1

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

3

4 u'''Exact ellipsoidal geodesy, intended I{for testing purposes only}.

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} based on module

9 L{geodsolve}, a wrapper invoking I{Karney}'s U{GeodSolve

10<https://GeographicLib.SourceForge.io/C++/doc/GeodSolve.1.html>} utility.

11'''

12

13# from pygeodesy.datums import _WGS84 # from .ellipsoidalBase

14 from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \

15 _nearestOn, _WGS84

16 from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, _TOL_M, \

17 _intersection3, _intersections2

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

19 from pygeodesy.karney import fabs, _polygon, Property_RO, _xkwds

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

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

22# from pygeodesy.props import Property_RO # from .karney

23

24# from math import fabs # from .karney

25

26__all__ = _ALL_LAZY.ellipsoidalGeodSolve

27__version__ = '24.08.13'

28

29

30 class Cartesian(CartesianEllipsoidalBase):

31 '''Extended to convert exact L{Cartesian} to exact L{LatLon} points.

32 '''

33

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

35 '''Convert this cartesian point to an exact geodetic point.

36

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}

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

41

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

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

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

45

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)

50

51

52 class LatLon(LatLonEllipsoidalBaseDI):

53 '''An ellipsoidal L{LatLon} like L{ellipsoidalKarney.LatLon} but using (exact)

54 geodesic I{wrapper} L{GeodesicSolve} to compute the geodesic distance,

55 initial and final bearing (azimuths) between two given points or the

56 destination point given a start point and an (initial) bearing.

57 '''

58

59 @Property_RO

60 def Equidistant(self):

61 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantGeodSolve}).

62 '''

63 return _MODS.azimuthal.EquidistantGeodSolve

64

65 @Property_RO

66 def geodesicx(self):

67 '''Get this C{LatLon}'s (exact) geodesic (L{GeodesicSolve}).

68 '''

69 return self.datum.ellipsoid.geodsolve

70

71 geodesic = geodesicx # for C{._Direct} and C{._Inverse}

72

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

74 '''Convert this point to exact cartesian (ECEF) coordinates.

75

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

77 arguments, ignored if C{B{Cartesian} is None}. Use C{B{Cartesian}=Class}

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

79

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

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

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

83

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

85 '''

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

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

88

89

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

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

92

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

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

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

96

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

98

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

100

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

102

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

104

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

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

107 '''

108 return fabs(_polygon(datum.ellipsoid.geodsolve, points, True, False, wrap))

109

110

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

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

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

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

115 (initial) bearing from North.

116

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

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

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

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

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

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

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

124 or C{None} for the mean height.

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

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

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

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

129 C{B{start1}.Equidistant}.

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

131 (C{meter}, conventionally).

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

133 or C{None}.

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

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

136

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

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

139 lon, height, datum)}.

140

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

142 non-intersecting lines or no convergence

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

144

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

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

147

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

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

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

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

152 earth perimeter).

153

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

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

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

157 BOUNDARIES} for more details about the iteration algorithm.

158 '''

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

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

161

162

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

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

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

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

167

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

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

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

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

172 B{C{radius1}}).

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

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

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

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

177 (C{bool}).

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

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

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

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

182 and B{C{radius2}}).

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

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

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

191 aka the I{radical center}.

192

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

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

195

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

197 or invalid B{C{equidistant}}.

198

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

200

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

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

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

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

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

206 intersections.

207 '''

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

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

210

211

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

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

214

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

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

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

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

219

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

221

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

223

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

225

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

227 area.

228

229 @see: L{pygeodesy.isclockwise}.

230 '''

231 a = _polygon(datum.ellipsoid.geodsolve, points, True, False, wrap)

232 if a < 0:

233 return True

234 elif a > 0:

235 return False

236 raise _areaError(points)

237

238

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

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

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

242 two other (ellipsoidal) points.

243

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

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

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

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

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

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

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

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

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

253 takes the heights of the points into account.

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

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

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

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

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

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

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

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

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

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

264

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

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

267

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

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

270

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

272

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

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

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

276 BOUNDARIES} for more details about the iteration algorithm.

277 '''

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

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

280

281

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

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

284

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

286 L{BooleanGH}).

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

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

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

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

291

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

293 ellipsoid axes).

294

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

296

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

298

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

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

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

302

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

304 L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf}

305 and L{sphericalTrigonometry.perimeterOf}.

306 '''

307 return _polygon(datum.ellipsoid.geodsolve, points, closed, True, wrap)

308

309

310__all__ += _ALL_OTHER(Cartesian, LatLon, # classes

311 areaOf, # functions

312 intersection3, intersections2, isclockwise, ispolar,

313 nearestOn, perimeterOf)

314

315# **) MIT License

316#

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

318#

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

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

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