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__ = '22.02.18' 

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 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 

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 B{C{Cartesian}} is C{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=LatLon, **LatLon_kwds): 

123 '''I{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: If C{True}, wrap or I{normalize} and unroll the B{C{start2}} 

136 and B{C{end*}} points (C{bool}). 

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

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

139 C{B{start1}.Equidistant}. 

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

141 (C{meter}, conventionally). 

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

143 or C{None}. 

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

145 ignored if C{B{LatLon} is None}. 

146 

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

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

149 lon, height, datum)}. 

150 

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

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

153 

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

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

156 

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

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

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

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

161 earth perimeter). 

162 

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

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

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

166 BOUNDARIES} for more details about the iteration algorithm. 

167 ''' 

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

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

170 

171 

172def intersections2(center1, radius1, center2, radius2, height=None, wrap=False, # was=True 

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

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

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

176 

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

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

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

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

181 B{C{radius1}}). 

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

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

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

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

186 (C{bool}). 

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

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

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

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

191 and B{C{radius2}}). 

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

193 or C{None}. 

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

195 ignored if C{B{LatLon} is None}. 

196 

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

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

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

200 aka the I{radical center}. 

201 

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

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

204 

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

206 or invalid B{C{equidistant}}. 

207 

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

209 

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

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

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

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

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

215 intersections. 

216 ''' 

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

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

219 

220 

221def isclockwise(points, datum=_WGS84, wrap=True): 

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

223 

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

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

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

227 B{C{points}} (C{bool}). 

228 

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

230 

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

232 

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

234 

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

236 

237 @see: L{pygeodesy.isclockwise}. 

238 ''' 

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

240 if a < 0: 

241 return True 

242 elif a > 0: 

243 return False 

244 raise _areaError(points) 

245 

246 

247def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 

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

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

250 two other (ellispoidal) points. 

251 

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

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

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

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

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

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

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

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

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

261 takes the heights of the points into account. 

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

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

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

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

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

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

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

269 (L{LatLon}) or C{None}. 

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

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

272 

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

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

275 

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

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

278 

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

280 

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

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

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

284 BOUNDARIES} for more details about the iteration algorithm. 

285 ''' 

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

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

288 

289 

290def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 

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

292 

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

294 L{BooleanGH}). 

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

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

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

298 B{C{points}} (C{bool}). 

299 

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

301 ellipsoid axes). 

302 

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

304 

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

306 

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

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

309 with C{B{points}} a composite. 

310 

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

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

313 L{sphericalTrigonometry.perimeterOf}. 

314 ''' 

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

316 

317 

318__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 

319 areaOf, intersecant2, # from .ellipsoidalBase 

320 intersection3, intersections2, isclockwise, ispolar, 

321 nearestOn, perimeterOf) 

322 

323# **) MIT License 

324# 

325# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved. 

326# 

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

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

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

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

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

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

333# 

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

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

336# 

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

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

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

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

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342# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR 

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