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, _TOL_M, \ 

16 _intersection3, _intersections2 

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

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

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

20from 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__ = '23.05.04' 

27 

28 

29class 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 

51class 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 

92def 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: If C{True}, wrap or I{normalize} and unroll the 

99 B{C{points}} (C{bool}). 

100 

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

102 ellipsoid axes). 

103 

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

105 

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

107 

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

109 longitudes not supported. 

110 

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

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

113 L{sphericalTrigonometry.areaOf}. 

114 

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

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

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

118 ''' 

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

120 

121 

122def intersection3(start1, end1, start2, end2, height=None, wrap=False, # was=True 

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

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

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

126 initial bearing from North. 

127 

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

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

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

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

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

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

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

135 or C{None} for the mean height. 

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

137 and B{C{end*}} points (C{bool}). 

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

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

140 C{B{start1}.Equidistant}. 

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

142 (C{meter}, conventionally). 

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

144 or C{None}. 

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

146 ignored if C{B{LatLon} is None}. 

147 

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

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

150 lon, height, datum)}. 

151 

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

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

154 

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

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

157 

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

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

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

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

162 earth perimeter). 

163 

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

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

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

167 BOUNDARIES} for more details about the iteration algorithm. 

168 ''' 

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

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

171 

172 

173def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True 

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

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

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

177 

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

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

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

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

182 B{C{radius1}}). 

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

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

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

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

187 (C{bool}). 

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

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

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

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

192 and B{C{radius2}}). 

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

194 or C{None}. 

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

196 ignored if C{B{LatLon} is None}. 

197 

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

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

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

201 aka the I{radical center}. 

202 

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

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

205 

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

207 or invalid B{C{equidistant}}. 

208 

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

210 

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

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

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

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

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

216 intersections. 

217 ''' 

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

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

220 

221 

222def isclockwise(points, datum=_WGS84, wrap=True): 

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

224 

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

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

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

228 B{C{points}} (C{bool}). 

229 

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

231 

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

233 

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

235 

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

237 

238 @see: L{pygeodesy.isclockwise}. 

239 ''' 

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

241 if a < 0: 

242 return True 

243 elif a > 0: 

244 return False 

245 raise _areaError(points) 

246 

247 

248def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

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

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

251 two other (ellispoidal) points. 

252 

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

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

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

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

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

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

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

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

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

262 takes the heights of the points into account. 

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

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

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

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

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

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

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

270 (L{LatLon}) or C{None}. 

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

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

273 

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

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

276 

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

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

279 

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

281 

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

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

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

285 BOUNDARIES} for more details about the iteration algorithm. 

286 ''' 

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

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

289 

290 

291def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 

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

293 

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

295 L{BooleanGH}). 

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

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

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

299 B{C{points}} (C{bool}). 

300 

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

302 ellipsoid axes). 

303 

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

305 

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

307 

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

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

310 with C{B{points}} a composite. 

311 

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

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

314 L{sphericalTrigonometry.perimeterOf}. 

315 ''' 

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

317 

318 

319__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

320 areaOf, # functions 

321 intersection3, intersections2, isclockwise, ispolar, 

322 nearestOn, perimeterOf) 

323 

324# **) MIT License 

325# 

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

327# 

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

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

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

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

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

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

334# 

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

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

337# 

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

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

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

341# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR 

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