Coverage for pygeodesy/ellipsoidalExact.py: 100%

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1 

2# -*- coding: utf-8 -*- 

3 

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

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 classes 

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

10''' 

11 

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

13from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \ 

14 _nearestOn, _WGS84 

15from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \ 

16 _intersection3, _intersections2, \ 

17 _TOL_M, intersecant2 

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.ellipsoidalExact 

27__version__ = '24.11.06' 

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} class 

40 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 

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

55 compute geodesic distances, bearings (azimuths), etc. 

56 ''' 

57 

58 @Property_RO 

59 def Equidistant(self): 

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

61 ''' 

62 return _MODS.azimuthal.EquidistantExact 

63 

64 @Property_RO 

65 def geodesicx(self): 

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

67 ''' 

68 return self.datum.ellipsoid.geodesicx 

69 

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

71 

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

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

74 

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

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

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

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

79 

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

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

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

83 

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

85 B{C{Cartesian_datum_kwds}}. 

86 ''' 

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

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

89 

90 

91def areaOf(points, datum=_WGS84, wrap=True): 

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

93 

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

95 L{BooleanGH}). 

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

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

98 B{C{points}} (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 

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

122 equidistant=None, tol=_TOL_M, **LatLon_and_kwds): 

123 '''I{Iteratively} compute the intersection point of two geodesic lines, each 

124 given as two points or as an start point and a bearing from North. 

125 

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

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

128 at B{C{start1}} (compass C{degrees360}). 

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

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

131 at B{C{start2}} (compass C{degrees360}). 

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

133 or C{None} for the mean height. 

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

135 both B{C{end*}} points (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_and_kwds: Optional class C{B{LatLon}=}L{LatLon} to return the 

142 intersection points and optionally, additional B{C{LatLon}} 

143 keyword arguments, ignored if C{B{LatLon}=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 non-intersecting 

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

151 

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

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

154 

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

156 computed as the C{destination} along that bearing at about 1.5 times the 

157 distance from the start point to an initial gu-/estimate of the intersection 

158 point (and between 1/8 and 3/8 of the authalic earth perimeter). 

159 

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

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

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

163 BOUNDARIES} for more details about the iteration algorithm. 

164 ''' 

165 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon) 

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

167 equidistant=equidistant, tol=tol, **kwds) 

168 

169 

170def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True 

171 equidistant=None, tol=_TOL_M, **LatLon_and_kwds): 

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

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

174 

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

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

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

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

179 B{C{radius1}}). 

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

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

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

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

184 (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_and_kwds: Optional class C{B{LatLon}=}L{LatLon} to return the 

191 intersection points and optionally, additional B{C{LatLon}} 

192 keyword arguments, ignored if C{B{LatLon}=None}. 

193 

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

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

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

197 aka the I{radical center}. 

198 

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

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

201 

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

203 or invalid B{C{equidistant}}. 

204 

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

206 

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

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

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

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

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

212 intersections. 

213 ''' 

214 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon) 

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

216 equidistant=equidistant, tol=tol, **kwds) 

217 

218 

219def 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: If C{True}, wrap or I{normalize} and unroll the 

225 B{C{points}} (C{bool}). 

226 

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

228 

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

230 

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

232 

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

234 

235 @see: L{pygeodesy.isclockwise}. 

236 ''' 

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

238 if a < 0: 

239 return True 

240 elif a > 0: 

241 return False 

242 raise _areaError(points) 

243 

244 

245def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

246 equidistant=None, tol=_TOL_M, **LatLon_and_kwds): 

247 '''I{Iteratively} locate the closest point on the geodesic (line) 

248 between two other (ellipsoidal) points. 

249 

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

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

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

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

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

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

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

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

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

259 takes the heights of the points into account. 

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

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

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

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

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

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

266 @kwarg LatLon_and_kwds: Optional class C{B{LatLon}=}L{LatLon} to return the 

267 closest point and optionally, additional B{C{LatLon}} keyword 

268 arguments, ignored if C{B{LatLon}=None}. 

269 

270 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon} is None}, 

271 a L{LatLon4Tuple}C{(lat, lon, height, datum)}. 

272 

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

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

275 

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

277 

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

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

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

281 BOUNDARIES} for more details about the iteration algorithm. 

282 ''' 

283 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon) 

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

285 equidistant=equidistant, tol=tol, **kwds) 

286 

287 

288def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 

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

290 

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

292 L{BooleanGH}). 

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

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

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

296 B{C{points}} (C{bool}). 

297 

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

299 ellipsoid axes). 

300 

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

302 

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

304 

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

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

307 with C{B{points}} a composite. 

308 

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

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

311 L{sphericalTrigonometry.perimeterOf}. 

312 ''' 

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

314 

315 

316__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

317 areaOf, intersecant2, # from .ellipsoidalBase 

318 intersection3, intersections2, isclockwise, ispolar, 

319 nearestOn, perimeterOf) 

320 

321# **) MIT License 

322# 

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

324# 

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

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

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

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

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

331# 

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

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

334# 

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

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

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

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