# Coverage for pygeodesy/ellipsoidalBaseDI.py : 96%

## 313 statements 301 run 12 missing 24 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 | # -*- 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 as _; del _ # PYCHOK semicolon from pygeodesy.basics import isnear0, isnear1, isscalar, issubclassof from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase, Property_RO, \ property_RO, _TOL_M from pygeodesy.errors import _AssertionError, IntersectionError, _IsnotError, \ _ValueError, _xellipsoidal, _xError, _xkwds_not from pygeodesy.fmath import favg, fmean_ from pygeodesy.fsums import Fmt, fsum_ from pygeodesy.formy import opposing, _radical2 from pygeodesy.interns import EPS, PI, PI2, PI_4, _antipodal_, _COMMASPACE_, \ _concentric_, _exceed_PI_radians_, _near_, _no_, \ _SPACE_, _too_, _0_0, _0_5, _1_5, _3_0 from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS from pygeodesy.namedTuples import Bearing2Tuple, Destination2Tuple, \ Intersection3Tuple, NearestOn2Tuple, \ NearestOn8Tuple, _LL4Tuple # from pygeodesy.props import Property_RO, property_RO # from .ellipsoidalBase # from pygeodesy.streprs import Fmt # from .fsums from pygeodesy.units import _fi_j2, Height, Radius_, Scalar from pygeodesy.utily import m2km, unroll180, _unrollon, wrap90, wrap180, wrap360 from math import degrees, radians __all__ = _ALL_LAZY.ellipsoidalBaseDI __version__ = '22.01.17' _polar__ = 'polar?' _tolerance_ = 'tolerance' _too_low_ = _too_('low') _B2END = _1_5 # _intersect3 bearing to pseudo-end point factor _TRIPS = 33 # _intersect3, _intersects2, _nearestOn interations, 6..9 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 _Direct(self, distance, bearing, LL, height): # overloaded by I{Vincenty} '''(INTERNAL) I{Karney}'s C{Direct} method. @return: A L{Destination2Tuple}C{(destination, final)} or a L{Destination3Tuple}C{(lat, lon, final)} if B{C{LL}} is C{None}. ''' g = self.geodesic r = g.Direct3(self.lat, self.lon, bearing, distance) if LL: r = self._Direct2Tuple(LL, height, r) return r def _Direct2Tuple(self, LL, height, r): '''(INTERNAL) Helper for C{._Direct} result L{Destination2Tuple}. ''' h = self.height if height is None else height d = LL(wrap90(r.lat), wrap180(r.lon), height=h, datum=self.datum, name=self.name, **_xkwds_not(None, epoch=self.epoch, reframe=self.reframe)) return Destination2Tuple(d, wrap360(r.final)) 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 @Property_RO def geodesic(self): # overloaded by I{Karney}'s, N/A for I{Vincenty} '''N/A, invalid (C{None} I{always}). ''' return None # PYCHOK no cover 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 (C{scalar}, 0.0 at this and 1.0 at the other point. @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}. ''' f = Scalar(fraction=fraction) if isnear0(f): r = self elif isnear1(f) and not wrap: r = self.others(other) else: # negative fraction OK t = self.distanceTo3(other, wrap=wrap) h = self._havg(other, f=f) if height is None else Height(height) r = self.destination(t.distance * f, t.initial, height=h) return r def _Inverse(self, other, wrap, **unused): # azis=False, overloaded by I{Vincenty} '''(INTERNAL) I{Karney}'s C{Inverse} method. @return: A L{Distance3Tuple}C{(distance, initial, final)}. @raise TypeError: The B{C{other}} point is not L{LatLon}. @raise ValueError: If this and the B{C{other}} point's L{Datum} ellipsoids are not compatible. ''' _ = self.ellipsoids(other) g = self.geodesic _, lon = unroll180(self.lon, other.lon, wrap=wrap) return g.Inverse3(self.lat, self.lon, other.lat, lon) def nearestOn8(self, points, closed=False, height=None, wrap=False, equidistant=None, tol=_TOL_M): '''Iteratively locate the point on a path or polygon closest to this point. @arg points: The path or polygon points (C{LatLon}[]). @kwarg closed: Optionally, close the polygon (C{bool}). @kwarg height: Optional height, overriding the height of this and all other points (C{meter}, conventionally). If B{C{height}} is C{None}, the height of each point is taken into account for distances. @return: A L{NearestOn8Tuple}C{(closest, distance, fi, j, start, end, initial, final)} with C{distance} in C{meter}, conventionally and with the C{closest}, the C{start} the C{end} point each an instance of this C{LatLon}. @raise PointsError: Insufficient number of B{C{points}}. @raise TypeError: Some B{C{points}} or B{C{equidistant}} invalid. @raise ValueError: Some B{C{points}}' datum or ellipsoid incompatible or no convergence for the given B{C{tol}}. @see: Function L{pygeodesy.nearestOn6} and method C{nearestOn6}. ''' D3 = self.distanceTo3 # Distance3Tuple try: Ps = self.PointsIter(points, loop=1) p1 = c = s = e = Ps[0] _ = self.ellipsoids(p1) c3 = D3(c, wrap=wrap) # XXX wrap=False? except (TypeError, ValueError) as x: raise _xError(x, Fmt.SQUARE(points=0), p1, this=self, tol=tol, closed=closed, height=height, wrap=wrap) # get the azimuthal equidistant projection, once A = _Equidistant00(equidistant, c) b = _Box(c, c3.distance) m = f = i = 0 # p1..p2 == points[i]..[j] kwds = dict(within=True, height=height, tol=tol, LatLon=self.classof, # this LatLon datum=self.datum, epoch=self.epoch, reframe=self.reframe) try: for j, p2 in Ps.enumerate(closed=closed): if wrap and j != 0: p2 = _unrollon(p1, p2) # skip edge if no overlap with box around closest if j < 4 or b.overlaps(p1.lat, p1.lon, p2.lat, p2.lon): p, t, _ = _nearestOn3_(self, p1, p2, A, **kwds) d3 = D3(p, wrap=False) # already unrolled if d3.distance < c3.distance: c3, c, s, e, f = d3, p, p1, p2, (i + t) b = _Box(c, c3.distance) m = max(m, c.iteration) p1, i = p2, j except (TypeError, ValueError) as x: raise _xError(x, Fmt.SQUARE(points=i), p1, Fmt.SQUARE(points=j), p2, this=self, tol=tol, closed=closed, height=height, wrap=wrap) f, j = _fi_j2(f, len(Ps)) # like .vector3d.nearestOn6 n = self.nearestOn8.__name__ c.rename(n) if s is not c: s = s.copy(name=n) if e is not c: e = e.copy(name=n) r = NearestOn8Tuple(c, c3.distance, f, j, s, e, c3.initial, c3.final) r._iteration = m # ._iteration for tests return r class _Box(object): '''Bounding box around a C{LatLon} point. @see: Function C{_box4} in .clipy.py. ''' def __init__(self, center, distance): '''New L{_Box} around point. @arg center: The center point (C{LatLon}). @arg distance: Radius, half-size of the box (C{meter}, conventionally) ''' E = center.ellipsoid() d = degrees(distance / max(E.a, E.b)) + _0_5 # some margin self._N = center.lat + d self._S = center.lat - d self._E = center.lon + d self._W = center.lon - d def overlaps(self, lat1, lon1, lat2, lon2): '''Check whether this box overlaps a line between 2 points. @arg lat1: Latitude of first point (C{degrees}). @arg lon1: Longitude of first point (C{degrees}). @arg lat2: Latitude of second point (C{degrees}). @arg lon2: Longitude of second point (C{degrees}). @return: C{False} if there is certainly no overlap, C{True} otherwise (C{bool}). ''' non_ = ((lat1 > self._N or lat2 < self._S) if lat1 < lat2 else (lat2 > self._N or lat1 < self._S)) or \ ((lon1 > self._E or lon2 < self._W) if lon1 < lon2 else (lon2 > self._E or lon1 < self._W)) return not non_ class _Tol(object): '''Handle a tolerance in C{meter} as C{degrees} and C{meter}. ''' _deg = 0 _lat = 0 _m = 0 _r = 0 def __init__(self, tol_m, E, lat, *lats): '''New L{_Tol}. @arg tol_m: Tolerance (C{meter}, only). @arg E: Earth ellispoid (L{Ellipsoid}). @arg lat: Latitude (C{degrees}). @arg lats: Additional latitudes (C{degrees}). ''' if lats: lat = fmean_(lat, *lats) self._lat = lat self._m = max(EPS, tol_m) self._r = max(EPS, E.rocMean(lat)) self._deg = max(EPS, degrees(self._m / self._r)) # avoid m2degrees! @property_RO def degrees(self): '''Get this tolerance in C{degrees}. ''' return self._deg def degrees2m(self, deg): '''Convert B{C{deg}} to meter at the same C{lat} and earth radius. ''' return self.radius * radians(deg) / PI2 # avoid degrees2m! def degError(self, deg, Error=_ValueError): '''Compose an error with C{deg}rees minimum. ''' return self.mError(self.degrees2m(deg), Error=Error) @property_RO def lat(self): '''Get the mean latitude in C{degrees}. ''' return self._lat def mError(self, m, Error=_ValueError): '''Compose an error with B{C{m}}eter minimum. ''' t = _SPACE_(_tolerance_, Fmt.PAREN(Fmt.g(self.meter)), _too_low_) if m2km(m) > self.meter: t = _COMMASPACE_(t, _antipodal_, _near_(_polar__)) return Error(_no_(Fmt.convergence(m)), txt=t) @property_RO def meter(self): '''Get this tolerance in C{meter}. ''' return self._m @property_RO def radius(self): '''Get the earth radius in C{meter}. ''' return self._r def _Equidistant00(equidistant, p1): '''(INTERNAL) Get an C{Equidistant*(0, 0, ...)} instance. ''' if equidistant is None or not callable(equidistant): equidistant = p1.Equidistant elif not issubclassof(equidistant, *_MODS.azimuthal._Equidistants): # PYCHOK no cover t = tuple(_.__name__ for _ in _MODS.azimuthal._Equidistants) raise _IsnotError(*t, equidistant=equidistant) return equidistant(0, 0, p1.datum) def _intersect3(s1, end1, s2, end2, height=None, wrap=True, # MCCABE 16 equidistant=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): '''(INTERNAL) Intersect two (ellipsoidal) path, see ellipsoidal method L{intersection3}, separated to allow callers to embellish any exceptions. ''' _LLS = _MODS.sphericalTrigonometry.LatLon _si = _MODS.sphericalTrigonometry._intersect _vi3 = _MODS.vector3d._intersect3d3 def _b_d(s, e, w, t, h=_0_0): # compute opposing and distance t = s.classof(t.lat, t.lon, height=h, name=t.name) t = s.distanceTo3(t, wrap=w) # Distance3Tuple b = opposing(e, t.initial) # "before" start return b, t.distance def _b_e(s, e, w, t): # compute an end point along the initial bearing # about 1.5 times the distance to the gu-/estimate, at # least 1/8 and at most 3/8 of the earth perimeter like # radians in .sphericalTrigonometry._int3d2 and bearing # comparison in .sphericalTrigonometry._intb b, d = _b_d(s, e, w, t, h=t.height) m = s.ellipsoid().R2x * PI_4 # authalic exact d = min(max(d * _B2END, m), m * _3_0) e = s.destination(d, e) return b, (_unrollon(s, e) if w else e) def _e_ll(s, e, w, **end): # return 2-tuple (end, False if bearing else True) ll = not isscalar(e) if ll: e = s.others(**end) if w: # unroll180 == .karney._unroll2 e = _unrollon(s, e) return e, ll def _o(o, b, n, s, t, e): # determine C{o}utside before, on or after start point if not o: # intersection may be on start if _MODS.latlonBase._isequalTo(s, t, eps=e.degrees): return o return -n if b else n E = s1.ellipsoids(s2) e1, ll1 = _e_ll(s1, end1, wrap, end1=end1) e2, ll2 = _e_ll(s2, end2, wrap, end2=end2) e = _Tol(tol, E, s1.lat, (e1.lat if ll1 else s1.lat), s2.lat, (e2.lat if ll2 else s2.lat)) # get the azimuthal equidistant projection A = _Equidistant00(equidistant, s1) # gu-/estimate initial intersection, spherically ... t = _si(_LLS(s1.lat, s1.lon, height=s1.height), (_LLS(e1.lat, e1.lon, height=e1.height) if ll1 else e1), _LLS(s2.lat, s2.lon, height=s2.height), (_LLS(e2.lat, e2.lon, height=e2.height) if ll2 else e2), height=height, wrap=False, LatLon=_LLS) # unrolled already h, n = t.height, t.name if not ll1: b1, e1 = _b_e(s1, e1, wrap, t) if not ll2: b2, e2 = _b_e(s2, e2, wrap, t) # ... and iterate as Karney describes, @see: # LatLonEllipsoidalBase.LatLon.intersections2 c = m = 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.meter, 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.degrees or d == c: t._iteration = i break if m is None or m > d: m = d # min tol in degrees c = d else: raise e.degError(m, Error=IntersectionError) # like .sphericalTrigonometry._intersect, if this intersection # is "before" the first point, use the antipodal intersection if not (ll1 or ll2): # end1 and end2 are an initial bearing b1, _ = _b_d(s1, end1, wrap, t) if b1: t = t.antipodal() b1 = not b1 b2, _ = _b_d(s2, end2, wrap, t) r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=s1, name=n) r._iteration = t._iteration # _NamedTuple._iteration return Intersection3Tuple(r, (o1 if ll1 else _o(o1, b1, 1, s1, t, e)), (o2 if ll2 else _o(o2, b2, 2, s2, t, e))) 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 two (ellipsoidal) points or an (ellipsoidal) start point and an initial bearing from North. ''' 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 16 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. ''' _LLS = _MODS.sphericalTrigonometry.LatLon _si2 = _MODS.sphericalTrigonometry._intersects2 _vi2 = _MODS.vector3d._intersects2 def _latlon4(t, h, n, c): r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=c, 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" e = _Tol(tol, E, favg(c1.lat, c2.lat, f=f)) # 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=e.radius, height=height, wrap=False, too_d=m) # unrolled already h, n = t1.height, t1.name # ... and iterate as Karney describes, @see: # LatLonEllipsoidalBase.LatLon.intersections2 ts, ta = [], None for t in ((t1,) if t1 is t2 else (t1, t2)): c = m = 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 # PYCHOK no cover 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.degrees or d == c: t._iteration = i # _NamedTuple._iteration ts.append(t) if v1 is v2: # abutting ta = t # PYCHOK no coves break c = d if m is None or m > d: m = d # min tol in degrees else: raise e.degError(m, Error=IntersectionError) if ta: # abutting circles pass # PYCHOK no cover elif len(ts) == 2: return (_latlon4(ts[0], h, n, c1), _latlon4(ts[1], h, n, c2)) elif len(ts) == 1: # PYCHOK no cover ta = ts[0] # assume abutting else: # PYCHOK no cover raise _AssertionError(ts=ts) r = _latlon4(ta, h, n, c1) return r, r def _nearestOn2(p, point1, point2, within=True, height=None, wrap=True, equidistant=None, tol=_TOL_M, **LatLon_and_kwds): '''(INTERNAL) Closest point and fraction, like L{_intersects2} above, separated to allow callers to embellish any exceptions. ''' p1 = p.others(point1=point1) p2 = p.others(point2=point2) _ = p.ellipsoids(p1) # E = p.ellipsoids(p2) # done in __nearestOn2__ # get the azimuthal equidistant projection A = _Equidistant00(equidistant, p) if wrap: p1 = _unrollon(p, p1) # XXX do not unroll? p2 = _unrollon(p, p2) # XXX do not unroll? p2 = _unrollon(p1, p2) r, f, e = _nearestOn3_(p, p1, p2, A, within=within, height=height, tol=tol, **LatLon_and_kwds) return NearestOn2Tuple(r, f) def _nearestOn3_(p, p1, p2, A, within=True, height=None, tol=_TOL_M, LatLon=None, **LatLon_kwds): # Only function C{_nearestOn2} and method C{nearestOn8} above _LLS = _MODS.sphericalNvector.LatLon _vnOn2 = _MODS.vector3d._nearestOn2 _V3d = _MODS.vector3d.Vector3d def _v3d(t, h): return _V3d(t.x, t.y, h) E = p.ellipsoids(p2) e = _Tol(tol, E, p.lat, p1.lat, p2.lat) # gu-/estimate initial nearestOn, spherically ... wrap=False, only! # using sphericalNvector.LatLon.nearestOn for within=False support 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, h = t.name, t.height if height is None: h1 = p1.height # use heights as pseudo-Z in projection space h2 = p2.height # to be included in the closest function h0 = favg(h1, h2) else: # ignore heights in distances, Z=0 h0 = h1 = h2 = _0_0 # ... and iterate as Karney describes, @see: # LatLonEllipsoidalBase.LatLon.intersections2 c = m = f = None # force first d == c to False # closest to origin, .z to interpolate height vp = _V3d(_0_0, _0_0, h0) 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, f = _vnOn2(vp, _v3d(A.forward(p1.lat, p1.lon), h1), _v3d(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.degrees or d == c: t._iteration = i # _NamedTuple._iteration break c = d if m is None or m > d: m = d # min tol in degrees else: raise e.degError(m) if height is None: h = v.z # nearest elif isscalar(height): h = height r = _LL4Tuple(t.lat, t.lon, h, t.datum, LatLon, LatLon_kwds, inst=p, name=n) r._iteration = t.iteration # for tests return r, f, e # fraction or None __all__ += _ALL_DOCS(LatLonEllipsoidalBaseDI) # **) MIT License # # Copyright (C) 2016-2022 -- 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.