# Coverage for pygeodesy/utily.py : 97%

## 245 statements 237 run 8 missing 14 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 | # -*- coding: utf-8 -*- u'''Various utility functions. 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>}. ''' # make sure int/int division yields float quotient, see .basics from __future__ import division as _; del _ # PYCHOK semicolon from pygeodesy.basics import copysign0, isint from pygeodesy.constants import EPS, EPS0, INF, NAN, NEG0, NINF, PI, PI2, PI_2, R_M, \ _float as _F, _isfinite, isnan, isnear0, isneg0, _M_KM, \ _M_NM, _M_SM, _0_0, _1__90, _0_5, _1_0, _N_1_0, _2__PI, \ _10_0, _90_0, _N_90_0, _180_0, _N_180_0, _360_0, _400_0 from pygeodesy.interns import _edge_, _radians_, _semi_circular_, _SPACE_ from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS from pygeodesy.units import Degrees, Feet, Float, Lam, Lam_, Meter, Meter2, Radians from math import acos, asin, atan2, cos, degrees, fabs, radians, sin, tan # pow __all__ = _ALL_LAZY.utily __version__ = '22.10.23' # read constant name "_M_UNIT" as "meter per unit" _M_CHAIN = _F( 20.1168) # yard2m(1) * 22 _M_FATHOM = _F( 1.8288) # yard2m(1) * 2 or _M_NM * 1e-3 _M_FOOT_GE = _F( 0.31608) # German Fuss (1 / 3.1637560111364) _M_FOOT_FR = _F( 0.3248406) # French Pied-du-Roi or pied (1 / 3.0784329298739) _M_FOOT_INTL = _F( 0.3048) # Int'l (1 / 3.2808398950131 = 10_000 / (254 * 12)) _M_FOOT_USRV = _F( 0.3048006096012192) # US Survey (1200 / 3937) _M_FURLONG = _F( 201.168) # 220 * yard2m(1) == 10 * m2chain(1) # _M_KM = _F(1000.0) # kilo meter # _M_NM = _F(1852.0) # nautical mile # _M_SM = _F(1609.344) # statute mile _M_TOISE = _F( 1.9490436) # French toise, 6 pieds (6 / 3.0784329298739) _M_YARD_UK = _F( 0.9144) # 254 * 12 * 3 / 10_000 == 3 * ft2m(1) Int'l def acos1(x): '''Return C{math.acos(max(-1, min(1, B{x})))}. ''' return acos(x) if fabs(x) < _1_0 else (PI if x < 0 else _0_0) def acre2ha(acres): '''Convert acres to hectare. @arg acres: Value in acres (C{scalar}). @return: Value in C{hectare} (C{float}). @raise ValueError: Invalid B{C{acres}}. ''' # 0.40468564224 == acre2m2(1) / 10_000 return Float(ha=Float(acres) * 0.40468564224) def acre2m2(acres): '''Convert acres to I{square} meter. @arg acres: Value in acres (C{scalar}). @return: Value in C{meter^2} (C{float}). @raise ValueError: Invalid B{C{acres}}. ''' # 4046.8564224 == chain2m(1) * furlong2m(1) return Meter2(Float(acres) * 4046.8564224) def asin1(x): '''Return C{math.asin(max(-1, min(1, B{x})))}. ''' return asin(x) if fabs(x) < _1_0 else (-PI_2 if x < 0 else PI_2) # -PI_2, not PI3_2! def atand(y_x): '''Return C{atan(B{y_x})} angle in C{degrees}. @see: Function L{pygeodesy.atan2d}. ''' return atan2d(y_x, _1_0) def atan2b(y, x): '''Return C{atan2(B{y}, B{x})} in degrees M{[0..+360]}. @see: Function L{pygeodesy.atan2d}. ''' d = atan2d(y, x) if d < 0: d += _360_0 return d def atan2d(y, x, reverse=False): '''Return C{atan2(B{y}, B{x})} in degrees M{[-180..+180]}, optionally reversed (by 180 degrees for C{azi2}). @see: I{Karney}'s C++ function U{Math.atan2d <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1Math.html>}. ''' if fabs(y) > fabs(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 = copysign0(_180_0, y) - degrees(atan2(y, -x)) elif x > 0: # q = 0 d = degrees(atan2(y, x)) if y else _0_0 elif isnan(x) or isnan(y): return NAN else: # x == 0 d = _N_90_0 if y < 0 else (_90_0 if y > 0 else _0_0) if reverse: d += _180_0 if d < 0 else _N_180_0 return d def chain2m(chains): '''Convert I{UK} chains to meter. @arg chains: Value in chains (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{chains}}. ''' return Meter(Float(chains=chains) * _M_CHAIN) def circle4(earth, lat): '''Get the equatorial or a parallel I{circle of latitude}. @arg earth: The earth radius, ellipsoid or datum (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @arg lat: Geodetic latitude (C{degrees90}, C{str}). @return: A L{Circle4Tuple}C{(radius, height, lat, beta)} instance. @raise RangeError: Latitude B{C{lat}} outside valid range and L{pygeodesy.rangerrors} set to C{True}. @raise TypeError: Invalid B{C{earth}}. @raise ValueError: B{C{earth}} or B{C{lat}}. ''' E = _MODS.datums._spherical_datum(earth).ellipsoid return E.circle4(lat) def cot(rad, **error_kwds): '''Return the C{cotangent} of an angle in C{radians}. @arg rad: Angle (C{radians}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: C{cot(B{rad})}. @raise ValueError: L{pygeodesy.isnear0}C{(sin(B{rad})}. ''' s, c = sincos2(rad) if isnear0(s): raise _valueError(cot, rad, **error_kwds) return c / s def cot_(*rads, **error_kwds): '''Return the C{cotangent} of angle(s) in C{radiansresection}. @arg rads: One or more angles (C{radians}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: Yield the C{cot(B{rad})} for each angle. @raise ValueError: See L{pygeodesy.cot}. ''' try: for r in rads: yield cot(r) except ValueError: raise _valueError(cot_, r, **error_kwds) def cotd(deg, **error_kwds): '''Return the C{cotangent} of an angle in C{degrees}. @arg deg: Angle (C{degrees}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: C{cot(B{deg})}. @raise ValueError: L{pygeodesy.isnear0}C{(sin(B{deg})}. ''' s, c = sincos2d(deg) if isnear0(s): raise _valueError(cotd, deg, **error_kwds) return c / s def cotd_(*degs, **error_kwds): '''Return the C{cotangent} of angle(s) in C{degrees}. @arg degs: One or more angles (C{degrees}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: Yield the C{cot(B{deg})} for each angle. @raise ValueError: See L{pygeodesy.cotd}. ''' try: for d in degs: yield cotd(d) except ValueError: raise _valueError(cotd_, d, **error_kwds) def degrees90(rad): '''Convert radians to degrees and wrap M{[-270..+90]}. @arg rad: Angle (C{radians}). @return: Angle, 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, 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, wrapped (C{degrees360}). ''' return _wrap(degrees(rad), _360_0, _360_0) def degrees2grades(deg): '''Convert degrees to I{grades} (aka I{gons} or I{gradians}). @arg deg: Angle (C{degrees}). @return: Angle (C{grades}). ''' return Degrees(deg) * _400_0 / _360_0 def degrees2m(deg, radius=R_M, lat=0): '''Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. @arg deg: The angle (C{degrees}). @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Distance (C{meter}, same units as B{C{radius}} or equatorial and polar radii) or C{0.0} for near-polar B{C{lat}}. @raise RangeError: Latitude B{C{lat}} outside valid range and L{pygeodesy.rangerrors} set to C{True}. @raise TypeError: Invalid B{C{radius}}. @raise ValueError: Invalid B{C{deg}}, B{C{radius}} or B{C{lat}}. @see: Function L{radians2m} and L{m2degrees}. ''' return _radians2m(Lam_(deg=deg, clip=0), radius, lat) def fathom2m(fathoms): '''Convert I{Imperial} fathom to meter. @arg fathoms: Value in fathoms (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{fathoms}}. @see: Function L{toise2m}, U{Fathom<https://WikiPedia.org/wiki/Fathom>} and U{Klafter<https://WikiPedia.org/wiki/Klafter>}. ''' return Meter(Float(fathoms=fathoms) * _M_FATHOM) def ft2m(feet, usurvey=False, pied=False, fuss=False): '''Convert I{International}, I{US Survey}, I{French} or I{German} B{C{feet}} to C{meter}. @arg feet: Value in feet (C{scalar}). @kwarg usurvey: Convert I{US Survey} foot if C{True} else ... @kwarg pied: Convert French I{pied-du-Roi} if C{True} else ... @kwarg fuss: Convert German I{Fuss} if C{True}, otherwise I{International} feet to C{meter}. @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{feet}}. ''' return Meter(Feet(feet) * (_M_FOOT_USRV if usurvey else (_M_FOOT_FR if pied else (_M_FOOT_GE if fuss else _M_FOOT_INTL)))) def furlong2m(furlongs): '''Convert a furlong to meter. @arg furlongs: Value in furlongs (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{furlongs}}. ''' return Meter(Float(furlongs=furlongs) * _M_FURLONG) def grades(rad): '''Convert radians to I{grades} (aka I{gons} or I{gradians}). @arg rad: Angle (C{radians}). @return: Angle (C{grades}). ''' return Float(grades=Float(rad=rad) * _400_0 / PI2) def grades400(rad): '''Convert radians to I{grades} (aka I{gons} or I{gradians}) and wrap M{[0..+400)}. @arg rad: Angle (C{radians}). @return: Angle, wrapped (C{grades}). ''' return Float(grades400=_wrap(grades(rad), _400_0, _400_0)) def grades2degrees(gon): '''Convert I{grades} (aka I{gons} or I{gradians}) to C{degrees}. @arg gon: Angle (C{grades}). @return: Angle (C{degrees}). ''' return Degrees(Float(gon=gon) * _360_0 / _400_0) def grades2radians(gon): '''Convert I{grades} (aka I{gons} or I{gradians}) to C{radians}. @arg gon: Angle (C{grades}). @return: Angle (C{radians}). ''' return Radians(Float(gon=gon) * PI2 / _400_0) def km2m(km): '''Convert kilo meter to meter (m). @arg km: Value in kilo meter (C{scalar}). @return: Value in meter (C{float}). @raise ValueError: Invalid B{C{km}}. ''' return Meter(Float(km=km) * _M_KM) def m2chain(meter): '''Convert meter to I{UK} chains. @arg meter: Value in meter (C{scalar}). @return: Value in C{chains} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Float(chain=Meter(meter) / _M_CHAIN) # * 0.049709695378986715 def m2degrees(distance, radius=R_M, lat=0): '''Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. @arg distance: Distance (C{meter}, same units as B{C{radius}}). @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, an L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Angle (C{degrees}) or C{INF} for near-polar B{C{lat}}. @raise RangeError: Latitude B{C{lat}} outside valid range and L{pygeodesy.rangerrors} set to C{True}. @raise TypeError: Invalid B{C{radius}}. @raise ValueError: Invalid B{C{distance}}, B{C{radius}} or B{C{lat}}. @see: Function L{m2radians} and L{degrees2m}. ''' return degrees(m2radians(distance, radius=radius, lat=lat)) def m2fathom(meter): '''Convert meter to I{Imperial} fathoms. @arg meter: Value in meter (C{scalar}). @return: Value in C{fathoms} (C{float}). @raise ValueError: Invalid B{C{meter}}. @see: Function L{m2toise}, U{Fathom<https://WikiPedia.org/wiki/Fathom>} and U{Klafter<https://WikiPedia.org/wiki/Klafter>}. ''' return Float(fathom=Meter(meter) / _M_FATHOM) # * 0.546806649 def m2ft(meter, usurvey=False, pied=False, fuss=False): '''Convert meter to I{International}, I{US Survey}, I{French} or or I{German} feet (C{ft}). @arg meter: Value in meter (C{scalar}). @kwarg usurvey: Convert to I{US Survey} foot if C{True} else ... @kwarg pied: Convert to French I{pied-du-Roi} if C{True} else ... @kwarg fuss: Convert to German I{Fuss} if C{True}, otherwise to I{International} foot. @return: Value in C{feet} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' # * 3.2808333333333333, US Survey 3937 / 1200 # * 3.2808398950131235, Int'l 10_000 / (254 * 12) return Float(feet=Meter(meter) / (_M_FOOT_USRV if usurvey else (_M_FOOT_FR if pied else (_M_FOOT_GE if fuss else _M_FOOT_INTL)))) def m2furlong(meter): '''Convert meter to furlongs. @arg meter: Value in meter (C{scalar}). @return: Value in C{furlongs} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Float(furlong=Meter(meter) / _M_FURLONG) # * 0.00497096954 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 Float(km=Meter(meter) / _M_KM) def m2NM(meter): '''Convert meter to nautical miles (NM). @arg meter: Value in meter (C{scalar}). @return: Value in C{NM} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Float(NM=Meter(meter) / _M_NM) # * 5.39956804e-4 def m2radians(distance, radius=R_M, lat=0): '''Convert a distance to an angle along the equator or along the parallel at an other (geodetic) latitude. @arg distance: Distance (C{meter}, same units as B{C{radius}}). @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, an L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Angle (C{radians}) or C{INF} for near-polar B{C{lat}}. @raise RangeError: Latitude B{C{lat}} outside valid range and L{pygeodesy.rangerrors} set to C{True}. @raise TypeError: Invalid B{C{radius}}. @raise ValueError: Invalid B{C{distance}}, B{C{radius}} or B{C{lat}}. @see: Function L{m2degrees} and L{radians2m}. ''' m = circle4(radius, lat).radius return INF if m < EPS0 else Radians(Float(distance=distance) / m) def m2SM(meter): '''Convert meter to statute miles (SM). @arg meter: Value in meter (C{scalar}). @return: Value in C{SM} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Float(SM=Meter(meter) / _M_SM) # * 6.21369949e-4 == 1 / 1609.344 def m2toise(meter): '''Convert meter to French U{toises<https://WikiPedia.org/wiki/Toise>}. @arg meter: Value in meter (C{scalar}). @return: Value in C{toises} (C{float}). @raise ValueError: Invalid B{C{meter}}. @see: Function L{m2fathom}. ''' return Float(toise=Meter(meter) / _M_TOISE) # * 0.513083632632119 def m2yard(meter): '''Convert meter to I{UK} yards. @arg meter: Value in meter (C{scalar}). @return: Value in C{yards} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Float(yard=Meter(meter) / _M_YARD_UK) # * 1.0936132983377078 def NM2m(nm): '''Convert nautical miles to meter (m). @arg nm: Value in nautical miles (C{scalar}). @return: Value in meter (C{float}). @raise ValueError: Invalid B{C{nm}}. ''' return Meter(Float(nm=nm) * _M_NM) def radians2m(rad, radius=R_M, lat=0): '''Convert an angle to a distance along the equator or along the parallel at an other (geodetic) latitude. @arg rad: The angle (C{radians}). @kwarg radius: Mean earth radius, ellipsoid or datum (C{meter}, L{Ellipsoid}, L{Ellipsoid2}, L{Datum} or L{a_f2Tuple}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Distance (C{meter}, same units as B{C{radius}} or equatorial and polar radii) or C{0.0} for near-polar B{C{lat}}. @raise RangeError: Latitude B{C{lat}} outside valid range and L{pygeodesy.rangerrors} set to C{True}. @raise TypeError: Invalid B{C{radius}}. @raise ValueError: Invalid B{C{rad}}, B{C{radius}} or B{C{lat}}. @see: Function L{degrees2m} and L{m2radians}. ''' return _radians2m(Lam(rad=rad, clip=0), radius, lat) def _radians2m(rad, radius, lat): '''(INTERNAL) Helper for C{degrees2m} and C{radians2m}. ''' m = circle4(radius, lat).radius return _0_0 if m < EPS0 else (rad * m) 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 _sin0cos2(q, r, sign): '''(INTERNAL) 2-tuple (C{sin(r), cos(r)}) in quadrant C{0 <= B{q} <= 3} and C{sin} zero I{signed} with B{C{sign}}. ''' if r < PI_2: s, c = sin(r), cos(r) t = s, c, -s, -c, s else: # r == PI_2 t = _1_0, _0_0, _N_1_0, _0_0, _1_0 # else: # r == 0, testUtility failures # t = _0_0, _1_0, _0_0, _N_1_0, _0_0 # q &= 3 s = t[q] or (NEG0 if sign < 0 else _0_0) c = t[q + 1] or _0_0 return s, c def sincos2(rad): '''Return the C{sine} and C{cosine} of an angle in C{radians}. @arg rad: Angle (C{radians}). @return: 2-Tuple (C{sin(B{rad})}, C{cos(B{rad})}). @see: U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/ 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>}. ''' if _isfinite(rad): q = int(rad * _2__PI) # int(math.floor) if q < 0: q -= 1 t = _sin0cos2(q & 3, rad - q * PI_2, rad) else: t = NAN, NAN return t def sincos2_(*rads): '''Return the C{sine} and C{cosine} of angle(s) in C{radians}. @arg rads: One or more angles (C{radians}). @return: Yield the C{sin(B{rad})} and C{cos(B{rad})} for each angle. @see: function L{sincos2}. ''' for r in rads: s, c = sincos2(r) yield s yield c def sincos2d(deg, **adeg): '''Return the C{sine} and C{cosine} of an angle in C{degrees}. @arg deg: Angle (C{degrees}). @kwarg adeg: Optional correction (C{degrees}). @return: 2-Tuple (C{sin(B{deg_})}, C{cos(B{deg_})}, C{B{deg_} = B{deg} + B{adeg}}). @see: U{GeographicLib<https://GeographicLib.SourceForge.io/C++/doc/ 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>}. ''' if _isfinite(deg): q = int(deg * _1__90) # int(math.floor) if q < 0: q -= 1 d = deg - q * _90_0 if adeg: t = _MODS.errors._xkwds_get(adeg, adeg=_0_0) d = _MODS.karney._around(d + t) t = _sin0cos2(q & 3, radians(d), deg) else: t = NAN, NAN return t def sincos2d_(*degs): '''Return the C{sine} and C{cosine} of angle(s) in C{degrees}. @arg degs: One or more angles (C{degrees}). @return: Yield the C{sin(B{deg})} and C{cos(B{deg})} for each angle. @see: Function L{sincos2d}. ''' for d in degs: s, c = sincos2d(d) yield s yield c def sincostan3(rad): '''Return the C{sine}, C{cosine} and C{tangent} of an angle in C{radians}. @arg rad: Angle (C{radians}). @return: 3-Tuple (C{sin(B{rad})}, C{cos(B{rad})}, C{tan(B{rad})}). @see: Function L{sincos2}. ''' rad %= PI2 # see ._wrap comments if rad: s, c = sincos2(rad) t = (s / c) if c else (NINF if s < 0 else (INF if s > 0 else s)) else: # sin(-0.0) == tan(-0.0) = -0.0 c = _1_0 s = t = NEG0 if isneg0(rad) else _0_0 return s, c, t def SM2m(sm): '''Convert statute miles to meter (m). @arg sm: Value in statute miles (C{scalar}). @return: Value in meter (C{float}). @raise ValueError: Invalid B{C{sm}}. ''' return Meter(Float(sm=sm) * _M_SM) def tan_2(rad, **semi): # edge=1 '''Compute the tangent of half angle. @arg rad: Angle (C{radians}). @kwarg semi: Angle or edge name and index for semi-circular error. @return: M{tan(rad / 2)} (C{float}). @raise ValueError: If B{C{rad}} is semi-circular and B{C{semi}} is given. ''' # .formy.excessKarney_, .sphericalTrigonometry.areaOf if semi and isnear0(fabs(rad) - PI): for n, v in semi.items(): break n = _SPACE_(n, _radians_) if not isint(v) else \ _SPACE_(_MODS.streprs.Fmt.SQUARE(**semi), _edge_) raise _MODS.errors._ValueError(n, rad, txt=_semi_circular_) return tan(rad * _0_5) def tand(deg, **error_kwds): '''Return the C{tangent} of an angle in C{degrees}. @arg deg: Angle (C{degrees}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: C{tan(B{deg})}. @raise ValueError: If L{pygeodesy.isnear0}C{(cos(B{deg})}. ''' s, c = sincos2d(deg) if isnear0(c): raise _valueError(tand, deg, **error_kwds) return s / c def tand_(*degs, **error_kwds): '''Return the C{tangent} of angle(s) in C{degrees}. @arg degs: One or more angles (C{degrees}). @kwarg error_kwds: Error to raise (C{ValueError}). @return: Yield the C{tan(B{deg})} for each angle. @raise ValueError: See L{pygeodesy.tand}. ''' for d in degs: yield tand(d, **error_kwds) 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 toise2m(toises): '''Convert French U{toises<https://WikiPedia.org/wiki/Toise>} to meter. @arg toises: Value in toises (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{toises}}. @see: Function L{fathom2m}. ''' return Meter(Float(toises=toises) * _M_TOISE) def truncate(x, ndigits=None): '''Truncate to the given number of digits. @arg x: Value to truncate (C{scalar}). @kwarg ndigits: Number of digits (C{int}), aka I{precision}. @return: Truncated B{C{x}} (C{float}). @see: Python function C{round}. ''' if isint(ndigits): p = _10_0**ndigits x = int(x * p) / p return x 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 C{(B{lon2}-B{lon1}, B{lon2})} unrolled (C{degrees}, C{degrees}). @see: Capability C{LONG_UNROLL} in U{GeographicLib <https://GeographicLib.SourceForge.io/C++/doc/python/interface.html#outmask>}. ''' d = lon2 - lon1 if wrap and fabs(d) > _180_0: u = _wrap(d, _180_0, _360_0) if u != d: return u, lon1 + u return d, lon2 def _unrollon(p1, p2): # unroll180 == .karney._unroll2 '''(INTERNAL) Wrap, unroll and replace longitude if different. ''' _, lon = unroll180(p1.lon, p2.lon, wrap=True) if fabs(lon - p2.lon) > EPS: p2 = p2.dup(lon=wrap180(lon)) return p2 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 C{(B{rad2}-B{rad1}, B{rad2})} unrolled (C{radians}, C{radians}). @see: Capability C{LONG_UNROLL} in U{GeographicLib <https://GeographicLib.SourceForge.io/C++/doc/python/interface.html#outmask>}. ''' r = rad2 - rad1 if wrap and fabs(r) > PI: u = _wrap(r, PI, PI2) if u != r: return u, rad1 + u return r, rad2 def _valueError(where, x, **kwds): '''(INTERNAL) Return a C{_ValueError}. ''' x = _MODS.streprs.Fmt.PAREN(where.__name__, x) return _MODS.errors._ValueError(x, **kwds) def _wrap(angle, wrap, modulo): '''(INTERNAL) Angle wrapper M{((wrap-modulo)..+wrap]}. @arg angle: Angle (C{degrees}, C{radians} or C{grades}). @arg wrap: Range (C{degrees}, C{radians} or C{grades}). @arg modulo: Upper limit (360 C{degrees}, PI2 C{radians} or 400 C{grades}). @return: The B{C{angle}}, wrapped (C{degrees}, C{radians} or C{grades}). ''' a = float(angle) if not (wrap - modulo) <= a < wrap: # 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 a %= modulo if a > wrap: a -= modulo return a 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): # see .streprs._umod_360 '''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) def yard2m(yards): '''Convert I{UK} yards to meter. @arg yards: Value in yards (C{scalar}). @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{yards}}. ''' return Float(yards=yards) * _M_YARD_UK # **) MIT License # # Copyright (C) 2016-2023 -- 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.