Coverage for pygeodesy/ellipsoidalGeodSolve.py: 100%

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1 

2# -*- coding: utf-8 -*- 

3 

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

5 

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

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

8L{isclockwise}, L{nearestOn} and L{perimeterOf} based on module 

9L{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 

14from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \ 

15 _nearestOn, _WGS84 

16from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, _TOL_M, \ 

17 _intersection3, _intersections2 

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

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

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

21from 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__ = '25.05.28' 

28 

29 

30class 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 

52class 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 

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

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 @kwarg polar: Use C{B{polar}=True} if the polygon encloses a pole (C{bool}), see 

97 function L{ispolar<pygeodesy.points.ispolar>} and U{area of a polygon 

98 enclosing a pole<https://GeographicLib.SourceForge.io/C++/doc/ 

99 classGeographicLib_1_1GeodesicExact.html#a3d7a9155e838a09a48dc14d0c3fac525>}. 

100 

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

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 longitudes not supported. 

108 

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

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

111 ''' 

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

113 

114 

115def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True 

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

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

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

119 (initial) bearing from North. 

120 

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

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

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

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

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

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

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

128 or C{None} for the mean height. 

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

130 and B{C{end*}} points (C{bool}). 

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

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

133 C{B{start1}.Equidistant}. 

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

135 (C{meter}, conventionally). 

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

137 or C{None}. 

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

139 ignored if C{B{LatLon} is None}. 

140 

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

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

143 lon, height, datum)}. 

144 

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

146 non-intersecting lines or no convergence 

147 for the given B{C{tol}}. 

148 

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

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

151 

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

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

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

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

156 earth perimeter). 

157 

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

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

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

161 BOUNDARIES} for more details about the iteration algorithm. 

162 ''' 

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

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

165 

166 

167def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True 

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

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

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

171 

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

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

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

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

176 B{C{radius1}}). 

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

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

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

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

181 (C{bool}). 

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

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

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

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

186 and B{C{radius2}}). 

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

188 or C{None}. 

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

190 ignored if C{B{LatLon} is None}. 

191 

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

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

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

195 aka the I{radical center}. 

196 

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

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

199 

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

201 or invalid B{C{equidistant}}. 

202 

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

204 

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

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

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

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

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

210 intersections. 

211 ''' 

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

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

214 

215 

216def isclockwise(points, datum=_WGS84, wrap=True, polar=False): 

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

218 

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

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

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

222 @kwarg polar: Use C{B{polar}=True} if the C{B{points}} enclose a pole (C{bool}), 

223 see function U{ispolar<pygeodeys.points.ispolar>}. 

224 

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

226 

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

228 

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

230 

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

232 

233 @see: L{pygeodesy.isclockwise}. 

234 ''' 

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

236 if a < 0: 

237 return True 

238 elif a > 0: 

239 return False 

240 raise _areaError(points) 

241 

242 

243def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

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

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

246 two other (ellipsoidal) points. 

247 

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

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

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

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

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

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

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

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

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

257 takes the heights of the points into account. 

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

259 B{C{point1}} and B{C{point2}} (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 

286def 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 L{BooleanGH}). 

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

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

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

293 

294 @return: Perimeter (C{meter}, same as units of the B{C{datum}}'s ellipsoid axes). 

295 

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

297 

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

299 

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

301 supported or C{B{closed}=False} 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, False) 

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# 

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

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

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

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

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

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

325# 

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

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

328# 

329# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

330# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 

331# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL 

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