Coverage for pygeodesy/ellipsoidalGeodSolve.py: 100%
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2# -*- coding: utf-8 -*-
4u'''Exact ellipsoidal geodesy, intended I{for testing purposes only}.
6Ellipsoidal geodetic (lat-/longitude) L{LatLon} and geocentric
7(ECEF) L{Cartesian} classes and functions L{areaOf}, L{intersections2},
8L{isclockwise}, L{nearestOn} and L{perimeterOf} based on module
9L{geodsolve}, a wrapper invoking I{Karney}'s U{GeodSolve
10<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} utility.
11'''
13# from pygeodesy.datums import _WGS84 # from .ellipsoidalBase
14from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \
15 _nearestOn, _WGS84
16from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, _TOL_M, \
17 _intersection3, _intersections2
18# from pygeodesy.errors import _xkwds # from .karney
19from pygeodesy.karney import fabs, _polygon, Property_RO, _xkwds
20from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
21from pygeodesy.points import _areaError, ispolar # PYCHOK exported
22# from pygeodesy.props import Property_RO # from .karney
24# from math import fabs # from .karney
26__all__ = _ALL_LAZY.ellipsoidalGeodSolve
27__version__ = '25.05.28'
30class Cartesian(CartesianEllipsoidalBase):
31 '''Extended to convert exact L{Cartesian} to exact L{LatLon} points.
32 '''
34 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
35 '''Convert this cartesian point to an exact geodetic point.
37 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword
38 arguments as C{datum}. Use C{B{LatLon}=...,
39 B{datum}=...} to override this L{LatLon}
40 class or specify C{B{LatLon}=None}.
42 @return: The geodetic point (L{LatLon}) or if C{B{LatLon} is None},
43 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
44 with C{C} and C{M} if available.
46 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.
47 '''
48 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
49 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
52class LatLon(LatLonEllipsoidalBaseDI):
53 '''An ellipsoidal L{LatLon} like L{ellipsoidalKarney.LatLon} but using (exact)
54 geodesic I{wrapper} L{GeodesicSolve} to compute the geodesic distance,
55 initial and final bearing (azimuths) between two given points or the
56 destination point given a start point and an (initial) bearing.
57 '''
59 @Property_RO
60 def Equidistant(self):
61 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantGeodSolve}).
62 '''
63 return _MODS.azimuthal.EquidistantGeodSolve
65 @Property_RO
66 def geodesicx(self):
67 '''Get this C{LatLon}'s (exact) geodesic (L{GeodesicSolve}).
68 '''
69 return self.datum.ellipsoid.geodsolve
71 geodesic = geodesicx # for C{._Direct} and C{._Inverse}
73 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None
74 '''Convert this point to exact cartesian (ECEF) coordinates.
76 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other keyword
77 arguments, ignored if C{B{Cartesian} is None}. Use C{B{Cartesian}=Class}
78 to override this L{Cartesian} class or set C{B{Cartesian}=None}.
80 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if C{B{Cartesian} is
81 None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with
82 C{C} and C{M} if available.
84 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other B{C{Cartesian_datum_kwds}}.
85 '''
86 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum)
87 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
90def areaOf(points, datum=_WGS84, wrap=True, polar=False):
91 '''Compute the area of an (ellipsoidal) polygon or composite.
93 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or L{BooleanGH}).
94 @kwarg datum: Optional datum (L{Datum}).
95 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{points}} (C{bool}).
96 @kwarg polar: Use C{B{polar}=True} if the polygon encloses a pole (C{bool}), see
97 function L{ispolar<pygeodesy.points.ispolar>} and U{area of a polygon
98 enclosing a pole<https://GeographicLib.SourceForge.io/C++/doc/
99 classGeographicLib_1_1GeodesicExact.html#a3d7a9155e838a09a48dc14d0c3fac525>}.
101 @return: Area (C{meter}, same as units of the B{C{datum}}'s ellipsoid axes, I{squared}).
103 @raise PointsError: Insufficient number of B{C{points}}.
105 @raise TypeError: Some B{C{points}} are not L{LatLon}.
107 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not supported.
109 @see: Functions L{pygeodesy.areaOf}, L{ellipsoidalExact.areaOf}, L{ellipsoidalKarney.areaOf},
110 L{sphericalNvector.areaOf} and L{sphericalTrigonometry.areaOf}.
111 '''
112 return fabs(_polygon(datum.ellipsoid.geodsolve, points, True, False, wrap, polar))
115def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
116 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
117 '''I{Iteratively} compute the intersection point of two lines, each defined
118 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
119 (initial) bearing from North.
121 @arg start1: Start point of the first line (L{LatLon}).
122 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
123 at the first point (compass C{degrees360}).
124 @arg start2: Start point of the second line (L{LatLon}).
125 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
126 at the second point (compass C{degrees360}).
127 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
128 or C{None} for the mean height.
129 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
130 and B{C{end*}} points (C{bool}).
131 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
132 L{pygeodesy.equidistant}) or C{None} for the preferred
133 C{B{start1}.Equidistant}.
134 @kwarg tol: Tolerance for convergence and for skew line distance and length
135 (C{meter}, conventionally).
136 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
137 or C{None}.
138 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
139 ignored if C{B{LatLon} is None}.
141 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
142 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
143 lon, height, datum)}.
145 @raise IntersectionError: Skew, colinear, parallel or otherwise
146 non-intersecting lines or no convergence
147 for the given B{C{tol}}.
149 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
150 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
152 @note: For each line specified with an initial bearing, a pseudo-end point
153 is computed as the C{destination} along that bearing at about 1.5
154 times the distance from the start point to an initial gu-/estimate
155 of the intersection point (and between 1/8 and 3/8 of the authalic
156 earth perimeter).
158 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
159 calculating-intersection-of-two-circles>} and U{Karney's paper
160 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
161 BOUNDARIES} for more details about the iteration algorithm.
162 '''
163 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
164 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
167def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
168 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
169 '''I{Iteratively} compute the intersection points of two circles, each defined
170 by an (ellipsoidal) center point and a radius.
172 @arg center1: Center of the first circle (L{LatLon}).
173 @arg radius1: Radius of the first circle (C{meter}, conventionally).
174 @arg center2: Center of the second circle (L{LatLon}).
175 @arg radius2: Radius of the second circle (C{meter}, same units as
176 B{C{radius1}}).
177 @kwarg height: Optional height for the intersection points (C{meter},
178 conventionally) or C{None} for the I{"radical height"}
179 at the I{radical line} between both centers.
180 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
181 (C{bool}).
182 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
183 function L{pygeodesy.equidistant}) or C{None} for
184 the preferred C{B{center1}.Equidistant}.
185 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
186 and B{C{radius2}}).
187 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
188 or C{None}.
189 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
190 ignored if C{B{LatLon} is None}.
192 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
193 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
194 None}. For abutting circles, both points are the same instance,
195 aka the I{radical center}.
197 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
198 circles or no convergence for the B{C{tol}}.
200 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
201 or invalid B{C{equidistant}}.
203 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
205 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
206 calculating-intersection-of-two-circles>}, U{Karney's paper
207 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
208 U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
209 U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
210 intersections.
211 '''
212 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
213 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
216def isclockwise(points, datum=_WGS84, wrap=True, polar=False):
217 '''Determine the direction of a path or polygon.
219 @arg points: The path or polygon points (C{LatLon}[]).
220 @kwarg datum: Optional datum (L{Datum}).
221 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{points}} (C{bool}).
222 @kwarg polar: Use C{B{polar}=True} if the C{B{points}} enclose a pole (C{bool}),
223 see function U{ispolar<pygeodeys.points.ispolar>}.
225 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
227 @raise PointsError: Insufficient number of B{C{points}}.
229 @raise TypeError: Some B{C{points}} are not C{LatLon}.
231 @raise ValueError: The B{C{points}} enclose a pole or zero area.
233 @see: L{pygeodesy.isclockwise}.
234 '''
235 a = _polygon(datum.ellipsoid.geodsolve, points, True, False, wrap, polar)
236 if a < 0:
237 return True
238 elif a > 0:
239 return False
240 raise _areaError(points)
243def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
244 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
245 '''I{Iteratively} locate the closest point on the geodesic between
246 two other (ellipsoidal) points.
248 @arg point: Reference point (C{LatLon}).
249 @arg point1: Start point of the geodesic (C{LatLon}).
250 @arg point2: End point of the geodesic (C{LatLon}).
251 @kwarg within: If C{True}, return the closest point I{between}
252 B{C{point1}} and B{C{point2}}, otherwise the
253 closest point elsewhere on the geodesic (C{bool}).
254 @kwarg height: Optional height for the closest point (C{meter},
255 conventionally) or C{None} or C{False} for the
256 interpolated height. If C{False}, the closest
257 takes the heights of the points into account.
258 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
259 B{C{point1}} and B{C{point2}} (C{bool}).
260 @kwarg equidistant: An azimuthal equidistant projection (I{class}
261 or function L{pygeodesy.equidistant}) or C{None}
262 for the preferred C{B{point}.Equidistant}.
263 @kwarg tol: Convergence tolerance (C{meter}).
264 @kwarg LatLon: Optional class to return the closest point
265 (L{LatLon}) or C{None}.
266 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
267 arguments, ignored if C{B{LatLon} is None}.
269 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
270 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
272 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
273 or B{C{point2}} or invalid B{C{equidistant}}.
275 @raise ValueError: No convergence for the B{C{tol}}.
277 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
278 calculating-intersection-of-two-circles>} and U{Karney's paper
279 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
280 BOUNDARIES} for more details about the iteration algorithm.
281 '''
282 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
283 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
286def perimeterOf(points, closed=False, datum=_WGS84, wrap=True):
287 '''Compute the perimeter of an (ellipsoidal) polygon or composite.
289 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or L{BooleanGH}).
290 @kwarg closed: Optionally, close the polygon (C{bool}).
291 @kwarg datum: Optional datum (L{Datum}).
292 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{points}} (C{bool}).
294 @return: Perimeter (C{meter}, same as units of the B{C{datum}}'s ellipsoid axes).
296 @raise PointsError: Insufficient number of B{C{points}}.
298 @raise TypeError: Some B{C{points}} are not L{LatLon}.
300 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not
301 supported or C{B{closed}=False} with C{B{points}} a composite.
303 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalExact.perimeterOf},
304 L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf}
305 and L{sphericalTrigonometry.perimeterOf}.
306 '''
307 return _polygon(datum.ellipsoid.geodsolve, points, closed, True, wrap, False)
310__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
311 areaOf, # functions
312 intersection3, intersections2, isclockwise, ispolar,
313 nearestOn, perimeterOf)
315# **) MIT License
316#
317# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
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