# Coverage for pygeodesy/vector3d.py : 95%

## 204 statements 194 run 10 missing 19 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 | # -*- coding: utf-8 -*- u'''Generic 3-D vector base class L{Vector3d} and function L{sumOf}. Pure Python implementation of vector-based functions by I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{Vector-based geodesy <https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. @newfield example: Example, Examples ''' from pygeodesy.basics import EPS, _isnotError, isscalar, len2, \ map1, property_doc_, property_RO from pygeodesy.fmath import fdot, fsum, hypot_ from pygeodesy.formy import n_xyz2latlon, n_xyz2philam from pygeodesy.lazily import _ALL_LAZY from pygeodesy.named import _NamedBase, Vector3Tuple from pygeodesy.streprs import strs from math import atan2, cos, sin # all public constants, classes and functions __all__ = _ALL_LAZY.vector3d + ('Vector3d', 'sumOf') __version__ = '20.03.23' def _xyzn4(xyz, y, z, Error=TypeError): # imported by .ecef.py '''(INTERNAL) Get an C{(x, y, z, name)} 4-tuple. ''' try: t = xyz.x, xyz.y, xyz.z except AttributeError: t = xyz, y, z try: x, y, z = map1(float, *t) except (TypeError, ValueError) as x: raise Error('%s invalid: %r, %s' % ('xyz, y or z', t, x)) return x, y, z, getattr(xyz, 'name', '') def _xyzhdn6(xyz, y, z, height, datum, ll, Error=TypeError): # .cartesianBase.py, .nvectorBase.py '''(INTERNAL) Get an C{(x, y, z, h, d, name)} 6-tuple. ''' x, y, z, n = _xyzn4(xyz, y, z, Error=Error) h = height or getattr(xyz, 'height', None) \ or getattr(xyz, 'h', None) \ or getattr(ll, 'height', None) d = datum or getattr(xyz, 'datum', None) \ or getattr(ll, 'datum', None) return x, y, z, h, d, n class CrossError(ValueError): '''Error raised for zero or near-zero vectorial cross products, occurring for coincident or colinear points, paths or bearings. ''' pass def crosserrors(raiser=None): '''Report or ignore vectorial cross product errors. @kwarg raiser: Use C{True} to throw or C{False} to ignore L{CrossError} exceptions. Use C{None} to leave the setting unchanged. @return: Previous setting (C{bool}). ''' t = Vector3d._crosserrors if raiser in (True, False): Vector3d._crosserrors = raiser return t class VectorError(ValueError): '''Issue with class L{Vector3d} or C{*Nvector}. ''' pass class Vector3d(_NamedBase): # XXX or _NamedTuple or Vector3Tuple? '''Generic 3-D vector manipulation. In a geodesy context, these may be used to represent: - n-vector representing a normal to point on earth's surface - earth-centered, earth-fixed vector (= n-vector for spherical model) - great circle normal to vector - motion vector on earth's surface - etc. ''' _crosserrors = True # set by function crosserrors above _fromll = None #: (INTERNAL) original ll. _length = None #: (INTERNAL) cached length. _united = None #: (INTERNAL) cached norm, unit (L{Vector3d}). _xyz = None #: (INTERNAL) cached xyz (L{Vector3Tuple}). _x = 0 #: (INTERNAL) X component. _y = 0 #: (INTERNAL) Y component. _z = 0 #: (INTERNAL) Z component. def __init__(self, x, y, z, ll=None, name=''): '''New 3-D vector. The vector may be normalised, or use x/y/z values for height relative to the surface of the sphere or ellipsoid, distance from earth centre, etc. @arg x: X component of vector (C{scalar}). @arg y: Y component of vector (C{scalar}). @arg z: Z component of vector (C{scalar}). @kwarg ll: Optional, original latlon (C{LatLon}). @kwarg name: Optional name (C{str}). ''' self._x = x self._y = y self._z = z if ll: self._fromll = ll if name: self.name = name def __add__(self, other): '''Add this to an other vector (L{Vector3d}). @return: Vectorial sum (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.plus(other) # __iadd__ = __add__ __radd__ = __add__ def __abs__(self): '''Return the norm of this vector. @return: Norm, unit length (C{float}); ''' return self.length def __cmp__(self, other): # Python 2- '''Compare this and an other vector @arg other: The other vector (L{Vector3d}). @return: -1, 0 or +1 (C{int}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return -1 if self.length < other.length else ( +1 if self.length > other.length else 0) cmp = __cmp__ def __div__(self, scalar): '''Divide this vector by a scalar. @arg scalar: The divisor (C{scalar}). @return: Quotient (L{Vector3d}). @raise TypeError: Non-scalar B{C{scalar}}. ''' return self.dividedBy(scalar) # __itruediv__ = __div__ __truediv__ = __div__ def __eq__(self, other): '''Is this vector equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if equal, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.isequalTo(other) def __ge__(self, other): '''Is this vector longer than or equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length >= other.length def __gt__(self, other): '''Is this vector longer than an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length > other.length def __le__(self, other): # Python 3+ '''Is this vector shorter than or equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length <= other.length def __lt__(self, other): # Python 3+ '''Is this vector shorter than an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length < other.length # Luciano Ramalho, "Fluent Python", page 397, O'Reilly 2016 def __matmul__(self, other): # PYCHOK Python 3.5+ ... c = a @ b '''Compute the cross product of this and an other vector. @arg other: The other vector (L{Vector3d}). @return: Cross product (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.cross(other) # __imatmul__ = __matmul__ def __mul__(self, scalar): '''Multiply this vector by a scalar @arg scalar: Factor (C{scalar}). @return: Product (L{Vector3d}). ''' return self.times(scalar) # __imul__ = __mul__ # __rmul__ = __mul__ def __ne__(self, other): '''Is this vector not equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return not self.isequalTo(other) def __neg__(self): '''Negate this vector. @return: Negative (L{Vector3d}) ''' return self.negate() def __pos__(self): '''Copy this vector. @return: Positive (L{Vector3d}) ''' return self.copy() # Luciano Ramalho, "Fluent Python", page 397, O'Reilly 2016 def __rmatmul__(self, other): # PYCHOK Python 3.5+ ... c = a @ b '''Compute the cross product of an other and this vector. @arg other: The other vector (L{Vector3d}). @return: Cross product (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return other.cross(self) def __rsub__(self, other): '''Subtract this vector from an other vector. @arg other: The other vector (L{Vector3d}). @return: Difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return other.minus(self) def __sub__(self, other): '''Subtract an other vector from this vector. @arg other: The other vector (L{Vector3d}). @return: Difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.minus(other) # __isub__ = __sub__ def _update(self, updated, *attrs): '''(INTERNAL) Zap cached attributes if updated. ''' if updated: _NamedBase._update(self, updated, '_length', # '_fromll' '_united', '_xyz', *attrs) def angleTo(self, other, vSign=None): '''Compute the angle between this and an other vector. @arg other: The other vector (L{Vector3d}). @kwarg vSign: Optional vector, if supplied (and out of the plane of this and the other), angle is signed positive if this->other is clockwise looking along vSign or negative in opposite direction, otherwise angle is unsigned. @return: Angle (C{radians}). @raise TypeError: If B{C{other}} or B{C{vSign}} not a L{Vector3d}. ''' x = self.cross(other) s = x.length if s < EPS: return 0.0 # use vSign as reference to get sign of s if vSign and x.dot(vSign) < 0: s = -s return atan2(s, self.dot(other)) def cross(self, other, raiser=None): '''Compute the cross product of this and an other vector. @arg other: The other vector (L{Vector3d}). @kwarg raiser: Optional, L{CrossError} label if raised (C{str}). @return: Cross product (L{Vector3d}). @raise CrossError: Zero or near-zero cross product and both B{C{raiser}} and L{crosserrors} set. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) x = self.y * other.z - self.z * other.y y = self.z * other.x - self.x * other.z z = self.x * other.y - self.y * other.x if raiser and self.crosserrors and max(map1(abs, x, y, z)) < EPS: t = 'coincident' if self.isequalTo(other) else 'colinear' r = getattr(other, '_fromll', None) or other raise CrossError('%s %s: %r' % (t, raiser, r)) return self.classof(x, y, z) @property_doc_('''raise or ignore L{CrossError} exceptions (C{bool}).''') def crosserrors(self): '''Get L{CrossError} exceptions (C{bool}). ''' return self._crosserrors @crosserrors.setter # PYCHOK setter! def crosserrors(self, raiser): '''Raise L{CrossError} exceptions (C{bool}). ''' self._crosserrors = bool(raiser) def dividedBy(self, factor): '''Divide this vector by a scalar. @arg factor: The divisor (C{scalar}). @return: New, scaled vector (L{Vector3d}). @raise TypeError: Non-scalar B{C{factor}}. @raise VectorError: Invalid or zero B{C{factor}}. ''' if not isscalar(factor): raise _isnotError('scalar', factor=factor) try: return self.times(1.0 / factor) except (ValueError, ZeroDivisionError): raise VectorError('%s invalid: %r' % ('factor', factor)) def dot(self, other): '''Compute the dot (scalar) product of this and an other vector. @arg other: The other vector (L{Vector3d}). @return: Dot product (C{float}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return fdot(self.xyz, *other.xyz) def equals(self, other, units=False): '''DEPRECATED, use method C{isequalTo}. ''' return self.isequalTo(other, units=units) # PYCHOK no cover def isequalTo(self, other, units=False, eps=EPS): '''Check if this and an other vector are equal or equivalent. @arg other: The other vector (L{Vector3d}). @kwarg units: Optionally, compare the normalized, unit version of both vectors. @kwarg eps: Tolerance for equality (C{scalar}). @return: C{True} if vectors are identical, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. @example: >>> v1 = Vector3d(52.205, 0.119) >>> v2 = Vector3d(52.205, 0.119) >>> e = v1.isequalTo(v2) # True ''' self.others(other) if units: d = self.unit().minus(other.unit()) else: d = self.minus(other) return max(map(abs, d.xyz)) < eps @property_RO def length(self): '''Get the length (norm, magnitude) of this vector (C{float}). ''' if self._length is None: self._length = hypot_(self.x, self.y, self.z) return self._length def minus(self, other): '''Subtract an other vector from this vector. @arg other: The other vector (L{Vector3d}). @return: New vector difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.classof(self.x - other.x, self.y - other.y, self.z - other.z) def negate(self): '''Return this vector in opposite direction. @return: New, opposite vector (L{Vector3d}). ''' return self.classof(-self.x, -self.y, -self.z) @property_RO def _N_vector(self): '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) ''' from pygeodesy.nvectorBase import _N_vector_ return _N_vector_(*(self._xyz or self.xyz)) def others(self, other, name='other'): '''Refined class comparison. @arg other: The other vector (L{Vector3d}). @kwarg name: Optional, other's name (C{str}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' try: _NamedBase.others(self, other, name=name) except TypeError: if not isinstance(other, Vector3d): raise def parse(self, str3d, sep=','): '''Parse an C{"x, y, z"} string. @arg str3d: X, y and z values (C{str}). @kwarg sep: Optional separator (C{str}). @return: New vector (L{Vector3d}). @raise VectorError: Invalid B{C{str3d}}. ''' try: v = [float(v.strip()) for v in str3d.split(sep)] if len(v) != 3: raise ValueError except (TypeError, ValueError): raise VectorError('%s invalid: %r' % ('str3d', str3d)) return self.classof(*v) def plus(self, other): '''Add this vector and an other vector. @arg other: The other vector (L{Vector3d}). @return: Vectorial sum (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.classof(self.x + other.x, self.y + other.y, self.z + other.z) sum = plus # alternate name def rotate(self, axis, theta): '''Rotate this vector around an axis by a specified angle. See U{Rotation matrix from axis and angle <https://WikiPedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle>} and U{Quaternion-derived rotation matrix <https://WikiPedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix>}. @arg axis: The axis being rotated around (L{Vector3d}). @arg theta: The angle of rotation (C{radians}). @return: New, rotated vector (L{Vector3d}). @JSname: I{rotateAround}. ''' self.others(axis, name='axis') c = cos(theta) a = axis.unit() # axis being rotated around b = a.times(1 - c) s = a.times(sin(theta)) p = self.unit().xyz # point being rotated # multiply p by a quaternion-derived rotation matrix return self.classof(fdot(p, a.x * b.x + c, a.x * b.y - s.z, a.x * b.z + s.y), fdot(p, a.y * b.x + s.z, a.y * b.y + c, a.y * b.z - s.x), fdot(p, a.z * b.x - s.y, a.z * b.y + s.x, a.z * b.z + c)) def rotateAround(self, axis, theta): '''DEPRECATED, use method C{rotate}. ''' return self.rotate(axis, theta) # PYCHOK no cover def times(self, factor): '''Multiply this vector by a scalar. @arg factor: Scale factor (C{scalar}). @return: New, scaled vector (L{Vector3d}). @raise TypeError: Non-scalar B{C{factor}}. ''' if not isscalar(factor): raise _isnotError('scalar', factor=factor) return self.classof(self.x * factor, self.y * factor, self.z * factor) def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property C{Nvector.philam}. @return: A L{PhiLam2Tuple}C{(phi, lam)}. ''' return n_xyz2philam(self.x, self.y, self.z) def to2ll(self): # PYCHOK no cover '''DEPRECATED, use property C{Nvector.latlon}. @return: A L{LatLon2Tuple}C{(lat, lon)}. ''' return n_xyz2latlon(self.x, self.y, self.z) def to3xyz(self): # PYCHOK no cover '''DEPRECATED, use property C{xyz}. @return: A L{Vector3Tuple}C{(x, y, z)}. ''' return self.xyz def toStr(self, prec=5, fmt='(%s)', sep=', '): # PYCHOK expected '''Return a string representation of this vector. @kwarg prec: Optional number of decimal places (C{int}). @kwarg fmt: Optional, enclosing format to use (C{str}). @kwarg sep: Optional separator between components (C{str}). @return: Vector as "(x, y, z)" (C{str}). ''' return fmt % (sep.join(strs(self.xyz, prec=prec)),) def unit(self, ll=None): '''Normalize this vector to unit length. @kwarg ll: Optional, original location (C{LatLon}). @return: Normalized vector (L{Vector3d}). ''' if self._united is None: n = self.length if n > EPS and abs(n - 1) > EPS: u = self._xnamed(self.dividedBy(n)) u._length = 1 else: u = self.copy() u._fromll = ll or self._fromll self._united = u._united = u return self._united @property_RO def x(self): '''Get the X component (C{float}). ''' return self._x @property_RO def xyz(self): '''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}). ''' if self._xyz is None: self._xyz = Vector3Tuple(self.x, self.y, self.z) return self._xnamed(self._xyz) @property_RO def y(self): '''Get the Y component (C{float}). ''' return self._y @property_RO def z(self): '''Get the Z component (C{float}). ''' return self._z def sumOf(vectors, Vector=Vector3d, **Vector_kwds): '''Compute the vectorial sum of several vectors. @arg vectors: Vectors to be added (L{Vector3d}[]). @kwarg Vector: Optional class for the vectorial sum (L{Vector3d}). @kwarg Vector_kwds: Optional B{C{Vector}} keyword arguments, ignored if B{C{Vector=None}}. @return: Vectorial sum (B{C{Vector}}). @raise VectorError: No B{C{vectors}}. ''' n, vectors = len2(vectors) if n < 1: raise VectorError('no vectors: %r' & (n,)) r = Vector3Tuple(fsum(v.x for v in vectors), fsum(v.y for v in vectors), fsum(v.z for v in vectors)) if Vector is not None: r = Vector(r.x, r.y, r.z, **Vector_kwds) # PYCHOK x, y, z return r # **) 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.