# Coverage for pygeodesy/ellipsoidalBaseDI.py : 91%

## 189 statements 172 run 17 missing 13 excluded

Hot-keys on this page

r m x p toggle line displays

j k next/prev highlighted chunk

0 (zero) top of page

1 (one) first highlighted chunk

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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 | # -*- coding: utf-8 -*- u'''(INTERNAL) Ellipsoidal direct/inverse geodesy base class C{LatLonEllipsoidalBaseDI} and functions. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division from pygeodesy.basics import issubclassof from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase from pygeodesy.errors import _AssertionError, IntersectionError, _IsnotError, \ _ValueError, _xellipsoidal, _xError from pygeodesy.fmath import favg, fmean_, fsum_ from pygeodesy.formy import _radical2 from pygeodesy.interns import _ellipsoidal_ # PYCHOK used! from pygeodesy.interns import EPS, PI, _exceed_PI_radians_, _no_, \ _near_concentric_, _too_, _0_0 from pygeodesy.lazily import _ALL_DOCS from pygeodesy.named import notOverloaded from pygeodesy.namedTuples import Bearing2Tuple, Intersection3Tuple, _LL4Tuple from pygeodesy.streprs import Fmt from pygeodesy.units import Height, Radius_, Scalar, _1mm as _TOL_M from pygeodesy.utily import m2degrees, unroll180 __all__ = () __version__ = '21.06.03' _TRIPS = 17 # _intersect3, _intersects2, _nearestOn interations, 6 is sufficient class LatLonEllipsoidalBaseDI(LatLonEllipsoidalBase): '''(INTERNAL) Base class for C{ellipsoidal*.LatLon} classes with I{overloaded} C{Direct} and C{Inverse} methods. ''' def bearingTo2(self, other, wrap=False): '''Compute the initial and final bearing (forward and reverse azimuth) from this to an other point, using this C{Inverse} method. See methods L{initialBearingTo} and L{finalBearingTo} for more details. @arg other: The other point (C{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: A L{Bearing2Tuple}C{(initial, final)}. @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are not compatible. ''' r = self._Inverse(other, wrap) return Bearing2Tuple(r.initial, r.final, name=self.name) def destination(self, distance, bearing, height=None): '''Compute the destination point after having travelled for the given distance from this point along a geodesic given by an initial bearing, using this C{Direct} method. See method L{destination2} for more details. @arg distance: Distance (C{meter}). @arg bearing: Initial bearing in (compass C{degrees360}). @kwarg height: Optional height, overriding the default height (C{meter}, same units as C{distance}). @return: The destination point (C{LatLon}). ''' return self._Direct(distance, bearing, self.classof, height).destination def destination2(self, distance, bearing, height=None): '''Compute the destination point and the final bearing (reverse azimuth) after having travelled for the given distance from this point along a geodesic given by an initial bearing, using this C{Direct} method. The distance must be in the same units as this point's datum axes, conventionally C{meter}. The distance is measured on the surface of the ellipsoid, ignoring this point's height. The initial and final bearing (forward and reverse azimuth) are in compass C{degrees360}. The destination point's height and datum are set to this point's height and datum, unless the former is overridden. @arg distance: Distance (C{meter}). @arg bearing: Initial bearing (compass C{degrees360}). @kwarg height: Optional height, overriding the default height (C{meter}, same units as C{distance}). @return: A L{Destination2Tuple}C{(destination, final)}. ''' r = self._Direct(distance, bearing, self.classof, height) return self._xnamed(r) def distanceTo(self, other, wrap=False, **unused): # ignore radius=R_M '''Compute the distance between this and an other point along a geodesic, using this C{Inverse} method. See method L{distanceTo3} for more details. @arg other: The other point (C{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Distance (C{meter}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are not compatible. ''' return self._Inverse(other, wrap, azis=False).distance def distanceTo3(self, other, wrap=False): '''Compute the distance, the initial and final bearing along a geodesic between this and an other point, using this C{Inverse} method. The distance is in the same units as this point's datum axes, conventionally meter. The distance is measured on the surface of the ellipsoid, ignoring this point's height. The initial and final bearing (forward and reverse azimuth) are in compass C{degrees360} from North. @arg other: Destination point (C{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: A L{Distance3Tuple}C{(distance, initial, final)}. @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are not compatible. ''' return self._xnamed(self._Inverse(other, wrap)) def finalBearingOn(self, distance, bearing): '''Compute the final bearing (reverse azimuth) after having travelled for the given distance along a geodesic given by an initial bearing from this point, using this C{Direct} method. See method L{destination2} for more details. @arg distance: Distance (C{meter}). @arg bearing: Initial bearing (compass C{degrees360}). @return: Final bearing (compass C{degrees360}). ''' return self._Direct(distance, bearing, None, None).final def finalBearingTo(self, other, wrap=False): '''Compute the final bearing (reverse azimuth) after having travelled along a geodesic from this point to an other point, using this C{Inverse} method. See method L{distanceTo3} for more details. @arg other: The other point (C{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Final bearing (compass C{degrees360}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are not compatible. ''' return self._Inverse(other, wrap).final def initialBearingTo(self, other, wrap=False): '''Compute the initial bearing (forward azimuth) to travel along a geodesic from this point to an other point, using this C{Inverse} method. See method L{distanceTo3} for more details. @arg other: The other point (C{LatLon}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Initial bearing (compass C{degrees360}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are not compatible. ''' return self._Inverse(other, wrap).initial def intermediateTo(self, other, fraction, height=None, wrap=False): '''Return the point at given fraction along the geodesic between this and an other point, using this C{Direct} and C{Inverse} methods. @arg other: The other point (C{LatLon}). @arg fraction: Fraction between both points ranging from 0, meaning this to 1, the other point (C{float}). @kwarg height: Optional height, overriding the fractional height (C{meter}). @kwarg wrap: Wrap and unroll longitudes (C{bool}). @return: Intermediate point (C{LatLon}). @raise TypeError: The B{C{other}} point is not C{LatLon}. @raise UnitError: Invalid B{C{fraction}} or B{C{height}}. @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are not compatible. @see: Methods L{distanceTo3} and L{destination}. ''' t = self.distanceTo3(other, wrap=wrap) f = Scalar(fraction=fraction) h = self._havg(other, f=f) if height is None else Height(height) return self.destination(t.distance * f, t.initial, height=h) def _Direct(self, distance, bearing, LL, height): '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self, distance, bearing, LL, height) def _Inverse(self, other, wrap, **kwds): # azis=True '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. ''' notOverloaded(self, other, wrap, **kwds) def _Equidistant00(equidistant, p1): '''(INTERNAL) Get an C{Equidistant*(0, 0, ...)} instance. ''' import pygeodesy.azimuthal as _az if equidistant is None or not callable(equidistant): equidistant = p1.Equidistant elif not issubclassof(equidistant, *_az._Equidistants): t = tuple(_.__name__ for _ in _az._Equidistants) raise _IsnotError(*t, equidistant=equidistant) return equidistant(0, 0, p1.datum) def _intersect3(s1, end1, s2, end2, height=None, wrap=True, # MCCABE? equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): '''(INTERNAL) Intersect two (ellipsoidal) path, see L{_intersection} above, separated to allow callers to embellish any exceptions. ''' from pygeodesy.sphericalTrigonometry import _intersect as _si, LatLon as _LLS from pygeodesy.vector3d import _intersect3d3 as _vi3 # E = s1.ellipsoids(s2) # assert E == s1.ellispoids(e1) == s1.ellipsoids(e2) e1 = s1.others(end1=end1) e2 = s1.others(end2=end2) if wrap: # unroll180 == .karney._unroll2 e1 = _unrollon(s1, e1) e2 = _unrollon(s2, e2) # get the azimuthal equidistant projection A = _Equidistant00(equidistant, s1) e = max(tol, EPS) # gu-/estimate initial intersection, spherically ... t = _si(_LLS(s1.lat, s1.lon, height=s1.height), _LLS(e1.lat, e1.lon, height=e1.height), _LLS(s2.lat, s2.lon, height=s2.height), _LLS(e2.lat, e2.lon, height=e2.height), height=height, wrap=False, LatLon=_LLS) # unrolled already h, n = t.height, t.name # ... and then iterate like Karney suggests to find # tri-points of median lines, @see: references under # method LatLonEllipsoidalBase.intersections2 above c = None # force first d == c to False for i in range(1, _TRIPS): A.reset(t.lat, t.lon) # gu-/estimate as origin # convert start and end points to projection # space and compute an intersection there v, o1, o2 = _vi3(A.forward(s1.lat, s1.lon), A.forward(e1.lat, e1.lon), A.forward(s2.lat, s2.lon), A.forward(e2.lat, e2.lon), eps=e, useZ=False) # convert intersection back to geodetic t, d = A._reverse2(v.x, v.y) # break if below tolerance or if unchanged if d < e or d == c: t._iteration = i break c = d else: raise IntersectionError(_no_(Fmt.convergence(e))) r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, name=n) r._iteration = t._iteration # _NamedTuple._iteration return Intersection3Tuple(r, o1, o2) def _intersection3(start1, end1, start2, end2, height=None, wrap=True, equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): '''(INTERNAL) Iteratively compute the intersection point of two paths, each defined by an (ellipsoidal) start and end point. ''' s1 = _xellipsoidal(start1=start1) s2 = s1.others(start2=start2) try: return _intersect3(s1, end1, s2, end2, height=height, wrap=wrap, equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) except (TypeError, ValueError) as x: raise _xError(x, start1=start1, end1=end1, start2=start2, end2=end2) def _intersections2(center1, radius1, center2, radius2, height=None, wrap=True, equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): '''(INTERNAL) Iteratively compute the intersection points of two circles, each defined by an (ellipsoidal) center point and a radius. ''' c1 = _xellipsoidal(center1=center1) c2 = c1.others(center2=center2) try: return _intersects2(c1, radius1, c2, radius2, height=height, wrap=wrap, equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) except (TypeError, ValueError) as x: raise _xError(x, center1=center1, radius1=radius1, center2=center2, radius2=radius2) def _intersects2(c1, radius1, c2, radius2, height=None, wrap=True, # MCCABE 15 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): '''(INTERNAL) Intersect two (ellipsoidal) circles, see L{_intersections2} above, separated to allow callers to embellish any exceptions. ''' from pygeodesy.sphericalTrigonometry import _intersects2 as _si2, LatLon as _LLS from pygeodesy.vector3d import _intersects2 as _vi2 def _latlon4(t, h, n): r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, name=n) r._iteration = t.iteration # ._iteration for tests return r r1 = Radius_(radius1=radius1) r2 = Radius_(radius2=radius2) E = c1.ellipsoids(c2) # get the azimuthal equidistant projection A = _Equidistant00(equidistant, c1) if r1 < r2: c1, c2 = c2, c1 r1, r2 = r2, r1 if r1 > (min(E.b, E.a) * PI): raise _ValueError(_exceed_PI_radians_) if wrap: # unroll180 == .karney._unroll2 c2 = _unrollon(c1, c2) # distance between centers and radii are # measured along the ellipsoid's surface m = c1.distanceTo(c2, wrap=False) # meter if m < max(r1 - r2, EPS): raise IntersectionError(_near_concentric_) if fsum_(r1, r2, -m) < 0: raise IntersectionError(_too_(Fmt.distant(m))) f = _radical2(m, r1, r2).ratio # "radical fraction" r = E.rocMean(favg(c1.lat, c2.lat, f=f)) e = max(m2degrees(tol, radius=r), EPS) # gu-/estimate initial intersections, spherically ... t1, t2 = _si2(_LLS(c1.lat, c1.lon, height=c1.height), r1, _LLS(c2.lat, c2.lon, height=c2.height), r2, radius=r, height=height, wrap=False, too_d=m) # unrolled already h, n = t1.height, t1.name # ... and then iterate like Karney suggests to find # tri-points of median lines, @see: references under # method LatLonEllipsoidalBase.intersections2 above ts, ta = [], None for t in ((t1,) if t1 is t2 else (t1, t2)): c = None # force first d == c to False for i in range(1, _TRIPS): A.reset(t.lat, t.lon) # gu-/estimate as origin # convert centers to projection space t1 = A.forward(c1.lat, c1.lon) t2 = A.forward(c2.lat, c2.lon) # compute intersections in projection space v1, v2 = _vi2(t1, r1, # XXX * t1.scale?, t2, r2, # XXX * t2.scale?, sphere=False, too_d=m) # convert intersections back to geodetic t1, d1 = A._reverse2(v1.x, v1.y) if v1 is v2: # abutting t, d = t1, d1 else: t2, d2 = A._reverse2(v2.x, v2.y) # consider only the closer intersection t, d = (t1, d1) if d1 < d2 else (t2, d2) # break if below tolerance or if unchanged if d < e or d == c: t._iteration = i # _NamedTuple._iteration ts.append(t) if v1 is v2: # abutting ta = t break c = d else: raise IntersectionError(_no_(Fmt.convergence(tol))) if ta: # abutting circles pass elif len(ts) == 2: return (_latlon4(ts[0], h, n), _latlon4(ts[1], h, n)) elif len(ts) == 1: # PYCHOK no cover ta = ts[0] # assume abutting else: raise _AssertionError(ts=ts) r = _latlon4(ta, h, n) return r, r def _nearestOn(point, point1, point2, within=True, height=None, wrap=True, equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): '''(INTERNAL) Get closest point, imported by .ellipsoidalExact, -GeodSolve, -Karney and -Vincenty to embellish exceptions. ''' try: p = _xellipsoidal(point=point) return _nearestOne(p, point1, point2, within=within, height=height, wrap=wrap, equidistant=equidistant, tol=tol, LatLon=LatLon, **LatLon_kwds) except (TypeError, ValueError) as x: raise _xError(x, point=point, point1=point1, point2=point2) def _nearestOne(p, point1, point2, within=True, height=None, wrap=True, equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): '''(INTERNAL) Get closest point, like L{_intersects2} above, separated to allow callers to embellish any exceptions. ''' from pygeodesy.sphericalNvector import LatLon as _LLS from pygeodesy.vector3d import _nearestOn as _vnOn, Vector3d def _v(t, h): return Vector3d(t.x, t.y, h) p1 = p.others(point1=point1) p2 = p.others(point2=point2) _ = p.ellipsoids(p1) E = p.ellipsoids(p2) if wrap: p1 = _unrollon(p, p1) p2 = _unrollon(p, p2) p2 = _unrollon(p1, p2) r = E.rocMean(fmean_(p.lat, p1.lat, p2.lat)) e = max(m2degrees(tol, radius=r), EPS) # get the azimuthal equidistant projection A = _Equidistant00(equidistant, p) # gu-/estimate initial nearestOn, spherically ... wrap=False, only! t = _LLS(p.lat, p.lon, height=p.height).nearestOn( _LLS(p1.lat, p1.lon, height=p1.height), _LLS(p2.lat, p2.lon, height=p2.height), within=within, height=height) n = t.name if height is False: # use height as Z component h = t.height h1 = p1.height h2 = p2.height else: h = h1 = h2 = _0_0 # ... and then iterate like Karney suggests to find # tri-points of median lines, @see: references under # method LatLonEllipsoidalBase.intersections2 above c = None # force first d == c to False # closest to origin, .z to interpolate height p = Vector3d(0, 0, h) for i in range(1, _TRIPS): A.reset(t.lat, t.lon) # gu-/estimate as origin # convert points to projection space # and compute the nearest one there v = _vnOn(p, _v(A.forward(p1.lat, p1.lon), h1), _v(A.forward(p2.lat, p2.lon), h2), within=within) # convert nearest one back to geodetic t, d = A._reverse2(v.x, v.y) # break if below tolerance or if unchanged if d < e or d == c: t._iteration = i # _NamedTuple._iteration if height is False: h = v.z # nearest interpolated break c = d else: raise _ValueError(_no_(Fmt.convergence(tol))) r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, name=n) r._iteration = t.iteration # ._iteration for tests return r def _unrollon(p1, p2): # unroll180 == .karney._unroll2 # wrap, unroll and replace longitude if different _, lon = unroll180(p1.lon, p2.lon, wrap=True) if abs(lon - p2.lon) > EPS: p2 = p2.classof(p2.lat, lon, p2.height, datum=p2.datum) return p2 __all__ += _ALL_DOCS(LatLonEllipsoidalBaseDI) # **) MIT License # # Copyright (C) 2016-2021 -- 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.