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, _TOL_M, \
16 _intersection3, _intersections2
17# from pygeodesy.errors import _xkwds # from .karney
18from pygeodesy.karney import fabs, _polygon, Property_RO, _xkwds
19from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER
20from pygeodesy.points import _areaError, ispolar # PYCHOK exported
21# from pygeodesy.props import Property_RO # from .karney
23# from math import fabs # from .karney
25__all__ = _ALL_LAZY.ellipsoidalExact
26__version__ = '23.04.11'
29class Cartesian(CartesianEllipsoidalBase):
30 '''Extended to convert exact L{Cartesian} to exact L{LatLon} points.
31 '''
33 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None
34 '''Convert this cartesian point to an exact geodetic point.
36 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword
37 arguments as C{datum}. Use C{B{LatLon}=...,
38 B{datum}=...} to override this L{LatLon} class
39 or specify C{B{LatLon}=None}.
41 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None},
42 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)}
43 with C{C} and C{M} if available.
45 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.
46 '''
47 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)
48 return CartesianEllipsoidalBase.toLatLon(self, **kwds)
51class LatLon(LatLonEllipsoidalBaseDI):
52 '''An ellipsoidal L{LatLon} like L{ellipsoidalKarney.LatLon} but using
53 exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact} to
54 compute the geodesic distance, initial and final bearing (azimuths)
55 between two given points or the destination point given a start point
56 and an (initial) bearing.
57 '''
59 @Property_RO
60 def Equidistant(self):
61 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantExact}).
62 '''
63 return _MODS.azimuthal.EquidistantExact
65 @Property_RO
66 def geodesicx(self):
67 '''Get this C{LatLon}'s exact geodesic (L{GeodesicExact}).
68 '''
69 return self.datum.ellipsoid.geodesicx
71 geodesic = geodesicx # for C{._Direct} and C{._Inverse}
73 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, ...
74 '''Convert this point to exact cartesian (ECEF) coordinates.
76 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and
77 other keyword arguments, ignored if C{B{Cartesian}
78 is None}. Use C{B{Cartesian}=...} to override this
79 L{Cartesian} class or set C{B{Cartesian}=None}.
81 @return: The cartesian (ECEF) coordinates as (L{Cartesian}) or if
82 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, lat,
83 lon, height, C, M, datum)} with C{C} and C{M} if available.
85 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other
86 B{C{Cartesian_datum_kwds}}.
87 '''
88 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum)
89 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)
92def areaOf(points, datum=_WGS84, wrap=True):
93 '''Compute the area of an (ellipsoidal) polygon or composite.
95 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or
96 L{BooleanGH}).
97 @kwarg datum: Optional datum (L{Datum}).
98 @kwarg wrap: Wrap and unroll longitudes (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=True,
122 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
123 '''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: Wrap and unroll longitudes (C{bool}).
136 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function
137 L{pygeodesy.equidistant}) or C{None} for the preferred
138 C{B{start1}.Equidistant}.
139 @kwarg tol: Tolerance for convergence and for skew line distance and length
140 (C{meter}, conventionally).
141 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
142 or C{None}.
143 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
144 ignored if C{B{LatLon} is None}.
146 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}
147 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,
148 lon, height, datum)}.
150 @raise IntersectionError: Skew, colinear, parallel or otherwise non-intersecting
151 lines or no convergence 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=True,
172 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
173 '''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: Wrap and unroll longitudes (C{bool}).
185 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
186 function L{pygeodesy.equidistant}) or C{None} for
187 the preferred C{B{center1}.Equidistant}.
188 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}
189 and B{C{radius2}}).
190 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})
191 or C{None}.
192 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,
193 ignored if C{B{LatLon} is None}.
195 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance
196 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is
197 None}. For abutting circles, both points are the same instance,
198 aka the I{radical center}.
200 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting
201 circles or no convergence for the B{C{tol}}.
203 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}
204 or invalid B{C{equidistant}}.
206 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
208 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
209 calculating-intersection-of-two-circles>}, U{Karney's paper
210 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
211 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
212 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
213 intersections.
214 '''
215 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,
216 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)
219def isclockwise(points, datum=_WGS84, wrap=True):
220 '''Determine the direction of a path or polygon.
222 @arg points: The path or polygon points (C{LatLon}[]).
223 @kwarg datum: Optional datum (L{Datum}).
224 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
226 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.
228 @raise PointsError: Insufficient number of B{C{points}}.
230 @raise TypeError: Some B{C{points}} are not C{LatLon}.
232 @raise ValueError: The B{C{points}} enclose a pole or zero area.
234 @see: L{pygeodesy.isclockwise}.
235 '''
236 a = _polygon(datum.ellipsoid.geodesicx, points, True, False, wrap)
237 if a < 0:
238 return True
239 elif a > 0:
240 return False
241 raise _areaError(points)
244def nearestOn(point, point1, point2, within=True, height=None, wrap=False,
245 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):
246 '''Iteratively locate the closest point on the geodesic between
247 two other (ellispoidal) points.
249 @arg point: Reference point (C{LatLon}).
250 @arg point1: Start point of the geodesic (C{LatLon}).
251 @arg point2: End point of the geodesic (C{LatLon}).
252 @kwarg within: If C{True} return the closest point I{between}
253 B{C{point1}} and B{C{point2}}, otherwise the
254 closest point elsewhere on the geodesic (C{bool}).
255 @kwarg height: Optional height for the closest point (C{meter},
256 conventionally) or C{None} or C{False} for the
257 interpolated height. If C{False}, the closest
258 takes the heights of the points into account.
259 @kwarg wrap: Wrap and unroll longitudes (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
290 L{BooleanGH}).
291 @kwarg closed: Optionally, close the polygon (C{bool}).
292 @kwarg datum: Optional datum (L{Datum}).
293 @kwarg wrap: Wrap and unroll longitudes (C{bool}).
295 @return: Perimeter (C{meter}, same units as the B{C{datum}}'s
296 ellipsoid axes).
298 @raise PointsError: Insufficient number of B{C{points}}.
300 @raise TypeError: Some B{C{points}} are not L{LatLon}.
302 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled
303 longitudes not supported or C{B{closed}=False}
304 with C{B{points}} a composite.
306 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalGeodSolve.perimeterOf},
307 L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf} and
308 L{sphericalTrigonometry.perimeterOf}.
309 '''
310 return _polygon(datum.ellipsoid.geodesicx, points, closed, True, wrap)
313__all__ += _ALL_OTHER(Cartesian, LatLon, # classes
314 areaOf, # functions
315 intersection3, intersections2, isclockwise, ispolar,
316 nearestOn, perimeterOf)
318# **) MIT License
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320# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
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