# Coverage for pygeodesy/utm.py : 98%

## 284 statements 277 run 7 missing 17 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 | # -*- coding: utf-8 -*- u'''I{Veness}' Universal Transverse Mercator (UTM) projection. Classes L{Utm} and L{UTMError} and functions L{parseUTM5}, L{toUtm8} and L{utmZoneBand5}. Pure Python implementation of UTM / WGS-84 conversion functions using an ellipsoidal earth model, transcoded from JavaScript originals by I{(C) Chris Veness 2011-2016} published under the same MIT Licence**, see U{UTM<https://www.Movable-Type.co.UK/scripts/latlong-utm-mgrs.html>} and U{Module utm<https://www.Movable-Type.co.UK/scripts/geodesy/docs/module-utm.html>}. The U{UTM<https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>} system is a 2-dimensional Cartesian coordinate system providing another way to identify locations on the surface of the earth. UTM is a set of 60 transverse Mercator projections, normally based on the WGS-84 ellipsoid. Within each zone, coordinates are represented as B{C{easting}}s and B{C{northing}}s, measured in metres. This module includes some of I{Charles Karney}'s U{'Transverse Mercator with an accuracy of a few nanometers'<https://Arxiv.org/pdf/1002.1417v3.pdf>}, 2011 (building on Krüger's U{'Konforme Abbildung des Erdellipsoids in der Ebene' <https://bib.GFZ-Potsdam.DE/pub/digi/krueger2.pdf>}, 1912) and C++ class U{TransverseMercator <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1TransverseMercator.html>}. Some other references are U{Universal Transverse Mercator coordinate system <https://WikiPedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>}, U{Transverse Mercator Projection<https://GeographicLib.SourceForge.io/tm.html>} and Henrik Seidel U{'Die Mathematik der Gauß-Krueger-Abbildung' <https://Henrik-Seidel.GMXhome.DE/gausskrueger.pdf>}, 2006. ''' from pygeodesy.basics import len2, map2, neg # splice from pygeodesy.datums import _ellipsoidal_datum, _WGS84 from pygeodesy.dms import degDMS, parseDMS2 from pygeodesy.errors import RangeError, _ValueError, \ _xkwds_get, _xkwds_not from pygeodesy.fmath import fdot3, Fsum, hypot, hypot1 from pygeodesy.interns import EPS, EPS0, MISSING, NN, _by_, \ _COMMASPACE_, _float, _NS_, \ _outside_, _range_, _S_, _SPACE_, \ _UTM_, _V_, _X_, _zone_, _0_0, _1_0 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import _xnamed from pygeodesy.namedTuples import EasNor2Tuple, UtmUps5Tuple, \ UtmUps8Tuple, UtmUpsLatLon5Tuple from pygeodesy.props import deprecated_method, Property_RO from pygeodesy.streprs import Fmt from pygeodesy.units import Band, Int, Lat, Lon, Zone from pygeodesy.utily import degrees90, degrees180, sincos2 from pygeodesy.utmupsBase import _LLEB, _hemi, _parseUTMUPS5, \ _to4lldn, _to3zBhp, _to3zll, \ _UTM_LAT_MAX, _UTM_LAT_MIN, \ _UTM_ZONE_MIN, _UTM_ZONE_MAX, \ _UTM_ZONE_OFF_MAX, UtmUpsBase from math import asinh, atan, atanh, atan2, cos, cosh, \ degrees, radians, sin, sinh, tan, tanh from operator import mul __all__ = _ALL_LAZY.utm __version__ = '21.06.21' # Latitude bands C..X of 8° each, covering 80°S to 84°N with X repeated # for 80-84°N _Bands = 'CDEFGHJKLMNPQRSTUVWXX' # latitude bands _FalseEasting = _float( 500e3) # falsed offset (C{meter}) _FalseNorthing = _float(10000e3) # falsed offset (C{meter}) _K0_UTM = _float(0.9996) # UTM scale, central meridian class UTMError(_ValueError): '''Universal Transverse Mercator (UTM parse or other L{Utm} issue. ''' pass class _Kseries(object): '''(INTERNAL) Alpha or Beta Krüger series. Krüger series summations for B{C{eta}}, B{C{ksi}}, B{C{p}} and B{C{q}}, caching the C{cos}, C{cosh}, C{sin} and C{sinh} values for the given B{C{eta}} and B{C{ksi}} angles (in C{radians}). ''' def __init__(self, AB, x, y): '''(INTERNAL) New Alpha or Beta Krüger series @arg AB: Krüger Alpha or Beta series coefficients (C{4-, 6- or 8-tuple}). @arg x: Eta angle (C{radians}). @arg y: Ksi angle (C{radians}). ''' n, j2 = len2(range(2, len(AB) * 2 + 1, 2)) self._ab = AB self._pq = map2(mul, j2, self._ab) # assert len(self._ab) == len(self._pq) == n x2 = map2(mul, j2, (x,) * n) self._chx = map2(cosh, x2) self._shx = map2(sinh, x2) # assert len(x2) == len(self._chx) == len(self._shx) == n y2 = map2(mul, j2, (y,) * n) self._cy = map2(cos, y2) self._sy = map2(sin, y2) # self._sy, self._cy = splice(sincos2(*y2)) # PYCHOK false # assert len(y2) == len(self._cy) == len(self._sy) == n def xs(self, x0): '''(INTERNAL) Eta summation (C{float}). ''' return fdot3(self._ab, self._cy, self._shx, start=x0) def ys(self, y0): '''(INTERNAL) Ksi summation (C{float}). ''' return fdot3(self._ab, self._sy, self._chx, start=y0) def ps(self, p0): '''(INTERNAL) P summation (C{float}). ''' return fdot3(self._pq, self._cy, self._chx, start=p0) def qs(self, q0): '''(INTERNAL) Q summation (C{float}). ''' return fdot3(self._pq, self._sy, self._shx, start=q0) def _cmlon(zone): '''(INTERNAL) Central meridian longitude (C{degrees180}). ''' return (zone * 6) - 183 def _false2(e, n, h): '''(INTERNAL) False easting and northing. ''' # Karney, "Test data for the transverse Mercator projection (2009)" # <https://GeographicLib.SourceForge.io/html/transversemercator.html> # and <https://Zenodo.org/record/32470#.W4LEJS2ZON8> e += _FalseEasting # make e relative to central meridian if h == _S_: n += _FalseNorthing # make n relative to equator return e, n def _to3zBlat(zone, band, Error=UTMError): # imported by .mgrs '''(INTERNAL) Check and return zone, Band and band latitude. @arg zone: Zone number or string. @arg band: Band letter. @arg Error: Exception to raise (L{UTMError}). @return: 3-Tuple (zone, Band, latitude). ''' z, B, _ = _to3zBhp(zone, band, Error=Error) if _UTM_ZONE_MIN > z or z > _UTM_ZONE_MAX: raise Error(zone=zone) b = None if B: b = _Bands.find(B) if b < 0: raise Error(band=band or B) b = Int((b << 3) - 80, name='bandLat') B = Band(B) elif Error is not UTMError: raise Error(band=band, txt=MISSING) return Zone(z), B, b def _to3zBll(lat, lon, cmoff=True): '''(INTERNAL) Return zone, Band and lat- and (central) longitude in degrees. @arg lat: Latitude (C{degrees}). @arg lon: Longitude (C{degrees}). @kwarg cmoff: Offset B{C{lon}} from zone's central meridian. @return: 4-Tuple (zone, Band, lat, lon). ''' z, lat, lon = _to3zll(lat, lon) # in .utmupsBase if _UTM_LAT_MIN > lat or lat >= _UTM_LAT_MAX: # [-80, 84) like Veness r = _range_(_UTM_LAT_MIN, _UTM_LAT_MAX, ropen=True) t = _SPACE_(_outside_, _UTM_, _range_, r) raise RangeError(lat=degDMS(lat), txt=t) B = _Bands[int(lat + 80) >> 3] x = lon - _cmlon(z) # z before Norway/Svaldbard if abs(x) > _UTM_ZONE_OFF_MAX: t = _SPACE_(_outside_, _UTM_, _zone_, str(z), _by_, degDMS(x, prec=6)) raise RangeError(lon=degDMS(lon), txt=t) if B == _X_: # and 0 <= int(lon) < 42: z = int(lon + 183) // 6 + 1 x = {32: 9, 34: 21, 36: 33}.get(z, None) if x: # Svalbard z += 1 if lon >= x else -1 elif B == _V_ and z == 31 and lon >= 3: z += 1 # SouthWestern Norway if cmoff: # lon off central meridian lon -= _cmlon(z) # z after Norway/Svaldbard return Zone(z), Band(B), Lat(lat), Lon(lon) def _to7zBlldfn(latlon, lon, datum, falsed, name, zone, Error, **cmoff): '''(INTERNAL) Determine 7-tuple (zone, band, lat, lon, datum, falsed, name) for L{toEtm8} and L{toUtm8}. ''' f = falsed and _xkwds_get(cmoff, cmoff=True) # DEPRECATED lat, lon, d, name = _to4lldn(latlon, lon, datum, name) z, B, lat, lon = _to3zBll(lat, lon, cmoff=f) if zone: # re-zone for ETM/UTM r, _, _ = _to3zBhp(zone, B) if r != z: if not _UTM_ZONE_MIN <= r <= _UTM_ZONE_MAX: raise Error(zone=zone) if f: # re-offset from central meridian lon += _cmlon(z) - _cmlon(r) z = r return z, B, lat, lon, d, f, name class Utm(UtmUpsBase): '''Universal Transverse Mercator (UTM) coordinate. ''' # _band = NN # latitude band letter ('C..X') _Error = UTMError # or etm.ETMError _latlon_args = () # (eps, unfalse) from _latlon (C{float}, C{bool}) # _scale = None # grid scale factor (C{scalar}) or C{None} _scale0 = _K0_UTM # central scale factor (C{scalar}) _zone = 0 # longitudinal zone (C{int} 1..60) def __init__(self, zone, hemisphere, easting, northing, band=NN, # PYCHOK expected datum=_WGS84, falsed=True, convergence=None, scale=None, name=NN): '''New L{Utm} UTM coordinate. @arg zone: Longitudinal UTM zone (C{int}, 1..60) or zone with/-out (latitudinal) Band letter (C{str}, '01C'..'60X'). @arg hemisphere: Northern or southern hemisphere (C{str}, C{'N[orth]'} or C{'S[outh]'}). @arg easting: Easting, see B{C{falsed}} (C{meter}). @arg northing: Northing, see B{C{falsed}} (C{meter}). @kwarg band: Optional, (latitudinal) band (C{str}, 'C'..'X'). @kwarg datum: Optional, this coordinate's datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg falsed: Both B{C{easting}} and B{C{northing}} are falsed (C{bool}). @kwarg convergence: Optional meridian convergence, bearing off grid North, clockwise from true North (C{degrees}) or C{None}. @kwarg scale: Optional grid scale factor (C{scalar}) or C{None}. @kwarg name: Optional name (C{str}). @raise TypeError: Invalid B{C{datum}}. @raise UTMError: Invalid B{C{zone}}, B{C{hemishere}}, B{C{easting}}, B{C{northing}}, B{C{band}}, B{C{convergence}} or B{C{scale}}. @example: >>> import pygeodesy >>> u = pygeodesy.Utm(31, 'N', 448251, 5411932) ''' if name: self.name = name self._zone, B, _ = _to3zBlat(zone, band) h = str(hemisphere)[:1].upper() if h not in _NS_: raise self._Error(hemisphere=hemisphere) e, n = easting, northing # Easting(easting), ... # if not falsed: # e, n = _false2(e, n, h) # # check easting/northing (with 40km overlap # # between zones) - is this worthwhile? # @raise RangeError: If B{C{easting}} or B{C{northing}} outside # the valid UTM range. # if 120e3 > e or e > 880e3: # raise RangeError(easting=easting) # if 0 > n or n > _FalseNorthing: # raise RangeError(northing=northing) self._hemisphere = h UtmUpsBase.__init__(self, e, n, band=B, datum=datum, falsed=falsed, convergence=convergence, scale=scale) def __eq__(self, other): return isinstance(other, Utm) and other.zone == self.zone \ and other.hemisphere == self.hemisphere \ and other.easting == self.easting \ and other.northing == self.northing \ and other.band == self.band \ and other.datum == self.datum def __repr__(self): return self.toRepr(B=True) def __str__(self): return self.toStr() def _xcopy2(self, Xtm, name=NN): '''(INTERNAL) Make copy as an B{C{Xtm}} instance. @arg Xtm: Class to return the copy (C{Xtm=Etm}, C{Xtm=Utm} or C{self.classof}). ''' return Xtm(self.zone, self.hemisphere, self.easting, self.northing, band=self.band, datum=self.datum, falsed=self.falsed, scale=self.scale, convergence=self.convergence, name=name or self.name) @Property_RO def band(self): '''Get the (latitudinal) band (C{str}, 'C'..'X' or ''). ''' return self._band @Property_RO def _etm(self): '''(INTERNAL) Cache for L{toEtm}. ''' from pygeodesy.etm import Etm return self._xcopy2(Etm) @Property_RO def falsed2(self): '''Get the easting and northing falsing (L{EasNor2Tuple}C{(easting, northing)}). ''' e = n = 0 if self.falsed: e = _FalseEasting # relative to central meridian if self.hemisphere == _S_: # relative to equator n = _FalseNorthing return EasNor2Tuple(e, n) @Property_RO def _lowerleft(self): # by .ellipsoidalBase.LatLon.toUtm '''Get this UTM C{un}-centered (L{Utm}) to its C{lowerleft}. ''' return _lowerleft(self, 0) @Property_RO def _mgrs(self): '''(INTERNAL) Cache for L{toMgrs}. ''' return _toMgrs(self) @Property_RO def _mgrs_lowerleft(self): '''(INTERNAL) Cache for L{toMgrs}, I{un}-centered. ''' u = self._lowerleft return self._mgrs if u is self else _toMgrs(u) def parse(self, strUTM, name=NN): '''Parse a string to a similar L{Utm} instance. @arg strUTM: The UTM coordinate (C{str}), see function L{parseUTM5}. @kwarg name: Optional instance name (C{str}), overriding this name. @return: The similar instance (L{Utm}). @raise UTMError: Invalid B{C{strUTM}}. @see: Function L{parseUPS5} and L{parseUTMUPS5}. ''' return parseUTM5(strUTM, datum=self.datum, Utm=self.classof, name=name or self.name) @deprecated_method def parseUTM(self, strUTM): # PYCHOK no cover '''DEPRECATED, use method L{Utm.parse}.''' return self.parse(strUTM) @Property_RO def pole(self): '''Get the top center of (stereographic) projection, C{""} always. ''' return NN # N/A for UTM def toEtm(self): '''Copy this UTM to an ETM coordinate. @return: The ETM coordinate (L{Etm}). ''' return self._etm def toLatLon(self, LatLon=None, eps=EPS, unfalse=True, **LatLon_kwds): '''Convert this UTM coordinate to an (ellipsoidal) geodetic point. @kwarg LatLon: Optional, ellipsoidal class to return the geodetic point (C{LatLon}) or C{None}. @kwarg eps: Optional convergence limit, L{EPS} or above (C{float}). @kwarg unfalse: Unfalse B{C{easting}} and B{C{northing}} if falsed (C{bool}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: This UTM as (B{C{LatLon}}) or if B{C{LatLon}} is C{None}, as L{LatLonDatum5Tuple}C{(lat, lon, datum, convergence, scale)}. @raise TypeError: If B{C{LatLon}} is not ellipsoidal. @raise UTMError: Invalid meridional radius or H-value. @example: >>> u = Utm(31, 'N', 448251.795, 5411932.678) >>> from pygeodesy import ellipsoidalVincenty as eV >>> ll = u.toLatLon(eV.LatLon) # 48°51′29.52″N, 002°17′40.20″E ''' if eps < EPS: eps = EPS # less doesn't converge if self._latlon and self._latlon_args == (eps, unfalse): return self._latlon5(LatLon) E = self.datum.ellipsoid # XXX vs LatLon.datum.ellipsoid x, y = self.eastingnorthing2(falsed=not unfalse) # from Karney 2011 Eq 15-22, 36 A0 = self.scale0 * E.A if A0 < EPS0: raise self._Error(meridional=A0) x /= A0 # η eta y /= A0 # ξ ksi K = _Kseries(E.BetaKs, x, y) # Krüger series y = neg(K.ys(-y)) # ξ' x = neg(K.xs(-x)) # η' shx = sinh(x) sy, cy = sincos2(y) H = hypot(shx, cy) if H < EPS0: raise self._Error(H=H) T = t0 = sy / H # τʹ S = Fsum(T) q = _1_0 / E.e12 P = 7 # -/+ toggle trips d = _1_0 + eps while abs(d) > eps and P > 0: p = -d # previous d, toggled h = hypot1(T) s = sinh(E.e * atanh(E.e * T / h)) t = T * hypot1(s) - s * h d = (t0 - t) / hypot1(t) * ((q + T**2) / h) T, d = S.fsum2_(d) # τi, (τi - τi-1) if d == p: # catch -/+ toggling of d P -= 1 # else: # P = 0 a = atan(T) # lat b = atan2(shx, cy) if unfalse and self.falsed: b += radians(_cmlon(self.zone)) ll = _LLEB(degrees90(a), degrees180(b), datum=self.datum, name=self.name) # convergence: Karney 2011 Eq 26, 27 p = neg(K.ps(-1)) q = K.qs(0) ll._convergence = degrees(atan(tan(y) * tanh(x)) + atan2(q, p)) # scale: Karney 2011 Eq 28 ll._scale = E.e2s(sin(a)) * hypot1(T) * H * (A0 / E.a / hypot(p, q)) self._latlon_to(ll, eps, unfalse) return self._latlon5(LatLon, **LatLon_kwds) def _latlon_to(self, ll, eps, unfalse): '''(INTERNAL) See C{.toLatLon}, C{toUtm8}, C{_toXtm8}. ''' self._latlon, self._latlon_args = ll, (eps, unfalse) def toMgrs(self, center=False): '''Convert this UTM coordinate to an MGRS grid reference. @kwarg center: If C{True}, I{un}-center this UTM to its C{lowerleft} (C{bool}) or by C{B{center} meter} (C{scalar}). @return: The MGRS grid reference (L{Mgrs}). @see: Function L{toMgrs} in L{mgrs} for more details. ''' return self._mgrs if center in (False, 0, _0_0) else ( self._mgrs_lowerleft if center in (True,) else _toMgrs(_lowerleft(self, center))) # PYCHOK indent def toRepr(self, prec=0, fmt=Fmt.SQUARE, sep=_COMMASPACE_, B=False, cs=False, **unused): # PYCHOK expected '''Return a string representation of this UTM coordinate. Note that UTM coordinates are rounded, not truncated (unlike MGRS grid references). @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg fmt: Optional, enclosing backets format (C{str}). @kwarg sep: Optional separator between name:value pairs (C{str}). @kwarg B: Optionally, include latitudinal band (C{bool}). @kwarg cs: Optionally, include meridian convergence and grid scale factor (C{bool} or non-zero C{int} to specify the precison like B{C{prec}}). @return: This UTM as a string C{"[Z:09[band], H:N|S, E:meter, N:meter]"} plus C{", C:degrees, S:float"} if B{C{cs}} is C{True} (C{str}). ''' return self._toRepr(fmt, B, cs, prec, sep) def toStr(self, prec=0, sep=_SPACE_, B=False, cs=False): # PYCHOK expected '''Return a string representation of this UTM coordinate. To distinguish from MGRS grid zone designators, a space is left between the zone and the hemisphere. Note that UTM coordinates are rounded, not truncated (unlike MGRS grid references). @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg sep: Optional separator to join (C{str}) or C{None} to return an unjoined C{tuple} of C{str}s. @kwarg B: Optionally, include latitudinal band (C{bool}). @kwarg cs: Optionally, include meridian convergence and grid scale factor (C{bool} or non-zero C{int} to specify the precison like B{C{prec}}). @return: This UTM as a string with C{zone[band], hemisphere, easting, northing, [convergence, scale]} in C{"00 N|S meter meter"} plus C{" degrees float"} if B{C{cs}} is C{True} (C{str}). @example: >>> u = Utm(3, 'N', 448251, 5411932.0001) >>> u.toStr(4) # 03 N 448251.0 5411932.0001 >>> u.toStr(sep=', ') # 03 N, 448251, 5411932 ''' return self._toStr(self.hemisphere, B, cs, prec, sep) def toUps(self, pole=NN, eps=EPS, falsed=True, **unused): '''Convert this UTM coordinate to a UPS coordinate. @kwarg pole: Optional top/center of the UPS projection, (C{str}, 'N[orth]'|'S[outh]'). @kwarg eps: Optional convergence limit, L{EPS} or above (C{float}), see method L{Utm.toLatLon}. @kwarg falsed: False both easting and northing (C{bool}). @return: The UPS coordinate (L{Ups}). ''' u = self._ups if u is None or u.pole != (pole or u.pole) or falsed != bool(u.falsed): from pygeodesy.ups import toUps8, Ups ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True) self._ups = u = toUps8(ll, Ups=Ups, falsed=falsed, pole=pole, strict=False, name=self.name) return u def toUtm(self, zone, eps=EPS, falsed=True, **unused): '''Convert this UTM coordinate to a different zone. @arg zone: New UTM zone (C{int}). @kwarg eps: Optional convergence limit, L{EPS} or above (C{float}), see method L{Utm.toLatLon}. @kwarg falsed: False both easting and northing (C{bool}). @return: The UTM coordinate (L{Utm}). ''' if zone == self.zone and falsed == self.falsed: return self.copy() elif zone: u = self._utm if u is None or u.zone != zone or falsed != u.falsed: ll = self.toLatLon(LatLon=_LLEB, eps=eps, unfalse=True) self._utm = u = toUtm8(ll, Utm=self.classof, falsed=falsed, name=self.name, zone=zone) return u raise self._Error(zone=zone) @Property_RO def zone(self): '''Get the (longitudinal) zone (C{int}, 1..60). ''' return self._zone def _lowerleft(utm, center): # by .ellipsoidalBase.LatLon.toUtm '''(INTERNAL) I{Un}-center a B{C{utm}} to its C{lowerleft} by C{B{center} meter} or by a I{guess} if B{C{center}} is C{0}. ''' if center: e = n = -center else: c = 5 # center for _ in range(3): c *= 10 # 50, 500, 5000 t = c * 2 e = int(utm.easting % t) n = int(utm.northing % t) if (e == c and n in (c, c - 1)) or \ (n == c and e in (c, c - 1)): break else: return utm # unchanged r = _xkwds_not(None, datum=utm.datum, scale=utm.scale, convergence=utm.convergence) return utm.classof(utm.zone, utm.hemisphere, utm.easting - e, utm.northing - n, band=utm.band, falsed=utm.falsed, **r) def _parseUTM5(strUTM, datum, Xtm, falsed, Error=UTMError, name=NN): # imported by .etm '''(INTERNAL) Parse a string representing a UTM coordinate, consisting of C{"zone[band] hemisphere easting northing"}, see L{parseETM5} and L{parseUTM5}. ''' z, h, e, n, B = _parseUTMUPS5(strUTM, None, Error=Error) if _UTM_ZONE_MIN > z or z > _UTM_ZONE_MAX or (B and B not in _Bands): raise Error(strUTM=strUTM, zone=z, band=B) if Xtm is None: r = UtmUps5Tuple(z, h, e, n, B, Error=Error, name=name) else: r = Xtm(z, h, e, n, band=B, datum=datum, falsed=falsed) if name: r = _xnamed(r, name, force=True) return r def parseUTM5(strUTM, datum=_WGS84, Utm=Utm, falsed=True, name=NN): '''Parse a string representing a UTM coordinate, consisting of C{"zone[band] hemisphere easting northing"}. @arg strUTM: A UTM coordinate (C{str}). @kwarg datum: Optional datum to use (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg Utm: Optional class to return the UTM coordinate (L{Utm}) or C{None}. @kwarg falsed: Both easting and northing are falsed (C{bool}). @kwarg name: Optional B{C{Utm}} name (C{str}). @return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}} is C{None}, a L{UtmUps5Tuple}C{(zone, hemipole, easting, northing, band)}. The C{hemipole} is the C{'N'|'S'} hemisphere. @raise UTMError: Invalid B{C{strUTM}}. @raise TypeError: Invalid B{C{datum}}. @example: >>> u = parseUTM5('31 N 448251 5411932') >>> u.toRepr() # [Z:31, H:N, E:448251, N:5411932] >>> u = parseUTM5('31 N 448251.8 5411932.7') >>> u.toStr() # 31 N 448252 5411933 ''' r = _parseUTM5(strUTM, datum, Utm, falsed, name=name) return r def _toMgrs(utm): '''(INTERNAL) Convert a L{Utm} to an L{Mgrs} instance. ''' from pygeodesy.mgrs import toMgrs return toMgrs(utm, datum=utm.datum, name=utm.name) def toUtm8(latlon, lon=None, datum=None, Utm=Utm, falsed=True, name=NN, zone=None, **cmoff): '''Convert a lat-/longitude point to a UTM coordinate. @arg latlon: Latitude (C{degrees}) or an (ellipsoidal) geodetic C{LatLon} point. @kwarg lon: Optional longitude (C{degrees}) or C{None}. @kwarg datum: Optional datum for this UTM coordinate, overriding B{C{latlon}}'s datum (L{Datum}, L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}). @kwarg Utm: Optional class to return the UTM coordinate (L{Utm}) or C{None}. @kwarg falsed: False both easting and northing (C{bool}). @kwarg name: Optional B{C{Utm}} name (C{str}). @kwarg zone: Optional UTM zone to enforce (C{int} or C{str}). @kwarg cmoff: DEPRECATED, use B{C{falsed}}. Offset longitude from the zone's central meridian (C{bool}). @return: The UTM coordinate (B{C{Utm}}) or if B{C{Utm}} is C{None} or not B{C{falsed}}, a L{UtmUps8Tuple}C{(zone, hemipole, easting, northing, band, datum, convergence, scale)}. The C{hemipole} is the C{'N'|'S'} hemisphere. @raise RangeError: If B{C{lat}} outside the valid UTM bands or if B{C{lat}} or B{C{lon}} outside the valid range and L{rangerrors} set to C{True}. @raise TypeError: Invalid B{C{datum}} or B{C{latlon}} not ellipsoidal. @raise UTMError: Invalid B{C{zone}}. @raise ValueError: If B{C{lon}} value is missing or if B{C{latlon}} is invalid. @note: Implements Karney’s method, using 8-th order Krüger series, giving results accurate to 5 nm (or better) for distances up to 3900 km from the central meridian. @example: >>> p = LatLon(48.8582, 2.2945) # 31 N 448251.8 5411932.7 >>> u = toUtm(p) # 31 N 448252 5411933 >>> p = LatLon(13.4125, 103.8667) # 48 N 377302.4 1483034.8 >>> u = toUtm(p) # 48 N 377302 1483035 ''' z, B, lat, lon, d, f, name = _to7zBlldfn(latlon, lon, datum, falsed, name, zone, UTMError, **cmoff) d = _ellipsoidal_datum(d, name=name) E = d.ellipsoid a, b = radians(lat), radians(lon) # easting, northing: Karney 2011 Eq 7-14, 29, 35 sb, cb = sincos2(b) T = tan(a) T12 = hypot1(T) S = sinh(E.e * atanh(E.e * T / T12)) T_ = T * hypot1(S) - S * T12 H = hypot(T_, cb) y = atan2(T_, cb) # ξ' ksi x = asinh(sb / H) # η' eta A0 = E.A * getattr(Utm, '_scale0', _K0_UTM) # Utm is class or None K = _Kseries(E.AlphaKs, x, y) # Krüger series y = K.ys(y) * A0 # ξ x = K.xs(x) * A0 # η # convergence: Karney 2011 Eq 23, 24 p_ = K.ps(1) q_ = K.qs(0) c = degrees(atan(T_ / hypot1(T_) * tan(b)) + atan2(q_, p_)) # scale: Karney 2011 Eq 25 k = E.e2s(sin(a)) * T12 / H * (A0 / E.a * hypot(p_, q_)) return _toXtm8(Utm, z, lat, x, y, B, d, c, k, f, name, latlon, EPS) def _toXtm8(Xtm, z, lat, x, y, B, d, c, k, f, # PYCHOK 13+ args name, latlon, eps, Error=UTMError): '''(INTERNAL) Helper for L{toEtm8} and L{toUtm8}. ''' h = _hemi(lat) if f: x, y = _false2(x, y, h) if Xtm is None: # DEPRECATED r = UtmUps8Tuple(z, h, x, y, B, d, c, k, Error=Error, name=name) else: r = _xnamed(Xtm(z, h, x, y, band=B, datum=d, falsed=f, convergence=c, scale=k), name) if isinstance(latlon, _LLEB) and d is latlon.datum: r._latlon_to(latlon, eps, f) # XXX weakref(latlon)? latlon._convergence = c latlon._scale = k return r def utmZoneBand5(lat, lon, cmoff=False, name=NN): '''Return the UTM zone number, Band letter, hemisphere and (clipped) lat- and longitude for a given location. @arg lat: Latitude in degrees (C{scalar} or C{str}). @arg lon: Longitude in degrees (C{scalar} or C{str}). @kwarg cmoff: Offset longitude from the zone's central meridian (C{bool}). @kwarg name: Optional name (C{str}). @return: A L{UtmUpsLatLon5Tuple}C{(zone, band, hemipole, lat, lon)} where C{hemipole} is the C{'N'|'S'} UTM hemisphere. @raise RangeError: If B{C{lat}} outside the valid UTM bands or if B{C{lat}} or B{C{lon}} outside the valid range and L{rangerrors} set to C{True}. @raise ValueError: Invalid B{C{lat}} or B{C{lon}}. ''' lat, lon = parseDMS2(lat, lon) z, B, lat, lon = _to3zBll(lat, lon, cmoff=cmoff) return UtmUpsLatLon5Tuple(z, B, _hemi(lat), lat, lon, name=name) # **) 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.