# Coverage for pygeodesy/lcc.py : 96%

## 211 statements 203 run 8 missing 7 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 | # -*- coding: utf-8 -*- u'''Lambert conformal conic projection for 1- or 2-Standard Parallels classes L{Conic}, L{Conics} registry, L{LCCError} and position class L{Lcc}. See U{LCC<https://WikiPedia.org/wiki/Lambert_conformal_conic_projection>}, U{Lambert Conformal Conic to Geographic Transformation Formulae <https://www.Linz.govt.NZ/data/geodetic-system/coordinate-conversion/ projection-conversions/lambert-conformal-conic-geographic>}, U{Lambert Conformal Conic Projection <https://MathWorld.Wolfram.com/LambertConformalConicProjection.html>} and John P. Snyder U{'Map Projections - A Working Manual' <https://pubs.er.USGS.gov/djvu/PP/PP_1395.pdf>}, 1987, pp 107-109. @newfield example: Example, Examples ''' from pygeodesy.ellipsoidalBase import LatLonEllipsoidalBase as _LLEB from pygeodesy.datum import Datums from pygeodesy.fmath import EPS, fStr, hypot, _IsNotError from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import EasNor3Tuple, LatLon4Tuple, LatLonDatum3Tuple, \ _NamedBase, _NamedEnum, _NamedEnumItem, nameof, \ _xnamed from pygeodesy.utily import PI_2, degrees90, degrees180, false2f, \ issubclassof, property_RO, sincos2, tanPI_2_2, \ _TypeError from math import atan, copysign, log, radians, sin, sqrt # all public constants, classes and functions __all__ = _ALL_LAZY.lcc __version__ = '20.01.22' class Conic(_NamedEnumItem): '''Lambert conformal conic projection (1- or 2-SP). ''' _auth = '' #: (INTERNAL) authorization (C{str}). _datum = None #: (INTERNAL) Datum (L{Datum}). _name = 'Conic' #: (INTERNAL) Conic (L{Conic}). _e = 0 #: (INTERNAL) Ellipsoid excentricity (C{float}). _E0 = 0 #: (INTERNAL) False easting (C{float}). _k0 = 1 #: (INTERNAL) Scale factor (C{float}). _N0 = 0 #: (INTERNAL) false northing (C{float}). _SP = 0 #: (INTERNAL) 1- or 2-SP (C{int}) _lat0 = 0 #: (INTERNAL) Origin lat (C{radians}). _lon0 = 0 #: (INTERNAL) Origin lon (C{radians}). _par1 = 0 #: (INTERNAL) 1st std parallel (C{radians}). _par2 = 0 #: (INTERNAL) 2nd std parallel (C{radians}). _opt3 = 0 #: (INTERNAL) Optional, longitude (C{radians}). _aF = 0 #: (INTERNAL) Precomputed F. _n = 0 #: (INTERNAL) Precomputed n. _n_ = 0 #: (INTERNAL) Precomputed 1 / n. _r0 = 0 #: (INTERNAL) Precomputed rho0. def __init__(self, latlon0, par1, par2=None, E0=0, N0=0, k0=1, opt3=0, name='', auth=''): '''New Lambert conformal conic projection. @param latlon0: Origin with (ellipsoidal) datum (C{LatLon}). @param par1: First standard parallel (C{degrees90}). @keyword par2: Optional, second standard parallel (C{degrees90}). @keyword E0: Optional, false easting (C{meter}). @keyword N0: Optional, false northing (C{meter}). @keyword k0: Optional scale factor (C{scalar}). @keyword opt3: Optional meridian (C{degrees180}). @keyword name: Optional name of the conic (C{str}). @keyword auth: Optional authentication authority (C{str}). @return: A Lambert projection (L{Conic}). @raise TypeError: Non-ellipsoidal B{C{latlon0}}. @example: >>> from pygeodesy import Conic, Datums, ellipsoidalNvector >>> ll0 = ellipsoidalNvector.LatLon(23, -96, datum=Datums.NAD27) >>> Snyder = Conic(ll0, 33, 45, E0=0, N0=0, name='Snyder') ''' if latlon0 is not None: _TypeError(_LLEB, latlon0=latlon0) self._lat0, self._lon0 = latlon0.to2ab() self._par1 = radians(par1) if par2 is None: self._par2 = self._par1 else: self._par2 = radians(par2) self._opt3 = radians(opt3) if k0 != 1: self._k0 = float(k0) if N0: self._N0 = float(N0) if E0: self._E0 = float(E0) self.toDatum(latlon0.datum)._dup2(self) self._register(Conics, name) elif name: self._name = name if auth: self._auth = auth @property_RO def auth(self): '''Get the authentication authority (C{str}). ''' return self._auth @property_RO def datum(self): '''Get the datum (L{Datum}). ''' return self._datum @property_RO def E0(self): '''Get the false easting (C{meter}). ''' return self._E0 @property_RO def k0(self): '''Get scale factor (C{float}). ''' return self._k0 @property_RO def lat0(self): '''Get the origin latitude (C{degrees90}). ''' return degrees90(self._lat0) @property_RO def lon0(self): '''Get the central meridian (C{degrees180}). ''' return degrees180(self._lon0) @property_RO def N0(self): '''Get the false northing (C{meter}). ''' return self._N0 @property_RO def name2(self): '''Get the conic and datum names as "conic.datum" (C{str}). ''' return self.name + '.' + self.datum.name @property_RO def par1(self): '''Get the 1st standard parallel (C{degrees90}). ''' return degrees90(self._par1) @property_RO def par2(self): '''Get the 2nd standard parallel (C{degrees90}). ''' return degrees90(self._par2) @property_RO def opt3(self): '''Get the optional meridian (C{degrees180}). ''' return degrees180(self._opt3) @property_RO def SP(self): '''Get the number of standard parallels (C{int}). ''' return self._SP def toDatum(self, datum): '''Convert this conic to the given datum. @param datum: Ellipsoidal datum to use (L{Datum}). @return: Converted conic, unregistered (L{Conic}). @raise TypeError: Non-ellipsoidal B{C{datum}}. ''' E = datum.ellipsoid if not E.isEllipsoidal: raise _IsNotError('ellipsoidal', datum=datum) c = self if c._e != E.e or c._datum != datum: c = Conic(None, 0, name=self._name) self._dup2(c) c._datum = datum c._e = E.e if abs(c._par1 - c._par2) < EPS: m1 = c._mdef(c._lat0) t1 = c._tdef(c._lat0) t0 = t1 k = 1 n = sin(c._lat0) sp = 1 else: m1 = c._mdef(c._par1) m2 = c._mdef(c._par2) t1 = c._tdef(c._par1) t2 = c._tdef(c._par2) t0 = c._tdef(c._lat0) k = c._k0 n = (log(m1) - log(m2)) \ / (log(t1) - log(t2)) sp = 2 F = m1 / (n * pow(t1, n)) c._aF = k * E.a * F c._n = n c._n_ = 1 / n c._r0 = c._rdef(t0) c._SP = sp return c convertDatum = toDatum # alternate name def toStr(self, prec=8): # PYCHOK expected '''Return this conic as a string. @keyword prec: Optional number of decimals, unstripped (C{int}). @return: Conic attributes (C{str}). ''' if self._SP == 1: return self._fStr(prec, 'lat0', 'lon0', 'par1', 'E0', 'N0', 'k0', 'SP', datum='(%s)' % (self.datum),) else: return self._fStr(prec, 'lat0', 'lon0', 'par1', 'par2', 'E0', 'N0', 'k0', 'SP', datum='(%s)' % (self.datum),) def _dup2(self, c): '''(INTERNAL) Copy this conic to c. @param c: Duplicate (L{Conic}). ''' c._auth = self._auth c._datum = self._datum c._e = self._e c._E0 = self._E0 c._k0 = self._k0 c._N0 = self._N0 c._SP = self._SP c._lat0 = self._lat0 c._lon0 = self._lon0 c._par1 = self._par1 c._par2 = self._par2 c._opt3 = self._opt3 c._aF = self._aF c._n = self._n c._n_ = self._n_ c._r0 = self._r0 def _mdef(self, lat): '''(INTERNAL) Compute m(lat). ''' s, c = sincos2(lat) s *= self._e return c / sqrt(1 - s**2) def _pdef(self, lat): '''(INTERNAL) Compute p(lat). ''' s = self._e * sin(lat) return pow((1 - s) / (1 + s), self._e / 2) def _rdef(self, t): '''(INTERNAL) Compute r(t). ''' return self._aF * pow(t, self._n) def _tdef(self, lat): '''(INTERNAL) Compute t(lat). ''' return max(0, tanPI_2_2(-lat) / self._pdef(lat)) def _xdef(self, t_x): '''(INTERNAL) Compute x(t_x). ''' return PI_2 - 2 * atan(t_x) # XXX + self._lat0 Conics = _NamedEnum('Conics', Conic) #: Registered conics. Conics._assert( # <https://SpatialReference.org/ref/sr-org/...> # AsLb = Conic(_LLEB(-14.2666667, 170, datum=Datums.NAD27), 0, 0, E0=500000, N0=0, name='AsLb', auth='EPSG:2155'), # American Samoa ... SP=1 ! Be08Lb = Conic(_LLEB(50.7978150, 4.359215833, datum=Datums.GRS80), 49.833333, 51.166667, E0=649328.0, N0=665262.0, name='Be08Lb', auth='EPSG:9802'), # Belgium Be72Lb = Conic(_LLEB(90, 4.3674867, datum=Datums.NAD83), 49.8333339, 51.1666672, E0=150000.013, N0=5400088.438, name='Be72Lb', auth='EPSG:31370'), # Belgium Fr93Lb = Conic(_LLEB(46.5, 3, datum=Datums.WGS84), 49, 44, E0=700000, N0=6600000, name='Fr93Lb', auth='EPSG:2154'), # RFG93, France MaNLb = Conic(_LLEB(33.3, -5.4, datum=Datums.NTF), 31.73, 34.87, E0=500000, N0=300000, name='MaNLb'), # Marocco MxLb = Conic(_LLEB(12, -102, datum=Datums.WGS84), 17.5, 29.5, E0=2500000, N0=0, name='MxLb', auth='EPSG:2155'), # Mexico PyT_Lb = Conic(_LLEB(46.8, 2.33722917, datum=Datums.NTF), 45.89893890000052, 47.69601440000037, E0=600000, N0=200000, name='PyT_Lb', auth='Test'), # France? USA_Lb = Conic(_LLEB(23, -96, datum=Datums.WGS84), 33, 45, E0=0, N0=0, name='USA_Lb'), # Conterminous, contiguous USA? WRF_Lb = Conic(_LLEB(40, -97, datum=Datums.WGS84), 33, 45, E0=0, N0=0, name='WRF_Lb', auth='EPSG:4326') # World ) class LCCError(ValueError): '''Lambert Conformal Conic C{LCC} or other L{Lcc} issue. ''' pass class Lcc(_NamedBase): '''Lambert conformal conic East-/Northing location. ''' _easting = 0 #: (INTERNAL) Easting (C{float}). _height = 0 #: (INTERNAL) Height (C{meter}). _northing = 0 #: (INTERNAL) Northing (C{float}). _conic = None #: (INTERNAL) Lamber projection (L{Conic}). def __init__(self, e, n, h=0, conic=Conics.WRF_Lb, name=''): '''New L{Lcc} Lamber conformal conic position. @param e: Easting (C{meter}). @param n: Northing (C{meter}). @keyword h: Optional height (C{meter}). @keyword conic: Optional, the conic projection (L{Conic}). @keyword name: Optional name (C{str}). @return: The Lambert location (L{Lcc}). @raise TypeError: If B{C{conic}} is not L{Conic}. @raise LCCError: Invalid or negative B{C{e}} or B{C{n}}. @example: >>> lb = Lcc(448251, 5411932.0001) ''' _TypeError(Conic, conic=conic) self._conic = conic self._easting = false2f(e, 'easting', false=conic.E0 > 0, Error=LCCError) self._northing = false2f(n, 'northing', false=conic.N0 > 0, Error=LCCError) if h: self._height = float(h) if name: self.name = name @property_RO def conic(self): '''Get the conic projection (L{Conic}). ''' return self._conic @property_RO def easting(self): '''Get the easting (C{meter}). ''' return self._easting @property_RO def height(self): '''Get the height (C{meter}). ''' return self._height @property_RO def northing(self): '''Get the northing (C{meter}). ''' return self._northing def to3lld(self, datum=None): '''Convert this L{Lcc} to a geodetic lat- and longitude. @keyword datum: Optional datum to use, otherwise use this B{C{Lcc}}'s conic.datum (C{Datum}). @return: A L{LatLonDatum3Tuple}C{(lat, lon, datum)}. @raise TypeError: If B{C{datum}} is not ellipsoidal. ''' c = self.conic if datum: c = c.toDatum(datum) e = self.easting - c._E0 n = c._r0 - self.northing + c._N0 r_ = copysign(hypot(e, n), c._n) t_ = pow(r_ / c._aF, c._n_) x = c._xdef(t_) # XXX c._lon0 while True: p, x = x, c._xdef(t_ * c._pdef(x)) if abs(x - p) < 1e-9: # XXX EPS too small? break # x, y == lon, lat a = degrees90(x) b = degrees180((atan(e / n) + c._opt3) * c._n_ + c._lon0) return LatLonDatum3Tuple(a, b, c.datum) def toLatLon(self, LatLon=None, datum=None, height=None): '''Convert this L{Lcc} to an (ellipsoidal) geodetic point. @keyword LatLon: Optional, ellipsoidal (sub-)class to return the geodetic point (C{LatLon}) or C{None}. @keyword datum: Optional datum to use, otherwise use this B{C{Lcc}}'s conic.datum (C{Datum}). @keyword height: Optional height for the point, overriding the default height (C{meter}). @return: The point (B{C{LatLon}}) or a L{LatLon4Tuple}C{(lat, lon, height, datum)} if B{C{LatLon}} is C{None}. @raise TypeError: If B{C{LatLon}} or B{C{datum}} is not ellipsoidal. ''' if LatLon and not issubclassof(LatLon, _LLEB): raise _IsNotError(_LLEB.__name__, LatLon=LatLon) a, b, d = self.to3lld(datum=datum) h = self.height if height is None else height r = LatLon4Tuple(a, b, h, d) if LatLon is None else \ LatLon(a, b, height=h, datum=d) return self._xnamed(r) def toStr(self, prec=0, sep=' ', m='m'): # PYCHOK expected '''Return a string representation of this L{Lcc} position. @keyword prec: Optional number of decimal, unstripped (C{int}). @keyword sep: Optional separator to join (C{str}). @keyword m: Optional height units, default C{meter} (C{str}). @return: This Lcc as "easting nothing" C{str} in C{meter} plus " height" and 'm' if heigth is non-zero (C{str}). @example: >>> lb = Lcc(448251, 5411932.0001) >>> lb.toStr(4) # 448251.0 5411932.0001 >>> lb.toStr(sep=', ') # 448251, 5411932 ''' t = [fStr(self._easting, prec=prec), fStr(self._northing, prec=prec)] if self._height: t += ['%+.2f%s' % (self._height, m)] return sep.join(t) def toStr2(self, prec=0, fmt='[%s]', sep=', ', m='m', C=False): # PYCHOK expected '''Return a string representation of this L{Lcc} position. @keyword prec: Optional number of decimals, unstripped (C{int}). @keyword fmt: Optional, enclosing backets format (C{str}). @keyword sep: Optional separator between name:values (C{str}). @keyword m: Optional unit of the height, default meter (C{str}). @keyword C: Optionally, include name of conic and datum (C{bool}). @return: This Lcc as "[E:meter, N:meter, H:m, C:Conic.Datum]" (C{str}). ''' t = self.toStr(prec=prec, sep=' ', m=m).split() k = 'ENH'[:len(t)] if C: k += 'C' t += [self.conic.name2] return fmt % (sep.join('%s:%s' % t for t in zip(k, t)),) def toLcc(latlon, conic=Conics.WRF_Lb, height=None, Lcc=Lcc, name=''): '''Convert an (ellipsoidal) geodetic point to a Lambert location. @param latlon: Ellipsoidal point (C{LatLon}). @keyword conic: Optional Lambert projection to use (L{Conic}). @keyword height: Optional height for the point, overriding the default height (C{meter}). @keyword Lcc: Optional (sub-)class to return the Lambert location (L{Lcc}). @keyword name: Optional B{C{Lcc}} name (C{str}). @return: The Lambert location (L{Lcc}) or an L{EasNor3Tuple}C{(easting, northing, height)} if B{C{Lcc}} is C{None}. @raise TypeError: If B{C{latlon}} is not ellipsoidal. ''' if not isinstance(latlon, _LLEB): raise _IsNotError(_LLEB.__name__, latlon=latlon) a, b = latlon.to2ab() c = conic.toDatum(latlon.datum) t = c._n * (b - c._lon0) - c._opt3 st, ct = sincos2(t) r = c._rdef(c._tdef(a)) e = c._E0 + r * st n = c._N0 + c._r0 - r * ct h = latlon.height if height is None else height r = EasNor3Tuple(e, n, h) if Lcc is None else \ Lcc(e, n, h=h, conic=c) return _xnamed(r, name or nameof(latlon)) if __name__ == '__main__': # print all for c in (Conics,): c = '\n' + repr(c) print('\n# '.join(c.split('\n'))) # **) 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. # % python -m pygeodesy.lcc # Conics.Be08Lb: Conic(name='Be08Lb', lat0=50.797815, lon0=4.35921583, par1=49.833333, par2=51.166667, E0=649328, N0=665262, k0=1, SP=2, datum=(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84), # Conics.Be72Lb: Conic(name='Be72Lb', lat0=90, lon0=4.3674867, par1=49.8333339, par2=51.1666672, E0=150000.013, N0=5400088.438, k0=1, SP=2, datum=(name='NAD83', ellipsoid=Ellipsoids.GRS80, transform=Transforms.NAD83), # Conics.Fr93Lb: Conic(name='Fr93Lb', lat0=46.5, lon0=3, par1=49, par2=44, E0=700000, N0=6600000, k0=1, SP=2, datum=(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84), # Conics.MaNLb: Conic(name='MaNLb', lat0=33.3, lon0=-5.4, par1=31.73, par2=34.87, E0=500000, N0=300000, k0=1, SP=2, datum=(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF), # Conics.MxLb: Conic(name='MxLb', lat0=12, lon0=-102, par1=17.5, par2=29.5, E0=2500000, N0=0, k0=1, SP=2, datum=(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84), # Conics.PyT_Lb: Conic(name='PyT_Lb', lat0=46.8, lon0=2.33722917, par1=45.8989389, par2=47.6960144, E0=600000, N0=200000, k0=1, SP=2, datum=(name='NTF', ellipsoid=Ellipsoids.Clarke1880IGN, transform=Transforms.NTF), # Conics.USA_Lb: Conic(name='USA_Lb', lat0=23, lon0=-96, par1=33, par2=45, E0=0, N0=0, k0=1, SP=2, datum=(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84), # Conics.WRF_Lb: Conic(name='WRF_Lb', lat0=40, lon0=-97, par1=33, par2=45, E0=0, N0=0, k0=1, SP=2, datum=(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Transforms.WGS84),