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
22from pygeodesy.interns import NN, _1_, _2_, _3_, _bearing_, _coincident_, \
23 _COMMASPACE_, _distance_, _h_, _insufficient_, \
24 _intersection_, _no_, _NorthPole_, _point_, \
25 _pole_, _SPACE_, _SouthPole_, _under
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
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, _xyzhdn3
38from math import fabs, sqrt
40__all__ = _ALL_LAZY.nvectorBase
41__version__ = '24.04.07'
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, ll=None, datum=None, name=NN):
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
56 L{Vector4Tuple}).
57 @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}}
58 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
59 @kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}}
60 is not C{scalar}, otherwise same units as B{C{x_xyz}}.
61 @kwarg h: Optional height above surface (C{meter}).
62 @kwarg ll: Optional, original latlon (C{LatLon}).
63 @kwarg datum: Optional, I{pass-thru} datum (L{Datum}).
64 @kwarg name: Optional name (C{str}).
66 @raise TypeError: Non-scalar B{C{x}}, B{C{y}} or B{C{z}}
67 coordinate or B{C{x}} not an C{Nvector},
68 L{Vector3Tuple} or L{Vector4Tuple} or
69 invalid B{C{datum}}.
70 '''
71 h, d, n = _xyzhdn3(x_xyz, h, datum, ll)
72 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=name or n)
73 if h:
74 self.h = h
75 if d is not None:
76 self._datum = _spherical_datum(d, name=self.name) # pass-thru
78 @Property_RO
79 def datum(self):
80 '''Get the I{pass-thru} datum (C{Datum}) or C{None}.
81 '''
82 return self._datum
84 @property_RO
85 def Ecef(self):
86 '''Get the ECEF I{class} (L{EcefKarney}), I{once}.
87 '''
88 NvectorBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO
89 return E
91 @property_RO
92 def ellipsoidalNvector(self):
93 '''Get the C{Nvector type} iff ellipsoidal, overloaded in L{pygeodesy.ellipsoidalNvector.Nvector}.
94 '''
95 return False
97 @property_doc_(''' the height above surface (C{meter}).''')
98 def h(self):
99 '''Get the height above surface (C{meter}).
100 '''
101 return self._h
103 @h.setter # PYCHOK setter!
104 def h(self, h):
105 '''Set the height above surface (C{meter}).
107 @raise TypeError: If B{C{h}} invalid.
109 @raise VectorError: If B{C{h}} invalid.
110 '''
111 h = Height(h=h, Error=VectorError)
112 if self._h != h:
113 _update_all(self)
114 self._h = h
116 @property_doc_(''' the height prefix (C{str}).''')
117 def H(self):
118 '''Get the height prefix (C{str}).
119 '''
120 return self._H
122 @H.setter # PYCHOK setter!
123 def H(self, H):
124 '''Set the height prefix (C{str}).
125 '''
126 self._H = str(H) if H else NN
128 def hStr(self, prec=-2, m=NN):
129 '''Return a string for the height B{C{h}}.
131 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
132 @kwarg m: Optional unit of the height (C{str}).
134 @see: Function L{pygeodesy.hstr}.
135 '''
136 return NN(self.H, hstr(self.h, prec=prec, m=m))
138 @Property_RO
139 def isEllipsoidal(self):
140 '''Check whether this n-vector is ellipsoidal (C{bool} or C{None} if unknown).
141 '''
142 return self.datum.isEllipsoidal if self.datum else None
144 @Property_RO
145 def isSpherical(self):
146 '''Check whether this n-vector is spherical (C{bool} or C{None} if unknown).
147 '''
148 return self.datum.isSpherical if self.datum else None
150 @Property_RO
151 def lam(self):
152 '''Get the (geodetic) longitude in C{radians} (C{float}).
153 '''
154 return self.philam.lam
156 @Property_RO
157 def lat(self):
158 '''Get the (geodetic) latitude in C{degrees} (C{float}).
159 '''
160 return self.latlon.lat
162 @Property_RO
163 def latlon(self):
164 '''Get the (geodetic) lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
165 '''
166 return n_xyz2latlon(self.x, self.y, self.z, name=self.name)
168 @Property_RO
169 def latlonheight(self):
170 '''Get the (geodetic) lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
171 '''
172 return self.latlon.to3Tuple(self.h)
174 @Property_RO
175 def latlonheightdatum(self):
176 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
177 '''
178 return self.latlonheight.to4Tuple(self.datum)
180 @Property_RO
181 def lon(self):
182 '''Get the (geodetic) longitude in C{degrees} (C{float}).
183 '''
184 return self.latlon.lon
186 @Property_RO
187 def phi(self):
188 '''Get the (geodetic) latitude in C{radians} (C{float}).
189 '''
190 return self.philam.phi
192 @Property_RO
193 def philam(self):
194 '''Get the (geodetic) lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
195 '''
196 return n_xyz2philam(self.x, self.y, self.z, name=self.name)
198 @Property_RO
199 def philamheight(self):
200 '''Get the (geodetic) lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
201 '''
202 return self.philam.to3Tuple(self.h)
204 @Property_RO
205 def philamheightdatum(self):
206 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
207 '''
208 return self.philamheight.to4Tuple(self.datum)
210 @property_RO
211 def sphericalNvector(self):
212 '''Get the C{Nvector type} iff spherical, overloaded in L{pygeodesy.sphericalNvector.Nvector}.
213 '''
214 return False
216 @deprecated_method
217 def to2ab(self): # PYCHOK no cover
218 '''DEPRECATED, use property L{philam}.
220 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
221 '''
222 return self.philam
224 @deprecated_method
225 def to3abh(self, height=None): # PYCHOK no cover
226 '''DEPRECATED, use property L{philamheight} or C{philam.to3Tuple(B{height})}.
228 @kwarg height: Optional height, overriding this
229 n-vector's height (C{meter}).
231 @return: A L{PhiLam3Tuple}C{(phi, lam, height)}.
233 @raise ValueError: Invalid B{C{height}}.
234 '''
235 return self.philamheight if height in (None, self.h) else \
236 self.philam.to3Tuple(height)
238 def toCartesian(self, h=None, Cartesian=None, datum=None, **Cartesian_kwds):
239 '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates.
241 @kwarg h: Optional height, overriding this n-vector's height (C{meter}).
242 @kwarg Cartesian: Optional class to return the (ECEF) coordinates
243 (C{Cartesian}).
244 @kwarg datum: Optional datum (C{Datum}), overriding this datum.
245 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
246 arguments, ignored if C{B{Cartesian} is None}.
248 @return: The cartesian (ECEF) coordinates (B{C{Cartesian}}) or
249 if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y, z,
250 lat, lon, height, C, M, datum)} with C{C} and C{M} if
251 available.
253 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}
254 argument.
256 @raise ValueError: Invalid B{C{h}}.
257 '''
258 D = _spherical_datum(datum or self.datum, name=self.name)
259 E = D.ellipsoid
260 h = self.h if h is None else Height(h)
262 x, y, z = self.x, self.y, self.z
263 # Kenneth Gade eqn 22
264 n = E.b / hypot_(x * E.a_b, y * E.a_b, z)
265 r = h + n * E.a2_b2
267 x *= r
268 y *= r
269 z *= h + n
271 if Cartesian is None:
272 r = self.Ecef(D).reverse(x, y, z, M=True)
273 else:
274 kwds = _xkwds(Cartesian_kwds, datum=D) # h=0
275 r = Cartesian(x, y, z, **kwds)
276 return self._xnamed(r)
278 @deprecated_method
279 def to2ll(self): # PYCHOK no cover
280 '''DEPRECATED, use property L{latlon}.
282 @return: A L{LatLon2Tuple}C{(lat, lon)}.
283 '''
284 return self.latlon
286 @deprecated_method
287 def to3llh(self, height=None): # PYCHOK no cover
288 '''DEPRECATED, use property C{latlonheight} or C{latlon.to3Tuple(B{height})}.
290 @kwarg height: Optional height, overriding this
291 n-vector's height (C{meter}).
293 @return: A L{LatLon3Tuple}C{(lat, lon, height)}.
295 @raise ValueError: Invalid B{C{height}}.
296 '''
297 return self.latlonheight if height in (None, self.h) else \
298 self.latlon.to3Tuple(height)
300 def toLatLon(self, height=None, LatLon=None, datum=None, **LatLon_kwds):
301 '''Convert this n-vector to an C{Nvector}-based geodetic point.
303 @kwarg height: Optional height, overriding this n-vector's
304 height (C{meter}).
305 @kwarg LatLon: Optional class to return the geodetic point
306 (C{LatLon}) or C{None}.
307 @kwarg datum: Optional, spherical datum (C{Datum}).
308 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
309 arguments, ignored if C{B{LatLon} is None}.
311 @return: The geodetic point (C{LatLon}) or if C{B{LatLon} is None},
312 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
313 datum)} with C{C} and C{M} if available.
315 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}
316 argument.
318 @raise ValueError: Invalid B{C{height}}.
319 '''
320 d = _spherical_datum(datum or self.datum, name=self.name)
321 h = self.h if height is None else Height(height)
322 # use self.Cartesian(Cartesian=None) for better accuracy of the height
323 # than self.Ecef(d).forward(self.lat, self.lon, height=h, M=True)
324 if LatLon is None:
325 r = self.toCartesian(h=h, Cartesian=None, datum=d)
326 else:
327 kwds = _xkwds(LatLon_kwds, height=h, datum=d)
328 r = self._xnamed(LatLon(self.lat, self.lon, **kwds))
329 return r
331 def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected
332 '''Return a string representation of this n-vector.
334 Height component is only included if non-zero.
336 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
337 @kwarg fmt: Enclosing backets format (C{str}).
338 @kwarg sep: Optional separator between components (C{str}).
340 @return: Comma-separated C{"(x, y, z [, h])"} enclosed in
341 B{C{fmt}} brackets (C{str}).
342 '''
343 t = Vector3d.toStr(self, prec=prec, fmt=NN, sep=sep)
344 if self.h:
345 t = sep.join((t, self.hStr()))
346 return (fmt % (t,)) if fmt else t
348 def toVector3d(self, norm=True):
349 '''Convert this n-vector to a 3-D vector, I{ignoring height}.
351 @kwarg norm: Normalize the 3-D vector (C{bool}).
353 @return: The (normalized) vector (L{Vector3d}).
354 '''
355 v = Vector3d.unit(self) if norm else self
356 return Vector3d(v.x, v.y, v.z, name=self.name)
358 @deprecated_method
359 def to4xyzh(self, h=None): # PYCHOK no cover
360 '''DEPRECATED, use property L{xyzh} or C{xyz.to4Tuple(B{h})}.'''
361 return self.xyzh if h in (None, self.h) else Vector4Tuple(
362 self.x, self.y, self.z, h, name=self.name)
364 def unit(self, ll=None):
365 '''Normalize this n-vector to unit length.
367 @kwarg ll: Optional, original latlon (C{LatLon}).
369 @return: Normalized vector (C{Nvector}).
370 '''
371 return _xattrs(Vector3d.unit(self, ll=ll), _under(_h_))
373 @Property_RO
374 def xyzh(self):
375 '''Get this n-vector's components (L{Vector4Tuple}C{(x, y, z, h)})
376 '''
377 return self.xyz.to4Tuple(self.h)
380NorthPole = NvectorBase(0, 0, +1, name=_NorthPole_) # North pole (C{Nvector})
381SouthPole = NvectorBase(0, 0, -1, name=_SouthPole_) # South pole (C{Nvector})
384class _N_vector_(NvectorBase):
385 '''(INTERNAL) Minimal, low-overhead C{n-vector}.
386 '''
387 def __init__(self, x, y, z, h=0, name=NN):
388 self._x, self._y, self._z = x, y, z
389 if h:
390 self._h = h
391 if name:
392 self.name = name
395class LatLonNvectorBase(LatLonBase):
396 '''(INTERNAL) Base class for n-vector-based ellipsoidal and
397 spherical C{LatLon} classes.
398 '''
400 def _update(self, updated, *attrs, **setters): # PYCHOK _Nv=None
401 '''(INTERNAL) Zap cached attributes if updated.
403 @see: C{ellipsoidalNvector.LatLon} and C{sphericalNvector.LatLon}
404 for the special case of B{C{_Nv}}.
405 '''
406 if updated:
407 _Nv, setters = _xkwds_pop2(setters, _Nv=None)
408 if _Nv is not None:
409 if _Nv._fromll is not None:
410 _Nv._fromll = None
411 self._Nv = None
412 LatLonBase._update(self, updated, *attrs, **setters)
414# def distanceTo(self, other, **kwds): # PYCHOK no cover
415# '''I{Must be overloaded}.'''
416# self._notOverloaded(other, **kwds)
418 def intersections2(self, radius1, other, radius2, **kwds): # PYCHOK expected
419 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
420 self._notImplemented(radius1, other, radius2, **kwds)
422 def others(self, *other, **name_other_up):
423 '''Refined class comparison.
425 @arg other: The other instance (C{LatLonNvectorBase}).
426 @kwarg name_other_up: Overriding C{name=other} and C{up=1}
427 keyword arguments.
429 @return: The B{C{other}} if compatible.
431 @raise TypeError: Incompatible B{C{other}} C{type}.
432 '''
433 if other:
434 other0 = other[0]
435 if isinstance(other0, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase?
436 return other0
438 other, name, up = _xother3(self, other, **name_other_up)
439 if not isinstance(other, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase?
440 LatLonBase.others(self, other, name=name, up=up + 1)
441 return other
443 def toNvector(self, **Nvector_and_kwds): # PYCHOK signature
444 '''Convert this point to C{Nvector} components, I{including height}.
446 @kwarg Nvector_and_kwds: Optional C{Nvector} class and C{Nvector} keyword arguments,
447 Specify C{B{Nvector}=...} to override this C{Nvector} class
448 or use C{B{Nvector}=None}.
450 @return: An C{Nvector} or if C{Nvector is None}, a L{Vector4Tuple}C{(x, y, z, h)}.
452 @raise TypeError: Invalid C{Nvector} or other B{C{Nvector_and_kwds}} item.
453 '''
454 return LatLonBase.toNvector(self, **_xkwds(Nvector_and_kwds, Nvector=NvectorBase))
456 def triangulate(self, bearing1, other, bearing2, height=None, wrap=False): # PYCHOK signature
457 '''Locate a point given this, an other point and the (initial) bearing
458 from this and the other point.
460 @arg bearing1: Bearing at this point (compass C{degrees360}).
461 @arg other: The other point (C{LatLon}).
462 @arg bearing2: Bearing at the other point (compass C{degrees360}).
463 @kwarg height: Optional height at the triangulated point,
464 overriding the mean height (C{meter}).
465 @kwarg wrap: If C{True}, use this and the B{C{other}} point
466 I{normalized} (C{bool}).
468 @return: Triangulated point (C{LatLon}).
470 @raise TypeError: Invalid B{C{other}} point.
472 @raise Valuerror: Points coincide.
473 '''
474 return _triangulate(self, bearing1, self.others(other), bearing2,
475 height=height, wrap=wrap, LatLon=self.classof)
477 def trilaterate(self, distance1, point2, distance2, point3, distance3,
478 radius=R_M, height=None, useZ=False, wrap=False):
479 '''Locate a point at given distances from this and two other points.
481 @arg distance1: Distance to this point (C{meter}, same units
482 as B{C{radius}}).
483 @arg point2: Second reference point (C{LatLon}).
484 @arg distance2: Distance to point2 (C{meter}, same units as
485 B{C{radius}}).
486 @arg point3: Third reference point (C{LatLon}).
487 @arg distance3: Distance to point3 (C{meter}, same units as
488 B{C{radius}}).
489 @kwarg radius: Mean earth radius (C{meter}).
490 @kwarg height: Optional height at trilaterated point, overriding
491 the mean height (C{meter}, same units as B{C{radius}}).
492 @kwarg useZ: Include Z component iff non-NaN, non-zero (C{bool}).
493 @kwarg wrap: If C{True}, use this, B{C{point2}} and B{C{point3}}
494 I{normalized} (C{bool}).
496 @return: Trilaterated point (C{LatLon}).
498 @raise IntersectionError: No intersection, trilateration failed.
500 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
502 @raise ValueError: Some B{C{points}} coincide or invalid B{C{distance1}},
503 B{C{distance2}}, B{C{distance3}} or B{C{radius}}.
505 @see: U{Trilateration<https://WikiPedia.org/wiki/Trilateration>},
506 Veness' JavaScript U{Trilateration<https://www.Movable-Type.co.UK/
507 scripts/latlong-vectors.html>} and method C{LatLon.trilaterate5}
508 of other, non-C{Nvector LatLon} classes.
509 '''
510 return _trilaterate(self, distance1, self.others(point2=point2), distance2,
511 self.others(point3=point3), distance3,
512 radius=radius, height=height, useZ=useZ,
513 wrap=wrap, LatLon=self.classof)
515 def trilaterate5(self, distance1, point2, distance2, point3, distance3, # PYCHOK signature
516 area=False, eps=EPS1, radius=R_M, wrap=False):
517 '''B{Not implemented} for C{B{area}=True} and falls back to method
518 C{trilaterate} otherwise.
520 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}
521 with a single trilaterated intersection C{minPoint I{is}
522 maxPoint}, C{min I{is} max} the nearest intersection
523 margin and count C{n = 1}.
525 @raise NotImplementedError: Keyword argument C{B{area}=True} not
526 (yet) supported.
528 @see: Method L{trilaterate} for other and more details.
529 '''
530 if area:
531 self._notImplemented(area=area)
533 t = _trilaterate(self, distance1, self.others(point2=point2), distance2,
534 self.others(point3=point3), distance3,
535 radius=radius, useZ=True, wrap=wrap,
536 LatLon=self.classof)
537 # ... and handle B{C{eps}} and C{IntersectionError}
538 # like function C{.latlonBase._trilaterate5}
539 d = self.distanceTo(t, radius=radius, wrap=wrap) # PYCHOK distanceTo
540 d = min(fabs(distance1 - d), fabs(distance2 - d), fabs(distance3 - d))
541 if d < eps: # min is max, minPoint is maxPoint
542 return Trilaterate5Tuple(d, t, d, t, 1) # n = 1
543 t = _SPACE_(_no_(_intersection_), Fmt.PAREN(min.__name__, Fmt.f(d, prec=3)))
544 raise IntersectionError(area=area, eps=eps, radius=radius, wrap=wrap, txt=t)
547def _nsumOf(nvs, h_None, Vector, Vector_kwds): # .sphericalNvector, .vector3d
548 '''(INTERNAL) Separated to allow callers to embellish exceptions.
549 '''
550 X, Y, Z, n = Fsum(), Fsum(), Fsum(), 0
551 H = Fsum() if h_None is None else n
552 for n, v in enumerate(nvs or ()): # one pass
553 X += v.x
554 Y += v.y
555 Z += v.z
556 H += v.h
557 if n < 1:
558 raise ValueError(_SPACE_(Fmt.PARENSPACED(len=n), _insufficient_))
560 x, y, z = map1(float, X, Y, Z)
561 h = H.fover(n) if h_None is None else h_None
562 return Vector3Tuple(x, y, z).to4Tuple(h) if Vector is None else \
563 Vector(x, y, z, **_xkwds(Vector_kwds, h=h))
566def sumOf(nvectors, Vector=None, h=None, **Vector_kwds):
567 '''Return the I{vectorial} sum of two or more n-vectors.
569 @arg nvectors: Vectors to be added (C{Nvector}[]).
570 @kwarg Vector: Optional class for the vectorial sum (C{Nvector})
571 or C{None}.
572 @kwarg h: Optional height, overriding the mean height (C{meter}).
573 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
574 arguments, ignored if C{B{Vector} is None}.
576 @return: Vectorial sum (B{C{Vector}}) or a L{Vector4Tuple}C{(x, y,
577 z, h)} if B{C{Vector}} is C{None}.
579 @raise VectorError: No B{C{nvectors}}.
580 '''
581 try:
582 return _nsumOf(nvectors, h, Vector, Vector_kwds)
583 except (TypeError, ValueError) as x:
584 raise VectorError(nvectors=nvectors, Vector=Vector, cause=x)
587def _triangulate(point1, bearing1, point2, bearing2, height=None,
588 wrap=False, **LatLon_and_kwds):
589 # (INTERNAL) Locate a point given two known points and initial
590 # bearings from those points, see C{LatLon.triangulate} above
592 def _gc(p, b, _i_):
593 n = p.toNvector()
594 de = NorthPole.cross(n, raiser=_pole_).unit() # east vector @ n
595 dn = n.cross(de) # north vector @ n
596 s, c = sincos2d(Bearing(b, name=_bearing_ + _i_))
597 dest = de.times(s)
598 dnct = dn.times(c)
599 d = dnct.plus(dest) # direction vector @ n
600 return n.cross(d) # great circle point + bearing
602 if wrap:
603 point2 = _unrollon(point1, point2, wrap=wrap)
604 if _isequalTo(point1, point2, eps=EPS):
605 raise _ValueError(points=point2, wrap=wrap, txt=_coincident_)
607 gc1 = _gc(point1, bearing1, _1_) # great circle p1 + b1
608 gc2 = _gc(point2, bearing2, _2_) # great circle p2 + b2
610 n = gc1.cross(gc2, raiser=_point_) # n-vector of intersection point
611 h = point1._havg(point2, h=height)
612 kwds = _xkwds(LatLon_and_kwds, height=h)
613 return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
616def _trilaterate(point1, distance1, point2, distance2, point3, distance3,
617 radius=R_M, height=None, useZ=False,
618 wrap=False, **LatLon_and_kwds):
619 # (INTERNAL) Locate a point at given distances from
620 # three other points, see LatLon.triangulate above
622 def _nr2(p, d, r, _i_, *qs): # .toNvector and angular distance squared
623 for q in qs:
624 if _isequalTo(p, q, eps=EPS):
625 raise _ValueError(points=p, txt=_coincident_)
626 return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2
628 p1, r = point1, Radius_(radius)
629 p2, p3, _ = _unrollon3(p1, point2, point3, wrap)
631 n1, r12 = _nr2(p1, distance1, r, _1_)
632 n2, r22 = _nr2(p2, distance2, r, _2_, p1)
633 n3, r32 = _nr2(p3, distance3, r, _3_, p1, p2)
635 # the following uses x,y coordinate system with origin at n1, x axis n1->n2
636 y = n3.minus(n1)
637 x = n2.minus(n1)
638 z = None
640 d = x.length # distance n1->n2
641 if d > EPS_2: # and y.length > EPS_2:
642 X = x.unit() # unit vector in x direction n1->n2
643 i = X.dot(y) # signed magnitude of x component of n1->n3
644 Y = y.minus(X.times(i)).unit() # unit vector in y direction
645 j = Y.dot(y) # signed magnitude of y component of n1->n3
646 if fabs(j) > EPS_2:
647 # courtesy of U{Carlos Freitas<https://GitHub.com/mrJean1/PyGeodesy/issues/33>}
648 x = fsumf_(r12, -r22, d**2) / (d * _2_0) # n1->intersection x- and ...
649 y = fsumf_(r12, -r32, i**2, j**2, x * i * _N_2_0) / (j * _2_0) # ... y-component
650 # courtesy of U{AleixDev<https://GitHub.com/mrJean1/PyGeodesy/issues/43>}
651 z = fsumf_(max(r12, r22, r32), -(x**2), -(y**2)) # XXX not just r12!
652 if z > EPS:
653 n = n1.plus(X.times(x)).plus(Y.times(y))
654 if useZ: # include Z component
655 Z = X.cross(Y) # unit vector perpendicular to plane
656 n = n.plus(Z.times(sqrt(z)))
657 if height is None:
658 h = fidw((point1.height, point2.height, point3.height),
659 map1(fabs, distance1, distance2, distance3))
660 else:
661 h = Height(height)
662 kwds = _xkwds(LatLon_and_kwds, height=h)
663 return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
665 # no intersection, d < EPS_2 or fabs(j) < EPS_2 or z < EPS
666 t = _SPACE_(_no_, _intersection_, NN)
667 raise IntersectionError(point1=point1, distance1=distance1,
668 point2=point2, distance2=distance2,
669 point3=point3, distance3=distance3,
670 txt=unstr(t, z=z, useZ=useZ, wrap=wrap))
673__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes
675# **) MIT License
676#
677# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
678#
679# Permission is hereby granted, free of charge, to any person obtaining a
680# copy of this software and associated documentation files (the "Software"),
681# to deal in the Software without restriction, including without limitation
682# the rights to use, copy, modify, merge, publish, distribute, sublicense,
683# and/or sell copies of the Software, and to permit persons to whom the
684# Software is furnished to do so, subject to the following conditions:
685#
686# The above copyright notice and this permission notice shall be included
687# in all copies or substantial portions of the Software.
688#
689# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
690# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
691# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
692# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
693# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
694# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
695# OTHER DEALINGS IN THE SOFTWARE.