Coverage for pygeodesy/ellipsoidalVincenty.py : 98%

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# -*- coding: utf-8 -*-
I{Thaddeus Vincenty}'s geodetic (lat-/longitude) L{LatLon}, geocentric (ECEF) L{Cartesian} and L{VincentyError} classes and functions L{areaOf}, L{intersections2}, L{nearestOn} and L{perimeterOf}.
Pure Python implementation of geodesy tools for ellipsoidal earth models, transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016} and published under the same MIT Licence**, see U{Vincenty geodesics <https://www.Movable-Type.co.UK/scripts/LatLongVincenty.html>}. More at U{geographiclib<https://PyPI.org/project/geographiclib>} and U{GeoPy<https://PyPI.org/project/geopy>}.
Calculate geodesic distance between two points using the U{Vincenty <https://WikiPedia.org/wiki/Vincenty's_formulae>} formulae and one of several ellipsoidal earth models. The default model is WGS-84, the most accurate and widely used globally-applicable model for the earth ellipsoid.
Other ellipsoids offering a better fit to the local geoid include Airy (1830) in the UK, Clarke (1880) in Africa, International 1924 in much of Europe, and GRS-67 in South America. North America (NAD83) and Australia (GDA) use GRS-80, which is equivalent to the WGS-84 model.
Great-circle distance uses a spherical model of the earth with the mean earth radius defined by the International Union of Geodesy and Geophysics (IUGG) as M{(2 * a + b) / 3 = 6371008.7714150598} meter or approx. 6371009 meter (for WGS-84, resulting in an error of up to about 0.5%).
Here's an example usage of C{ellipsoidalVincenty}:
>>> from pygeodesy.ellipsoidalVincenty import LatLon >>> Newport_RI = LatLon(41.49008, -71.312796) >>> Cleveland_OH = LatLon(41.499498, -81.695391) >>> Newport_RI.distanceTo(Cleveland_OH) 866,455.4329158525 # meter
To change the ellipsoid model used by the Vincenty formulae use:
>>> from pygeodesy import Datums >>> from pygeodesy.ellipsoidalVincenty import LatLon >>> p = LatLon(0, 0, datum=Datums.OSGB36)
or by converting to anothor datum:
>>> p = p.toDatum(Datums.OSGB36) ''' # make sure int/int division yields float quotient, see .basics
# from pygeodesy.basics import isnear0 # from .fmath # from pygeodesy.datums import _WGS84 # from .ellipsoidalBase LatLonEllipsoidalBaseDI, _TOL_M Distance3Tuple Property_RO, property_doc_ # from pygeodesy.streprs import Fmt # from .points
'''Error raised from I{Vincenty}'s C{direct} and C{inverse} methods for coincident points or lack of convergence. '''
'''Extended to convert geocentric, L{Cartesian} points to Vincenty-based, ellipsoidal, geodetic L{LatLon}. ''' '''Get the ECEF I{class} (L{EcefVeness}), I{lazily}. '''
'''Convert this cartesian point to a C{Vincenty}-based geodetic point.
@kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword arguments as C{datum}. Use C{B{LatLon}=..., B{datum}=...} 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_and_kwds}} argument. '''
'''Using the formulae devised by U{I{Thaddeus Vincenty (1975)} <https://WikiPedia.org/wiki/Vincenty's_formulae>} for an (oblate) ellipsoidal model of the earth to compute the geodesic distance and bearings between two given points or the destination point given an start point and (initial) bearing.
Set the earth model to be used with the keyword argument datum. The default is Datums.WGS84, which is the most globally accurate. For other models, see the Datums in module datum.
Note: This implementation of I{Vincenty} methods may not converge for some valid points, raising a L{VincentyError}. In that case, a result may be obtained by increasing the tolerance C{epsilon} and/or iteration C{limit}, see properties L{LatLon.epsilon} and L{LatLon.iterations}. ''' # _iteration = None # iteration number from .named._NamedBase
def bearingTo(self, other, wrap=False): # PYCHOK no cover '''DEPRECATED, use method L{initialBearingTo} or L{bearingTo2}. ''' return self.initialBearingTo(other, wrap=wrap)
'''Get the ECEF I{class} (L{EcefVeness}), I{lazily}. '''
'''Get the convergence epsilon (C{radians}). '''
'''Set the convergence epsilon (C{radians}).
@raise TypeError: Non-scalar B{C{epsilon}}.
@raise ValueError: Out of bounds B{C{epsilon}}. '''
'''Get the iteration limit (C{int}). '''
'''Set the iteration limit (C{int}).
@raise TypeError: Non-scalar B{C{limit}}.
@raise ValueError: Out-of-bounds B{C{limit}}. '''
'''Convert this point to C{Vincenty}-based cartesian (ECEF) coordinates.
@kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other keyword arguments, ignored if C{B{Cartesian} is None}. Use C{B{Cartesian}=...} to override this L{Cartesian} class or specify C{B{Cartesian} is None}.
@return: The cartesian point (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}}. ''' datum=self.datum)
'''(INTERNAL) Direct 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} limits. '''
ca2 = _0_0
else: t = self._no_convergence(t) raise VincentyError(t, txt=repr(self)) # self.toRepr()
# final bearing (reverse azimuth +/- 180)
else:
'''(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} limits and/or if this and the B{C{other}} point are coincident or near-antipodal. '''
raise VincentyError(_ambiguous_, txt=t) # return zeros like Karney, but unlike Veness
else:
# # 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(_ambiguous_, self._is_to(other, True)) else: raise VincentyError(self._no_convergence(c), txt=t)
# if self.height or other.height: # b += self._havg(other)
else:
'''(INTERNAL) Return I{'<self> [antipodal] to <other>'} text (C{str}). '''
'''(INTERNAL) Return I{'no convergence (..): ...'} text (C{str}). ''' (LatLon.iterations.name, self.iterations)))
'''(INTERNAL) C{2 * c2sm**2 - 1}. '''
'''(INTERNAL) C{Dl}. ''' C * cs * _c2sm2(c2sm)))
'''(INTERNAL) C{Ds - d}. ''' B / _6_0 * c2sm * ss2))
'''(INTERNAL) Compute A, B polynomials. ''' return _1_0, _0_0
'''(INTERNAL) Reduced C{(sin(B{a}), cos(B{a}), tan(B{a}))}. '''
def areaOf(points, datum=_WGS84, wrap=True): # PYCHOK no cover '''DEPRECATED, use function L{ellipsoidalExact.areaOf} or L{ellipsoidalKarney.areaOf}. ''' try: return _MODS.ellipsoidalKarney.areaOf(points, datum=datum, wrap=wrap) except ImportError: return _MODS.ellipsoidalExact.areaOf(points, datum=datum, wrap=wrap)
equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): '''Iteratively compute the intersection point of two paths, each defined by two (ellipsoidal) points or by an (ellipsoidal) start point and a bearing from North.
@arg start1: Start point of the first path (L{LatLon}). @arg end1: End point of the first path (L{LatLon}) or the initial bearing at the first point (compass C{degrees360}). @arg start2: Start point of the second path (L{LatLon}). @arg end2: End point of the second path (L{LatLon}) or the initial bearing at the second point (compass C{degrees360}). @kwarg height: Optional height at the intersection (C{meter}, conventionally) or C{None} for the mean height. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection (I{class} or function L{pygeodesy.equidistant}) or C{None} for the preferred C{B{start1}.Equidistant}. @kwarg tol: Tolerance for convergence and for skew line distance and length (C{meter}, conventionally). @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} is None}.
@return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point} a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
@raise IntersectionError: Skew, colinear, parallel or otherwise non-intersecting paths or no convergence for the given B{C{tol}}.
@raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}}, B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
@note: For each path specified with an initial bearing, a pseudo-end point is computed as the C{destination} along that bearing at about 1.5 times the distance from the start point to an initial gu-/estimate of the intersection point (and between 1/8 and 3/8 of the authalic earth perimeter).
@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>} and U{Karney's paper <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm. ''' equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
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 (C{meter}, conventionally) or C{None} for the I{"radical height"} at the I{radical line} between both centers. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection (I{class} or function L{pygeodesy.equidistant}) or C{None} for the preferred C{B{center1}.Equidistant}. @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} is None}.
@return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is None}. For abutting circles, both points are the same instance, aka the I{radical center}.
@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{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. ''' equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): '''Iteratively locate the closest point on the geodesic between two other (ellipsoidal) points.
@arg point: Reference point (C{LatLon}). @arg point1: Start point of the geodesic (C{LatLon}). @arg point2: End point of the geodesic (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 geodesic (C{bool}). @kwarg height: Optional height for the closest point (C{meter}, conventionally) or C{None} or C{False} for the interpolated height. If C{False}, the closest takes the heights of the points into account. @kwarg wrap: Wrap and unroll longitudes (C{bool}). @kwarg equidistant: An azimuthal equidistant projection (I{class} or function L{pygeodesy.equidistant}) or C{None} for the preferred C{B{point}.Equidistant}. @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} is None}.
@return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
@raise ImportError: Package U{geographiclib <https://PyPI.org/project/geographiclib>} not installed or not found, but only if C{B{equidistant}=}L{EquidistantKarney}.
@raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}} or B{C{point2}} or invalid B{C{equidistant}}.
@raise ValueError: No convergence for the B{C{tol}}.
@see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ calculating-intersection-of-two-circles>} and U{Karney's paper <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm. ''' equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): # PYCHOK no cover '''DEPRECATED, use function L{ellipsoidalExact.perimeterOf} or L{ellipsoidalKarney.perimeterOf}. ''' return _MODS.ellipsoidalKarney.perimeterOf(points, closed=closed, datum=datum, wrap=wrap)
intersection3, intersections2, ispolar, # from .points nearestOn) + _ALL_DOCS(areaOf, perimeterOf) # deprecated
# **) MIT License # # Copyright (C) 2016-2022 -- 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. |