1 2# -*- coding: utf-8 -*- 3 4u'''Ellipsoidal, I{Karney}-based geodesy. 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}, all requiring I{Charles 9Karney}'s U{geographiclib <https://PyPI.org/project/geographiclib>} 10Python package to be installed. 11 12Here's an example usage of C{ellipsoidalKarney}: 13 14 >>> from pygeodesy.ellipsoidalKarney import LatLon 15 >>> Newport_RI = LatLon(41.49008, -71.312796) 16 >>> Cleveland_OH = LatLon(41.499498, -81.695391) 17 >>> Newport_RI.distanceTo(Cleveland_OH) 18 866,455.4329098687 # meter 19 20You can change the ellipsoid model used by the I{Karney} formulae 21as follows: 22 23 >>> from pygeodesy import Datums 24 >>> from pygeodesy.ellipsoidalKarney import LatLon 25 >>> p = LatLon(0, 0, datum=Datums.OSGB36) 26 27or by converting to anothor datum: 28 29 >>> p = p.toDatum(Datums.OSGB36) 30''' 31 32from pygeodesy.datums import _WGS84 33from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase 34from pygeodesy.ellipsoidalBaseDI import LatLonEllipsoidalBaseDI, \ 35 _intersection3, _intersections2, \ 36 _nearestOn 37# from pygeodesy.errors import _xkwds # from .karney 38from pygeodesy.karney import _polygon, _TOL_M, _xkwds 39from pygeodesy.lazily import _ALL_LAZY, _ALL_OTHER 40from pygeodesy.points import _areaError, ispolar # PYCHOK exported 41from pygeodesy.props import deprecated_method, Property_RO 42# from pygeodesy.units import _1mm as _TOL_M # from .karney 43 44__all__ = _ALL_LAZY.ellipsoidalKarney 45__version__ = '21.09.12' 46 47 48class Cartesian(CartesianEllipsoidalBase): 49 '''Extended to convert C{Karney}-based L{Cartesian} to 50 C{Karney}-based L{LatLon} points. 51 ''' 52 53 def toLatLon(self, **LatLon_and_kwds): # PYCHOK LatLon=LatLon, datum=None 54 '''Convert this cartesian point to a C{Karney}-based geodetic point. 55 56 @kwarg LatLon_and_kwds: Optional L{LatLon} and L{LatLon} keyword 57 arguments as C{datum}. Use C{B{LatLon}=..., 58 B{datum}=...} to override this L{LatLon} 59 class or specify C{B{LatLon}=None}. 60 61 @return: The geodetic point (L{LatLon}) or if B{C{LatLon}} is C{None}, 62 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} 63 with C{C} and C{M} if available. 64 65 @raise TypeError: Invalid B{C{LatLon_and_kwds}} argument. 66 ''' 67 kwds = _xkwds(LatLon_and_kwds, LatLon=LatLon, datum=self.datum) 68 return CartesianEllipsoidalBase.toLatLon(self, **kwds) 69 70 71class LatLon(LatLonEllipsoidalBaseDI): 72 '''An ellipsoidal L{LatLon} similar to L{ellipsoidalVincenty.LatLon} 73 but using I{Charles F. F. Karney}'s Python U{geographiclib 74 <https://PyPI.org/project/geographiclib>} to compute the geodesic 75 distance, initial and final bearing (azimuths) between two given 76 points or the destination point given a start point and an (initial) 77 bearing. 78 79 @note: This L{LatLon} require the U{geographiclib 80 <https://PyPI.org/project/geographiclib>} package. 81 ''' 82 83 @deprecated_method 84 def bearingTo(self, other, wrap=False): # PYCHOK no cover 85 '''DEPRECATED, use method L{initialBearingTo}. 86 ''' 87 return self.initialBearingTo(other, wrap=wrap) 88 89 @Property_RO 90 def Equidistant(self): 91 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney}). 92 ''' 93 from pygeodesy.azimuthal import EquidistantKarney 94 return EquidistantKarney 95 96 @Property_RO 97 def geodesic(self): 98 '''Get this C{LatLon}'s I{wrapped} U{Karney Geodesic 99 <https://GeographicLib.SourceForge.io/html/python/code.html>}, 100 provided package U{geographiclib 101 <https://PyPI.org/project/geographiclib>} is installed. 102 ''' 103 return self.datum.ellipsoid.geodesic 104 105 def toCartesian(self, **Cartesian_datum_kwds): # PYCHOK Cartesian=Cartesian, datum=None 106 '''Convert this point to C{Karney}-based cartesian (ECEF) coordinates. 107 108 @kwarg Cartesian_datum_kwds: Optional L{Cartesian}, B{C{datum}} 109 and other keyword arguments, ignored if C{B{Cartesian} is None}. 110 Use C{B{Cartesian}=...} to override this L{Cartesian} class 111 or set C{B{Cartesian} is None}. 112 113 @return: The cartesian (ECEF) coordinates (L{Cartesian}) or if 114 B{C{Cartesian}} is C{None}, an L{Ecef9Tuple}C{(x, y, z, 115 lat, lon, height, C, M, datum)} with C{C} and C{M} if 116 available. 117 118 @raise TypeError: Invalid B{C{Cartesian}}, B{C{datum}} or other 119 B{C{Cartesian_datum_kwds}}. 120 ''' 121 kwds = _xkwds(Cartesian_datum_kwds, Cartesian=Cartesian, datum=self.datum) 122 return LatLonEllipsoidalBaseDI.toCartesian(self, **kwds) 123 124 125def areaOf(points, datum=_WGS84, wrap=True): 126 '''Compute the area of an (ellipsoidal) polygon. 127 128 @arg points: The polygon points (L{LatLon}[]). 129 @kwarg datum: Optional datum (L{Datum}). 130 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 131 132 @return: Area (C{meter}, same as units of the 133 B{C{datum}}'s ellipsoid axes, I{squared}). 134 135 @raise ImportError: Package U{geographiclib 136 <https://PyPI.org/project/geographiclib>} 137 not installed or not found. 138 139 @raise PointsError: Insufficient number of B{C{points}}. 140 141 @raise TypeError: Some B{C{points}} are not L{LatLon}. 142 143 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, 144 unrolled longitudes not supported. 145 146 @note: This function requires the U{geographiclib 147 <https://PyPI.org/project/geographiclib>} package. 148 149 @see: L{pygeodesy.areaOf}, L{ellipsoidalExact.areaOf}, 150 L{ellipsoidalGeodSolve.areaOf}, L{sphericalNvector.areaOf} 151 and L{sphericalTrigonometry.areaOf}. 152 ''' 153 return abs(_polygon(datum.ellipsoid.geodesic, points, True, False, wrap)) 154 155 156def intersection3(start1, end1, start2, end2, height=None, wrap=True, 157 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): 158 '''Interatively compute the intersection point of two paths, each defined 159 by two (ellipsoidal) points or by an (ellipsoidal) start point and a 160 bearing from North. 161 162 @arg start1: Start point of the first path (L{LatLon}). 163 @arg end1: End point of the first path (L{LatLon}) or the initial bearing 164 at the first point (compass C{degrees360}). 165 @arg start2: Start point of the second path (L{LatLon}). 166 @arg end2: End point of the second path (L{LatLon}) or the initial bearing 167 at the second point (compass C{degrees360}). 168 @kwarg height: Optional height at the intersection (C{meter}, conventionally) 169 or C{None} for the mean height. 170 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 171 @kwarg equidistant: An azimuthal equidistant projection (I{class} or function 172 L{equidistant}) or C{None} for the preferred 173 C{B{start1}.Equidistant}. 174 @kwarg tol: Tolerance for convergence and for skew line distance and length 175 (C{meter}, conventionally). 176 @kwarg LatLon: Optional class to return the intersection points (L{LatLon}) 177 or C{None}. 178 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, 179 ignored if C{B{LatLon} is None}. 180 181 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)} with C{point} 182 a B{C{LatLon}} or if C{B{LatLon} is None}, a L{LatLon4Tuple}C{(lat, 183 lon, height, datum)}. 184 185 @raise IntersectionError: Skew, colinear, parallel or otherwise 186 non-intersecting paths or no convergence 187 for the given B{C{tol}}. 188 189 @raise TypeError: Invalid or non-ellipsoidal B{C{start1}}, B{C{end1}}, 190 B{C{start2}} or B{C{end2}} or invalid B{C{equidistant}}. 191 192 @note: For each path specified with an initial bearing, a pseudo-end point 193 is computed as the C{destination} along that bearing at about 1.5 194 times the distance from the start point to an initial gu-/estimate 195 of the intersection point (and between 1/8 and 3/8 of the authalic 196 earth perimeter). 197 ''' 198 return _intersection3(start1, end1, start2, end2, height=height, wrap=wrap, 199 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) 200 201 202def intersections2(center1, radius1, center2, radius2, height=None, wrap=True, 203 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): 204 '''Iteratively compute the intersection points of two circles, each defined 205 by an (ellipsoidal) center point and a radius. 206 207 @arg center1: Center of the first circle (L{LatLon}). 208 @arg radius1: Radius of the first circle (C{meter}, conventionally). 209 @arg center2: Center of the second circle (L{LatLon}). 210 @arg radius2: Radius of the second circle (C{meter}, same units as 211 B{C{radius1}}). 212 @kwarg height: Optional height for the intersection points (C{meter}, 213 conventionally) or C{None} for the I{"radical height"} 214 at the I{radical line} between both centers. 215 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 216 @kwarg equidistant: An azimuthal equidistant projection (I{class} or 217 function L{equidistant}) or C{None} for the preferred 218 C{B{center1}.Equidistant}. 219 @kwarg tol: Convergence tolerance (C{meter}, same units as B{C{radius1}} 220 and B{C{radius2}}). 221 @kwarg LatLon: Optional class to return the intersection points (L{LatLon}) 222 or C{None}. 223 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, 224 ignored if C{B{LatLon} is None}. 225 226 @return: 2-Tuple of the intersection points, each a B{C{LatLon}} instance 227 or L{LatLon4Tuple}C{(lat, lon, height, datum)} if C{B{LatLon} is 228 None}. For abutting circles, both points are the same instance, 229 aka the I{radical center}. 230 231 @raise IntersectionError: Concentric, antipodal, invalid or non-intersecting 232 circles or no convergence for the B{C{tol}}. 233 234 @raise TypeError: Invalid or non-ellipsoidal B{C{center1}} or B{C{center2}} 235 or invalid B{C{equidistant}}. 236 237 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}. 238 239 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/ 240 calculating-intersection-of-two-circles>}, U{Karney's paper 241 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES}, 242 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and 243 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>} 244 intersections. 245 ''' 246 return _intersections2(center1, radius1, center2, radius2, height=height, wrap=wrap, 247 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) 248 249 250def isclockwise(points, datum=_WGS84, wrap=True): 251 '''Determine the direction of a path or polygon. 252 253 @arg points: The path or polygon points (C{LatLon}[]). 254 @kwarg datum: Optional datum (L{Datum}). 255 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 256 257 @return: C{True} if B{C{points}} are clockwise, C{False} otherwise. 258 259 @raise ImportError: Package U{geographiclib 260 <https://PyPI.org/project/geographiclib>} 261 not installed or not found. 262 263 @raise PointsError: Insufficient number of B{C{points}}. 264 265 @raise TypeError: Some B{C{points}} are not C{LatLon}. 266 267 @raise ValueError: The B{C{points}} enclose a pole or zero 268 area. 269 270 @note: This function requires the U{geographiclib 271 <https://PyPI.org/project/geographiclib>} package. 272 273 @see: L{pygeodesy.isclockwise}. 274 ''' 275 a = _polygon(datum.ellipsoid.geodesic, points, True, False, wrap) 276 if a > 0: 277 return True 278 elif a < 0: 279 return False 280 raise _areaError(points) 281 282 283def nearestOn(point, point1, point2, within=True, height=None, wrap=False, 284 equidistant=None, tol=_TOL_M, LatLon=LatLon, **LatLon_kwds): 285 '''Iteratively locate the closest point on the arc between two 286 other (ellipsoidal) points. 287 288 @arg point: Reference point (C{LatLon}). 289 @arg point1: Start point of the arc (C{LatLon}). 290 @arg point2: End point of the arc (C{LatLon}). 291 @kwarg within: If C{True} return the closest point I{between} 292 B{C{point1}} and B{C{point2}}, otherwise the 293 closest point elsewhere on the arc (C{bool}). 294 @kwarg height: Optional height for the closest point (C{meter}, 295 conventionally) or C{None} or C{False} for the 296 interpolated height. If C{False}, the distance 297 between points takes height into account. 298 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 299 @kwarg equidistant: An azimuthal equidistant projection (I{class} 300 or function L{equidistant}) or C{None} for 301 the preferred C{B{point}.Equidistant}. 302 @kwarg tol: Convergence tolerance (C{meter}). 303 @kwarg LatLon: Optional class to return the closest point 304 (L{LatLon}) or C{None}. 305 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword 306 arguments, ignored if C{B{LatLon} is None}. 307 308 @return: Closest point, a B{C{LatLon}} instance or if C{B{LatLon} 309 is None}, a L{LatLon4Tuple}C{(lat, lon, height, datum)}. 310 311 @raise ImportError: Package U{geographiclib 312 <https://PyPI.org/project/geographiclib>} 313 not installed or not found. 314 315 @raise TypeError: Invalid or non-ellipsoidal B{C{point}}, B{C{point1}} 316 or B{C{point2}} or invalid B{C{equidistant}}. 317 318 @raise ValueError: No convergence for the B{C{tol}}. 319 ''' 320 return _nearestOn(point, point1, point2, within=within, height=height, wrap=wrap, 321 equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) 322 323 324def perimeterOf(points, closed=False, datum=_WGS84, wrap=True): 325 '''Compute the perimeter of an (ellipsoidal) polygon. 326 327 @arg points: The polygon points (L{LatLon}[]). 328 @kwarg closed: Optionally, close the polygon (C{bool}). 329 @kwarg datum: Optional datum (L{Datum}). 330 @kwarg wrap: Wrap and unroll longitudes (C{bool}). 331 332 @return: Perimeter (C{meter}, same as units of the 333 B{C{datum}}'s ellipsoid axes). 334 335 @raise ImportError: Package U{geographiclib 336 <https://PyPI.org/project/geographiclib>} 337 not installed or not found. 338 339 @raise PointsError: Insufficient number of B{C{points}}. 340 341 @raise TypeError: Some B{C{points}} are not L{LatLon}. 342 343 @raise ValueError: Invalid C{B{wrap}=False}, unwrapped, 344 unrolled longitudes not supported. 345 346 @note: This function requires the U{geographiclib 347 <https://PyPI.org/project/geographiclib>} package. 348 349 @see: L{pygeodesy.perimeterOf}, L{ellipsoidalExact.perimeterOf}, 350 L{ellipsoidalGeodSolve.perimeterOf}, L{sphericalNvector.perimeterOf} 351 and L{sphericalTrigonometry.perimeterOf}. 352 ''' 353 return _polygon(datum.ellipsoid.geodesic, points, closed, True, wrap) 354 355 356__all__ += _ALL_OTHER(Cartesian, LatLon, # classes 357 areaOf, # functions 358 intersection3, intersections2, isclockwise, ispolar, 359 nearestOn, perimeterOf) 360 361# **) MIT License 362# 363# Copyright (C) 2016-2021 -- mrJean1 at Gmail -- All Rights Reserved. 364# 365# Permission is hereby granted, free of charge, to any person obtaining a 366# copy of this software and associated documentation files (the "Software"), 367# to deal in the Software without restriction, including without limitation 368# the rights to use, copy, modify, merge, publish, distribute, sublicense, 369# and/or sell copies of the Software, and to permit persons to whom the 370# Software is furnished to do so, subject to the following conditions: 371# 372# The above copyright notice and this permission notice shall be included 373# in all copies or substantial portions of the Software. 374# 375# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 376# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 377# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 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