1

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

3

4 u'''Exact ellipsoidal geodesy using I{Karney}'s Exact Geodesic.

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 classes

9 L{GeodesicExact}, L{GeodesicAreaExact} and L{GeodesicLineExact}.

10'''

11

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

13 from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \

14 _nearestOn, _WGS84

15 from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \

16 _intersection3, _intersections2, \

17 _TOL_M, intersecant2

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.ellipsoidalExact

27__version__ = '23.11.08'

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} class

40 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

54 exact geodesic classes L{GeodesicExact} and L{GeodesicLineExact} to

55 compute the geodesic distance, initial and final bearing (azimuths)

56 between two given points or the destination point given a start point

57 and an (initial) bearing.

58 '''

59

60 @Property_RO

61 def Equidistant(self):

62 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantExact}).

63 '''

64 return _MODS.azimuthal.EquidistantExact

65

66 @Property_RO

67 def geodesicx(self):

68 '''Get this C{LatLon}'s exact geodesic (L{GeodesicExact}).

69 '''

70 return self.datum.ellipsoid.geodesicx

71

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

73

74 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, ...

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

76

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

78 other keyword arguments, ignored if C{B{Cartesian}

79 is None}. Use C{B{Cartesian}=...} to override this

80 L{Cartesian} class or set C{B{Cartesian}=None}.

81

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

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

84 lon, height, C, M, datum)} with C{C} and C{M} if 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} I{squared}, same units as the B{C{datum}}'s

103 ellipsoid axes).

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{ellipsoidalGeodSolve.areaOf},

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

114 L{sphericalTrigonometry.areaOf}.

115

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

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

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

119 '''

120 return fabs(_polygon(datum.ellipsoid.geodesicx, points, True, False, wrap))

121

122

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

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

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

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

127 initial bearing from North.

128

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

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

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

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

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

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

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

136 or C{None} for the mean height.

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

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

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

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

141 C{B{start1}.Equidistant}.

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

143 (C{meter}, conventionally).

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

145 or C{None}.

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

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

148

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

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

151 lon, height, datum)}.

152

153 @raise IntersectionError: Skew, colinear, parallel or otherwise non-intersecting

154 lines or no convergence for the given B{C{tol}}.

155

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

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

158

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

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

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

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

163 earth perimeter).

164

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

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

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

168 BOUNDARIES} for more details about the iteration algorithm.

169 '''

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

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

172

173

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

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

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

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

178

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

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

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

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

183 B{C{radius1}}).

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

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

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

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

188 (C{bool}).

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

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

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

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

193 and B{C{radius2}}).

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

195 or C{None}.

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

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

198

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

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

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

202 aka the I{radical center}.

203

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

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

206

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

208 or invalid B{C{equidistant}}.

209

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

211

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

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

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

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

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

217 intersections.

218 '''

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

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

221

222

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

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

225

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

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

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

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

230

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

232

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

234

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

236

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

238

239 @see: L{pygeodesy.isclockwise}.

240 '''

241 a = _polygon(datum.ellipsoid.geodesicx, points, True, False, wrap)

242 if a < 0:

243 return True

244 elif a > 0:

245 return False

246 raise _areaError(points)

247

248

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

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

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

252 two other (ellispoidal) points.

253

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

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

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

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

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

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

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

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

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

263 takes the heights of the points into account.

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

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

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

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

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

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

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

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

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

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

274

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

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

277

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

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

280

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

282

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

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

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

286 BOUNDARIES} for more details about the iteration algorithm.

287 '''

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

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

290

291

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

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

294

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

296 L{BooleanGH}).

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

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

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

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

301

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

303 ellipsoid axes).

304

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

306

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

308

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

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

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

312

313 @see: Functions L{pygeodesy.perimeterOf}, L{ellipsoidalGeodSolve.perimeterOf},

314 L{ellipsoidalKarney.perimeterOf}, L{sphericalNvector.perimeterOf} and

315 L{sphericalTrigonometry.perimeterOf}.

316 '''

317 return _polygon(datum.ellipsoid.geodesicx, points, closed, True, wrap)

318

319

320__all__ += _ALL_OTHER(Cartesian, LatLon, # classes

321 areaOf, intersecant2, # from .ellipsoidalBase

322 intersection3, intersections2, isclockwise, ispolar,

323 nearestOn, perimeterOf)

324

325# **) MIT License

326#

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

328#

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

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

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

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

335#

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

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