Coverage for pygeodesy/ellipsoidalExact.py: 100%
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2# -*- coding: utf-8 -*-
4u'''Exact ellipsoidal geodesy using I{Karney}'s Exact Geodesic.
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 classes
9L{GeodesicExact}, L{GeodesicAreaExact} and L{GeodesicLineExact}.
10'''
12# from pygeodesy.datums import _WGS84 # from .ellipsoidalBase
13from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \
14 _nearestOn, _WGS84
15from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \
16 _intersection3, _intersections2, \
17 _TOL_M, intersecant2
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.ellipsoidalExact
27__version__ = '23.11.08'
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} class
40 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
54 exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact} to
55 compute the geodesic distance, initial and final bearing (azimuths)
56 between two given points or the destination point given a start point
57 and an (initial) bearing.
58 '''
60 @Property_RO
61 def Equidistant(self):
62 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantExact}).
63 '''
64 return _MODS.azimuthal.EquidistantExact
66 @Property_RO
67 def geodesicx(self):
68 '''Get this C{LatLon}'s exact geodesic (L{GeodesicExact}).
69 '''
70 return self.datum.ellipsoid.geodesicx
72 geodesic = geodesicx # for C{._Direct} and C{._Inverse}
74 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, ...
75 '''Convert this point to exact cartesian (ECEF) coordinates.
77 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and
78 other keyword arguments, ignored if C{B{Cartesian}
79 is None}. Use C{B{Cartesian}=...} to override this
80 L{Cartesian} class or set C{B{Cartesian}=None}.
82 @return: The cartesian (ECEF) coordinates as (L{Cartesian}) or if
83 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat,
84 lon, height, C, M, datum)} with C{C} and C{M} if 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} I{squared}, same units as the B{C{datum}}'s
103 ellipsoid axes).
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{ellipsoidalGeodSolve.areaOf},
113 L{ellipsoidalKarney.areaOf}, L{sphericalNvector.areaOf} and
114 L{sphericalTrigonometry.areaOf}.
116 @note: The U{area of a polygon enclosing a pole<https://GeographicLib.SourceForge.io/
117 C++/doc/classGeographicLib_1_1GeodesicExact.html#a3d7a9155e838a09a48dc14d0c3fac525>}
118 can be found by adding half the datum's ellipsoid surface area to the polygon's area.
119 '''
120 return fabs(_polygon(datum.ellipsoid.geodesicx, points, True, False, wrap))
123def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
124 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
125 '''I{Iteratively} compute the intersection point of two lines, each defined
126 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
127 initial bearing from North.
129 @arg start1: Start point of the first line (L{LatLon}).
130 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
131 at the first point (compass C{degrees360}).
132 @arg start2: Start point of the second line (L{LatLon}).
133 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
134 at the second point (compass C{degrees360}).
135 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
136 or C{None} for the mean height.
137 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
138 and B{C{end*}} points (C{bool}).
139 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
140 L{pygeodesy.equidistant}) or C{None} for the preferred
141 C{B{start1}.Equidistant}.
142 @kwarg tol: Tolerance for convergence and for skew line distance and length
143 (C{meter}, conventionally).
144 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
145 or C{None}.
146 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
147 ignored if C{B{LatLon} is None}.
149 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
150 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
151 lon, height, datum)}.
153 @raise IntersectionError: Skew, colinear, parallel or otherwise non-intersecting
154 lines or no convergence for the given B{C{tol}}.
156 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
157 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
159 @note: For each line specified with an initial bearing, a pseudo-end point
160 is computed as the C{destination} along that bearing at about 1.5
161 times the distance from the start point to an initial gu-/estimate
162 of the intersection point (and between 1/8 and 3/8 of the authalic
163 earth perimeter).
165 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
166 calculating-intersection-of-two-circles>} and U{Karney's paper
167 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
168 BOUNDARIES} for more details about the iteration algorithm.
169 '''
170 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
171 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
174def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
175 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
176 '''I{Iteratively} compute the intersection points of two circles, each defined
177 by an (ellipsoidal) center point and a radius.
179 @arg center1: Center of the first circle (L{LatLon}).
180 @arg radius1: Radius of the first circle (C{meter}, conventionally).
181 @arg center2: Center of the second circle (L{LatLon}).
182 @arg radius2: Radius of the second circle (C{meter}, same units as
183 B{C{radius1}}).
184 @kwarg height: Optional height for the intersection points (C{meter},
185 conventionally) or C{None} for the I{"radical height"}
186 at the I{radical line} between both centers.
187 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
188 (C{bool}).
189 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
190 function L{pygeodesy.equidistant}) or C{None} for
191 the preferred C{B{center1}.Equidistant}.
192 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
193 and B{C{radius2}}).
194 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
195 or C{None}.
196 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
197 ignored if C{B{LatLon} is None}.
199 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
200 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
201 None}. For abutting circles, both points are the same instance,
202 aka the I{radical center}.
204 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
205 circles or no convergence for the B{C{tol}}.
207 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
208 or invalid B{C{equidistant}}.
210 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
212 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
213 calculating-intersection-of-two-circles>}, U{Karney's paper
214 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
215 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
216 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
217 intersections.
218 '''
219 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
220 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
223def isclockwise(points, datum=_WGS84, wrap=True):
224 '''Determine the direction of a path or polygon.
226 @arg points: The path or polygon points (C{LatLon}[]).
227 @kwarg datum: Optional datum (L{Datum}).
228 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
229 B{C{points}} (C{bool}).
231 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
233 @raise PointsError: Insufficient number of B{C{points}}.
235 @raise TypeError: Some B{C{points}} are not C{LatLon}.
237 @raise ValueError: The B{C{points}} enclose a pole or zero area.
239 @see: L{pygeodesy.isclockwise}.
240 '''
241 a = _polygon(datum.ellipsoid.geodesicx, points, True, False, wrap)
242 if a < 0:
243 return True
244 elif a > 0:
245 return False
246 raise _areaError(points)
249def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
250 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
251 '''I{Iteratively} locate the closest point on the geodesic between
252 two other (ellispoidal) points.
254 @arg point: Reference point (C{LatLon}).
255 @arg point1: Start point of the geodesic (C{LatLon}).
256 @arg point2: End point of the geodesic (C{LatLon}).
257 @kwarg within: If C{True} return the closest point I{between}
258 B{C{point1}} and B{C{point2}}, otherwise the
259 closest point elsewhere on the geodesic (C{bool}).
260 @kwarg height: Optional height for the closest point (C{meter},
261 conventionally) or C{None} or C{False} for the
262 interpolated height. If C{False}, the closest
263 takes the heights of the points into account.
264 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
265 B{C{point1}} and B{C{point2}} (C{bool}).
266 @kwarg equidistant: An azimuthal equidistant projection (I{class}
267 or function L{pygeodesy.equidistant}) or C{None}
268 for the preferred C{B{point}.Equidistant}.
269 @kwarg tol: Convergence tolerance (C{meter}).
270 @kwarg LatLon: Optional class to return the closest point
271 (L{LatLon}) or C{None}.
272 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
273 arguments, ignored if C{B{LatLon} is None}.
275 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}
276 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.
278 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}
279 or B{C{point2}} or invalid B{C{equidistant}}.
281 @raise ValueError: No convergence for the B{C{tol}}.
283 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
284 calculating-intersection-of-two-circles>} and U{Karney's paper
285 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
286 BOUNDARIES} for more details about the iteration algorithm.
287 '''
288 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,
289 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
292def perimeterOf(points, closed=False, datum=_WGS84, wrap=True):
293 '''Compute the perimeter of an (ellipsoidal) polygon or composite.
295 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
296 L{BooleanGH}).
297 @kwarg closed: Optionally, close the polygon (C{bool}).
298 @kwarg datum: Optional datum (L{Datum}).
299 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
300 B{C{points}} (C{bool}).
302 @return: Perimeter (C{meter}, same units as the B{C{datum}}'s
303 ellipsoid axes).
305 @raise PointsError: Insufficient number of B{C{points}}.
307 @raise TypeError: Some B{C{points}} are not L{LatLon}.
309 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
310 longitudes not supported or C{B{closed}=False}
311 with C{B{points}} a composite.
313 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalGeodSolve.perimeterOf},
314 L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf} and
315 L{sphericalTrigonometry.perimeterOf}.
316 '''
317 return _polygon(datum.ellipsoid.geodesicx, points, closed, True, wrap)
320__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
321 areaOf, intersecant2, # from .ellipsoidalBase
322 intersection3, intersections2, isclockwise, ispolar,
323 nearestOn, perimeterOf)
325# **) MIT License
326#
327# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
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330# copy of this software and associated documentation files (the "Software"),
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