# Coverage for pygeodesy/utily.py : 97%

## 157 statements 153 run 4 missing 3 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 | # -*- coding: utf-8 -*- u'''Geometric and other utility functions and constants. After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>} and U{Vector-based geodesy<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. @newfield example: Example, Examples ''' from pygeodesy.basics import isint from pygeodesy.errors import _xkwds_get, _ValueError from pygeodesy.interns import PI, PI2, PI_2, R_M, _Missing, \ _0_0, _0_5, _1_0, _90_0, _180_0, _360_0 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.units import Feet, Lam_, Meter, Phi_, Radius from math import acos, asin, atan2, cos, degrees, radians, sin, tan # pow __all__ = _ALL_LAZY.utily __version__ = '20.10.02' # <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html> _1_90 = _1_0 / _90_0 # 0.011111111111111111111111111111111111111111111111 _2_PI = _1_0 / PI_2 # 0.63661977236758134307553505349005744813783858296182 # sqrt(2) + 1 <https://WikiPedia.org/wiki/Square_root_of_2> # _R2_1 = 2.41421356237309504880 # _16887_24209_69807_85696_71875_37694_80731_76679_73799 _iterNumpy2len = 1 # adjustable for testing purposes def acos1(x): '''Return M{math.acos(max(-1, min(1, x)))}. ''' return acos(max(-_1_0, min(_1_0, x))) def asin1(x): '''Return M{math.asin(max(-1, min(1, x)))}. ''' return asin(max(-_1_0, min(_1_0, x))) def atan2b(y, x): '''Compute C{atan2(y, x)} as degrees M{[0..+360]}. @see: Function L{atan2d}. ''' d = atan2d(y, x) if d < 0: d += _360_0 return d def atan2d(y, x): '''Compute C{atan2(y, x)} as degrees M{[-180..+180]}. @see: I{Karney}'s C++ function U{Math.atan2d <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Math.html>}. ''' if abs(y) > abs(x) > 0: if y < 0: # q = 3 d = degrees(atan2(x, -y)) - _90_0 else: # q = 2 d = _90_0 - degrees(atan2(x, y)) elif x < 0: # q = 1 d = (-_180_0 if y < 0 else _180_0) - degrees(atan2(y, -x)) elif x > 0: # q = 0 d = degrees(atan2(y, x)) if y else _0_0 else: d = -_90_0 if y < 0 else (_90_0 if y > 0 else _0_0) return d def degrees90(rad): '''Convert radians to degrees and wrap M{[-270..+90]}. @arg rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees90}). ''' return _wrap(degrees(rad), _90_0, _360_0) def degrees180(rad): '''Convert radians to degrees and wrap M{[-180..+180]}. @arg rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees180}). ''' return _wrap(degrees(rad), _180_0, _360_0) def degrees360(rad): '''Convert radians to degrees and wrap M{[0..+360)}. @arg rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees360}). ''' return _wrap(degrees(rad), _360_0, _360_0) def degrees2m(deg, radius=R_M, lat=0): '''Convert angle to distance along the equator or along a parallel at an other latitude. @arg deg: Angle (C{degrees}). @kwarg radius: Mean earth radius (C{meter}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise ValueError: Invalid B{C{deg}}, B{C{radius}} or B{C{lat}}. @see: Function L{m2degrees}. ''' m = Lam_(deg=deg, clip=0) * Radius(radius) if lat: m *= cos(Phi_(lat)) return Meter(m) def ft2m(feet, usurvey=False): '''Convert I{International} or I{US Survey} feet to meter. @arg feet: Value in feet (C{scalar}). @kwarg usurvery: Convert I{US Survey} feet (C{bool}), I{International} feet otherwise. @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{feet}}. ''' # US Survey 1200./3937. == 0.3048006096012192 return Feet(feet) * (0.3048006096012192 if usurvey else 0.3048) def isNumpy2(obj): '''Check for an B{C{Numpy2LatLon}} points wrapper. @arg obj: The object (any C{type}). @return: C{True} if B{C{obj}} is an B{C{Numpy2LatLon}} instance, C{False} otherwise. ''' # isinstance(self, (Numpy2LatLon, ...)) return getattr(obj, isNumpy2.__name__, False) def isPoints2(obj): '''Check for an B{C{LatLon2psxy}} points wrapper. @arg obj: The object (any C{type}). @return: C{True} if B{C{obj}} is an B{C{LatLon2psxy}} instance, C{False} otherwise. ''' # isinstance(self, (LatLon2psxy, ...)) return getattr(obj, isPoints2.__name__, False) def isTuple2(obj): '''Check for an B{C{Tuple2LatLon}} points wrapper. @arg obj: The object (any). @return: C{True} if B{C{obj}} is an B{C{Tuple2LatLon}} instance, C{False} otherwise. ''' # isinstance(self, (Tuple2LatLon, ...)) return getattr(obj, isTuple2.__name__, False) def iterNumpy2(obj): '''Iterate over Numpy2 wrappers or other sequences exceeding the threshold. @arg obj: Points array, list, sequence, set, etc. (any). @return: C{True} do, C{False} don't iterate. ''' try: return isNumpy2(obj) or len(obj) > _iterNumpy2len except TypeError: return False def iterNumpy2over(n=None): '''Get or set the L{iterNumpy2} threshold. @kwarg n: Optional, new threshold (C{int}). @return: Previous threshold (C{int}). @raise ValueError: Invalid B{C{n}}. ''' global _iterNumpy2len p = _iterNumpy2len if n is not None: try: i = int(n) if i > 0: _iterNumpy2len = i else: raise ValueError except (TypeError, ValueError): raise _ValueError(n=n) return p def m2degrees(meter, radius=R_M, lat=0): '''Convert distance to angle along equator or along a parallel at an other latitude. @arg meter: Distance (C{meter}, same units as B{C{radius}}). @kwarg radius: Mean earth radius (C{meter}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Angle (C{degrees}). @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise ValueError: Invalid B{C{meter}}, B{C{radius}} or B{C{lat}}. @see: Function L{degrees2m}. ''' r = Radius(radius) if lat: r *= cos(Phi_(lat)) return degrees(Meter(meter) / r) def m2ft(meter, usurvey=False): '''Convert meter to I{International} or I{US Survey} feet (C{ft}). @arg meter: Value in meter (C{scalar}). @kwarg usurvery: Convert to I{US Survey} feet (C{bool}), I{International} feet otherwise. @return: Value in C{feet} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' # US Survey == 3937./1200. = 3.2808333333333333 return Meter(meter) * (3.2808333333333333 if usurvey else 3.2808399) def m2km(meter): '''Convert meter to kilo meter (km). @arg meter: Value in meter (C{scalar}). @return: Value in km (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 1.0e-3 def m2NM(meter): '''Convert meter to nautical miles (NM). @arg meter: Value in meter (C{scalar}). @return: Value in NM (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 5.39956804e-4 # == * _1_0 / 1852.0 def m2SM(meter): '''Convert meter to statute miles (SM). @arg meter: Value in meter (C{scalar}). @return: Value in SM (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 6.21369949e-4 # == _1_0 / 1609.344 def radiansPI(deg): '''Convert and wrap degrees to radians M{[-PI..+PI]}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI}) ''' return _wrap(radians(deg), PI, PI2) def radiansPI2(deg): '''Convert and wrap degrees to radians M{[0..+2PI)}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI2}) ''' return _wrap(radians(deg), PI2, PI2) def radiansPI_2(deg): '''Convert and wrap degrees to radians M{[-3PI/2..+PI/2]}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI_2}) ''' return _wrap(radians(deg), PI_2, PI2) def _sincos2(q, r): '''(INTERNAL) 2-tuple (C{sin(r), cos(r)}) in quadrant M{0 <= q <= 3}. ''' if r: s, c = sin(r), cos(r) t = s, c, -s, -c, s else: t = _0_0, _1_0, -_0_0, -_1_0, _0_0 # q &= 3 return t[q], t[q + 1] def sincos2(*rad): '''Return the C{sine} and C{cosine} of angle(s). @arg rad: One or more angles (C{radians}). @return: The C{sin(rad)} and C{cos(rad)} for each angle. @see: U{GeographicLib<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Math.html#sincosd>} function U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ python/geographiclib/geomath.py#l155>} and C++ U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ include/GeographicLib/Math.hpp#l558>}. ''' for r in rad: q = int(r * _2_PI) # int(math.floor) if r < 0: q -= 1 s, c = _sincos2(q & 3, r - q * PI_2) # _0_0 <= r < PI_2 yield s yield c def sincos2d(*deg): '''Return the C{sine} and C{cosine} of angle(s) in C{degrees}. @arg deg: One or more angles (C{degrees}). @return: The C{sin(deg)} and C{cos(deg)} for each angle. @see: U{GeographicLib<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Math.html#sincosd>} function U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ python/geographiclib/geomath.py#l155>} and C++ U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ include/GeographicLib/Math.hpp#l558>}. ''' for d in deg: q = int(d * _1_90) # int(math.floor) if d < 0: q -= 1 s, c = _sincos2(q & 3, radians(d - q * _90_0)) # _0_0 <= r < PI_2 yield s yield c def splice(iterable, n=2, **fill): '''Split an iterable into C{n} slices. @arg iterable: Items to be spliced (C{list}, C{tuple}, ...). @kwarg n: Number of slices to generate (C{int}). @kwarg fill: Optional fill value for missing items. @return: A generator for each of B{C{n}} slices, M{iterable[i::n] for i=0..n}. @raise ValueError: Invalid B{C{n}}. @note: Each generated slice is a C{tuple} or a C{list}, the latter only if the B{C{iterable}} is a C{list}. @example: >>> from pygeodesy import splice >>> a, b = splice(range(10)) >>> a, b ((0, 2, 4, 6, 8), (1, 3, 5, 7, 9)) >>> a, b, c = splice(range(10), n=3) >>> a, b, c ((0, 3, 6, 9), (1, 4, 7), (2, 5, 8)) >>> a, b, c = splice(range(10), n=3, fill=-1) >>> a, b, c ((0, 3, 6, 9), (1, 4, 7, -1), (2, 5, 8, -1)) >>> tuple(splice(list(range(9)), n=5)) ([0, 5], [1, 6], [2, 7], [3, 8], [4]) >>> splice(range(9), n=1) <generator object splice at 0x0...> ''' if not (isint(n) and n > 0): raise _ValueError(n=n) t = iterable if not isinstance(t, (list, tuple)): t = tuple(t) # force tuple, also for PyPy3 if n > 1: fill = _xkwds_get(fill, fill=_Missing) if fill is not _Missing: m = len(t) % n if m > 0: # fill with same type t += type(t)((fill,)) * (n - m) for i in range(n): yield t[i::n] # slice [i:None:n] pychok -Tb ... else: yield t def tan_2(rad): '''Compute the tangent of half angle. @arg rad: Angle (C{radians}). @return: M{tan(rad / 2)} (C{float}). ''' return tan(rad * _0_5) def tanPI_2_2(rad): '''Compute the tangent of half angle, 90 degrees rotated. @arg rad: Angle (C{radians}). @return: M{tan((rad + PI/2) / 2)} (C{float}). ''' return tan((rad + PI_2) * _0_5) def unroll180(lon1, lon2, wrap=True): '''Unroll longitudinal delta and wrap longitude in degrees. @arg lon1: Start longitude (C{degrees}). @arg lon2: End longitude (C{degrees}). @kwarg wrap: Wrap and unroll to the M{(-180..+180]} range (C{bool}). @return: 2-Tuple (B{C{lon2-lon1}}, B{C{lon2}}) unrolled (C{degrees}, C{degrees}). @see: Capability C{LONG_UNROLL} in U{GeographicLib <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. ''' d = lon2 - lon1 if wrap and abs(d) > _180_0: u = _wrap(d, _180_0, _360_0) if u != d: return u, lon1 + u return d, lon2 def unrollPI(rad1, rad2, wrap=True): '''Unroll longitudinal delta and wrap longitude in radians. @arg rad1: Start longitude (C{radians}). @arg rad2: End longitude (C{radians}). @kwarg wrap: Wrap and unroll to the M{(-PI..+PI]} range (C{bool}). @return: 2-Tuple (B{C{rad2 - rad1}}, B{C{rad2}}) unrolled (C{radians}, C{radians}). @see: Capability C{LONG_UNROLL} in U{GeographicLib <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. ''' r = rad2 - rad1 if wrap and abs(r) > PI: u = _wrap(r, PI, PI2) if u != r: return u, rad1 + u return r, rad2 def _wrap(angle, wrap, modulo): '''(INTERNAL) Angle wrapper M{((wrap-modulo)..+wrap]}. @arg angle: Angle (C{degrees} or C{radians}). @arg wrap: Range (C{degrees} or C{radians}). @arg modulo: Upper limit (360 C{degrees} or PI2 C{radians}). @return: The B{C{angle}}, wrapped (C{degrees} or C{radians}). ''' if wrap > angle >= (wrap - modulo): angle = float(angle) else: # math.fmod(-1.5, 3.14) == -1.5, but -1.5 % 3.14 == 1.64 # math.fmod(-1.5, 360) == -1.5, but -1.5 % 360 == 358.5 angle %= modulo if angle > wrap: angle -= modulo return angle def wrap90(deg): '''Wrap degrees to M{[-270..+90]}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees90}). ''' return _wrap(deg, _90_0, _360_0) def wrap180(deg): '''Wrap degrees to M{[-180..+180]}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees180}). ''' return _wrap(deg, _180_0, _360_0) def wrap360(deg): '''Wrap degrees to M{[0..+360)}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees360}). ''' return _wrap(deg, _360_0, _360_0) def wrapPI(rad): '''Wrap radians to M{[-PI..+PI]}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI}). ''' return _wrap(rad, PI, PI2) def wrapPI2(rad): '''Wrap radians to M{[0..+2PI)}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI2}). ''' return _wrap(rad, PI2, PI2) def wrapPI_2(rad): '''Wrap radians to M{[-3PI/2..+PI/2]}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI_2}). ''' return _wrap(rad, PI_2, PI2) # **) 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.