# Coverage for pygeodesy/nvectorBase.py : 97%

## 234 statements 226 run 8 missing 21 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 | # -*- coding: utf-8 -*- u'''(INTERNAL) Base classes for elliposiodal and spherical C{Nvector}s. Classes L{LatLonNvectorBase} for C{n-vectorial} ellipsoidal and spherical C{LatLon}s, class L{NvectorBase} for C{Cartesian}s and function L{sumOf}. Pure Python implementation of C{n-vector}-based geodesy tools for ellipsoidal earth models, transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016} and published under the same MIT Licence**, see U{Vector-based geodesy <https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. ''' from pygeodesy.basics import len2, map1 from pygeodesy.datums import _spherical_datum from pygeodesy.errors import IntersectionError, _ValueError, \ _xkwds, _xkwds_pop from pygeodesy.fmath import fidw, fsum, fsum_, hypot_ from pygeodesy.formy import n_xyz2latlon, n_xyz2philam from pygeodesy.interns import EPS, EPS1, EPS_2, MISSING, NN, R_M, \ _bearing_, _coincident_, _COMMASPACE_, \ _distance_, _intersection_, _no_, _NorthPole_, \ _points_, _pole_, _SPACE_, _SouthPole_, \ _1_, _2_, _3_, _2_0 from pygeodesy.latlonBase import LatLonBase from pygeodesy.lazily import _ALL_DOCS from pygeodesy.named import notImplemented, _xother3 from pygeodesy.namedTuples import Trilaterate5Tuple, Vector3Tuple, \ Vector4Tuple from pygeodesy.props import deprecated_method, property_doc_, Property_RO from pygeodesy.streprs import Fmt, hstr, unstr, _xattrs from pygeodesy.units import Bearing, Height, Radius_, Scalar from pygeodesy.utily import sincos2d from pygeodesy.vector3d import Vector3d, VectorError, \ sumOf as _sumOf, _xyzhdn6 from math import fabs, sqrt # atan2, cos, sin __all__ = (_NorthPole_, _SouthPole_) # constants __version__ = '21.06.25' class NvectorBase(Vector3d): # XXX kept private '''Base class for ellipsoidal and spherical C{Nvector}s. ''' _datum = None # L{Datum}, overriden _h = 0 # height (C{meter}) _H = NN # height prefix (C{str}), '↑' in JS version def __init__(self, x, y=None, z=None, h=0, ll=None, datum=None, name=NN): '''New n-vector normal to the earth's surface. @arg x: An C{Nvector}, L{Vector3Tuple}, L{Vector4Tuple} or the C{X} coordinate (C{scalar}). @arg y: The C{Y} coordinate (C{scalar}) if B{C{x}} C{scalar}. @arg z: The C{Z} coordinate (C{scalar}) if B{C{x}} C{scalar}. @kwarg h: Optional height above surface (C{meter}). @kwarg ll: Optional, original latlon (C{LatLon}). @kwarg datum: Optional, I{pass-thru} datum (L{Datum}). @kwarg name: Optional name (C{str}). @raise TypeError: Non-scalar B{C{x}}, B{C{y}} or B{C{z}} coordinate or B{C{x}} not an C{Nvector}, L{Vector3Tuple} or L{Vector4Tuple} or invalid B{C{datum}}. @example: >>> from pygeodesy.sphericalNvector import Nvector >>> v = Nvector(0.5, 0.5, 0.7071, 1) >>> v.toLatLon() # 45.0°N, 045.0°E, +1.00m ''' x, y, z, h, d, n = _xyzhdn6(x, y, z, h, datum, ll) Vector3d.__init__(self, x, y, z, ll=ll, name=name or n) if h: self.h = h if d: self._datum = _spherical_datum(d, name=self.name) # pass-thru @Property_RO def datum(self): '''Get the I{pass-thru} datum (C{Datum}) or C{None}. ''' return self._datum @Property_RO def Ecef(self): '''Get the ECEF I{class} (L{EcefKarney}), I{lazily}. ''' from pygeodesy.ecef import EcefKarney return EcefKarney # default @property_doc_(''' the height above surface (C{meter}).''') def h(self): '''Get the height above surface (C{meter}). ''' return self._h @h.setter # PYCHOK setter! def h(self, h): '''Set the height above surface. @arg h: New height (C{meter}). @raise TypeError: If B{C{h}} invalid. @raise VectorError: If B{C{h}} invalid. ''' h = Height(h=h, Error=VectorError) self._update(h != self._h) self._h = h @property_doc_(''' the height prefix (C{str}).''') def H(self): '''Get the height prefix (C{str}). ''' return self._H @H.setter # PYCHOK setter! def H(self, H): '''Set the height prefix. @arg H: New height prefix (C{str}). ''' self._H = str(H) if H else NN def hStr(self, prec=-2, m=NN): '''Return a string for the height B{C{h}}. @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg m: Optional unit of the height (C{str}). @see: Function L{hstr}. ''' return NN(self.H, hstr(self.h, prec=prec, m=m)) @Property_RO def isEllipsoidal(self): '''Check whether this n-vector is ellipsoidal (C{bool} or C{None} if unknown). ''' return self.datum.isEllipsoidal if self.datum else None @Property_RO def isSpherical(self): '''Check whether this n-vector is spherical (C{bool} or C{None} if unknown). ''' return self.datum.isSpherical if self.datum else None @Property_RO def lam(self): '''Get the (geodetic) longitude in C{radians} (C{float}). ''' return self.philam.lam @Property_RO def lat(self): '''Get the (geodetic) latitude in C{degrees} (C{float}). ''' return self.latlon.lat @Property_RO def latlon(self): '''Get the (geodetic) lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}). ''' return n_xyz2latlon(self.x, self.y, self.z, name=self.name) @Property_RO def latlonheight(self): '''Get the (geodetic) lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}). ''' return self.latlon.to3Tuple(self.h) @Property_RO def latlonheightdatum(self): '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}). ''' return self.latlonheight.to4Tuple(self.datum) @Property_RO def lon(self): '''Get the (geodetic) longitude in C{degrees} (C{float}). ''' return self.latlon.lon @Property_RO def phi(self): '''Get the (geodetic) latitude in C{radians} (C{float}). ''' return self.philam.phi @Property_RO def philam(self): '''Get the (geodetic) lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}). ''' return n_xyz2philam(self.x, self.y, self.z, name=self.name) @Property_RO def philamheight(self): '''Get the (geodetic) lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}). ''' return self.philam.to3Tuple(self.h) @Property_RO def philamheightdatum(self): '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}). ''' return self.philamheight.to4Tuple(self.datum) @deprecated_method def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property L{philam}. @return: A L{PhiLam2Tuple}C{(phi, lam)}. ''' return self.philam @deprecated_method def to3abh(self, height=None): # PYCHOK no cover '''DEPRECATED, use method L{philamheight} or C{philam.to3Tuple(B{height})}. @kwarg height: Optional height, overriding this n-vector's height (C{meter}). @return: A L{PhiLam3Tuple}C{(phi, lam, height)}. @raise ValueError: Invalid B{C{height}}. ''' return self.philamheight if height in (None, self.h) else \ self.philam.to3Tuple(height) def toCartesian(self, h=None, Cartesian=None, datum=None, **Cartesian_kwds): '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates. @kwarg h: Optional height, overriding this n-vector's height (C{meter}). @kwarg Cartesian: Optional class to return the (ECEF) coordinates (C{Cartesian}). @kwarg datum: Optional datum (C{Datum}), overriding this datum. @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian}=None}. @return: The cartesian (ECEF) coordinates (B{C{Cartesian}}) or if C{B{Cartesian}=None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} and C{M} if available. @raise TypeError: Invalid B{C{Cartesian}}. @raise ValueError: Invalid B{C{h}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> c = v.toCartesian() # [3194434, 3194434, 4487327] >>> p = c.toLatLon() # 45.0°N, 45.0°E ''' d = _spherical_datum(datum or self.datum, name=self.name) E = d.ellipsoid h = self.h if h is None else Height(h=h) x, y, z = self.x, self.y, self.z # Kenneth Gade eqn (22) n = E.b / hypot_(x * E.a_b, y * E.a_b, z) r = h + n * E.a2_b2 x *= r y *= r z *= n + h if Cartesian is None: r = self.Ecef(d).reverse(x, y, z, M=True) else: kwds = _xkwds(Cartesian_kwds, datum=d) # h=0 r = Cartesian(x, y, z, **kwds) return self._xnamed(r) @deprecated_method def to2ll(self): # PYCHOK no cover '''DEPRECATED, use property L{latlon}. @return: A L{LatLon2Tuple}C{(lat, lon)}. ''' return self.latlon @deprecated_method def to3llh(self, height=None): # PYCHOK no cover '''DEPRECATED, use property C{latlonheight} or C{latlon.to3Tuple}C{)}B{C{height}}C{)}. @kwarg height: Optional height, overriding this n-vector's height (C{meter}). @return: A L{LatLon3Tuple}C{(lat, lon, height)}. @raise ValueError: Invalid B{C{height}}. ''' return self.latlonheight if height in (None, self.h) else \ self.latlon.to3Tuple(height) def toLatLon(self, height=None, LatLon=None, datum=None, **LatLon_kwds): '''Convert this n-vector to an C{Nvector}-based geodetic point. @kwarg height: Optional height, overriding this n-vector's height (C{meter}). @kwarg LatLon: Optional class to return the geodetic point (C{LatLon}) or C{None}. @kwarg datum: Optional, spherical datum (C{Datum}). @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. @return: The geodetic point (C{LatLon}) or if C{B{LatLon}=None}, an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)} with C{C} and C{M} if available. @raise TypeError: Invalid B{C{LatLon}}. @raise ValueError: Invalid B{C{height}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> p = v.toLatLon() # 45.0°N, 45.0°E ''' d = _spherical_datum(datum or self.datum, name=self.name) h = self.h if height is None else Height(height) # use self.Cartesian(Cartesian=None) for better accuracy of the height # than self.Ecef(d).forward(self.lat, self.lon, height=h, M=True) if LatLon is None: r = self.toCartesian(h=h, Cartesian=None, datum=d) else: kwds = _xkwds(LatLon_kwds, height=h, datum=d) r = self._xnamed(LatLon(self.lat, self.lon, **kwds)) return r def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected '''Return a string representation of this n-vector. Height component is only included if non-zero. @kwarg prec: Optional number of decimals, unstripped (C{int}). @kwarg fmt: Optional enclosing backets format (C{str}). @kwarg sep: Optional separator between components (C{str}). @return: Comma-separated C{"(x, y, z [, h])"} enclosed in B{C{fmt}} brackets (C{str}). @example: >>> Nvector(0.5, 0.5, 0.7071).toStr() # (0.5, 0.5, 0.7071) >>> Nvector(0.5, 0.5, 0.7071, 1).toStr(-3) # (0.500, 0.500, 0.707, +1.00) ''' t = Vector3d.toStr(self, prec=prec, fmt=NN, sep=sep) if self.h: t = sep.join((t, self.hStr())) return (fmt % (t,)) if fmt else t def toVector3d(self, norm=True): '''Convert this n-vector to a 3-D vector, I{ignoring the height}. @kwarg norm: Normalize the 3-D vector (C{bool}). @return: The (normalized) vector (L{Vector3d}). ''' v = Vector3d.unit(self) if norm else self return Vector3d(v.x, v.y, v.z, name=self.name) @deprecated_method def to4xyzh(self, h=None): # PYCHOK no cover '''DEPRECATED, use property L{xyzh} or C{xyz.to4Tuple(B{h})}. ''' return self.xyzh if h in (None, self.h) else Vector4Tuple( self.x, self.y, self.z, h, name=self.name) def unit(self, ll=None): '''Normalize this n-vector to unit length. @kwarg ll: Optional, original latlon (C{LatLon}). @return: Normalized vector (C{Nvector}). ''' return _xattrs(Vector3d.unit(self, ll=ll), '_h') @Property_RO def xyzh(self): '''Get this n-vector's components (L{Vector4Tuple}C{(x, y, z, h)}) ''' return self.xyz.to4Tuple(self.h) NorthPole = NvectorBase(0, 0, +1, name=_NorthPole_) # North pole (C{Nvector}) SouthPole = NvectorBase(0, 0, -1, name=_SouthPole_) # South pole (C{Nvector}) class _N_vector_(NvectorBase): '''(INTERNAL) Minimal, low-overhead C{n-vector}. ''' def __init__(self, x, y, z, h=0, name=NN): self._x, self._y, self._z = x, y, z if h: self._h = h if name: self.name = name class LatLonNvectorBase(LatLonBase): '''(INTERNAL) Base class for n-vector-based ellipsoidal and spherical C{LatLon} classes. ''' def _update(self, updated, *attrs, **kwds): # PYCHOK _Nv=None '''(INTERNAL) Zap cached attributes if updated. @see: C{ellipsoidalNvector.LatLon} and C{sphericalNvector.LatLon} for the special case of B{C{_Nv}}. ''' if updated: _Nv = _xkwds_pop(kwds, _Nv=None) if _Nv is not None: if _Nv._fromll is not None: _Nv._fromll = None self._Nv = None LatLonBase._update(self, updated, *attrs) # def distanceTo(self, other, **kwds): # PYCHOK no cover # '''(INTERNAL) I{Must be overloaded}, see function C{notOverloaded}. # ''' # from pygeodesy.named import notOverloaded # notOverloaded(self, other, **kwds) def intersections2(self, radius1, other, radius2, **kwds): # PYCHOK expected '''B{Not implemented}, throws a C{NotImplementedError} always. ''' notImplemented(self, radius1, other, radius2, **kwds) def others(self, *other, **name_other_up): '''Refined class comparison. @arg other: The other instance (C{LatLonNvectorBase}). @kwarg name_other_up: Overriding C{name=other} and C{up=1} keyword arguments. @return: The B{C{other}} if compatible. @raise TypeError: Incompatible B{C{other}} C{type}. ''' if other: other0 = other[0] if isinstance(other0, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase? return other0 other, name, up = _xother3(self, other, **name_other_up) if not isinstance(other, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase? LatLonBase.others(self, other, name=name, up=up + 1) return other def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature '''Convert this point to C{Nvector} components, I{including height}. @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector}=None}. @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if B{C{Nvector}} is C{None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}. ''' return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds) def triangulate(self, bearing1, other, bearing2, height=None): '''Locate a point given this and an other point and a bearing at this and the other point. @arg bearing1: Bearing at this point (compass C{degrees360}). @arg other: The other point (C{LatLon}). @arg bearing2: Bearing at the other point (compass C{degrees360}). @kwarg height: Optional height at the triangulated point, overriding the mean height (C{meter}). @return: Triangulated point (C{LatLon}). @raise TypeError: Invalid B{C{other}} point. @raise Valuerror: Points coincide. @example: >>> p = LatLon("47°18.228'N","002°34.326'W") # Basse Castouillet >>> q = LatLon("47°18.664'N","002°31.717'W") # Basse Hergo >>> t = p.triangulate(7, q, 295) # 47.323667°N, 002.568501°W' ''' return _triangulate(self, bearing1, self.others(other), bearing2, height=height, LatLon=self.classof) def trilaterate(self, distance1, point2, distance2, point3, distance3, radius=R_M, height=None, useZ=False): '''Locate a point at given distances from this and two other points. @arg distance1: Distance to this point (C{meter}, same units as B{C{radius}}). @arg point2: Second reference point (C{LatLon}). @arg distance2: Distance to point2 (C{meter}, same units as B{C{radius}}). @arg point3: Third reference point (C{LatLon}). @arg distance3: Distance to point3 (C{meter}, same units as B{C{radius}}). @kwarg radius: Mean earth radius (C{meter}). @kwarg height: Optional height at trilaterated point, overriding the mean height (C{meter}, same units as B{C{radius}}). @kwarg useZ: Include Z component iff non-NaN, non-zero (C{bool}). @return: Trilaterated point (C{LatLon}). @raise IntersectionError: No intersection, trilateration failed. @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. @raise ValueError: Some B{C{points}} coincide or invalid B{C{distance1}}, B{C{distance2}}, B{C{distance3}} or B{C{radius}}. @see: U{Trilateration<https://WikiPedia.org/wiki/Trilateration>}, Veness' JavaScript U{Trilateration<https://www.Movable-Type.co.UK/ scripts/latlong-vectors.html>} and method C{LatLon.trilaterate2} of other, non-C{Nvector LatLon} classes. ''' return _trilaterate(self, distance1, self.others(point2=point2), distance2, self.others(point3=point3), distance3, radius=radius, height=height, useZ=useZ, LatLon=self.classof) def trilaterate5(self, distance1, point2, distance2, point3, distance3, # PYCHOK signature area=False, eps=EPS1, radius=R_M, wrap=False): '''B{Not implemented} for C{B{area}=True} or C{B{wrap}=True} and falls back to method C{trilaterate} otherwise. @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)} with a single trilaterated intersection C{minPoint I{is} maxPoint}, C{min I{is} max} the nearest intersection margin and count C{n = 1}. @raise IntersectionError: No intersection, trilateration failed. @raise NotImplementedError: Keyword argument C{B{area}=True} or C{B{wrap}=True} not (yet) supported. @raise TypeError: Invalid B{C{point2}} or B{C{point3}}. @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}}, B{C{distance2}}, B{C{distance3}} or B{C{radius}}. ''' if area or wrap: notImplemented(self, area=area, wrap=wrap) t = _trilaterate(self, distance1, self.others(point2=point2), distance2, self.others(point3=point3), distance3, radius=radius, height=None, useZ=True, LatLon=self.classof) # ... and handle B{C{eps}} and C{IntersectionError} # like function C{.latlonBase._trilaterate5} d = self.distanceTo(t, radius=radius, wrap=wrap) # PYCHOK distanceTo d = min(fabs(distance1 - d), fabs(distance2 - d), fabs(distance3 - d)) if d < eps: # min is max, minPoint is maxPoint return Trilaterate5Tuple(d, t, d, t, 1) # n = 1 t = _SPACE_(_no_(_intersection_), Fmt.PAREN(min.__name__, Fmt.f(d, prec=3))) raise IntersectionError(area=area, eps=eps, wrap=wrap, txt=t) def sumOf(nvectors, Vector=None, h=None, **Vector_kwds): '''Return the vectorial sum of two or more n-vectors. @arg nvectors: Vectors to be added (C{Nvector}[]). @kwarg Vector: Optional class for the vectorial sum (C{Nvector}) or C{None}. @kwarg h: Optional height, overriding the mean height (C{meter}). @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments, ignored if C{B{Vector}=None}. @return: Vectorial sum (B{C{Vector}}) or a L{Vector4Tuple}C{(x, y, z, h)} if B{C{Vector}} is C{None}. @raise VectorError: No B{C{nvectors}}. ''' n, nvectors = len2(nvectors) if n < 1: raise VectorError(nvectors=n, txt=MISSING) if h is None: h = fsum(v.h for v in nvectors) / float(n) if Vector is None: r = _sumOf(nvectors, Vector=Vector3Tuple).to4Tuple(h) else: r = _sumOf(nvectors, Vector=Vector, h=h, **Vector_kwds) return r def _triangulate(point1, bearing1, point2, bearing2, height=None, **LatLon_LatLon_kwds): # (INTERNAL)Locate a point given two known points and initial # bearings from those points, see LatLon.triangulate above def _gc(p, b, _i_): n = p.toNvector() de = NorthPole.cross(n, raiser=_pole_).unit() # east vector @ n dn = n.cross(de) # north vector @ n s, c = sincos2d(Bearing(b, name=_bearing_ + _i_)) dest = de.times(s) dnct = dn.times(c) d = dnct.plus(dest) # direction vector @ n return n.cross(d) # great circle point + bearing if point1.isequalTo(point2, EPS): raise _ValueError(points=point2, txt=_coincident_) gc1 = _gc(point1, bearing1, _1_) # great circle p1 + b1 gc2 = _gc(point2, bearing2, _2_) # great circle p2 + b2 n = gc1.cross(gc2, raiser=_points_) # n-vector of intersection point h = point1._havg(point2) if height is None else Height(height) kwds = _xkwds(LatLon_LatLon_kwds, height=h) return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...) def _trilaterate(point1, distance1, point2, distance2, point3, distance3, radius=R_M, height=None, useZ=False, **LatLon_LatLon_kwds): # (INTERNAL) Locate a point at given distances from # three other points, see LatLon.triangulate above def _nd2(p, d, r, _i_, *qs): # .toNvector and angular distance squared for q in qs: if p.isequalTo(q, EPS): raise _ValueError(points=p, txt=_coincident_) return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2 r = Radius_(radius) n1, r12 = _nd2(point1, distance1, r, _1_) n2, r22 = _nd2(point2, distance2, r, _2_, point1) n3, r32 = _nd2(point3, distance3, r, _3_, point1, point2) # the following uses x,y coordinate system with origin at n1, x axis n1->n2 y = n3.minus(n1) x = n2.minus(n1) z = None d = x.length # distance n1->n2 if d > EPS_2: # and y.length > EPS_2: X = x.unit() # unit vector in x direction n1->n2 i = X.dot(y) # signed magnitude of x component of n1->n3 Y = y.minus(X.times(i)).unit() # unit vector in y direction j = Y.dot(y) # signed magnitude of y component of n1->n3 if abs(j) > EPS_2: # courtesy Carlos Freitas <https://GitHub.com/mrJean1/PyGeodesy/issues/33> x = fsum_(r12, -r22, d**2) / (_2_0 * d) # n1->intersection x- and ... y = fsum_(r12, -r32, i**2, j**2, -2 * x * i) / (_2_0 * j) # ... y-component # courtesy AleixDev <https://GitHub.com/mrJean1/PyGeodesy/issues/43> z = fsum_(max(r12, r22, r32), -(x**2), -(y**2)) # XXX not just r12! if z > EPS: n = n1.plus(X.times(x)).plus(Y.times(y)) if useZ: # include Z component Z = X.cross(Y) # unit vector perpendicular to plane n = n.plus(Z.times(sqrt(z))) if height is None: h = fidw((point1.height, point2.height, point3.height), map1(fabs, distance1, distance2, distance3)) else: h = Height(height) kwds = _xkwds(LatLon_LatLon_kwds, height=h) return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...) # no intersection, d < EPS_2 or abs(j) < EPS_2 or z < EPS t = _SPACE_(_no_, _intersection_, NN) raise IntersectionError(point1=point1, distance1=distance1, point2=point2, distance2=distance2, point3=point3, distance3=distance3, txt=unstr(t, z=z, useZ=useZ)) __all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes # **) MIT License # # Copyright (C) 2016-2021 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.