# Coverage for pygeodesy/resections.py : 99%

## 313 statements 309 run 4 missing 61 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 | # -*- coding: utf-8 -*- u'''3-Point resection functions L{cassini}, L{collins5}, L{pierlot} and L{tienstra7}, survey functions L{snellius3} and L{wildberger3} and triangle functions L{triAngle}, L{triAngle4}, L{triSide}, L{triSide2} and L{triSide4}. @note: Function L{pierlot} is transcoded with permission from U{triangulationPierlot <http://www.Telecom.ULg.ac.Be/triangulation/doc/total_8c.html>} and U{Pierlot <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree>}. ''' from pygeodesy.basics import isnear0, map1 from pygeodesy.errors import _and, _or, TriangleError, _ValueError, _xkwds from pygeodesy.fmath import favg, Fdot, fidw, fmean, hypot, hypot2_ from pygeodesy.fsums import Fsum, fsum_, fsum1, fsum1_ from pygeodesy.interns import EPS, EPS0, EPS02, PI, PI2, PI_2, PI_4, _a_, _A_, \ _b_, _B_, _c_, _C_, _coincident_, _colinear_, _d_, \ _invalid_, _negative_, _not_, _rIn_, _SPACE_, \ _0_0, _0_5, _1_0, _N_1_0, _2_0, _N_2_0, _4_0, _360_0 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import Fmt, _NamedTuple, _Pass # from pygeodesy.streprs import Fmt # from .named from pygeodesy.units import Degrees, Distance, Radians from pygeodesy.utily import acos1, asin1, sincos2, sincos2_, sincos2d, sincos2d_ from pygeodesy.vector3d import _otherV3d, Vector3d from math import cos, atan2, degrees, radians, sin, sqrt __all__ = _ALL_LAZY.resections __version__ = '22.03.01' _concyclic_ = 'concyclic' _PA_ = 'PA' _PB_ = 'PB' _PC_ = 'PC' _pointH_ = 'pointH' _pointP_ = 'pointP' _R3_ = 'R3' _radA_ = 'radA' _radB_ = 'radB' _radC_ = 'radC' class Collins5Tuple(_NamedTuple): '''5-Tuple C{(pointP, pointH, a, b, c)} with survey C{pointP}, auxiliary C{pointH}, each an instance of B{C{pointA}}'s (sub-)class and triangle sides C{a}, C{b} and C{c} in C{meter}, conventionally. ''' _Names_ = (_pointP_, _pointH_, _a_, _b_, _c_) _Units_ = (_Pass, _Pass, Distance, Distance, Distance) class ResectionError(_ValueError): '''Error raised for issues in L{pygeodesy.resections}. ''' pass class Survey3Tuple(_NamedTuple): '''3-Tuple C{(PA, PB, PC)} with distance from survey point C{P} to each of the triangle corners C{A}, C{B} and C{C} in C{meter}, conventionally. ''' _Names_ = (_PA_, _PB_, _PC_) _Units_ = ( Distance, Distance, Distance) class Tienstra7Tuple(_NamedTuple): '''7-Tuple C{(pointP, A, B, C, a, b, c)} with survey C{pointP}, interior triangle angles C{A}, C{B} and C{C} in C{degrees} and triangle sides C{a}, C{b} and C{c} in C{meter}, conventionally. ''' _Names_ = (_pointP_, _A_, _B_, _C_, _a_, _b_, _c_) _Units_ = (_Pass, Degrees, Degrees, Degrees, Distance, Distance, Distance) class TriAngle4Tuple(_NamedTuple): '''4-Tuple C{(radA, radB, radC, rIn)} with the interior angles at triangle corners C{A}, C{B} and C{C} in C{radians} and the C{InCircle} radius C{rIn} aka C{inradius} in C{meter}, conventionally. ''' _Names_ = (_radA_, _radB_, _radC_, _rIn_) _Units_ = ( Radians, Radians, Radians, Distance) class TriSide2Tuple(_NamedTuple): '''2-Tuple C{(a, radA)} with triangle side C{a} in C{meter}, conventionally and angle C{radA} at the opposite triangle corner in C{radians}. ''' _Names_ = (_a_, _radA_) _Units_ = ( Distance, Radians) class TriSide4Tuple(_NamedTuple): '''4-Tuple C{(a, b, radC, d)} with interior angle C{radC} at triangle corner C{C} in C{radians}with the length of triangle sides C{a} and C{b} and with triangle height C{d} perpendicular to triangle side C{c}, in the same units as triangle sides C{a} and C{b}. ''' _Names_ = (_a_, _b_, _radC_, _d_) _Units_ = ( Distance, Distance, Radians, Distance) def cassini(pointA, pointB, pointC, alpha, beta, useZ=False, Clas=None, **Clas_kwds): '''3-Point resection using U{Cassini<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>}'s method. @arg pointA: First point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg alpha: Angle subtended by triangle side B{C{pointA}} to B{C{pointC}} (C{degrees}, non-negative). @arg beta: Angle subtended by triangle side B{C{pointB}} to B{C{pointC}} (C{degrees}, non-negative). @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=0} (C{bool}). @kwarg Clas: Optional class to return the survey and auxiliary point or C{None} for B{C{pointA}}'s (sub-)class. @kwarg Clas_kwds: Optional additional keyword argument for the survey and auxiliary point instance. @note: Typically, B{C{pointC}} is between B{C{pointA}} and B{C{pointB}}. @return: The survey point, an instance of B{C{Clas}} or if C{B{Clas} is None} of B{C{pointA}}'s (sub-)class. @raise ResectionError: Near-coincident, -colinear or -concyclic points or negative or invalid B{C{alpha}} or B{C{beta}}. @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}. @see: U{Three Point Resection Problem<https://Dokumen.tips/documents/ three-point-resection-problem-introduction-kaestner-burkhardt-method.html>} and functions L{pygeodesy.collins5}, L{pygeodesy.pierlot} and L{pygeodesy.tienstra7}. ''' def _H(A, C, sa): s, c = sincos2d(sa) if isnear0(s): raise ValueError(_or(_coincident_, _colinear_)) t = s, c, c x = Fdot(t, A.x, C.y, -A.y).fover(s) y = Fdot(t, A.y, -C.x, A.x).fover(s) return Vector3d(x, y, 0) A = _otherV3d(useZ=useZ, pointA=pointA) B = _otherV3d(useZ=useZ, pointB=pointB) C = _otherV3d(useZ=useZ, pointC=pointC) try: sa, sb = map1(float, alpha, beta) if min(sa, sb) < 0: raise ValueError(_negative_) if fsum_(_360_0, -sa, -sb) < EPS0: raise ValueError(_invalid_) H1 = _H(A, C, sa) H2 = _H(B, C, -sb) x = H1.x - H2.x y = H1.y - H2.y if isnear0(x) or isnear0(y): raise ValueError(_SPACE_(_concyclic_, (x, y))) m = y / x n = x / y N = n + m if isnear0(N): raise ValueError(_SPACE_(_concyclic_, (m, n, N))) t = n, m, _1_0, _N_1_0 x = Fdot(t, C.x, H1.x, C.y, H1.y).fover(N) y = Fdot(t, H1.y, C.y, C.x, H1.x).fover(N) z = _zidw(A, B, C, x, y) if useZ else 0 clas = Clas or pointA.classof return clas(x, y, z, **_xkwds(Clas_kwds, name=cassini.__name__)) except (TypeError, ValueError) as x: raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, alpha=alpha, beta=beta, txt=str(x)) def collins5(pointA, pointB, pointC, alpha, beta, useZ=False, Clas=None, **Clas_kwds): '''3-Point resection using U{Collins<https://Dokumen.tips/documents/ three-point-resection-problem-introduction-kaestner-burkhardt-method.html>}' method. @arg pointA: First point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointC: Center point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg alpha: Angle subtended by triangle side C{b} from B{C{pointA}} to B{C{pointC}} (C{degrees}, non-negative). @arg beta: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees}, non-negative). @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=0} (C{bool}). @kwarg Clas: Optional class to return the survey point or C{None} for B{C{pointA}}'s (sub-)class. @kwarg Clas_kwds: Optional additional keyword argument for the survey point instance. @note: Typically, B{C{pointC}} is between B{C{pointA}} and B{C{pointB}}. @return: L{Collins5Tuple}C{(pointP, pointH, a, b, c)} with survey C{pointP}, auxiliary C{pointH}, each an instance of B{C{Clas}} or if C{B{Clas} is None} of B{C{pointA}}'s (sub-)class and triangle sides C{a}, C{b} and C{c} in C{meter}, conventionally. @raise ResectionError: Near-coincident, -colinear or -concyclic points or negative or invalid B{C{alpha}} or B{C{beta}}. @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointM}}. @see: U{Collins' methode<https://NL.WikiPedia.org/wiki/Achterwaartse_insnijding>} and functions L{pygeodesy.cassini}, L{pygeodesy.pierlot} and L{pygeodesy.tienstra7}. ''' def _azi_len2(A, B, pi2): v = B.minus(A) r = atan2(v.x, v.y) if pi2 and r < 0: r += pi2 return r, v.length def _cV3(d, r, A, B, C, useZ, V3, **kwds): s, c = sincos2(r) x = A.x + d * s y = A.y + d * c z = _zidw(A, B, C, x, y) if useZ else 0 return V3(x, y, z, **kwds) A = _otherV3d(useZ=useZ, pointA=pointA) B = _otherV3d(useZ=useZ, pointB=pointB) C = _otherV3d(useZ=useZ, pointC=pointC) try: ra, rb = radians(alpha), radians(beta) if min(ra, rb) < 0: raise ValueError(_negative_) sra, srH = sin(ra), sin(ra + rb - PI) # rH = PI - ((PI - ra) + (PI - rb)) if isnear0(sra) or isnear0(srH): raise ValueError(_or(_coincident_, _colinear_, _concyclic_)) clas = Clas or pointA.classof kwds = _xkwds(Clas_kwds, name=collins5.__name__) # za, a = _azi_len2(C, B, PI2) zb, b = _azi_len2(C, A, PI2) zc, c = _azi_len2(A, B, 0) # d = c * sin(PI - rb) / srH # B.minus(H).length d = c * sin(PI - ra) / srH # A.minus(H).length r = zc + PI - rb # zh = zc + (PI - rb) H = _cV3(d, r, A, B, C, useZ, Vector3d) zh, _ = _azi_len2(C, H, PI2) # d = a * sin(za - zh) / sin(rb) # B.minus(P).length d = b * sin(zb - zh) / sra # A.minus(P).length r = zh - ra # zb - PI + (PI - ra - (zb - zh)) P = _cV3(d, r, A, B, C, useZ, clas, **kwds) H = clas(H.x, H.y, H.z, **kwds) a = B.minus(C).length return Collins5Tuple(P, H, a, b, c) except (TypeError, ValueError) as x: raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, alpha=alpha, beta=beta, txt=str(x)) def pierlot(point1, point2, point3, alpha12, alpha23, useZ=False, Clas=None, **Clas_kwds): '''3-Point resection using U{Pierlot<http://www.Telecom.ULg.ac.Be/publi/publications/ pierlot/Pierlot2014ANewThree>}'s method C{ToTal}. @arg point1: First point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg point2: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg point3: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg alpha12: Angle subtended from B{C{point1}} to B{C{point2}} (C{degrees}). @arg alpha23: Angle subtended from B{C{point2}} to B{C{point3}} (C{degrees}). @kwarg useZ: If C{True}, interpolate the Z component, otherwise use C{z=0} (C{bool}). @kwarg Clas: Optional class to return the survey point or C{None} for B{C{point1}}'s (sub-)class. @kwarg Clas_kwds: Optional additional keyword arguments for the survey point instance. @note: Points B{C{point1}}, B{C{point2}} and B{C{point3}} are ordered counter-clockwise, typically. @return: The survey (or robot) point, an instance of B{C{Clas}} or if C{B{Clas} is None} of B{C{point1}}'s (sub-)class. @raise ResectionError: Near-coincident, -colinear or -concyclic points or invalid B{C{alpha12}} or B{C{alpha23}}. @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or B{C{point3}}. @see: U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation Algorithm for Mobile Robot Positioning"<https://ORBi.ULiege.Be/ bitstream/2268/157469/1/Pierlot2014ANewThree.pdf>}, U{Vincent Pierlot, Marc Van Droogenbroeck, "18 Triangulation Algorithms for 2D Positioning (also known as the Resection Problem)"<http://www.Telecom.ULg.ac.Be/ triangulation>} and functions L{pygeodesy.cassini}, L{pygeodesy.collins5} and L{pygeodesy.tienstra7}. ''' B1 = _otherV3d(useZ=useZ, point1=point1) B2 = _otherV3d(useZ=useZ, point2=point2) B3 = _otherV3d(useZ=useZ, point3=point3) try: # (INTERNAL) Raises error for (pseudo-)singularities s12, c12, s23, c23 = sincos2d_(alpha12, alpha23) if isnear0(s12) or isnear0(s23): raise ValueError(_or(_coincident_, _colinear_)) cot12 = c12 / s12 cot23 = c23 / s23 # cot31 = (1 - cot12 * cot23) / (cot12 + cot32) d = fsum1_(c12 * s23, s12 * c23) if isnear0(d): raise ValueError(_or(_colinear_, _coincident_)) cot31 = fsum1_(s12 * s23, -c12 * c23) / d x1_, y1_, _ = B1.minus(B2).xyz x3_, y3_, _ = B3.minus(B2).xyz # x23 = x3_ - cot23 * y3_ # y23 = y3_ + cot23 * x3_ X12_23 = Fsum(x1_, cot12 * y1_, -x3_, cot23 * y3_) Y12_23 = Fsum(y1_, -cot12 * x1_, -y3_, -cot23 * x3_) X31_23 = Fsum(x1_, -cot31 * y1_, cot31 * y3_, cot23 * y3_) Y31_23 = Fsum(y1_, cot31 * x1_, -cot31 * x3_, -cot23 * x3_) d = float(X31_23 * Y12_23 - X12_23 * Y31_23) if isnear0(d): raise ValueError(_or(_coincident_, _colinear_, _concyclic_)) K = Fsum(x3_ * x1_, cot31 * (y3_ * x1_), y3_ * y1_, -cot31 * (x3_ * y1_)) x = (B2.x * d + K * Y12_23).fover(d) y = (B2.y * d - K * X12_23).fover(d) z = _zidw(B1, B2, B3, x, y) if useZ else 0 clas = Clas or point1.classof return clas(x, y, z, **_xkwds(Clas_kwds, name=pierlot.__name__)) except (TypeError, ValueError) as x: raise ResectionError(point1=point1, point2=point2, point3=point3, alpha12=alpha12, alpha23=alpha23, txt=str(x)) def snellius3(a, b, degC, alpha, beta): '''Snellius' surveying using U{Snellius Pothenot<https://WikiPedia.org/wiki/Snellius–Pothenot_problem>}. @arg a: Length of the triangle side between corners C{B} and C{C} and opposite of triangle corner C{A} (C{scalar}, non-negative C{meter}, conventionally). @arg b: Length of the triangle side between corners C{C} and C{A} and opposite of triangle corner C{B} (C{scalar}, non-negative C{meter}, conventionally). @arg degC: Angle at triangle corner C{C}, opposite triangle side C{c} (non-negative C{degrees}). @arg alpha: Angle subtended by triangle side B{C{b}} (non-negative C{degrees}). @arg beta: Angle subtended by triangle side B{C{a}} (non-negative C{degrees}). @return: L{Survey3Tuple}C{(PA, PB, PC)} with distance from survey point C{P} to each of the triangle corners C{A}, C{B} and C{C}, same units as triangle sides B{C{a}}, B{C{b}} and B{C{c}}. @raise TriangleError: Invalid B{C{a}}, B{C{b}} or B{C{degC}} or negative B{C{alpha}} or B{C{beta}}. @see: Function L{pygeodesy.wildberger3}. ''' try: a, b, degC, alpha, beta = map1(float, a, b, degC, alpha, beta) ra, rb, rC = map1(radians, alpha, beta, degC) if min(ra, rb, rC, a, b) < 0: raise ValueError(_negative_) r = fsum_(ra, rb, rC) * _0_5 k = PI - r if min(k, r) < 0: raise ValueError(_or(_coincident_, _colinear_)) sa, _, sb, _ = sincos2_(ra, rb) p = atan2(a * sa, b * sb) sp, cp, sr, cr = sincos2_(PI_4 - p, r) w = atan2(sp * sr, cp * cr) x = k + w y = k - w s = abs(sa) if abs(sb) > s: pc = abs(a * sin(y) / sb) elif s: pc = abs(b * sin(x) / sa) else: raise ValueError(_or(_colinear_, _coincident_)) pa = _triSide(b, pc, fsum_(PI, -ra, -x)) pb = _triSide(a, pc, fsum_(PI, -rb, -y)) return Survey3Tuple(pa, pb, pc) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, degC=degC, alpha=alpha, beta=beta, txt=str(x)) def tienstra7(pointA, pointB, pointC, alpha, beta=None, gamma=None, useZ=False, Clas=None, **Clas_kwds): '''3-Point resection using U{Tienstra<https://WikiPedia.org/wiki/Tienstra_formula>}'s formula. @arg pointA: First point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointB: Second point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg pointC: Third point (C{Cartesian}, L{Vector3d}, C{Vector3Tuple}, C{Vector4Tuple} or C{Vector2Tuple} if C{B{useZ}=False}). @arg alpha: Angle subtended by triangle side C{a} from B{C{pointB}} to B{C{pointC}} (C{degrees}, non-negative). @kwarg beta: Angle subtended by triangle side C{b} from B{C{pointA}} to B{C{pointC}} (C{degrees}, non-negative) or C{None} if C{B{gamma} is not None}. @kwarg gamma: Angle subtended by triangle side C{c} from B{C{pointA}} to B{C{pointB}} (C{degrees}, non-negative) or C{None} if C{B{beta} is not None}. @kwarg useZ: If C{True}, use and interpolate the Z component, otherwise force C{z=0} (C{bool}). @kwarg Clas: Optional class to return the survey point or C{None} for B{C{pointA}}'s (sub-)class. @kwarg Clas_kwds: Optional additional keyword arguments for the survey point instance. @note: Points B{C{pointA}}, B{C{pointB}} and B{C{pointC}} are ordered clockwise. @return: L{Tienstra7Tuple}C{(pointP, A, B, C, a, b, c)} with survey C{pointP}, an instance of B{C{Clas}} or if C{B{Clas} is None} of B{C{pointA}}'s (sub-)class, with triangle angles C{A} at B{C{pointA}}, C{B} at B{C{pointB}} and C{C} at B{C{pointC}} in C{degrees} and with triangle sides C{a}, C{b} and C{c} in C{meter}, conventionally. @raise ResectionError: Near-coincident, -colinear or -concyclic points or sum of B{C{alpha}}, B{C{beta}} and B{C{gamma}} not C{360} or negative B{C{alpha}}, B{C{beta}} or B{C{gamma}}. @raise TypeError: Invalid B{C{pointA}}, B{C{pointB}} or B{C{pointC}}. @see: U{3-Point Resection Solver<http://MesaMike.org/geocache/GC1B0Q9/tienstra/>}, U{V. Pierlot, M. Van Droogenbroeck, "A New Three Object Triangulation..." <http://www.Telecom.ULg.ac.Be/publi/publications/pierlot/Pierlot2014ANewThree/>}, U{18 Triangulation Algorithms...<http://www.Telecom.ULg.ac.Be/triangulation/>} and functions L{pygeodesy.cassini}, L{pygeodesy.collins5} and L{pygeodesy.pierlot}. ''' def _deg_ks(r, s, ks, N): if isnear0(fsum_(PI, r, -s)): # r + (PI2 - s) == PI raise ValueError(Fmt.PARENSPACED(concyclic=N)) # k = 1 / (cot(r) - cot(s)) # = 1 / (cos(r) / sin(r) - cos(s) / sin(s)) # = 1 / (cos(r) * sin(s) - cos(s) * sin(r)) / (sin(r) * sin(s)) # = sin(r) * sin(s) / (cos(r) * sin(s) - cos(s) * sin(r)) sr, cr, ss, cs = sincos2_(r, s) c = cr * ss - cs * sr if isnear0(c): raise ValueError(Fmt.PARENSPACED(cotan=N)) ks.append(sr * ss / c) return Degrees(degrees(r), name=N) # C degrees A = _otherV3d(useZ=useZ, pointA=pointA) B = _otherV3d(useZ=useZ, pointB=pointB) C = _otherV3d(useZ=useZ, pointC=pointC) try: sa, sb, sc = map1(radians, alpha, (beta or 0), (gamma or 0)) if beta is None: if gamma is None: raise ValueError(_and(Fmt.EQUAL(beta=beta), Fmt.EQUAL(gamma=gamma))) sb = fsum_(PI2, -sa, -sc) elif gamma is None: sc = fsum_(PI2, -sa, -sb) else: # subtended angles must add to 360 degrees r = fsum1_(sa, sb, sc) if abs(r - PI2) > EPS: raise ValueError(Fmt.EQUAL(sum=degrees(r))) if min(sa, sb, sc) < 0: raise ValueError(_negative_) # triangle sides a = B.minus(C).length b = A.minus(C).length c = A.minus(B).length ks = [] # 3 Ks and triangle angles dA = _deg_ks(_triAngle(b, c, a), sa, ks, _A_) dB = _deg_ks(_triAngle(a, c, b), sb, ks, _B_) dC = _deg_ks(_triAngle(a, b, c), sc, ks, _C_) k = fsum1(ks) if isnear0(k): raise ValueError(Fmt.EQUAL(K=k)) x = Fdot(ks, A.x, B.x, C.x).fover(k) y = Fdot(ks, A.y, B.y, C.y).fover(k) z = _zidw(A, B, C, x, y) if useZ else 0 clas = Clas or pointA.classof P = clas(x, y, z, **_xkwds(Clas_kwds, name=tienstra7.__name__)) return Tienstra7Tuple(P, dA, dB, dC, a, b, c) except (TypeError, ValueError) as x: raise ResectionError(pointA=pointA, pointB=pointB, pointC=pointC, alpha=alpha, beta=beta, gamma=gamma, txt=str(x)) def triAngle(a, b, c): '''Compute one angle of a triangle. @arg a: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg b: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg c: Opposite triangle side length (C{scalar}, non-negative C{meter}, conventionally). @return: Angle in C{radians} at triangle corner C{C}, opposite triangle side B{C{c}}. @raise TriangleError: Invalid or negative B{C{a}}, B{C{b}} or B{C{c}}. @see: Functions L{pygeodesy.triAngle4} and L{pygeodesy.triSide}. ''' try: return _triAngle(a, b, c) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, c=c, tx=str(x)) def _triAngle(a, b, c): # (INTERNAL) To allow callers to embellish errors a, b, c = map1(float, a, b, c) if a < b: a, b = b, a if b < 0 or c < 0: raise ValueError(_negative_) if a < EPS0: raise ValueError(_coincident_) b_a = b / a if b_a < EPS0: raise ValueError(_coincident_) return acos1(fsum_(_1_0, b_a**2, -(c / a)**2) / (b_a * _2_0)) def triAngle4(a, b, c): '''Compute the angles of a triangle. @arg a: Length of the triangle side opposite of triangle corner C{A} (C{scalar}, non-negative C{meter}, conventionally). @arg b: Length of the triangle side opposite of triangle corner C{B} (C{scalar}, non-negative C{meter}, conventionally). @arg c: Length of the triangle side opposite of triangle corner C{C} (C{scalar}, non-negative C{meter}, conventionally). @return: L{TriAngle4Tuple}C{(radA, radB, radC, rIn)} with angles C{radA}, C{radB} and C{radC} at triangle corners C{A}, C{B} and C{C}, all in C{radians} and the C{InCircle} radius C{rIn} aka C{inradius}, same units as triangle sides B{C{a}}, B{C{b}} and B{C{c}}. @raise TriangleError: Invalid or negative B{C{a}}, B{C{b}} or B{C{c}}. @see: Function L{pygeodesy.triAngle}. ''' try: a, b, c = map1(float, a, b, c) ab = a < b if ab: a, b = b, a bc = b < c if bc: b, c = c, b if c > EPS0: # c = min(a, b, c) s = float(Fsum(a, b, c) * _0_5) if s < EPS0: raise ValueError(_negative_) sa, sb, sc = (s - a), (s - b), (s - c) r = sa * sb * sc / s if r < EPS02: raise ValueError(_coincident_) r = sqrt(r) rA = atan2(r, sa) * _2_0 rB = atan2(r, sb) * _2_0 rC = fsum_(PI, -rA, -rB) if min(rA, rB, rC) < 0: raise ValueError(_colinear_) elif c < 0: raise ValueError(_negative_) else: # 0 <= c <= EPS0 rA = rB = PI_2 rC = r = _0_0 if bc: rB, rC = rC, rB if ab: rA, rB = rB, rA return TriAngle4Tuple(rA, rB, rC, r) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, c=c, txt=str(x)) def triSide(a, b, radC): '''Compute one side of a triangle. @arg a: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg b: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg radC: Angle included by sides B{C{a}} and B{C{b}}, opposite triangle side C{c} (C{radians}). @return: Length of triangle side C{c}, opposite triangle corner C{C} and angle B{C{radC}}, same units as B{C{a}} and B{C{b}}. @raise TriangleError: Invalid B{C{a}}, B{C{b}} or B{C{radC}}. @see: Functions L{pygeodesy.sqrt_a}, L{pygeodesy.triAngle}, L{pygeodesy.triSide2} and L{pygeodesy.triSide4}. ''' try: return _triSide(a, b, radC) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, radC=radC, txt=str(x)) def _triSide(a, b, radC): # (INTERNAL) To allow callers to embellish errors a, b, r = map1(float, a, b, radC) if min(a, b, r) < 0: raise ValueError(_negative_) if a < b: a, b = b, a if a > EPS0: ba = b / a c2 = fsum_(_1_0, ba**2, _N_2_0 * ba * cos(r)) if c2 > EPS02: return a * sqrt(c2) elif c2 < 0: raise ValueError(_invalid_) return hypot(a, b) def triSide2(b, c, radB): '''Compute one side and the opposite angle of a triangle. @arg b: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg c: Adjacent triangle side length (C{scalar}, non-negative C{meter}, conventionally). @arg radB: Angle included by sides B{C{a}} and B{C{c}}, opposite triangle side C{b} (C{radians}). @return: L{TriSide2Tuple}C{(a, radA)} with triangle angle C{radA} in C{radians} and length of the opposite triangle side C{a}, same units as B{C{b}} and B{C{c}}. @raise TriangleError: Invalid B{C{b}} or B{C{c}} or either B{C{b}} or B{C{radB}} near zero. @see: Functions L{pygeodesy.sqrt_a}, L{pygeodesy.triSide} and L{pygeodesy.triSide4}. ''' try: return _triSide2(b, c, radB) except (TypeError, ValueError) as x: raise TriangleError(b=b, c=c, radB=radB, txt=str(x)) def _triSide2(b, c, radB): # (INTERNAL) To allow callers to embellish errors b, c, rB = map1(float, b, c, radB) if min(b, c, rB) < 0: raise ValueError(_negative_) sB, cB = sincos2(rB) if isnear0(sB): if not isnear0(b): raise ValueError(_invalid_) if cB < 0: a, rA = (b + c), PI else: a, rA = abs(b - c), _0_0 elif isnear0(b): raise ValueError(_invalid_) else: rA = fsum_(PI, -rB, -asin1(c * sB / b)) a = sin(rA) * b / sB return TriSide2Tuple(a, rA) def triSide4(radA, radB, c): '''Compute two sides and the height of a triangle. @arg radA: Angle at triangle corner C{A}, opposite triangle side C{a} (non-negative C{radians}). @arg radB: Angle at triangle corner C{B}, opposite triangle side C{b} (non-negative C{radians}). @arg c: Length of triangle side between triangle corners C{A} and C{B}, (C{scalar}, non-negative C{meter}, conventionally). @return: L{TriSide4Tuple}C{(a, b, radC, d)} with triangle sides C{a} and C{b} and triangle height C{d} perpendicular to triangle side B{C{c}}, all in the same units as B{C{c}} and interior angle C{radC} in C{radians} at triangle corner C{C}, opposite triangle side B{C{c}}. @raise TriangleError: Invalid or negative B{C{radA}}, B{C{radB}} or B{C{c}}. @see: U{Triangulation, Surveying<https://WikiPedia.org/wiki/Triangulation_(surveying)>} and functions L{pygeodesy.sqrt_a}, L{pygeodesy.triSide} and L{pygeodesy.triSide2}. ''' try: rA, rB, c = map1(float, radA, radB, c) rC = fsum_(PI, -rA, -rB) if min(rC, rA, rB, c) < 0: raise ValueError(_negative_) sa, ca, sb, cb = sincos2_(rA, rB) sc = fsum1_(sa * cb, sb * ca) if sc < EPS0 or min(sa, sb) < 0: raise ValueError(_invalid_) sc = c / sc return TriSide4Tuple((sa * sc), (sb * sc), rC, (sa * sb * sc)) except (TypeError, ValueError) as x: raise TriangleError(radA=radA, radB=radB, c=c, txt=str(x)) def wildberger3(a, b, c, alpha, beta, R3=min): '''Snellius' surveying using U{Rational Trigonometry<https://WikiPedia.org/wiki/Snellius–Pothenot_problem>}. @arg a: Length of the triangle side between corners C{B} and C{C} and opposite of triangle corner C{A} (C{scalar}, non-negative C{meter}, conventionally). @arg b: Length of the triangle side between corners C{C} and C{A} and opposite of triangle corner C{B} (C{scalar}, non-negative C{meter}, conventionally). @arg c: Length of the triangle side between corners C{A} and C{B} and opposite of triangle corner C{C} (C{scalar}, non-negative C{meter}, conventionally). @arg alpha: Angle subtended by triangle side B{C{b}} (C{degrees}, non-negative). @arg beta: Angle subtended by triangle side B{C{a}} (C{degrees}, non-negative). @kwarg R3: Callable to determine C{R3} from C{(R3 - C)**2 = D}, typically standard function C{min} or C{max}, invoked with 2 arguments. @return: L{Survey3Tuple}C{(PA, PB, PC)} with distance from survey point C{P} to each of the triangle corners C{A}, C{B} and C{C}, same units as B{C{a}}, B{C{b}} and B{C{c}}. @raise TriangleError: Invalid B{C{a}}, B{C{b}} or B{C{c}} or negative B{C{alpha}} or B{C{beta}} or B{C{R3}} not C{callable}. @see: U{Wildberger, Norman J.<https://math.sc.chula.ac.th/cjm/content/ survey-article-greek-geometry-rational-trigonometry-and-snellius-–-pothenot-surveying>}, U{Devine Proportions, page 252<http://www.ms.LT/derlius/WildbergerDivineProportions.pdf>} and function L{pygeodesy.snellius3}. ''' def _s(x): return sin(x)**2 def _vpa(r1, r3, q2, q3_r3): r = r1 * r3 * _4_0 n = float(r - Fsum(r1, r3, -q2).fpow(2)) if n < 0 or isnear0(r): raise ValueError(_coincident_) return sqrt((n / r) * q3_r3) if n else _0_0 try: a, b, c, da, db = map1(float, a, b, c, alpha, beta) if min(a, b, c, da, db) < 0: raise ValueError(_negative_) ra, rb = radians(da), radians(db) s1, s2, s3 = s = map1(_s, rb, ra, ra + rb) # rb, ra! if min(s) < EPS02: raise ValueError(_or(_coincident_, _colinear_)) q1, q2, q3 = q = a**2, b**2, c**2 if min(q) < EPS02: raise ValueError(_coincident_) q3_s3 = q3 / s3 r1 = s2 * q3_s3 # s2! r2 = s1 * q3_s3 # s1! Qs = Fsum(*q) # == hypot2_(a, b, c) ss = fsum1(s) s += float(Qs * _0_5), # tuple! C0 = Fdot(s, q1, q2, q3, -ss) r3 = C0.fover(-s3) d0 = float(Qs.fpow(2).fsub_(hypot2_(*q) * _2_0).fmul(s1 * s2 / s3)) if d0 > EPS02: # > c0 d0 = sqrt(d0) if not callable(R3): raise ValueError(_SPACE_(_R3_, _not_(callable.__name__))) r3 = R3(float(d0 + C0), -float(d0 - C0)) # XXX min or max elif d0 < 0: raise ValueError(_negative_) pa = _vpa(r1, r3, q2, q3_s3) pb = _vpa(r2, r3, q1, q3_s3) pc = favg(_triSide2(b, pa, ra).a, _triSide2(a, pb, rb).a) return Survey3Tuple(pa, pb, pc) except (TypeError, ValueError) as x: raise TriangleError(a=a, b=b, c=c, alpha=alpha, beta=beta, R3=R3, txt=str(x)) def _zidw(A, B, C, x, y): # interpolate z or coplanar with A, B and C? t = A.z, B.z, C.z v = Vector3d(x, y, fmean(t)) m = v.minus return fidw(t, (m(A).length, m(B).length, m(C).length)) # **) MIT License # # Copyright (C) 2016-2022 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.