# Coverage for pygeodesy/sphericalBase.py : 93%

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 | # -*- coding: utf-8 -*- u'''(INTERNAL) Spherical base classes C{CartesianSphericalBase} and C{LatLonSphericalBase}. Pure Python implementation of geodetic (lat-/longitude) functions, transcribed in part from JavaScript originals by I{(C) Chris Veness 2011-2016} and published under the same MIT Licence**, see U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>}. @newfield example: Example, Examples ''' from pygeodesy.cartesianBase import CartesianBase from pygeodesy.datum import R_M, R_MA, Datum, Datums from pygeodesy.dms import parse3llh from pygeodesy.ecef import EcefKarney from pygeodesy.fmath import EPS, acos1, favg, fsum_, _IsNotError from pygeodesy.latlonBase import LatLonBase from pygeodesy.lazily import _ALL_DOCS from pygeodesy.named import Bearing2Tuple from pygeodesy.utily import PI, PI2, PI_2, degrees90, degrees180, \ degrees360, property_RO, sincos2d, \ tanPI_2_2, _TypeError, wrapPI from math import atan2, cos, hypot, log, radians, sin # XXX the following classes are listed only to get # Epydoc to include class and method documentation __all__ = _ALL_DOCS('CartesianSphericalBase', 'LatLonSphericalBase') __version__ = '19.10.21' class CartesianSphericalBase(CartesianBase): '''(INTERNAL) Base class for spherical C{Cartesian}s. ''' _datum = Datums.Sphere #: (INTERNAL) L{Datum}. _Ecef = EcefKarney #: (INTERNAL) Preferred C{Ecef...} class. class LatLonSphericalBase(LatLonBase): '''(INTERNAL) Base class for spherical C{LatLon}s. ''' _datum = Datums.Sphere #: (INTERNAL) Spherical L{Datum}. _Ecef = EcefKarney #: (INTERNAL) Preferred C{Ecef...} class. def __init__(self, lat, lon, height=0, datum=None, name=''): '''Create a spherical C{LatLon} point frome the given lat-, longitude and height on the given datum. @param lat: Latitude (C{degrees} or DMS C{[N|S]}). @param lon: Longitude (C{degrees} or DMS C{str[E|W]}). @keyword height: Optional elevation (C{meter}, the same units as the datum's half-axes). @keyword datum: Optional, shperical datum to use (L{Datum}). @keyword name: Optional name (string). @raise TypeError: B{C{datum}} is not a L{datum} or not spherical. @example: >>> p = LatLon(51.4778, -0.0016) # height=0, datum=Datums.WGS84 ''' LatLonBase.__init__(self, lat, lon, height=height, name=name) if datum: self.datum = datum def bearingTo2(self, other, wrap=False, raiser=False): '''Return the initial and final bearing (forward and reverse azimuth) from this to an other point. @param other: The other point (C{LatLon}). @keyword wrap: Wrap and unroll longitudes (C{bool}). @keyword raiser: Optionally, raise L{CrossError} (C{bool}). @return: A L{Bearing2Tuple}C{(initial, final)}. @raise TypeError: The I{other} point is not spherical. @see: Methods C{initialBearingTo} and C{finalBearingTo}. ''' # .initialBearingTo is inside .-Nvector and .-Trigonometry r = Bearing2Tuple(self.initialBearingTo(other, wrap=wrap, raiser=raiser), # PYCHOK .initialBearingTo self.finalBearingTo( other, wrap=wrap, raiser=raiser)) return self._xnamed(r) @property def datum(self): '''Get this point's datum (L{Datum}). ''' return self._datum @datum.setter # PYCHOK setter! def datum(self, datum): '''Set this point's datum I{without conversion}. @param datum: New datum (L{Datum}). @raise TypeError: If B{C{datum}} is not a L{Datum} or not spherical. ''' _TypeError(Datum, datum=datum) if not datum.isSpherical: raise _IsNotError('spherical', datum=datum) self._update(datum != self._datum) self._datum = datum def finalBearingTo(self, other, wrap=False, raiser=False): '''Return the final bearing (reverse azimuth) from this to an other point. @param other: The other point (spherical C{LatLon}). @keyword wrap: Wrap and unroll longitudes (C{bool}). @keyword raiser: Optionally, raise L{CrossError} (C{bool}). @return: Final bearing (compass C{degrees360}). @raise TypeError: The I{other} point is not spherical. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(48.857, 2.351) >>> b = p.finalBearingTo(q) # 157.9 ''' self.others(other) # final bearing is the reverse of the other, initial one; # .initialBearingTo is inside .-Nvector and .-Trigonometry b = other.initialBearingTo(self, wrap=wrap, raiser=raiser) return (b + 180) % 360 # == wrap360 since b >= 0 @property_RO def isEllipsoidal(self): '''Check whether this C{LatLon} is ellipsoidal (C{bool}). ''' return self.datum.isEllipsoidal @property_RO def isSpherical(self): '''Check whether this C{LatLon} is spherical (C{bool}). ''' return self.datum.isSpherical def maxLat(self, bearing): '''Return the maximum latitude reached when travelling on a great circle on given bearing from this point based on Clairaut's formula. The maximum latitude is independent of longitude and the same for all points on a given latitude. Negate the result for the minimum latitude (on the Southern hemisphere). @param bearing: Initial bearing (compass C{degrees360}). @return: Maximum latitude (C{degrees90}). @JSname: I{maxLatitude}. ''' a, _ = self.to2ab() m = acos1(abs(sin(radians(bearing)) * cos(a))) return degrees90(m) def minLat(self, bearing): '''Return the minimum latitude reached when travelling on a great circle on given bearing from this point. @param bearing: Initial bearing (compass C{degrees360}). @return: Minimum latitude (C{degrees90}). @see: Method L{maxLat} for more details. @JSname: I{minLatitude}. ''' return -self.maxLat(bearing) def parse(self, strll, height=0, sep=','): '''Parse a string representing lat-/longitude point and return a C{LatLon}. The lat- and longitude must be separated by a sep[arator] character. If height is present it must follow and be separated by another sep[arator]. Lat- and longitude may be swapped, provided at least one ends with the proper compass direction. For more details, see functions L{parse3llh} and L{parseDMS} in module L{dms}. @param strll: Lat, lon [, height] (C{str}). @keyword height: Optional , default height (C{meter}). @keyword sep: Optional separator (C{str}). @return: The point (spherical C{LatLon}). @raise ValueError: Invalid I{strll}. ''' return self.classof(*parse3llh(strll, height=height, sep=sep)) def _rhumb3(self, other): '''(INTERNAL) Rhumb_ helper function. @param other: The other point (spherical C{LatLon}). ''' self.others(other) a1, b1 = self.to2ab() a2, b2 = other.to2ab() # if |db| > 180 take shorter rhumb # line across the anti-meridian db = wrapPI(b2 - b1) dp = log(tanPI_2_2(a2) / tanPI_2_2(a1)) return (a2 - a1), db, dp def rhumbBearingTo(self, other): '''Return the initial bearing (forward azimuth) from this to an other point along a rhumb (loxodrome) line. @param other: The other point (spherical C{LatLon}). @return: Initial bearing (compass C{degrees360}). @raise TypeError: The I{other} point is not spherical. @example: >>> p = LatLon(51.127, 1.338) >>> q = LatLon(50.964, 1.853) >>> b = p.rhumbBearingTo(q) # 116.7 ''' _, db, dp = self._rhumb3(other) return degrees360(atan2(db, dp)) def rhumbDestination(self, distance, bearing, radius=R_M, height=None): '''Return the destination point having travelled along a rhumb (loxodrome) line from this point the given distance on the given bearing. @param distance: Distance travelled (C{meter}, same units as I{radius}). @param bearing: Bearing from this point (compass C{degrees360}). @keyword radius: Optional, mean earth radius (C{meter}). @keyword height: Optional height, overriding the default height (C{meter}, same unit as I{radius}). @return: The destination point (spherical C{LatLon}). @example: >>> p = LatLon(51.127, 1.338) >>> q = p.rhumbDestination(40300, 116.7) # 50.9642°N, 001.8530°E @JSname: I{rhumbDestinationPoint} ''' a1, b1 = self.to2ab() r = float(distance) / float(radius) # angular distance in radians sb, cb = sincos2d(bearing) da = r * cb a2 = a1 + da # normalize latitude if past pole if a2 > PI_2: a2 = PI - a2 elif a2 < -PI_2: a2 = -PI - a2 dp = log(tanPI_2_2(a2) / tanPI_2_2(a1)) # E-W course becomes ill-conditioned with 0/0 q = (da / dp) if abs(dp) > EPS else cos(a1) b2 = (b1 + r * sb / q) if abs(q) > EPS else b1 h = self.height if height is None else height return self.classof(degrees90(a2), degrees180(b2), height=h) def rhumbDistanceTo(self, other, radius=R_M): '''Return the distance from this to an other point along a rhumb (loxodrome) line. @param other: The other point (spherical C{LatLon}). @keyword radius: Optional, mean earth radius (C{meter}). @return: Distance (C{meter}, the same units as I{radius}). @raise TypeError: The I{other} point is not spherical. @example: >>> p = LatLon(51.127, 1.338) >>> q = LatLon(50.964, 1.853) >>> d = p.rhumbDistanceTo(q) # 403100 ''' # see <https://www.EdWilliams.org/avform.htm#Rhumb> da, db, dp = self._rhumb3(other) # on Mercator projection, longitude distances shrink # by latitude; the 'stretch factor' q becomes ill- # conditioned along E-W line (0/0); use an empirical # tolerance to avoid it if abs(dp) > EPS: q = da / dp else: a, _ = self.to2ab() q = cos(a) return float(radius) * hypot(da, q * db) def rhumbMidpointTo(self, other, height=None): '''Return the (loxodromic) midpoint between this and an other point. @param other: The other point (spherical LatLon). @keyword height: Optional height, overriding the mean height (C{meter}). @return: The midpoint (spherical C{LatLon}). @raise TypeError: The I{other} point is not spherical. @example: >>> p = LatLon(51.127, 1.338) >>> q = LatLon(50.964, 1.853) >>> m = p.rhumb_midpointTo(q) >>> m.toStr() # '51.0455°N, 001.5957°E' ''' self.others(other) # see <https://MathForum.org/library/drmath/view/51822.html> a1, b1 = self.to2ab() a2, b2 = other.to2ab() if abs(b2 - b1) > PI: b1 += PI2 # crossing anti-meridian a3 = favg(a1, a2) b3 = favg(b1, b2) f1 = tanPI_2_2(a1) if abs(f1) > EPS: f2 = tanPI_2_2(a2) f = f2 / f1 if abs(f) > EPS: f = log(f) if abs(f) > EPS: f3 = tanPI_2_2(a3) b3 = fsum_(b1 * log(f2), -b2 * log(f1), (b2 - b1) * log(f3)) / f h = self._havg(other) if height is None else height return self.classof(degrees90(a3), degrees180(b3), height=h) def toWm(self, radius=R_MA): '''Convert this C{LatLon} point to a I{WM} coordinate. @keyword radius: Optional earth radius (C{meter}). @return: The WM coordinate (L{Wm}). @see: Function L{toWm} in module L{webmercator} for details. ''' from pygeodesy.webmercator import toWm # PYCHOK recursive import return toWm(self, radius=radius) # **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.