1

2# -*- coding: utf-8 -*-

3

4 u'''Ellipsoidal, I{Karney}-based geodesy.

5

6 Ellipsoidal geodetic (lat-/longitude) L{LatLon} and geocentric (ECEF) L{Cartesian}

7 classes and functions L{areaOf}, L{intersection3}, L{intersections2}, L{isclockwise},

8 L{nearestOn} and L{perimeterOf}, requiring I{Charles F.F. Karney}'s U{geographiclib

9<https://PyPI.org/project/geographiclib>} Python package to be installed.

10

11 A usage example of C{ellipsoidalKarney}:

12

13 >>> from pygeodesy.ellipsoidalKarney import LatLon

14 >>> Newport_RI = LatLon(41.49008, -71.312796)

15 >>> Cleveland_OH = LatLon(41.499498, -81.695391)

16 >>> Newport_RI.distanceTo(Cleveland_OH)

17 866,455.4329098687 # meter

18

19 You can change the ellipsoid model used by the I{Karney} formulae

20 as follows:

21

22 >>> from pygeodesy import Datums

23 >>> from pygeodesy.ellipsoidalKarney import LatLon

24 >>> p = LatLon(0, 0, datum=Datums.OSGB36)

25

26 or by converting to anothor datum:

27

28 >>> p = p.toDatum(Datums.OSGB36)

29'''

30

31 from pygeodesy.datums import _WGS84

32 from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, _nearestOn

33 from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \

34 _intersection3, _intersections2, \

35 _TOL_M, intersecant2

36# from pygeodesy.errors import _xkwds # from .karney

37 from pygeodesy.karney import _polygon, fabs, _xkwds

38 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _ALL_OTHER

39 from pygeodesy.points import _areaError, ispolar # PYCHOK exported

40 from pygeodesy.props import deprecated_method, Property_RO

41

42# from math import fabs # from .karney

43

44__all__ = _ALL_LAZY.ellipsoidalKarney

45__version__ = '24.08.13'

46

47

48 class Cartesian(CartesianEllipsoidalBase):

49 '''Extended to convert C{Karney}-based L{Cartesian} to C{Karney}-based L{LatLon} points.

50 '''

51

52 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None

53 '''Convert this cartesian point to a C{Karney}-based geodetic point.

54

55 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword arguments

56 as C{datum}. Use C{B{LatLon}=..., B{datum}=...} to override

57 this L{LatLon} class or specify C{B{LatLon}=None}.

58

59 @return: The geodetic point (L{LatLon}) or if C{B{LatLon} is None}, an

60 L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C}

61 and C{M} if available.

62

63 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument.

64 '''

65 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum)

66 return CartesianEllipsoidalBase.toLatLon(self, **kwds)

67

68

69 class LatLon(LatLonEllipsoidalBaseDI):

70 '''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon} but using

71 I{Karney}'s Python U{geographiclib<https://PyPI.org/project/geographiclib>}

72 to compute geodesic distances, bearings (azimuths), etc.

73 '''

74

75 @deprecated_method

76 def bearingTo(self, other, wrap=False): # PYCHOK no cover

77 '''DEPRECATED, use method L{initialBearingTo}.

78 '''

79 return self.initialBearingTo(other, wrap=wrap)

80

81 @Property_RO

82 def Equidistant(self):

83 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney}).

84 '''

85 return _MODS.azimuthal.EquidistantKarney

86

87 @Property_RO

88 def geodesic(self):

89 '''Get this C{LatLon}'s I{wrapped} U{geodesic.Geodesic

90 <https://GeographicLib.SourceForge.io/Python/doc/code.html>}, provided

91 I{Karney}'s U{geographiclib<https://PyPI.org/project/geographiclib>}

92 package is installed.

93 '''

94 return self.datum.ellipsoid.geodesic

95

96 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None

97 '''Convert this point to C{Karney}-based cartesian (ECEF) coordinates.

98

99 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} and other keyword

100 arguments, ignored if C{B{Cartesian} is None}. Use C{B{Cartesian}=...} to

101 override this L{Cartesian} class or set C{B{Cartesian}=None}.

102

103 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if C{B{Cartesian} is

104 None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with

105 C{C} and C{M} if available.

106

107 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other B{C{Cartesian_datum_kwds}}.

108 '''

109 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum)

110 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds)

111

112

113 def areaOf(points, datum=_WGS84, wrap=True):

114 '''Compute the area of an (ellipsoidal) polygon or composite using I{Karney}'s

115 U{geographiclib<https://PyPI.org/project/geographiclib>} package.

116

117 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or L{BooleanGH}).

118 @kwarg datum: Optional datum (L{Datum}).

119 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{points}} (C{bool}).

120

121 @return: Area (C{meter}, same as units of the B{C{datum}}'s ellipsoid axes, I{squared}).

122

123 @raise ImportError: Package U{geographiclib<https://PyPI.org/project/geographiclib>}

124 not installed or not found.

125

126 @raise PointsError: Insufficient number of B{C{points}}.

127

128 @raise TypeError: Some B{C{points}} are not L{LatLon}.

129

130 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled longitudes not supported.

131

132 @see: Functions L{pygeodesy.areaOf}, L{ellipsoidalExact.areaOf}, L{ellipsoidalGeodSolve.areaOf},

133 L{sphericalNvector.areaOf} and L{sphericalTrigonometry.areaOf}.

134

135 @note: The U{area of a polygon enclosing a pole<https://GeographicLib.SourceForge.io/

136 C++/doc/classGeographicLib_1_1GeodesicExact.html#a3d7a9155e838a09a48dc14d0c3fac525>}

137 can be found by adding half the datum's ellipsoid surface area to the polygon's area.

138 '''

139 return fabs(_polygon(datum.ellipsoid.geodesic, points, True, False, wrap))

140

141

142 def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True

143 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):

144 '''I{Iteratively} compute the intersection point of two lines, each defined

145 by two (ellipsoidal) points or by an (ellipsoidal) start point and an

146 (initial) bearing from North.

147

148 @arg start1: Start point of the first line (L{LatLon}).

149 @arg end1: End point of the first line (L{LatLon}) or the initial bearing

150 at the first point (compass C{degrees360}).

151 @arg start2: Start point of the second line (L{LatLon}).

152 @arg end2: End point of the second line (L{LatLon}) or the initial bearing

153 at the second point (compass C{degrees360}).

154 @kwarg height: Optional height at the intersection (C{meter}, conventionally)

155 or C{None} for the mean height.

156 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{start2}}

157 and B{C{end*}} points (C{bool}).

158 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function

159 L{pygeodesy.equidistant}) or C{None} for the preferred

160 C{B{start1}.Equidistant}.

161 @kwarg tol: Tolerance for convergence and for skew line distance and length

162 (C{meter}, conventionally).

163 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})

164 or C{None}.

165 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,

166 ignored if C{B{LatLon} is None}.

167

168 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point}

169 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat,

170 lon, height, datum)}.

171

172 @raise IntersectionError: Skew, colinear, parallel or otherwise

173 non-intersecting lines or no convergence

174 for the given B{C{tol}}.

175

176 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}},

177 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}.

178

179 @note: For each line specified with an initial bearing, a pseudo-end point

180 is computed as the C{destination} along that bearing at about 1.5

181 times the distance from the start point to an initial gu-/estimate

182 of the intersection point (and between 1/8 and 3/8 of the authalic

183 earth perimeter).

184

185 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/

186 calculating-intersection-of-two-circles>} and U{Karney's paper

187 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME

188 BOUNDARIES} for more details about the iteration algorithm.

189 '''

190 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap,

191 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)

192

193

194 def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True

195 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):

196 '''I{Iteratively} compute the intersection points of two circles, each defined

197 by an (ellipsoidal) center point and a radius.

198

199 @arg center1: Center of the first circle (L{LatLon}).

200 @arg radius1: Radius of the first circle (C{meter}, conventionally).

201 @arg center2: Center of the second circle (L{LatLon}).

202 @arg radius2: Radius of the second circle (C{meter}, same units as

203 B{C{radius1}}).

204 @kwarg height: Optional height for the intersection points (C{meter},

205 conventionally) or C{None} for the I{"radical height"}

206 at the I{radical line} between both centers.

207 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{center2}}

208 (C{bool}).

209 @kwarg equidistant: An azimuthal equidistant projection (I{class} or

210 function L{pygeodesy.equidistant}) or C{None} for

211 the preferred C{B{center1}.Equidistant}.

212 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}}

213 and B{C{radius2}}).

214 @kwarg LatLon: Optional class to return the intersection points (L{LatLon})

215 or C{None}.

216 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments,

217 ignored if C{B{LatLon} is None}.

218

219 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance

220 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is

221 None}. For abutting circles, both points are the same instance,

222 aka the I{radical center}.

223

224 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting

225 circles or no convergence for the B{C{tol}}.

226

227 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}}

228 or invalid B{C{equidistant}}.

229

230 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.

231

232 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/

233 calculating-intersection-of-two-circles>}, U{Karney's paper

234 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},

235 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and

236 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}

237 intersections.

238 '''

239 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap,

240 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)

241

242

243 def isclockwise(points, datum=_WGS84, wrap=True):

244 '''Determine the direction of a path or polygon using I{Karney}'s

245 U{geographiclib<https://PyPI.org/project/geographiclib>} package.

246

247 @arg points: The path or polygon points (C{LatLon}[]).

248 @kwarg datum: Optional datum (L{Datum}).

249 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

250 B{C{points}} (C{bool}).

251

252 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise.

253

254 @raise ImportError: Package U{geographiclib

255 <https://PyPI.org/project/geographiclib>}

256 not installed or not found.

257

258 @raise PointsError: Insufficient number of B{C{points}}.

259

260 @raise TypeError: Some B{C{points}} are not C{LatLon}.

261

262 @raise ValueError: The B{C{points}} enclose a pole or zero area.

263

264 @see: L{pygeodesy.isclockwise}.

265 '''

266 a = _polygon(datum.ellipsoid.geodesic, points, True, False, wrap)

267 if a < 0:

268 return True

269 elif a > 0:

270 return False

271 raise _areaError(points)

272

273

274 def nearestOn(point, point1, point2, within=True, height=None, wrap=False,

275 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds):

276 '''I{Iteratively} locate the closest point on the geodesic between

277 two other (ellipsoidal) points.

278

279 @arg point: Reference point (C{LatLon}).

280 @arg point1: Start point of the geodesic (C{LatLon}).

281 @arg point2: End point of the geodesic (C{LatLon}).

282 @kwarg within: If C{True}, return the closest point I{between}

283 B{C{point1}} and B{C{point2}}, otherwise the

284 closest point elsewhere on the geodesic (C{bool}).

285 @kwarg height: Optional height for the closest point (C{meter},

286 conventionally) or C{None} or C{False} for the

287 interpolated height. If C{False}, the closest

288 takes the heights of the points into account.

289 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both

290 B{C{point1}} and B{C{point2}} (C{bool}).

291 @kwarg equidistant: An azimuthal equidistant projection (I{class}

292 or function L{pygeodesy.equidistant}) or C{None}

293 for the preferred C{B{point}.Equidistant}.

294 @kwarg tol: Convergence tolerance (C{meter}).

295 @kwarg LatLon: Optional class to return the closest point

296 (L{LatLon}) or C{None}.

297 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword

298 arguments, ignored if C{B{LatLon} is None}.

299

300 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon}

301 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}.

302

303 @raise ImportError: Package U{geographiclib

304 <https://PyPI.org/project/geographiclib>}

305 not installed or not found.

306

307 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}}

308 or B{C{point2}} or invalid B{C{equidistant}}.

309

310 @raise ValueError: No convergence for the B{C{tol}}.

311

312 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/

313 calculating-intersection-of-two-circles>} and U{Karney's paper

314 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME

315 BOUNDARIES} for more details about the iteration algorithm.

316 '''

317 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap,

318 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds)

319

320

321 def perimeterOf(points, closed=False, datum=_WGS84, wrap=True):

322 '''Compute the perimeter of an (ellipsoidal) polygon or composite using I{Karney}'s

323 U{geographiclib<https://PyPI.org/project/geographiclib>} package.

324

325 @arg points: The polygon points (L{LatLon}[], L{BooleanFHP} or

326 L{BooleanGH}).

327 @kwarg closed: Optionally, close the polygon (C{bool}).

328 @kwarg datum: Optional datum (L{Datum}).

329 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the

330 B{C{points}} (C{bool}).

331

332 @return: Perimeter (C{meter}, same as units of the B{C{datum}}'s

333 ellipsoid axes).

334

335 @raise ImportError: Package U{geographiclib

336 <https://PyPI.org/project/geographiclib>}

337 not installed or not found.

338

339 @raise PointsError: Insufficient number of B{C{points}}.

340

341 @raise TypeError: Some B{C{points}} are not L{LatLon} or C{B{closed}=False}

342 with B{C{points}} a composite.

343

344 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, unrolled

345 longitudes not supported or C{B{closed}=False}

346 with C{B{points}} a composite.

347

348 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalExact.perimeterOf},

349 L{ellipsoidalGeodSolve.perimeterOf}, L{sphericalNvector.perimeterOf}

350 and L{sphericalTrigonometry.perimeterOf}.

351 '''

352 return _polygon(datum.ellipsoid.geodesic, points, closed, True, wrap)

353

354

355__all__ += _ALL_OTHER(Cartesian, LatLon, # classes

356 areaOf, intersecant2, # from .ellipsoidalBase

357 intersection3, intersections2, isclockwise, ispolar,

358 nearestOn, perimeterOf)

359

360# **) MIT License

361#

362# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.

363#

364# Permission is hereby granted, free of charge, to any person obtaining a

365# copy of this software and associated documentation files (the "Software"),

366# to deal in the Software without restriction, including without limitation

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369# Software is furnished to do so, subject to the following conditions:

370#

371# The above copyright notice and this permission notice shall be included

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373#

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