Coverage for pygeodesy/ellipsoidalExact.py: 100%
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« prev ^ index » next coverage.py v7.2.2, created at 2024-06-10 14:08 -0400
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__ = '22.02.18'
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 geodesic distances, bearings (azimuths), etc.
56 '''
58 @Property_RO
59 def Equidistant(self):
60 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantExact}).
61 '''
62 return _MODS.azimuthal.EquidistantExact
64 @Property_RO
65 def geodesicx(self):
66 '''Get this C{LatLon}'s exact geodesic (L{GeodesicExact}).
67 '''
68 return self.datum.ellipsoid.geodesicx
70 geodesic = geodesicx # for C{._Direct} and C{._Inverse}
72 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, ...
73 '''Convert this point to exact cartesian (ECEF) coordinates.
75 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and
76 other keyword arguments, ignored if C{B{Cartesian}
77 is None}. Use C{B{Cartesian}=...} to override this
78 L{Cartesian} class or set C{B{Cartesian}=None}.
80 @return: The cartesian (ECEF) coordinates as (L{Cartesian}) or if
81 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat,
82 lon, height, C, M, datum)} with C{C} and C{M} if available.
84 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other
85 B{C{Cartesian_datum_kwds}}.
86 '''
87 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum)
88 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
91def areaOf(points, datum=_WGS84, wrap=True):
92 '''Compute the area of an (ellipsoidal) polygon or composite.
94 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
95 L{BooleanGH}).
96 @kwarg datum: Optional datum (L{Datum}).
97 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
98 B{C{points}} (C{bool}).
100 @return: Area (C{meter} I{squared}, same units as the B{C{datum}}'s
101 ellipsoid axes).
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
108 longitudes not supported.
110 @see: Functions L{pygeodesy.areaOf}, L{ellipsoidalGeodSolve.areaOf},
111 L{ellipsoidalKarney.areaOf}, L{sphericalNvector.areaOf} and
112 L{sphericalTrigonometry.areaOf}.
114 @note: The U{area of a polygon enclosing a pole<https://GeographicLib.SourceForge.io/
115 C++/doc/classGeographicLib_1_1GeodesicExact.html#a3d7a9155e838a09a48dc14d0c3fac525>}
116 can be found by adding half the datum's ellipsoid surface area to the polygon's area.
117 '''
118 return fabs(_polygon(datum.ellipsoid.geodesicx, points, True, False, wrap))
121def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True
122 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
123 '''I{Iteratively} compute the intersection point of two lines, each defined
124 by two (ellipsoidal) points or by an (ellipsoidal) start point and an
125 initial bearing from North.
127 @arg start1: Start point of the first line (L{LatLon}).
128 @arg end1: End point of the first line (L{LatLon}) or the initial bearing
129 at the first point (compass C{degrees360}).
130 @arg start2: Start point of the second line (L{LatLon}).
131 @arg end2: End point of the second line (L{LatLon}) or the initial bearing
132 at the second point (compass C{degrees360}).
133 @kwarg height: Optional height at the intersection (C{meter}, conventionally)
134 or C{None} for the mean height.
135 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}
136 and B{C{end*}} points (C{bool}).
137 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
138 L{pygeodesy.equidistant}) or C{None} for the preferred
139 C{B{start1}.Equidistant}.
140 @kwarg tol: Tolerance for convergence and for skew line distance and length
141 (C{meter}, conventionally).
142 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
143 or C{None}.
144 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
145 ignored if C{B{LatLon} is None}.
147 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
148 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
149 lon, height, datum)}.
151 @raise IntersectionError: Skew, colinear, parallel or otherwise non-intersecting
152 lines or no convergence for the given B{C{tol}}.
154 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},
155 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.
157 @note: For each line specified with an initial bearing, a pseudo-end point
158 is computed as the C{destination} along that bearing at about 1.5
159 times the distance from the start point to an initial gu-/estimate
160 of the intersection point (and between 1/8 and 3/8 of the authalic
161 earth perimeter).
163 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
164 calculating-intersection-of-two-circles>} and U{Karney's paper
165 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME
166 BOUNDARIES} for more details about the iteration algorithm.
167 '''
168 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,
169 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
172def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True
173 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
174 '''I{Iteratively} compute the intersection points of two circles, each defined
175 by an (ellipsoidal) center point and a radius.
177 @arg center1: Center of the first circle (L{LatLon}).
178 @arg radius1: Radius of the first circle (C{meter}, conventionally).
179 @arg center2: Center of the second circle (L{LatLon}).
180 @arg radius2: Radius of the second circle (C{meter}, same units as
181 B{C{radius1}}).
182 @kwarg height: Optional height for the intersection points (C{meter},
183 conventionally) or C{None} for the I{"radical height"}
184 at the I{radical line} between both centers.
185 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}
186 (C{bool}).
187 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
188 function L{pygeodesy.equidistant}) or C{None} for
189 the preferred C{B{center1}.Equidistant}.
190 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
191 and B{C{radius2}}).
192 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
193 or C{None}.
194 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
195 ignored if C{B{LatLon} is None}.
197 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
198 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
199 None}. For abutting circles, both points are the same instance,
200 aka the I{radical center}.
202 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
203 circles or no convergence for the B{C{tol}}.
205 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
206 or invalid B{C{equidistant}}.
208 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
210 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
211 calculating-intersection-of-two-circles>}, U{Karney's paper
212 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
213 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
214 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
215 intersections.
216 '''
217 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
218 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
221def isclockwise(points, datum=_WGS84, wrap=True):
222 '''Determine the direction of a path or polygon.
224 @arg points: The path or polygon points (C{LatLon}[]).
225 @kwarg datum: Optional datum (L{Datum}).
226 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
227 B{C{points}} (C{bool}).
229 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
231 @raise PointsError: Insufficient number of B{C{points}}.
233 @raise TypeError: Some B{C{points}} are not C{LatLon}.
235 @raise ValueError: The B{C{points}} enclose a pole or zero area.
237 @see: L{pygeodesy.isclockwise}.
238 '''
239 a = _polygon(datum.ellipsoid.geodesicx, 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 (ellispoidal) 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 units as 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{ellipsoidalGeodSolve.perimeterOf},
312 L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf} and
313 L{sphericalTrigonometry.perimeterOf}.
314 '''
315 return _polygon(datum.ellipsoid.geodesicx, points, closed, True, wrap)
318__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
319 areaOf, intersecant2, # from .ellipsoidalBase
320 intersection3, intersections2, isclockwise, ispolar,
321 nearestOn, perimeterOf)
323# **) MIT License
324#
325# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
326#
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328# copy of this software and associated documentation files (the "Software"),
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332# Software is furnished to do so, subject to the following conditions:
333#
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