Coverage for pygeodesy/nvectorBase.py: 96%
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Private elliposiodal and spherical C{Nvector} base classes
5L{LatLonNvectorBase} and L{NvectorBase} and function L{sumOf}.
7Pure Python implementation of C{n-vector}-based geodesy tools for ellipsoidal
8earth models, transcoded from JavaScript originals by I{(C) Chris Veness 2005-2016}
9and published under the same MIT Licence**, see U{Vector-based geodesy
10<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}.
11'''
13# from pygeodesy.basics import map1 # from .namedTuples
14from pygeodesy.constants import EPS, EPS1, EPS_2, R_M, _2_0, _N_2_0
15# from pygeodesy.datums import _spherical_datum # from .formy
16from pygeodesy.errors import IntersectionError, _ValueError, VectorError, \
17 _xkwds, _xkwds_pop2
18from pygeodesy.fmath import fdot, fidw, hypot_ # PYCHOK fdot shared
19from pygeodesy.fsums import Fsum, fsumf_
20from pygeodesy.formy import _isequalTo, n_xyz2latlon, n_xyz2philam, \
21 _spherical_datum
22# from pygeodesy.internals import _under # from .named
23from pygeodesy.interns import NN, _1_, _2_, _3_, _bearing_, _coincident_, \
24 _COMMASPACE_, _distance_, _h_, _insufficient_, \
25 _intersection_, _no_, _point_, _pole_, _SPACE_
26from pygeodesy.latlonBase import LatLonBase, _ALL_DOCS, _ALL_LAZY, _MODS
27# from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS # from .latlonBase
28from pygeodesy.named import _xother3, _under
29from pygeodesy.namedTuples import Trilaterate5Tuple, Vector3Tuple, \
30 Vector4Tuple, map1
31from pygeodesy.props import deprecated_method, Property_RO, property_doc_, \
32 property_RO, _update_all
33from pygeodesy.streprs import Fmt, hstr, unstr, _xattrs
34from pygeodesy.units import Bearing, Height, Radius_, Scalar
35from pygeodesy.utily import sincos2d, _unrollon, _unrollon3
36from pygeodesy.vector3d import Vector3d, _xyzhdlln4
38from math import fabs, sqrt
40__all__ = _ALL_LAZY.nvectorBase
41__version__ = '24.06.06'
44class NvectorBase(Vector3d): # XXX kept private
45 '''Base class for ellipsoidal and spherical C{Nvector}s.
46 '''
47 _datum = None # L{Datum}, overriden
48 _h = Height(h=0) # height (C{meter})
49 _H = NN # height prefix (C{str}), '↑' in JS version
51 def __init__(self, x_xyz, y=None, z=None, h=0, datum=None, **ll_name):
52 '''New n-vector normal to the earth's surface.
54 @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector
55 (C{Nvector}, L{Vector3d}, L{Vector3Tuple} or L{Vector4Tuple}).
56 @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}} is not
57 C{scalar}, otherwise same units as B{C{x_xyz}}.
58 @kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}} is not
59 C{scalar}, otherwise same units as B{C{x_xyz}}.
60 @kwarg h: Optional height above surface (C{meter}).
61 @kwarg datum: Optional, I{pass-thru} datum (L{Datum}).
62 @kwarg ll_name: Optional C{B{name}=NN} (C{str}) and optional, original
63 latlon C{B{ll}=None} (C{LatLon}).
65 @raise TypeError: Non-scalar B{C{x}}, B{C{y}} or B{C{z}} coordinate or
66 B{C{x_xyz}} not an C{Nvector}, L{Vector3Tuple} or
67 L{Vector4Tuple} or invalid B{C{datum}}.
68 '''
69 h, d, ll, n = _xyzhdlln4(x_xyz, h, datum, **ll_name)
70 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=n)
71 if h:
72 self.h = h
73 if d is not None:
74 self._datum = _spherical_datum(d, name=n) # pass-thru
76 @Property_RO
77 def datum(self):
78 '''Get the I{pass-thru} datum (C{Datum}) or C{None}.
79 '''
80 return self._datum
82 @property_RO
83 def Ecef(self):
84 '''Get the ECEF I{class} (L{EcefKarney}), I{once}.
85 '''
86 NvectorBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO
87 return E
89 @property_RO
90 def ellipsoidalNvector(self):
91 '''Get the C{Nvector type} iff ellipsoidal, overloaded in L{pygeodesy.ellipsoidalNvector.Nvector}.
92 '''
93 return False
95 @property_doc_(''' the height above surface (C{meter}).''')
96 def h(self):
97 '''Get the height above surface (C{meter}).
98 '''
99 return self._h
101 @h.setter # PYCHOK setter!
102 def h(self, h):
103 '''Set the height above surface (C{meter}).
105 @raise TypeError: If B{C{h}} invalid.
107 @raise VectorError: If B{C{h}} invalid.
108 '''
109 h = Height(h=h, Error=VectorError)
110 if self._h != h:
111 _update_all(self)
112 self._h = h
114 @property_doc_(''' the height prefix (C{str}).''')
115 def H(self):
116 '''Get the height prefix (C{str}).
117 '''
118 return self._H
120 @H.setter # PYCHOK setter!
121 def H(self, H):
122 '''Set the height prefix (C{str}).
123 '''
124 self._H = str(H) if H else NN
126 def hStr(self, prec=-2, m=NN):
127 '''Return a string for the height B{C{h}}.
129 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
130 @kwarg m: Optional unit of the height (C{str}).
132 @see: Function L{pygeodesy.hstr}.
133 '''
134 return NN(self.H, hstr(self.h, prec=prec, m=m))
136 @Property_RO
137 def isEllipsoidal(self):
138 '''Check whether this n-vector is ellipsoidal (C{bool} or C{None} if unknown).
139 '''
140 return self.datum.isEllipsoidal if self.datum else None
142 @Property_RO
143 def isSpherical(self):
144 '''Check whether this n-vector is spherical (C{bool} or C{None} if unknown).
145 '''
146 return self.datum.isSpherical if self.datum else None
148 @Property_RO
149 def lam(self):
150 '''Get the (geodetic) longitude in C{radians} (C{float}).
151 '''
152 return self.philam.lam
154 @Property_RO
155 def lat(self):
156 '''Get the (geodetic) latitude in C{degrees} (C{float}).
157 '''
158 return self.latlon.lat
160 @Property_RO
161 def latlon(self):
162 '''Get the (geodetic) lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
163 '''
164 return n_xyz2latlon(self.x, self.y, self.z, name=self.name)
166 @Property_RO
167 def latlonheight(self):
168 '''Get the (geodetic) lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
169 '''
170 return self.latlon.to3Tuple(self.h)
172 @Property_RO
173 def latlonheightdatum(self):
174 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
175 '''
176 return self.latlonheight.to4Tuple(self.datum)
178 @Property_RO
179 def lon(self):
180 '''Get the (geodetic) longitude in C{degrees} (C{float}).
181 '''
182 return self.latlon.lon
184 @Property_RO
185 def phi(self):
186 '''Get the (geodetic) latitude in C{radians} (C{float}).
187 '''
188 return self.philam.phi
190 @Property_RO
191 def philam(self):
192 '''Get the (geodetic) lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
193 '''
194 return n_xyz2philam(self.x, self.y, self.z, name=self.name)
196 @Property_RO
197 def philamheight(self):
198 '''Get the (geodetic) lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
199 '''
200 return self.philam.to3Tuple(self.h)
202 @Property_RO
203 def philamheightdatum(self):
204 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
205 '''
206 return self.philamheight.to4Tuple(self.datum)
208 @property_RO
209 def sphericalNvector(self):
210 '''Get the C{Nvector type} iff spherical, overloaded in L{pygeodesy.sphericalNvector.Nvector}.
211 '''
212 return False
214 @deprecated_method
215 def to2ab(self): # PYCHOK no cover
216 '''DEPRECATED, use property L{philam}.
218 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
219 '''
220 return self.philam
222 @deprecated_method
223 def to3abh(self, height=None): # PYCHOK no cover
224 '''DEPRECATED, use property L{philamheight} or C{philam.to3Tuple(B{height})}.
226 @kwarg height: Optional height, overriding this
227 n-vector's height (C{meter}).
229 @return: A L{PhiLam3Tuple}C{(phi, lam, height)}.
231 @raise ValueError: Invalid B{C{height}}.
232 '''
233 return self.philamheight if height in (None, self.h) else \
234 self.philam.to3Tuple(height)
236 def toCartesian(self, h=None, Cartesian=None, datum=None, **Cartesian_kwds):
237 '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates.
239 @kwarg h: Optional height, overriding this n-vector's height (C{meter}).
240 @kwarg Cartesian: Optional class to return the (ECEF) coordinates
241 (C{Cartesian}).
242 @kwarg datum: Optional datum (C{Datum}), overriding this datum.
243 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
244 arguments, ignored if C{B{Cartesian} is None}.
246 @return: The cartesian (ECEF) coordinates (B{C{Cartesian}}) or
247 if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y, z,
248 lat, lon, height, C, M, datum)} with C{C} and C{M} if
249 available.
251 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}
252 argument.
254 @raise ValueError: Invalid B{C{h}}.
255 '''
256 D = _spherical_datum(datum or self.datum, name=self.name)
257 E = D.ellipsoid
258 h = self.h if h is None else Height(h)
260 x, y, z = self.x, self.y, self.z
261 # Kenneth Gade eqn 22
262 n = E.b / hypot_(x * E.a_b, y * E.a_b, z)
263 r = h + n * E.a2_b2
265 x *= r
266 y *= r
267 z *= h + n
269 if Cartesian is None:
270 r = self.Ecef(D).reverse(x, y, z, M=True)
271 else:
272 kwds = _xkwds(Cartesian_kwds, datum=D) # h=0
273 r = Cartesian(x, y, z, **kwds)
274 return self._xnamed(r)
276 @deprecated_method
277 def to2ll(self): # PYCHOK no cover
278 '''DEPRECATED, use property L{latlon}.
280 @return: A L{LatLon2Tuple}C{(lat, lon)}.
281 '''
282 return self.latlon
284 @deprecated_method
285 def to3llh(self, height=None): # PYCHOK no cover
286 '''DEPRECATED, use property C{latlonheight} or C{latlon.to3Tuple(B{height})}.
288 @kwarg height: Optional height, overriding this
289 n-vector's height (C{meter}).
291 @return: A L{LatLon3Tuple}C{(lat, lon, height)}.
293 @raise ValueError: Invalid B{C{height}}.
294 '''
295 return self.latlonheight if height in (None, self.h) else \
296 self.latlon.to3Tuple(height)
298 def toLatLon(self, height=None, LatLon=None, datum=None, **LatLon_kwds):
299 '''Convert this n-vector to an C{Nvector}-based geodetic point.
301 @kwarg height: Optional height, overriding this n-vector's
302 height (C{meter}).
303 @kwarg LatLon: Optional class to return the geodetic point
304 (C{LatLon}) or C{None}.
305 @kwarg datum: Optional, spherical datum (C{Datum}).
306 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
307 arguments, ignored if C{B{LatLon} is None}.
309 @return: The geodetic point (C{LatLon}) or if C{B{LatLon} is None},
310 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
311 datum)} with C{C} and C{M} if available.
313 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}
314 argument.
316 @raise ValueError: Invalid B{C{height}}.
317 '''
318 d = _spherical_datum(datum or self.datum, name=self.name)
319 h = self.h if height is None else Height(height)
320 # use self.Cartesian(Cartesian=None) for better accuracy of the height
321 # than self.Ecef(d).forward(self.lat, self.lon, height=h, M=True)
322 if LatLon is None:
323 r = self.toCartesian(h=h, Cartesian=None, datum=d)
324 else:
325 kwds = _xkwds(LatLon_kwds, height=h, datum=d)
326 r = LatLon(self.lat, self.lon, **self._name1__(kwds))
327 return r
329 def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected
330 '''Return a string representation of this n-vector.
332 Height component is only included if non-zero.
334 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
335 @kwarg fmt: Enclosing backets format (C{str}).
336 @kwarg sep: Optional separator between components (C{str}).
338 @return: Comma-separated C{"(x, y, z [, h])"} enclosed in
339 B{C{fmt}} brackets (C{str}).
340 '''
341 t = Vector3d.toStr(self, prec=prec, fmt=NN, sep=sep)
342 if self.h:
343 t = sep.join((t, self.hStr()))
344 return (fmt % (t,)) if fmt else t
346 def toVector3d(self, norm=True):
347 '''Convert this n-vector to a 3-D vector, I{ignoring height}.
349 @kwarg norm: Normalize the 3-D vector (C{bool}).
351 @return: The (normalized) vector (L{Vector3d}).
352 '''
353 v = Vector3d.unit(self) if norm else self
354 return Vector3d(v.x, v.y, v.z, name=self.name)
356 @deprecated_method
357 def to4xyzh(self, h=None): # PYCHOK no cover
358 '''DEPRECATED, use property L{xyzh} or C{xyz.to4Tuple(B{h})}.'''
359 return self.xyzh if h in (None, self.h) else Vector4Tuple(
360 self.x, self.y, self.z, h, name=self.name)
362 def unit(self, ll=None):
363 '''Normalize this n-vector to unit length.
365 @kwarg ll: Optional, original latlon (C{LatLon}).
367 @return: Normalized vector (C{Nvector}).
368 '''
369 return _xattrs(Vector3d.unit(self, ll=ll), _under(_h_))
371 @Property_RO
372 def xyzh(self):
373 '''Get this n-vector's components (L{Vector4Tuple}C{(x, y, z, h)})
374 '''
375 return self.xyz.to4Tuple(self.h)
378NorthPole = NvectorBase(0, 0, +1, name='NorthPole') # North pole (C{Nvector})
379SouthPole = NvectorBase(0, 0, -1, name='SouthPole') # South pole (C{Nvector})
382class _N_vector_(NvectorBase):
383 '''(INTERNAL) Minimal, low-overhead C{n-vector}.
384 '''
385 def __init__(self, x, y, z, h=0, **name):
386 self._x, self._y, self._z = x, y, z
387 if h:
388 self._h = h
389 if name:
390 self.name = name
393class LatLonNvectorBase(LatLonBase):
394 '''(INTERNAL) Base class for n-vector-based ellipsoidal and
395 spherical C{LatLon} classes.
396 '''
398 def _update(self, updated, *attrs, **setters): # PYCHOK _Nv=None
399 '''(INTERNAL) Zap cached attributes if updated.
401 @see: C{ellipsoidalNvector.LatLon} and C{sphericalNvector.LatLon}
402 for the special case of B{C{_Nv}}.
403 '''
404 if updated:
405 _Nv, setters = _xkwds_pop2(setters, _Nv=None)
406 if _Nv is not None:
407 if _Nv._fromll is not None:
408 _Nv._fromll = None
409 self._Nv = None
410 LatLonBase._update(self, updated, *attrs, **setters)
412# def distanceTo(self, other, **kwds): # PYCHOK no cover
413# '''I{Must be overloaded}.'''
414# self._notOverloaded(other, **kwds)
416 def intersections2(self, radius1, other, radius2, **kwds): # PYCHOK expected
417 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
418 self._notImplemented(radius1, other, radius2, **kwds)
420 def others(self, *other, **name_other_up):
421 '''Refined class comparison.
423 @arg other: The other instance (C{LatLonNvectorBase}).
424 @kwarg name_other_up: Overriding C{name=other} and C{up=1}
425 keyword arguments.
427 @return: The B{C{other}} if compatible.
429 @raise TypeError: Incompatible B{C{other}} C{type}.
430 '''
431 if other:
432 other0 = other[0]
433 if isinstance(other0, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase?
434 return other0
436 other, name, up = _xother3(self, other, **name_other_up)
437 if not isinstance(other, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase?
438 LatLonBase.others(self, other, name=name, up=up + 1)
439 return other
441 def toNvector(self, **Nvector_and_kwds): # PYCHOK signature
442 '''Convert this point to C{Nvector} components, I{including height}.
444 @kwarg Nvector_and_kwds: Optional C{Nvector} class and C{Nvector} keyword arguments,
445 Specify C{B{Nvector}=...} to override this C{Nvector} class
446 or use C{B{Nvector}=None}.
448 @return: An C{Nvector} or if C{Nvector is None}, a L{Vector4Tuple}C{(x, y, z, h)}.
450 @raise TypeError: Invalid C{Nvector} or other B{C{Nvector_and_kwds}} item.
451 '''
452 return LatLonBase.toNvector(self, **_xkwds(Nvector_and_kwds, Nvector=NvectorBase))
454 def triangulate(self, bearing1, other, bearing2, height=None, wrap=False): # PYCHOK signature
455 '''Locate a point given this, an other point and the (initial) bearing
456 from this and the other point.
458 @arg bearing1: Bearing at this point (compass C{degrees360}).
459 @arg other: The other point (C{LatLon}).
460 @arg bearing2: Bearing at the other point (compass C{degrees360}).
461 @kwarg height: Optional height at the triangulated point, overriding
462 the mean height (C{meter}).
463 @kwarg wrap: If C{True}, use this and the B{C{other}} point
464 I{normalized} (C{bool}).
466 @return: Triangulated point (C{LatLon}).
468 @raise TypeError: Invalid B{C{other}} point.
470 @raise Valuerror: Points coincide.
471 '''
472 return _triangulate(self, bearing1, self.others(other), bearing2,
473 height=height, wrap=wrap, LatLon=self.classof)
475 def trilaterate(self, distance1, point2, distance2, point3, distance3,
476 radius=R_M, height=None, useZ=False, wrap=False):
477 '''Locate a point at given distances from this and two other points.
479 @arg distance1: Distance to this point (C{meter}, same units
480 as B{C{radius}}).
481 @arg point2: Second reference point (C{LatLon}).
482 @arg distance2: Distance to point2 (C{meter}, same units as
483 B{C{radius}}).
484 @arg point3: Third reference point (C{LatLon}).
485 @arg distance3: Distance to point3 (C{meter}, same units as
486 B{C{radius}}).
487 @kwarg radius: Mean earth radius (C{meter}).
488 @kwarg height: Optional height at trilaterated point, overriding
489 the mean height (C{meter}, same units as B{C{radius}}).
490 @kwarg useZ: Include Z component iff non-NaN, non-zero (C{bool}).
491 @kwarg wrap: If C{True}, use this, B{C{point2}} and B{C{point3}}
492 I{normalized} (C{bool}).
494 @return: Trilaterated point (C{LatLon}).
496 @raise IntersectionError: No intersection, trilateration failed.
498 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
500 @raise ValueError: Some B{C{points}} coincide or invalid B{C{distance1}},
501 B{C{distance2}}, B{C{distance3}} or B{C{radius}}.
503 @see: U{Trilateration<https://WikiPedia.org/wiki/Trilateration>},
504 Veness' JavaScript U{Trilateration<https://www.Movable-Type.co.UK/
505 scripts/latlong-vectors.html>} and method C{LatLon.trilaterate5}
506 of other, non-C{Nvector LatLon} classes.
507 '''
508 return _trilaterate(self, distance1, self.others(point2=point2), distance2,
509 self.others(point3=point3), distance3,
510 radius=radius, height=height, useZ=useZ,
511 wrap=wrap, LatLon=self.classof)
513 def trilaterate5(self, distance1, point2, distance2, point3, distance3, # PYCHOK signature
514 area=False, eps=EPS1, radius=R_M, wrap=False):
515 '''B{Not implemented} for C{B{area}=True} and falls back to method
516 C{trilaterate} otherwise.
518 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}
519 with a single trilaterated intersection C{minPoint I{is}
520 maxPoint}, C{min I{is} max} the nearest intersection
521 margin and count C{n = 1}.
523 @raise NotImplementedError: Keyword argument C{B{area}=True} not
524 (yet) supported.
526 @see: Method L{trilaterate} for other and more details.
527 '''
528 if area:
529 self._notImplemented(area=area)
531 t = _trilaterate(self, distance1, self.others(point2=point2), distance2,
532 self.others(point3=point3), distance3,
533 radius=radius, useZ=True, wrap=wrap,
534 LatLon=self.classof)
535 # ... and handle B{C{eps}} and C{IntersectionError}
536 # like function C{.latlonBase._trilaterate5}
537 d = self.distanceTo(t, radius=radius, wrap=wrap) # PYCHOK distanceTo
538 d = min(fabs(distance1 - d), fabs(distance2 - d), fabs(distance3 - d))
539 if d < eps: # min is max, minPoint is maxPoint
540 return Trilaterate5Tuple(d, t, d, t, 1) # n = 1
541 t = _SPACE_(_no_(_intersection_), Fmt.PAREN(min.__name__, Fmt.f(d, prec=3)))
542 raise IntersectionError(area=area, eps=eps, radius=radius, wrap=wrap, txt=t)
545def _nsumOf(nvs, h_None, Vector, Vector_kwds): # .sphericalNvector, .vector3d
546 '''(INTERNAL) Separated to allow callers to embellish exceptions.
547 '''
548 X, Y, Z, n = Fsum(), Fsum(), Fsum(), 0
549 H = Fsum() if h_None is None else n
550 for n, v in enumerate(nvs or ()): # one pass
551 X += v.x
552 Y += v.y
553 Z += v.z
554 H += v.h
555 if n < 1:
556 raise ValueError(_SPACE_(Fmt.PARENSPACED(len=n), _insufficient_))
558 x, y, z = map1(float, X, Y, Z)
559 h = H.fover(n) if h_None is None else h_None
560 return Vector3Tuple(x, y, z).to4Tuple(h) if Vector is None else \
561 Vector(x, y, z, **_xkwds(Vector_kwds, h=h))
564def sumOf(nvectors, Vector=None, h=None, **Vector_kwds):
565 '''Return the I{vectorial} sum of two or more n-vectors.
567 @arg nvectors: Vectors to be added (C{Nvector}[]).
568 @kwarg Vector: Optional class for the vectorial sum (C{Nvector})
569 or C{None}.
570 @kwarg h: Optional height, overriding the mean height (C{meter}).
571 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
572 arguments, ignored if C{B{Vector} is None}.
574 @return: Vectorial sum (B{C{Vector}}) or a L{Vector4Tuple}C{(x, y,
575 z, h)} if B{C{Vector}} is C{None}.
577 @raise VectorError: No B{C{nvectors}}.
578 '''
579 try:
580 return _nsumOf(nvectors, h, Vector, Vector_kwds)
581 except (TypeError, ValueError) as x:
582 raise VectorError(nvectors=nvectors, Vector=Vector, cause=x)
585def _triangulate(point1, bearing1, point2, bearing2, height=None,
586 wrap=False, **LatLon_and_kwds):
587 # (INTERNAL) Locate a point given two known points and initial
588 # bearings from those points, see C{LatLon.triangulate} above
590 def _gc(p, b, _i_):
591 n = p.toNvector()
592 de = NorthPole.cross(n, raiser=_pole_).unit() # east vector @ n
593 dn = n.cross(de) # north vector @ n
594 s, c = sincos2d(Bearing(b, name=_bearing_ + _i_))
595 dest = de.times(s)
596 dnct = dn.times(c)
597 d = dnct.plus(dest) # direction vector @ n
598 return n.cross(d) # great circle point + bearing
600 if wrap:
601 point2 = _unrollon(point1, point2, wrap=wrap)
602 if _isequalTo(point1, point2, eps=EPS):
603 raise _ValueError(points=point2, wrap=wrap, txt=_coincident_)
605 gc1 = _gc(point1, bearing1, _1_) # great circle p1 + b1
606 gc2 = _gc(point2, bearing2, _2_) # great circle p2 + b2
608 n = gc1.cross(gc2, raiser=_point_) # n-vector of intersection point
609 h = point1._havg(point2, h=height)
610 kwds = _xkwds(LatLon_and_kwds, height=h)
611 return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
614def _trilaterate(point1, distance1, point2, distance2, point3, distance3,
615 radius=R_M, height=None, useZ=False,
616 wrap=False, **LatLon_and_kwds):
617 # (INTERNAL) Locate a point at given distances from
618 # three other points, see LatLon.triangulate above
620 def _nr2(p, d, r, _i_, *qs): # .toNvector and angular distance squared
621 for q in qs:
622 if _isequalTo(p, q, eps=EPS):
623 raise _ValueError(points=p, txt=_coincident_)
624 return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2
626 p1, r = point1, Radius_(radius)
627 p2, p3, _ = _unrollon3(p1, point2, point3, wrap)
629 n1, r12 = _nr2(p1, distance1, r, _1_)
630 n2, r22 = _nr2(p2, distance2, r, _2_, p1)
631 n3, r32 = _nr2(p3, distance3, r, _3_, p1, p2)
633 # the following uses x,y coordinate system with origin at n1, x axis n1->n2
634 y = n3.minus(n1)
635 x = n2.minus(n1)
636 z = None
638 d = x.length # distance n1->n2
639 if d > EPS_2: # and y.length > EPS_2:
640 X = x.unit() # unit vector in x direction n1->n2
641 i = X.dot(y) # signed magnitude of x component of n1->n3
642 Y = y.minus(X.times(i)).unit() # unit vector in y direction
643 j = Y.dot(y) # signed magnitude of y component of n1->n3
644 if fabs(j) > EPS_2:
645 # courtesy of U{Carlos Freitas<https://GitHub.com/mrJean1/PyGeodesy/issues/33>}
646 x = fsumf_(r12, -r22, d**2) / (d * _2_0) # n1->intersection x- and ...
647 y = fsumf_(r12, -r32, i**2, j**2, x * i * _N_2_0) / (j * _2_0) # ... y-component
648 # courtesy of U{AleixDev<https://GitHub.com/mrJean1/PyGeodesy/issues/43>}
649 z = fsumf_(max(r12, r22, r32), -(x**2), -(y**2)) # XXX not just r12!
650 if z > EPS:
651 n = n1.plus(X.times(x)).plus(Y.times(y))
652 if useZ: # include Z component
653 Z = X.cross(Y) # unit vector perpendicular to plane
654 n = n.plus(Z.times(sqrt(z)))
655 if height is None:
656 h = fidw((point1.height, point2.height, point3.height),
657 map1(fabs, distance1, distance2, distance3))
658 else:
659 h = Height(height)
660 kwds = _xkwds(LatLon_and_kwds, height=h)
661 return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
663 # no intersection, d < EPS_2 or fabs(j) < EPS_2 or z < EPS
664 t = _SPACE_(_no_, _intersection_, NN)
665 raise IntersectionError(point1=point1, distance1=distance1,
666 point2=point2, distance2=distance2,
667 point3=point3, distance3=distance3,
668 txt=unstr(t, z=z, useZ=useZ, wrap=wrap))
671__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes
673# **) MIT License
674#
675# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
676#
677# Permission is hereby granted, free of charge, to any person obtaining a
678# copy of this software and associated documentation files (the "Software"),
679# to deal in the Software without restriction, including without limitation
680# the rights to use, copy, modify, merge, publish, distribute, sublicense,
681# and/or sell copies of the Software, and to permit persons to whom the
682# Software is furnished to do so, subject to the following conditions:
683#
684# The above copyright notice and this permission notice shall be included
685# in all copies or substantial portions of the Software.
686#
687# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
688# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
689# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
690# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
691# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
692# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
693# OTHER DEALINGS IN THE SOFTWARE.