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__ = '23.05.12'

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 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.

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}}

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

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

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

80

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

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

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

84 available.

85

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

87 B{C{Cartesian_datum_kwds}}.

88 '''

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

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

91

92

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

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

95

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

97 L{BooleanGH}).

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

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

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

101

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

103 ellipsoid axes, I{squared}).

104

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

106

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

108

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

110 longitudes not supported.

111

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

113 L{ellipsoidalKarney.areaOf}, L{sphericalNvector.areaOf}

114 and L{sphericalTrigonometry.areaOf}.

115 '''

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

117

118

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

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

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

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

123 (initial) bearing from North.

124

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

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

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

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

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

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

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

132 or C{None} for the mean height.

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

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

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

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

137 C{B{start1}.Equidistant}.

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

139 (C{meter}, conventionally).

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

141 or C{None}.

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

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

144

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

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

147 lon, height, datum)}.

148

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

150 non-intersecting lines or no convergence

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

152

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}}.

155

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).

161

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)

169

170

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

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

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

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

175

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

185 (C{bool}).

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

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

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

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

190 and B{C{radius2}}).

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

192 or C{None}.

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

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

195

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

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

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

199 aka the I{radical center}.

200

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

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

203

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

205 or invalid B{C{equidistant}}.

206

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

208

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

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

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

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

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

214 intersections.

215 '''

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

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

218

219

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

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

222

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

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

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

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

227

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

229

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

231

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

233

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

235 area.

236

237 @see: L{pygeodesy.isclockwise}.

238 '''

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

240 if a < 0:

241 return True

242 elif a > 0:

243 return False

244 raise _areaError(points)

245

246

247 def 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 (ellipsoidal) points.

251

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}.

272

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)}.

275

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

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

278

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

280

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)

288

289

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

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

292

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}).

299

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

301 ellipsoid axes).

302

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

304

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

306

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.

310

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

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

313 and L{sphericalTrigonometry.perimeterOf}.

314 '''

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

316

317

318__all__ += _ALL_OTHER(Cartesian, LatLon, # classes

319 areaOf, # functions

320 intersection3, intersections2, isclockwise, ispolar,

321 nearestOn, perimeterOf)

322

323# **) MIT License

324#

325# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.

326#

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

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333#

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

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