLon(50.06632, -5.71475) >>> q = LatLon(58.64402, -3.07009) >>> b = p.initialBearingTo(q) # 9.141877488906045° >>> p = LatLon(52.205, 0.119) >>> q = LatLon(48.857, 2.351) >>> b = p.initialBearingTo(q) # 156.1106404059787° @JSname: I{bearingTo}. ''' return self._inverse(other, wrap).initial def intermediateTo(self, other, fraction, height=None, wrap=False): '''Return the point at given fraction along the geodesic between this and an other point, using I{Karney}'s C{Direct} and C{Inverse} methods. @arg other: The other point (L{LatLon}). @arg fraction: Fraction between both points ranging from 0, meaning this to 1, the other point (C{float}). @kwarg height: Optional height, overriding the fractional height (C{meter}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Intermediate point (L{LatLon}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise TypeError: The B{C{other}} point is not L{LatLon}. @raise UnitError: Invalid B{C{fraction}} or B{C{height}}. @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are not compatible. @see: Methods L{distanceTo3} and L{destination}. @example: >>> p = ellipsoidalKarney.LatLon(52.205, 0.119) >>> q = ellipsoidalKarney.LatLon(48.857, 2.351) >>> i = p.intermediateTo(q, 0.25) # 51.372275°N, 000.707253°E ''' return _intermediateTo(self, other, fraction, height, wrap) def intersections2(self, radius1, other, radius2, height=None, wrap=True, # PYCHOK expected tol=_TOL_M): '''Compute the intersection points of two circles each defined by a center point and a radius. @arg radius1: Radius of the this circle (C{meter}, conventionally). @arg other: Center of the other circle (C{LatLon}). @arg radius2: Radius of the other circle (C{meter}, same units as B{C{radius1}}). @kwarg height: Optional height for the intersection points, overriding the "radical height" at the "radical line" between both centers (C{meter}, conventionally) or C{None}. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}} and B{C{radius2}}). @return: 2-Tuple of the intersection points, each a C{LatLon} instance. For abutting circles, both intersection points are the same instance. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting circles or no convergence. @raise TypeError: Invalid B{C{other}} or B{C{equidistant}}. @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}. @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>}, U{Karney's paper <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{I{14. MARITIME BOUNDARIES}}, U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>} intersections. ''' self.others(other) return intersections2(self, radius1, other, radius2, height=height, wrap=wrap, tol=tol, LatLon=self.classof, datum=self.datum) def nearestOn(self, point1, point2, within=True, height=None, wrap=False, # PYCHOK expected tol=_TOL_M): '''Locate the closest point on the arc between two other points and this point. @arg point1: Start point of the arc (C{LatLon}). @arg point2: End point of the arc (C{LatLon}). @kwarg within: If C{True} return the closest point I{between} B{C{point1}} and B{C{point2}}, otherwise the closest point elsewhere on the arc (C{bool}). @kwarg height: Optional height for the closest point (C{meter}) or C{None}. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg tol: Convergence tolerance (C{meter}). @return: Closest point (B{C{LatLon}}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise TypeError: Invalid or non-ellipsoidal B{C{point1}} or B{C{point2}}. ''' # use .nearestOn to get C{azimuthal.EquidistantKarney} or ImportError return nearestOn(self, point1, point2, within=within, height=height, wrap=wrap, tol=tol, LatLon=self.classof, datum=self.datum) def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None '''Convert this point to C{Karney}-based cartesian (ECEF) coordinates. @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other keyword arguments, ignored if B{C{Cartesian=None}}. Use B{C{Cartesian=...}} to override this L{Cartesian} class or set B{C{Cartesian=None}}. @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} and C{M} if available. @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other B{C{Cartesian_datum_kwds}}. ''' kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum) return LatLonEllipsoidalBase.toCartesian(self, **kwds) def _direct(self, distance, bearing, LL, height): '''(INTERNAL) I{Karney}'s C{Direct} method. @return: A L{Destination2Tuple}C{(destination, final)} or a L{Destination3Tuple}C{(lat, lon, final)} if B{C{LL}} is C{None}. ''' g = self.datum.ellipsoid.geodesic r = g.Direct3(self.lat, self.lon, bearing, distance) if LL: h = self.height if height is None else height d = LL(wrap90(r.lat), wrap180(r.lon), height=h, datum=self.datum) r = Destination2Tuple(self._xnamed(d), wrap360(r.final)) return r def _inverse(self, other, wrap): '''(INTERNAL) I{Karney}'s C{Inverse} method. @return: A L{Distance3Tuple}C{(distance, initial, final)}. @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. ''' g = self.ellipsoids(other).geodesic _, lon = unroll180(self.lon, other.lon, wrap=wrap) return g.Inverse3(self.lat, self.lon, other.lat, lon) def _EquidistantKarney(equidistant): # (INTERNAL) Get the C{EquidistantKarney} class. if equidistant is None or not callable(equidistant): from pygeodesy.azimuthal import EquidistantKarney as equidistant return equidistant def _geodesic(datum, points, closed, line, wrap): # Compute the area or perimeter of a polygon, # using the geographiclib package, iff installed g = datum.ellipsoid.geodesic if not wrap: # capability LONG_UNROLL can't be off raise _ValueError(wrap=wrap) _, points = points2(points, closed=closed) # base=LatLonEllipsoidalBase(0, 0) g = g.Polygon(line) # note, lon deltas are unrolled, by default for p in points: g.AddPoint(p.lat, p.lon) if closed and line: p = points[0] g.AddPoint(p.lat, p.lon) # g.Compute returns (number_of_points, perimeter, signed area) return g.Compute(False, True)[1 if line else 2] def areaOf(points, datum=Datums.WGS84, wrap=True): '''Compute the area of an (ellipsoidal) polygon. @arg points: The polygon points (L{LatLon}[]). @kwarg datum: Optional datum (L{Datum}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Area (C{meter}, same as units of the B{C{datum}} ellipsoid, squared). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} are not L{LatLon}. @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not supported. @note: This function requires the U{geographiclib <https://PyPI.org/project/geographiclib>} package. @see: L{pygeodesy.areaOf}, L{sphericalNvector.areaOf} and L{sphericalTrigonometry.areaOf}. ''' return abs(_geodesic(datum, points, True, False, wrap)) def intersections2(center1, radius1, center2, radius2, height=None, wrap=True, equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): '''Iteratively compute the intersection points of two circles each defined by an (ellipsoidal) center point and a radius. @arg center1: Center of the first circle (L{LatLon}). @arg radius1: Radius of the first circle (C{meter}, conventionally). @arg center2: Center of the second circle (L{LatLon}). @arg radius2: Radius of the second circle (C{meter}, same units as B{C{radius1}}). @kwarg height: Optional height for the intersection points, overriding the "radical height" at the "radical line" between both centers (C{meter}, conventionally) or C{None}. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection (class L{Equidistant} or function L{equidistant}) or C{None} for L{EquidistantKarney}. @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}} and B{C{radius2}}). @kwarg LatLon: Optional class to return the intersection points (L{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance or L{LatLon4Tuple}C{(lat, lon, height, datum)} if B{C{LatLon}} is C{None}. For abutting circles, both intersection points are the same instance. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting circles or no convergence for the B{C{tol}}. @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}} or invalid B{C{equidistant}}. @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}. @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>}, U{Karney's paper <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{I{14. MARITIME BOUNDARIES}}, U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>} intersections. ''' E = _EquidistantKarney(equidistant) return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap, equidistant=E, tol=tol, LatLon=LatLon, **LatLon_kwds) def isclockwise(points, datum=Datums.WGS84, wrap=True): '''Determine the direction of a path or polygon. @arg points: The path or polygon points (C{LatLon}[]). @kwarg datum: Optional datum (L{Datum}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: C{True} if B{C{points}} are clockwise, C{False} otherwise. @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} are not C{LatLon}. @raise ValueError: The B{C{points}} enclose a pole or zero area. @note: This function requires the U{geographiclib <https://PyPI.org/project/geographiclib>} package. @see: L{pygeodesy.isclockwise}. ''' a = _geodesic(datum, points, True, False, wrap) if a > 0: return True elif a < 0: return False raise _areaError(points) def nearestOn(point, point1, point2, within=True, height=None, wrap=False, equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): '''Iteratively locate the closest point on the arc between two other points. @arg point: Reference point (C{LatLon}). @arg point1: Start point of the arc (C{LatLon}). @arg point2: End point of the arc (C{LatLon}). @kwarg within: If C{True} return the closest point I{between} B{C{point1}} and B{C{point2}}, otherwise the closest point elsewhere on the arc (C{bool}). @kwarg height: Optional height for the closest point (C{meter}) or C{None}. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection (class L{Equidistant} or function L{equidistant}) or C{None} for L{EquidistantKarney}. @kwarg tol: Convergence tolerance (C{meter}). @kwarg LatLon: Optional class to return the closest point (L{LatLon}) or C{None}. @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: Closest point (B{C{LatLon}}). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}} or B{C{point2}} or invalid B{C{equidistant}}. ''' p = _xellipsoidal(point=point) p1 = p.others(point1=point1) p2 = p.others(point2=point2) E = _EquidistantKarney(equidistant) return _nearestOn(p, p1, p2, within=within, height=height, wrap=wrap, equidistant=E, tol=tol, LatLon=LatLon, **LatLon_kwds) def perimeterOf(points, closed=False, datum=Datums.WGS84, wrap=True): '''Compute the perimeter of an (ellipsoidal) polygon. @arg points: The polygon points (L{LatLon}[]). @kwarg closed: Optionally, close the polygon (C{bool}). @kwarg datum: Optional datum (L{Datum}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Perimeter (C{meter}, same as units of the B{C{datum}} ellipsoid). @raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} are not L{LatLon}. @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not supported. @note: This function requires the U{geographiclib <https://PyPI.org/project/geographiclib>} package. @see: L{pygeodesy.perimeterOf} and L{sphericalTrigonometry.perimeterOf}. ''' return _geodesic(datum, points, closed, True, wrap) __all__ += _ALL_OTHER(Cartesian, LatLon, # classes areaOf, intersections2, isclockwise, ispolar, # functions nearestOn, perimeterOf) # **) 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.