1

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

3

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

5

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

7(ECEF) L{Cartesian} classes and functions L{areaOf}, L{intersections2},

8 L{isclockwise}, L{nearestOn} and L{perimeterOf}, all requiring I{Charles

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

10 Python package to be installed.

11

12 Here's an example usage of C{ellipsoidalKarney}:

13

14 >>> from pygeodesy.ellipsoidalKarney import LatLon

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

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

17 >>> Newport_RI.distanceTo(Cleveland_OH)

18 866,455.4329098687 # meter

19

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

21 as follows:

22

23 >>> from pygeodesy import Datums

24 >>> from pygeodesy.ellipsoidalKarney import LatLon

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

26

27 or by converting to anothor datum:

28

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

30'''

31

32 from pygeodesy.datums import _WGS84

33 from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \

34 intersecant2, _nearestOn

35 from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, _TOL_M, \

36 _intersection3, _intersections2

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

38 from pygeodesy.karney import fabs, _polygon, _xkwds

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

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

41 from pygeodesy.props import deprecated_method, Property_RO

42

43# from math import fabs # from .karney

44

45__all__ = _ALL_LAZY.ellipsoidalKarney

46__version__ = '23.10.08'

47

48

49 class Cartesian(CartesianEllipsoidalBase):

50 '''Extended to convert C{Karney}-based L{Cartesian} to

51 C{Karney}-based L{LatLon} points.

52 '''

53

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

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

56

57 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword

58 arguments as C{datum}. Use C{B{LatLon}=...,

59 B{datum}=...} to override this L{LatLon}

60 class or specify C{B{LatLon}=None}.

61

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

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

64 with C{C} and C{M} if available.

65

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

67 '''

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

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

70

71

72 class LatLon(LatLonEllipsoidalBaseDI):

73 '''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon}

74 but using I{Charles F. F. Karney}'s Python U{geographiclib

75 <https://PyPI.org/project/geographiclib>} to compute the geodesic

76 distance, initial and final bearing (azimuths) between two given

77 points or the destination point given a start point and an (initial)

78 bearing.

79

80 @note: This L{LatLon} require the U{geographiclib

81 <https://PyPI.org/project/geographiclib>} package.

82 '''

83

84 @deprecated_method

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

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

87 '''

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

89

90 @Property_RO

91 def Equidistant(self):

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

93 '''

94 return _MODS.azimuthal.EquidistantKarney

95

96 @Property_RO

97 def geodesic(self):

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

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

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

101 package is installed.

102 '''

103 return self.datum.ellipsoid.geodesic

104

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

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

107

108 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}}

109 and other keyword arguments, ignored if C{B{Cartesian} is None}.

110 Use C{B{Cartesian}=...} to override this L{Cartesian} class

111 or set C{B{Cartesian} is None}.

112

113 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if

114 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z,

115 lat, lon, height, C, M, datum)} with C{C} and C{M} if

116 available.

117

118 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other

119 B{C{Cartesian_datum_kwds}}.

120 '''

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

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

123

124

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

126 '''Compute the area of an (ellipsoidal) polygon or composite.

127

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

129 or L{BooleanGH}).

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

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

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

133

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

135 ellipsoid axes, I{squared}).

136

137 @raise ImportError: Package U{geographiclib

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

139 not installed or not found.

140

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

142

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

144

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

146 longitudes not supported.

147

148 @note: This function requires the U{geographiclib

149 <https://PyPI.org/project/geographiclib>} package.

150

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

152 L{ellipsoidalGeodSolve.areaOf}, L{sphericalNvector.areaOf}

153 and L{sphericalTrigonometry.areaOf}.

154

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

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

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

158 '''

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

160

161

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

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

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

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

166 (initial) bearing from North.

167

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

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

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

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

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

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

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

175 or C{None} for the mean height.

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

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

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

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

180 C{B{start1}.Equidistant}.

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

182 (C{meter}, conventionally).

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

184 or C{None}.

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

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

187

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

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

190 lon, height, datum)}.

191

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

193 non-intersecting lines or no convergence

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

195

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

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

198

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

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

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

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

203 earth perimeter).

204

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

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

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

208 BOUNDARIES} for more details about the iteration algorithm.

209 '''

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

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

212

213

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

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

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

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

218

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

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

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

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

223 B{C{radius1}}).

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

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

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

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

228 (C{bool}).

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

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

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

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

233 and B{C{radius2}}).

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

235 or C{None}.

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

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

238

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

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

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

242 aka the I{radical center}.

243

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

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

246

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

248 or invalid B{C{equidistant}}.

249

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

251

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

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

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

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

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

257 intersections.

258 '''

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

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

261

262

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

264 '''Determine the direction of a path or polygon.

265

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

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

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

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

270

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

272

273 @raise ImportError: Package U{geographiclib

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

275 not installed or not found.

276

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

278

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

280

281 @raise ValueError: The B{C{points}} enclose a pole or zero

282 area.

283

284 @note: This function requires the U{geographiclib

285 <https://PyPI.org/project/geographiclib>} package.

286

287 @see: L{pygeodesy.isclockwise}.

288 '''

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

290 if a < 0:

291 return True

292 elif a > 0:

293 return False

294 raise _areaError(points)

295

296

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

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

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

300 two other (ellipsoidal) points.

301

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

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

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

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

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

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

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

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

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

311 takes the heights of the points into account.

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

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

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

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

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

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

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

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

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

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

322

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

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

325

326 @raise ImportError: Package U{geographiclib

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

328 not installed or not found.

329

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

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

332

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

334

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

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

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

338 BOUNDARIES} for more details about the iteration algorithm.

339 '''

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

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

342

343

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

345 '''Compute the perimeter of an (ellipsoidal) polygon or composite.

346

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

348 L{BooleanGH}).

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

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

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

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

353

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

355 ellipsoid axes).

356

357 @raise ImportError: Package U{geographiclib

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

359 not installed or not found.

360

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

362

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

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

365

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

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

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

369

370 @note: This function requires the U{geographiclib

371 <https://PyPI.org/project/geographiclib>} package.

372

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

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

375 and L{sphericalTrigonometry.perimeterOf}.

376 '''

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

378

379

380__all__ += _ALL_OTHER(Cartesian, LatLon, # classes

381 areaOf, intersecant2, # from .ellipsoidalBase

382 intersection3, intersections2, isclockwise, ispolar,

383 nearestOn, perimeterOf)

384

385# **) MIT License

386#

387# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.

388#

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

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

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

392# the rights to use, copy, modify, merge, publish, distribute, sublicense,

393# and/or sell copies of the Software, and to permit persons to whom the

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

395#

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

397# in all copies or substantial portions of the Software.

398#

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