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__ = '24.05.25'
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 B{C{LatLon}} is C{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}}
77 and other keyword arguments, ignored if C{B{Cartesian} is None}.
78 Use C{B{Cartesian}=...} to override this L{Cartesian} class
79 or set C{B{Cartesian}=None}.
81 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if
82 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z,
83 lat, lon, height, C, M, datum)} with C{C} and C{M} if
84 available.
86 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other
87 B{C{Cartesian_datum_kwds}}.
88 '''
89 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum)
90 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
93def areaOf(points, datum=_WGS84, wrap=True):
94 '''Compute the area of an (ellipsoidal) polygon or composite.
96 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
97 L{BooleanGH}).
98 @kwarg datum: Optional datum (L{Datum}).
99 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
100 B{C{points}} (C{bool}).
102 @return: Area (C{meter}, same as units of the B{C{datum}}'s
103 ellipsoid axes, I{squared}).
105 @raise PointsError: Insufficient number of B{C{points}}.
107 @raise TypeError: Some B{C{points}} are not L{LatLon}.
109 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
110 longitudes not supported.
112 @see: Functions L{pygeodesy.areaOf}, L{ellipsoidalExact.areaOf},
113 L{ellipsoidalKarney.areaOf}, L{sphericalNvector.areaOf}
114 and L{sphericalTrigonometry.areaOf}.
115 '''
116 return fabs(_polygon(datum.ellipsoid.geodsolve, points, True, False, wrap))
119def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
120 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
121 '''I{Iteratively} compute the intersection point of two lines, each defined
122 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
123 (initial) bearing from North.
125 @arg start1: Start point of the first line (L{LatLon}).
126 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
127 at the first point (compass C{degrees360}).
128 @arg start2: Start point of the second line (L{LatLon}).
129 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
130 at the second point (compass C{degrees360}).
131 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
132 or C{None} for the mean height.
133 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
134 and B{C{end*}} points (C{bool}).
135 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
136 L{pygeodesy.equidistant}) or C{None} for the preferred
137 C{B{start1}.Equidistant}.
138 @kwarg tol: Tolerance for convergence and for skew line distance and length
139 (C{meter}, conventionally).
140 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
141 or C{None}.
142 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
143 ignored if C{B{LatLon} is None}.
145 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
146 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
147 lon, height, datum)}.
149 @raise IntersectionError: Skew, colinear, parallel or otherwise
150 non-intersecting lines or no convergence
151 for the given B{C{tol}}.
153 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
154 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
156 @note: For each line specified with an initial bearing, a pseudo-end point
157 is computed as the C{destination} along that bearing at about 1.5
158 times the distance from the start point to an initial gu-/estimate
159 of the intersection point (and between 1/8 and 3/8 of the authalic
160 earth perimeter).
162 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
163 calculating-intersection-of-two-circles>} and U{Karney's paper
164 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
165 BOUNDARIES} for more details about the iteration algorithm.
166 '''
167 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
168 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
171def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
172 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
173 '''I{Iteratively} compute the intersection points of two circles, each defined
174 by an (ellipsoidal) center point and a radius.
176 @arg center1: Center of the first circle (L{LatLon}).
177 @arg radius1: Radius of the first circle (C{meter}, conventionally).
178 @arg center2: Center of the second circle (L{LatLon}).
179 @arg radius2: Radius of the second circle (C{meter}, same units as
180 B{C{radius1}}).
181 @kwarg height: Optional height for the intersection points (C{meter},
182 conventionally) or C{None} for the I{"radical height"}
183 at the I{radical line} between both centers.
184 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
185 (C{bool}).
186 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
187 function L{pygeodesy.equidistant}) or C{None} for
188 the preferred C{B{center1}.Equidistant}.
189 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
190 and B{C{radius2}}).
191 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
192 or C{None}.
193 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
194 ignored if C{B{LatLon} is None}.
196 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
197 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
198 None}. For abutting circles, both points are the same instance,
199 aka the I{radical center}.
201 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
202 circles or no convergence for the B{C{tol}}.
204 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
205 or invalid B{C{equidistant}}.
207 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
209 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
210 calculating-intersection-of-two-circles>}, U{Karney's paper
211 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
212 U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
213 U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
214 intersections.
215 '''
216 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
217 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
220def isclockwise(points, datum=_WGS84, wrap=True):
221 '''Determine the direction of a path or polygon.
223 @arg points: The path or polygon points (C{LatLon}[]).
224 @kwarg datum: Optional datum (L{Datum}).
225 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
226 B{C{points}} (C{bool}).
228 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
230 @raise PointsError: Insufficient number of B{C{points}}.
232 @raise TypeError: Some B{C{points}} are not C{LatLon}.
234 @raise ValueError: The B{C{points}} enclose a pole or zero
235 area.
237 @see: L{pygeodesy.isclockwise}.
238 '''
239 a = _polygon(datum.ellipsoid.geodsolve, points, True, False, wrap)
240 if a < 0:
241 return True
242 elif a > 0:
243 return False
244 raise _areaError(points)
247def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
248 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
249 '''I{Iteratively} locate the closest point on the geodesic between
250 two other (ellipsoidal) points.
252 @arg point: Reference point (C{LatLon}).
253 @arg point1: Start point of the geodesic (C{LatLon}).
254 @arg point2: End point of the geodesic (C{LatLon}).
255 @kwarg within: If C{True} return the closest point I{between}
256 B{C{point1}} and B{C{point2}}, otherwise the
257 closest point elsewhere on the geodesic (C{bool}).
258 @kwarg height: Optional height for the closest point (C{meter},
259 conventionally) or C{None} or C{False} for the
260 interpolated height. If C{False}, the closest
261 takes the heights of the points into account.
262 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
263 B{C{point1}} and B{C{point2}} (C{bool}).
264 @kwarg equidistant: An azimuthal equidistant projection (I{class}
265 or function L{pygeodesy.equidistant}) or C{None}
266 for the preferred C{B{point}.Equidistant}.
267 @kwarg tol: Convergence tolerance (C{meter}).
268 @kwarg LatLon: Optional class to return the closest point
269 (L{LatLon}) or C{None}.
270 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
271 arguments, ignored if C{B{LatLon} is None}.
273 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
274 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
276 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
277 or B{C{point2}} or invalid B{C{equidistant}}.
279 @raise ValueError: No convergence for the B{C{tol}}.
281 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
282 calculating-intersection-of-two-circles>} and U{Karney's paper
283 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
284 BOUNDARIES} for more details about the iteration algorithm.
285 '''
286 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
287 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
290def perimeterOf(points, closed=False, datum=_WGS84, wrap=True):
291 '''Compute the perimeter of an (ellipsoidal) polygon or composite.
293 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
294 L{BooleanGH}).
295 @kwarg closed: Optionally, close the polygon (C{bool}).
296 @kwarg datum: Optional datum (L{Datum}).
297 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
298 B{C{points}} (C{bool}).
300 @return: Perimeter (C{meter}, same as units of the B{C{datum}}'s
301 ellipsoid axes).
303 @raise PointsError: Insufficient number of B{C{points}}.
305 @raise TypeError: Some B{C{points}} are not L{LatLon}.
307 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
308 longitudes not supported or C{B{closed}=False}
309 with C{B{points}} a composite.
311 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalExact.perimeterOf},
312 L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf}
313 and L{sphericalTrigonometry.perimeterOf}.
314 '''
315 return _polygon(datum.ellipsoid.geodsolve, points, closed, True, wrap)
318__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
319 areaOf, # functions
320 intersection3, intersections2, isclockwise, ispolar,
321 nearestOn, perimeterOf)
323# **) MIT License
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325# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
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