# Coverage for pygeodesy/ellipsoidalNvector.py : 89%

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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 | # -*- coding: utf-8 -*- u'''N-vector-based classes geodetic (lat-/longitude) L{LatLon}, geocentric (ECEF) L{Cartesian}, L{Ned} and L{Nvector} and functions L{meanOf} and L{toNed}, I{all ellipsoidal}. Pure Python implementation of n-vector-based geodetic (lat-/longitude) methods by I{(C) Chris Veness 2011-2016} published under the same MIT Licence**, see U{Vector-based geodesy <https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. These classes and functions work with: (a) geodesic (polar) lat-/longitude points on the earth's surface and (b) 3-D vectors used as n-vectors representing points on the earth's surface or vectors normal to the plane of a great circle. See also Kenneth Gade U{'A Non-singular Horizontal Position Representation' <https://www.NavLab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf>}, The Journal of Navigation (2010), vol 63, nr 3, pp 395-417. @newfield example: Example, Examples ''' from pygeodesy.datum import Datum, Datums from pygeodesy.ecef import EcefVeness from pygeodesy.ellipsoidalBase import CartesianEllipsoidalBase, \ LatLonEllipsoidalBase from pygeodesy.fmath import fdot, fStr, hypot_ from pygeodesy.lazily import _ALL_LAZY, _2kwds from pygeodesy.named import LatLon3Tuple, _Named, Ned3Tuple, _xnamed from pygeodesy.nvectorBase import NorthPole, LatLonNvectorBase, \ NvectorBase, sumOf as _sumOf from pygeodesy.utily import degrees90, degrees360, property_RO, _TypeError from math import asin, atan2, cos, radians, sin # all public contants, classes and functions __all__ = _ALL_LAZY.ellipsoidalNvector + ( 'Cartesian', 'LatLon', 'Ned', 'Nvector', # classes 'meanOf', 'sumOf', 'toNed') # functions __version__ = '20.01.22' class Cartesian(CartesianEllipsoidalBase): '''Extended to convert geocentric, L{Cartesian} points to L{Nvector} and n-vector-based, geodetic L{LatLon}. ''' def toLatLon(self, **kwds): # PYCHOK LatLon=LatLon, datum=None '''Convert this cartesian point to an C{Nvector}-based geodetic point. @keyword kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. Specify C{LatLon=...} to override this L{LatLon} class or set C{B{LatLon}=None}. @return: The B{C{LatLon}} point (L{LatLon}) or when 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}} or B{C{kwds}}. ''' kwds = _2kwds(kwds, LatLon=LatLon, datum=self.datum) return CartesianEllipsoidalBase.toLatLon(self, **kwds) def toNvector(self, **kwds): # PYCHOK Datums.WGS84 '''Convert this cartesian to L{Nvector} components, I{including height}. @keyword kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector}=None}. Specify C{Nvector=...} to override this L{Nvector} class or set C{B{Nvector}=None}. @return: The B{C{Nvector}} components (L{Nvector}) or a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Nvector}=None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{kwds}}. @example: >>> from ellipsoidalNvector import LatLon >>> c = Cartesian(3980581, 97, 4966825) >>> n = c.toNvector() # (0.62282, 0.000002, 0.78237, +0.24) ''' kwds = _2kwds(kwds, Nvector=Nvector, datum=self.datum) return CartesianEllipsoidalBase.toNvector(self, **kwds) class LatLon(LatLonNvectorBase, LatLonEllipsoidalBase): '''An n-vector-based, ellipsoidal L{LatLon} point. @example: >>> from ellipsoidalNvector import LatLon >>> p = LatLon(52.205, 0.119) # height=0, datum=Datums.WGS84 ''' _Ecef = EcefVeness #: (INTERNAL) Preferred C{Ecef...} class, backward compatible. _Nv = None #: (INTERNAL) Cached toNvector (L{Nvector}). # _v3d = None #: (INTERNAL) Cached toVector3d (L{Vector3d}). _r3 = None #: (INTERNAL) Cached _rotation3 (3-Tuple L{Nvector}). def _rotation3(self): '''(INTERNAL) Build the rotation matrix from n-vector coordinate frame axes. ''' if self._r3 is None: nv = self.toNvector() # local (n-vector) coordinate frame d = nv.negate() # down (opposite to n-vector) e = NorthPole.cross(nv, raiser='pole').unit() # east (pointing perpendicular to the plane) n = e.cross(d) # north (by right hand rule) self._r3 = n, e, d # matrix rows return self._r3 def _update(self, updated): '''(INTERNAL) Clear caches if updated. ''' if updated: # reset caches if self._Nv: self._Nv._fromll = None self._Nv = None self._r3 = None LatLonNvectorBase._update(self, updated) LatLonEllipsoidalBase._update(self, updated) # def crossTrackDistanceTo(self, start, end, radius=R_M): # '''Return the (signed) distance from this point to the great # circle defined by a start point and an end point or bearing. # # @param start: Start point of great circle path (L{LatLon}). # @param end: End point of great circle path (L{LatLon}) or # initial bearing (compass C{degrees360}) at # the start point. # @keyword radius: Optional, mean earth radius (C{meter}). # # @return: Distance to great circle, negative if to left or # positive if to right of path (C{meter}, same units # as B{C{radius}}). # # @raise TypeError: If B{C{start}} or B{C{end}} point is not L{LatLon}. # # @example: # # >>> p = LatLon(53.2611, -0.7972) # # >>> s = LatLon(53.3206, -1.7297) # >>> b = 96.0 # >>> d = p.crossTrackDistanceTo(s, b) # -305.7 # # >>> e = LatLon(53.1887, 0.1334) # >>> d = p.crossTrackDistanceTo(s, e) # -307.5 # ''' # self.others(start, name='start') # # if isscalar(end): # gc from point and bearing # gc = start.greatCircle(end) # else: # gc by two points # gc = start.toNvector().cross(end.toNvector()) # # # (signed) angle between point and gc normal vector # v = self.toNvector() # a = gc.angleTo(v, vSign=v.cross(gc)) # if a < 0: # a = -PI_2 - a # else: # a = PI_2 - a # return a * float(radius) def deltaTo(self, other): '''Calculate the NED delta from this to an other point. The delta is returned as a North-East-Down (NED) vector. Note, this is a linear delta, unrelated to a geodesic on the ellipsoid. The points need not be defined on the same datum. @param other: The other point (L{LatLon}). @return: Delta of this point (L{Ned}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @raise ValueError: If ellipsoids are incompatible. @example: >>> a = LatLon(49.66618, 3.45063) >>> b = LatLon(48.88667, 2.37472) >>> delta = a.deltaTo(b) # [N:-86126, E:-78900, D:1069] >>> d = delta.length # 116807.681 m >>> b = delta.bearing # 222.493° >>> e = delta.elevation # -0.5245° ''' self.ellipsoids(other) # throws TypeError and ValueError n, e, d = self._rotation3() # get delta in cartesian frame dc = other.toCartesian().minus(self.toCartesian()) # rotate dc to get delta in n-vector reference # frame using the rotation matrix row vectors return Ned(dc.dot(n), dc.dot(e), dc.dot(d), name=self.name) # def destination(self, distance, bearing, radius=R_M, height=None): # '''Return the destination point after traveling from this # point the given distance on the given initial bearing. # # @param distance: Distance traveled (C{meter}, same units as # given earth B{C{radius}}). # @param bearing: Initial bearing (compass C{degrees360}). # @keyword radius: Optional, mean earth radius (C{meter}). # @keyword height: Optional height at destination point, # overriding default (C{meter}, same units # as B{C{radius}}). # # @return: Destination point (L{LatLon}). # # @example: # # >>> p = LatLon(51.4778, -0.0015) # >>> q = p.destination(7794, 300.7) # >>> q.toStr() # '51.5135°N, 000.0983°W' ? # ''' # r = float(distance) / float(radius) # angular distance in radians # # great circle by starting from this point on given bearing # gc = self.greatCircle(bearing) # # v1 = self.toNvector() # x = v1.times(cos(r)) # component of v2 parallel to v1 # y = gc.cross(v1).times(sin(r)) # component of v2 perpendicular to v1 # # v2 = x.plus(y).unit() # return v2.toLatLon(height=self.height if height is C{None} else height) def destinationNed(self, delta): '''Calculate the destination point using the supplied NED delta from this point. @param delta: Delta from this to the other point in the local tangent plane (LTP) of this point (L{Ned}). @return: Destination point (L{Cartesian}). @raise TypeError: If {delta} is not L{Ned}. @example: >>> a = LatLon(49.66618, 3.45063) >>> delta = toNed(116807.681, 222.493, -0.5245) # [N:-86126, E:-78900, D:1069] >>> b = a.destinationNed(delta) # 48.88667°N, 002.37472°E @JSname: I{destinationPoint}. ''' _TypeError(Ned, delta=delta) n, e, d = self._rotation3() # convert NED delta to standard Vector3d in coordinate frame of n-vector dn = delta.toVector3d().to3xyz() # rotate dn to get delta in cartesian (ECEF) coordinate # reference frame using the rotation matrix column vectors dc = Cartesian(fdot(dn, n.x, e.x, d.x), fdot(dn, n.y, e.y, d.y), fdot(dn, n.z, e.z, d.z)) # apply (cartesian) delta to this Cartesian to # obtain destination point as cartesian v = self.toCartesian().plus(dc) # the plus() gives a plain vector return v.toLatLon(datum=self.datum, LatLon=self.classof) # Cartesian(v.x, v.y, v.z).toLatLon(...) def distanceTo(self, other, radius=None): '''Approximate the distance from this to an other point. @param other: The other point (L{LatLon}). @keyword radius: Optional, mean earth radius (C{meter}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(48.857, 2.351); >>> d = p.distanceTo(q) # 404300 ''' self.others(other) v1 = self.toVector3d() v2 = other.toVector3d() r = self.datum.ellipsoid.R1 if radius is None else radius return v1.angleTo(v2) * float(r) def equals(self, other, eps=None): '''DEPRECATED, use method C{isequalTo}. ''' return self.isequalTo(other, eps=eps) def isequalTo(self, other, eps=None): '''Compare this point with an other point. @param other: The other point (L{LatLon}). @keyword eps: Optional margin (C{float}). @return: C{True} if points are identical, including datum, I{ignoring height}, C{False} otherwise. @raise TypeError: The B{C{other}} point is not L{LatLon}. @see: Use method L{isequalTo3} to include I{height}. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(52.205, 0.119) >>> e = p.isequalTo(q) # True ''' return LatLonEllipsoidalBase.isequalTo(self, other, eps=eps) \ if self.datum == other.datum else False # def greatCircle(self, bearing): # '''Return the great circle heading on the given bearing # from this point. # # Direction of vector is such that initial bearing vector # b = c × p, where p is representing this point. # # @param bearing: Bearing from this point (compass C{degrees360}). # # @return: N-vector representing great circle (L{Nvector}). # # @example: # # >>> p = LatLon(53.3206, -1.7297) # >>> g = p.greatCircle(96.0) # >>> g.toStr() # '(-0.794, 0.129, 0.594)' # ''' # b, a = self.to2ab() # c = radians(bearing) # # ca, sa = cos(a), sin(a) # cb, sb = cos(b), sin(b) # cc, sc = cos(c), sin(c) # # return self._xnamed(Nvector(sa * cc - ca * sb * sc, # -ca * cc - sa * sb * sc, # cb * sc) # def initialBearingTo(self, other): # '''Return the initial bearing (forward azimuth) from this # to an other point. # # @param other: The other point (L{LatLon}). # # @return: Initial bearing (compass C{degrees360}). # # @raise TypeError: The B{C{other}} point is not L{LatLon}. # # @example: # # >>> p1 = LatLon(52.205, 0.119) # >>> p2 = LatLon(48.857, 2.351) # >>> b = p1.bearingTo(p2) # 156.2 # # @JSname: I{bearingTo}. # ''' # self.others(other) # # v1 = self.toNvector() # v2 = other.toNvector() # # gc1 = v1.cross(v2) # gc through v1 & v2 # gc2 = v1.cross(_NP3) # gc through v1 & North pole # # # bearing is (signed) angle between gc1 & gc2 # return degrees360(gc1.angleTo(gc2, vSign=v1)) def intermediateTo(self, other, fraction, height=None): '''Return the point at given fraction between this and an other point. @param other: The other point (L{LatLon}). @param fraction: Fraction between both points ranging from 0 = this point to 1 = other point (C{float}). @keyword height: Optional height, overriding the fractional height (C{meter}). @return: Intermediate point (L{LatLon}). @raise TypeError: The B{C{other}} point is not L{LatLon}. @example: >>> p = LatLon(52.205, 0.119) >>> q = LatLon(48.857, 2.351) >>> p = p.intermediateTo(q, 0.25) # 51.3721°N, 000.7073°E @JSname: I{intermediatePointTo}. ''' self.others(other) i = other.toNvector().times(fraction).plus( self.toNvector().times(1 - fraction)) if height is None: h = self._havg(other, f=fraction) else: h = height return i.toLatLon(height=h, LatLon=self.classof) # Nvector(i.x, i.y, i.z).toLatLon(...) def toCartesian(self, **kwds): # PYCHOK Cartesian=Cartesian, datum=None '''Convert this point to an C{Nvector}-based geodetic point. @keyword kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. Specify C{LatLon=...} to override this L{LatLon} class or set C{B{LatLon}=None}. @return: The B{C{LatLon}} point (L{LatLon}) or when 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}} or B{C{kwds}}. ''' kwds = _2kwds(kwds, Cartesian=Cartesian, datum=self.datum) return LatLonEllipsoidalBase.toCartesian(self, **kwds) def toNvector(self, **kwds): # PYCHOK signature '''Convert this point to L{Nvector} components, I{including height}. @keyword kwds: Optional, additional B{C{Nvector}} keyword arguments, ignored if C{B{Nvector}=None}. Specify C{Nvector=...} to override this L{Nvector} class or set C{B{Nvector}=None}. @return: The B{C{Nvector}} components (L{Nvector}) or a L{Vector4Tuple}C{(x, y, z, h)} if C{B{Nvector}=None}. @raise TypeError: Invalid B{C{Nvector}} or B{C{kwds}}. @example: >>> p = LatLon(45, 45) >>> n = p.toNvector() >>> n.toStr() # [0.50, 0.50, 0.70710] ''' kwds = _2kwds(kwds, Nvector=Nvector, datum=self.datum) return LatLonNvectorBase.toNvector(self, **kwds) # def toVector3d(self): # '''Convert this point to a L{Vector3d} normal to the # earth's surface. # # @return: Vector representing this point (L{Vector3d}). # # @example: # # >>> p = LatLon(45, 45) # >>> v = p.toVector3d() # >>> v.toStr() # '(0.50, 0.50, 0.707)' # ''' # if self._v3d is None: # x, y, z, _ = self.toNvector() # self._v3d = Vector3d(x, y, z) # return self._v3d class Ned(_Named): '''North-Eeast-Down (NED), also known as Local Tangent Plane (LTP), is a vector in the local coordinate frame of a body. ''' _bearing = None #: (INTERNAL) Cache bearing (compass C{degrees360}). _down = None #: (INTERNAL) Down component (C{meter}). _east = None #: (INTERNAL) East component (C{meter}). _elevation = None #: (INTERNAL) Cache elevation (C{degrees}). _length = None #: (INTERNAL) Cache length (C{float}). _north = None #: (INTERNAL) North component (C{meter}). def __init__(self, north, east, down, name=''): '''New North-East-Down vector. @param north: North component (C{meter}). @param east: East component (C{meter}). @param down: Down component, normal to the surface of the ellipsoid (C{meter}). @keyword name: Optional name (C{str}). @example: >>> from ellipsiodalNvector import Ned >>> delta = Ned(110569, 111297, 1936) >>> delta.toStr(prec=0) # [N:110569, E:111297, D:1936] ''' self._north = north or 0 self._east = east or 0 self._down = down or 0 if name: self.name = name def __str__(self): return self.toStr() @property_RO def bearing(self): '''Get the bearing of this NED vector (compass C{degrees360}). ''' if self._bearing is None: self._bearing = degrees360(atan2(self.east, self.north)) return self._bearing @property_RO def down(self): '''Gets the Down component of this NED vector (C{meter}). ''' return self._down @property_RO def east(self): '''Gets the East component of this NED vector (C{meter}). ''' return self._east @property_RO def elevation(self): '''Get the elevation, tilt of this NED vector in degrees from horizontal, i.e. tangent to ellipsoid surface (C{degrees90}). ''' if self._elevation is None: self._elevation = -degrees90(asin(self.down / self.length)) return self._elevation @property_RO def length(self): '''Gets the length of this NED vector (C{meter}). ''' if self._length is None: self._length = hypot_(self.north, self.east, self.down) return self._length @property_RO def north(self): '''Gets the North component of this NED vector (C{meter}). ''' return self._north def to3ned(self): '''Return this NED vector as north/east/down components. @return: An L{Ned3Tuple}C{(north, east, down)}. ''' r = Ned3Tuple(self.north, self.east, self.down) return self._xnamed(r) def toStr(self, prec=3, fmt='[%s]', sep=', '): # PYCHOK expected '''Return a string representation of this NED vector. @keyword prec: Optional number of decimals, unstripped (C{int}). @keyword fmt: Optional enclosing backets format (C{str}). @keyword sep: Optional separator between NEDs (C{str}). @return: This Ned as "[N:f, E:f, D:f]" (C{str}). ''' t3 = fStr(self.to3ned(), prec=prec, sep=' ').split() return fmt % (sep.join('%s:%s' % t for t in zip('NED', t3)),) def toStr2(self, prec=None, fmt='[%s]', sep=', '): # PYCHOK expected '''Return a string representation of this NED vector as length, bearing and elevation. @keyword prec: Optional number of decimals, unstripped (C{int}). @keyword fmt: Optional enclosing backets format (C{str}). @keyword sep: Optional separator between NEDs (C{str}). @return: This Ned as "[L:f, B:degrees360, E:degrees90]" (C{str}). ''' from pygeodesy.dms import F_D, toDMS t3 = (fStr(self.length, prec=3 if prec is None else prec), toDMS(self.bearing, form=F_D, prec=prec, ddd=0), toDMS(self.elevation, form=F_D, prec=prec, ddd=0)) return fmt % (sep.join('%s:%s' % t for t in zip('LBE', t3)),) def toVector3d(self): '''Return this NED vector as a 3-d vector. @return: The vector(north, east, down) (L{Vector3d}). ''' from pygeodesy.vector3d import Vector3d return Vector3d(*self.to3ned(), name=self.name) _Nvll = LatLon(0, 0) #: (INTERNAL) Reference instance (L{LatLon}). class Nvector(NvectorBase): '''An n-vector is a position representation using a (unit) vector normal to the earth ellipsoid. Unlike lat-/longitude points, n-vectors have no singularities or discontinuities. For many applications, n-vectors are more convenient to work with than other position representations like lat-/longitude, earth-centred earth-fixed (ECEF) vectors, UTM coordinates, etc. Note commonality with L{sphericalNvector.Nvector}. ''' _datum = Datums.WGS84 #: (INTERNAL) Default datum (L{Datum}). _Ecef = EcefVeness #: (INTERNAL) Preferred C{Ecef...} class, backward compatible. def __init__(self, x, y, z, h=0, datum=None, ll=None, name=''): '''New n-vector normal to the earth's surface. @param x: X component (C{meter}). @param y: Y component (C{meter}). @param z: Z component (C{meter}). @keyword h: Optional height above model surface (C{meter}). @keyword datum: Optional datum this n-vector is defined within (L{Datum}). @keyword ll: Optional, original latlon (C{LatLon}). @keyword name: Optional name (C{str}). @raise TypeError: If B{C{datum}} is not a L{Datum}. @example: >>> from ellipsoidalNvector import Nvector >>> v = Nvector(0.5, 0.5, 0.7071, 1) >>> v.toLatLon() # 45.0°N, 045.0°E, +1.00m ''' NvectorBase.__init__(self, x, y, z, h=h, ll=ll, name=name) if datum: _TypeError(Datum, datum=datum) self._datum = datum @property_RO def datum(self): '''Get this n-vector's datum (L{Datum}). ''' return self._datum def toCartesian(self, **kwds): # PYCHOK Cartesian=Cartesian '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates. @keyword kwds: Optional, additional B{C{Cartesian}} keyword arguments, ignored if C{B{Cartesian}=None}. Specify C{Cartesian=...} to override this L{Cartesian} class or set C{B{Cartesian}=None}. @return: The B{C{Cartesian}} point (L{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}}, B{C{datum}} or B{C{kwds}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> c = v.toCartesian() # [3194434, 3194434, 4487327] >>> p = c.toLatLon() # 45.0°N, 45.0°E ''' kwds = _2kwds(kwds, h=self.h, Cartesian=Cartesian, datum=self.datum) return NvectorBase.toCartesian(self, **kwds) # class or .classof def toLatLon(self, **kwds): # PYCHOK height=None, LatLon=LatLon '''Convert this n-vector to an C{Nvector}-based geodetic point. @keyword kwds: Optional, additional B{C{LatLon}} keyword arguments, ignored if C{B{LatLon}=None}. Specify C{LatLon=...} to override this L{LatLon} class or set C{B{LatLon}=None}. @return: The B{C{LatLon}} point (L{LatLon}) or a L{LatLon3Tuple}C{(lat, lon, height)} if C{B{LatLon}=None}. @raise TypeError: Invalid B{C{LatLon}} or B{C{kwds}}. @example: >>> v = Nvector(0.5, 0.5, 0.7071) >>> p = v.toLatLon() # 45.0°N, 45.0°E ''' kwds = _2kwds(kwds, height=self.h, LatLon=LatLon, datum=self.datum) return NvectorBase.toLatLon(self, **kwds) # class or .classof def unit(self, ll=None): '''Normalize this vector to unit length. @keyword ll: Optional, original latlon (C{LatLon}). @return: Normalised vector (L{Nvector}). ''' if self._united is None: u = NvectorBase.unit(self, ll=ll) if u.datum != self.datum: u._datum = self.datum # self._united = u._united = u return self._united def meanOf(points, datum=Datums.WGS84, height=None, LatLon=LatLon): '''Compute the geographic mean of several points. @param points: Points to be averaged (L{LatLon}[]). @keyword datum: Optional datum to use (L{Datum}). @keyword height: Optional height at mean point, overriding the mean height (C{meter}). @keyword LatLon: Optional (sub-)class to return the mean point (L{LatLon}) or C{None}. @return: Geographic mean point and mean height (B{C{LatLon}}) or a L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}} is C{None}. @raise ValueError: Insufficient number of B{C{points}}. ''' _, points = _Nvll.points2(points, closed=False) # geographic mean m = sumOf(p.toNvector() for p in points) a, b, h = m.to3llh() if height is not None: h = height r = LatLon3Tuple(a, b, h) if LatLon is None else \ LatLon(a, b, height=h, datum=datum) return _xnamed(r, meanOf.__name__) def sumOf(nvectors, Vector=Nvector, h=None, **kwds): '''Return the vectorial sum of two or more n-vectors. @param nvectors: Vectors to be added (L{Nvector}[]). @keyword Vector: Optional class for the vectorial sum (L{Nvector}). @keyword h: Optional height, overriding the mean height (C{meter}). @keyword kwds: Optional, additional B{C{Vector}} keyword arguments. @return: Vectorial sum (B{C{Vector}}). @raise VectorError: No B{C{nvectors}}. ''' return _sumOf(nvectors, Vector=Vector, h=h, **kwds) def toNed(distance, bearing, elevation, name=''): '''Create an NED vector from distance, bearing and elevation (in local coordinate system). @param distance: NED vector length (C{meter}). @param bearing: NED vector bearing (compass C{degrees360}). @param elevation: NED vector elevation from local coordinate frame horizontal (C{degrees}). @keyword name: Optional name (C{str}). @return: NED vector equivalent to this B{C{distance}}, B{C{bearing}} and B{C{elevation}} (L{Ned}). @JSname: I{fromDistanceBearingElevation}. ''' b, e = radians(bearing), radians(elevation) d = float(distance) dce = d * cos(e) return Ned(cos(b) * dce, sin(b) * dce, -sin(e) * d, name=name) # **) 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.