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, _TOL_M, \

16 _intersection3, _intersections2

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

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

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

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

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

22

23# from math import fabs # from .karney

24

25__all__ = _ALL_LAZY.ellipsoidalExact

26__version__ = '23.04.11'

27

28

29 class Cartesian(CartesianEllipsoidalBase):

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

31 '''

32

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

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

35

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

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

38 B{datum}=...} to override this L{LatLon} class

39 or specify C{B{LatLon}=None}.

40

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

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

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

44

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

46 '''

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

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

49

50

51 class LatLon(LatLonEllipsoidalBaseDI):

52 '''An ellipsoidal L{LatLon} like L{ellipsoidalKarney.LatLon} but using

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

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

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

56 and an (initial) bearing.

57 '''

58

59 @Property_RO

60 def Equidistant(self):

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

62 '''

63 return _MODS.azimuthal.EquidistantExact

64

65 @Property_RO

66 def geodesicx(self):

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

68 '''

69 return self.datum.ellipsoid.geodesicx

70

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

72

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

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

75

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

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

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

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

80

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

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

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

84

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

86 B{C{Cartesian_datum_kwds}}.

87 '''

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

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

90

91

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

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

94

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

96 L{BooleanGH}).

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

98 @kwarg wrap: Wrap and unroll longitudes (C{bool}).

99

100 @return: Area (C{meter} I{squared}, same units as the B{C{datum}}'s

101 ellipsoid axes).

102

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

104

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

106

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

108 longitudes not supported.

109

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

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

112 L{sphericalTrigonometry.areaOf}.

113

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

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

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

117 '''

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

119

120

121 def intersection3(start1, end1, start2, end2, height=None, wrap=True,

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

123 '''Iteratively compute the intersection point of two lines, each defined

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

125 initial bearing from North.

126

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

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

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

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

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

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

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

134 or C{None} for the mean height.

135 @kwarg wrap: Wrap and unroll longitudes (C{bool}).

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

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

138 C{B{start1}.Equidistant}.

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

140 (C{meter}, conventionally).

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

142 or C{None}.

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

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

145

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

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

148 lon, height, datum)}.

149

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

151 lines or no convergence 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=True,

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

173 '''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: Wrap and unroll longitudes (C{bool}).

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

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

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

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

189 and B{C{radius2}}).

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

191 or C{None}.

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

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

194

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

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

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

198 aka the I{radical center}.

199

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

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

202

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

204 or invalid B{C{equidistant}}.

205

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

207

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

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

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

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

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

213 intersections.

214 '''

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

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

217

218

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

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

221

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

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

224 @kwarg wrap: Wrap and unroll longitudes (C{bool}).

225

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

227

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

229

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

231

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

233

234 @see: L{pygeodesy.isclockwise}.

235 '''

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

237 if a < 0:

238 return True

239 elif a > 0:

240 return False

241 raise _areaError(points)

242

243

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

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

246 '''Iteratively locate the closest point on the geodesic between

247 two other (ellispoidal) points.

248

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

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

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

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

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

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

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

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

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

258 takes the heights of the points into account.

259 @kwarg wrap: Wrap and unroll longitudes (C{bool}).

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

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

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

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

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

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

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

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

268

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

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

271

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

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

274

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

276

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

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

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

280 BOUNDARIES} for more details about the iteration algorithm.

281 '''

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

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

284

285

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

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

288

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

290 L{BooleanGH}).

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

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

293 @kwarg wrap: Wrap and unroll longitudes (C{bool}).

294

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

296 ellipsoid axes).

297

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

299

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

301

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

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

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

305

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

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

308 L{sphericalTrigonometry.perimeterOf}.

309 '''

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

311

312

313__all__ += _ALL_OTHER(Cartesian, LatLon, # classes

314 areaOf, # functions

315 intersection3, intersections2, isclockwise, ispolar,

316 nearestOn, perimeterOf)

317

318# **) MIT License

319#

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

321#

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

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