Coverage for pygeodesy/ellipsoidalGeodSolve.py: 100%
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« prev ^ index » next coverage.py v7.6.1, created at 2025-04-25 13:15 -0400
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__ = '24.08.13'
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):
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}).
97 @return: Area (C{meter}, same as units of the B{C{datum}}'s ellipsoid axes, I{squared}).
99 @raise PointsError: Insufficient number of B{C{points}}.
101 @raise TypeError: Some B{C{points}} are not L{LatLon}.
103 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not supported.
105 @see: Functions L{pygeodesy.areaOf}, L{ellipsoidalExact.areaOf}, L{ellipsoidalKarney.areaOf},
106 L{sphericalNvector.areaOf} and L{sphericalTrigonometry.areaOf}.
107 '''
108 return fabs(_polygon(datum.ellipsoid.geodsolve, points, True, False, wrap))
111def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
112 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
113 '''I{Iteratively} compute the intersection point of two lines, each defined
114 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
115 (initial) bearing from North.
117 @arg start1: Start point of the first line (L{LatLon}).
118 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
119 at the first point (compass C{degrees360}).
120 @arg start2: Start point of the second line (L{LatLon}).
121 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
122 at the second point (compass C{degrees360}).
123 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
124 or C{None} for the mean height.
125 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
126 and B{C{end*}} points (C{bool}).
127 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
128 L{pygeodesy.equidistant}) or C{None} for the preferred
129 C{B{start1}.Equidistant}.
130 @kwarg tol: Tolerance for convergence and for skew line distance and length
131 (C{meter}, conventionally).
132 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
133 or C{None}.
134 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
135 ignored if C{B{LatLon} is None}.
137 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
138 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
139 lon, height, datum)}.
141 @raise IntersectionError: Skew, colinear, parallel or otherwise
142 non-intersecting lines or no convergence
143 for the given B{C{tol}}.
145 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
146 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
148 @note: For each line specified with an initial bearing, a pseudo-end point
149 is computed as the C{destination} along that bearing at about 1.5
150 times the distance from the start point to an initial gu-/estimate
151 of the intersection point (and between 1/8 and 3/8 of the authalic
152 earth perimeter).
154 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
155 calculating-intersection-of-two-circles>} and U{Karney's paper
156 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
157 BOUNDARIES} for more details about the iteration algorithm.
158 '''
159 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
160 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
163def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
164 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
165 '''I{Iteratively} compute the intersection points of two circles, each defined
166 by an (ellipsoidal) center point and a radius.
168 @arg center1: Center of the first circle (L{LatLon}).
169 @arg radius1: Radius of the first circle (C{meter}, conventionally).
170 @arg center2: Center of the second circle (L{LatLon}).
171 @arg radius2: Radius of the second circle (C{meter}, same units as
172 B{C{radius1}}).
173 @kwarg height: Optional height for the intersection points (C{meter},
174 conventionally) or C{None} for the I{"radical height"}
175 at the I{radical line} between both centers.
176 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
177 (C{bool}).
178 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
179 function L{pygeodesy.equidistant}) or C{None} for
180 the preferred C{B{center1}.Equidistant}.
181 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
182 and B{C{radius2}}).
183 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
184 or C{None}.
185 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
186 ignored if C{B{LatLon} is None}.
188 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
189 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
190 None}. For abutting circles, both points are the same instance,
191 aka the I{radical center}.
193 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
194 circles or no convergence for the B{C{tol}}.
196 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
197 or invalid B{C{equidistant}}.
199 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
201 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
202 calculating-intersection-of-two-circles>}, U{Karney's paper
203 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
204 U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
205 U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
206 intersections.
207 '''
208 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
209 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
212def isclockwise(points, datum=_WGS84, wrap=True):
213 '''Determine the direction of a path or polygon.
215 @arg points: The path or polygon points (C{LatLon}[]).
216 @kwarg datum: Optional datum (L{Datum}).
217 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
218 B{C{points}} (C{bool}).
220 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
222 @raise PointsError: Insufficient number of B{C{points}}.
224 @raise TypeError: Some B{C{points}} are not C{LatLon}.
226 @raise ValueError: The B{C{points}} enclose a pole or zero
227 area.
229 @see: L{pygeodesy.isclockwise}.
230 '''
231 a = _polygon(datum.ellipsoid.geodsolve, points, True, False, wrap)
232 if a < 0:
233 return True
234 elif a > 0:
235 return False
236 raise _areaError(points)
239def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
240 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
241 '''I{Iteratively} locate the closest point on the geodesic between
242 two other (ellipsoidal) points.
244 @arg point: Reference point (C{LatLon}).
245 @arg point1: Start point of the geodesic (C{LatLon}).
246 @arg point2: End point of the geodesic (C{LatLon}).
247 @kwarg within: If C{True}, return the closest point I{between}
248 B{C{point1}} and B{C{point2}}, otherwise the
249 closest point elsewhere on the geodesic (C{bool}).
250 @kwarg height: Optional height for the closest point (C{meter},
251 conventionally) or C{None} or C{False} for the
252 interpolated height. If C{False}, the closest
253 takes the heights of the points into account.
254 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
255 B{C{point1}} and B{C{point2}} (C{bool}).
256 @kwarg equidistant: An azimuthal equidistant projection (I{class}
257 or function L{pygeodesy.equidistant}) or C{None}
258 for the preferred C{B{point}.Equidistant}.
259 @kwarg tol: Convergence tolerance (C{meter}).
260 @kwarg LatLon: Optional class to return the closest point
261 (L{LatLon}) or C{None}.
262 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
263 arguments, ignored if C{B{LatLon} is None}.
265 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
266 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
268 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
269 or B{C{point2}} or invalid B{C{equidistant}}.
271 @raise ValueError: No convergence for the B{C{tol}}.
273 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
274 calculating-intersection-of-two-circles>} and U{Karney's paper
275 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
276 BOUNDARIES} for more details about the iteration algorithm.
277 '''
278 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
279 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
282def perimeterOf(points, closed=False, datum=_WGS84, wrap=True):
283 '''Compute the perimeter of an (ellipsoidal) polygon or composite.
285 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
286 L{BooleanGH}).
287 @kwarg closed: Optionally, close the polygon (C{bool}).
288 @kwarg datum: Optional datum (L{Datum}).
289 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
290 B{C{points}} (C{bool}).
292 @return: Perimeter (C{meter}, same as units of the B{C{datum}}'s
293 ellipsoid axes).
295 @raise PointsError: Insufficient number of B{C{points}}.
297 @raise TypeError: Some B{C{points}} are not L{LatLon}.
299 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
300 longitudes not supported or C{B{closed}=False}
301 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)
310__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
311 areaOf, # functions
312 intersection3, intersections2, isclockwise, ispolar,
313 nearestOn, perimeterOf)
315# **) MIT License
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317# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
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