Coverage for pygeodesy/nvectorBase.py: 96%
249 statements
« prev ^ index » next coverage.py v7.2.2, created at 2024-06-27 20:21 -0400
« prev ^ index » next coverage.py v7.2.2, created at 2024-06-27 20:21 -0400
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 _xattrs, _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
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__ = '24.06.12'
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}), required if B{C{x_xyz}} is
57 C{scalar} and same units as B{C{x_xyz}}, ignored otherwise.
58 @kwarg z: Z component of vector (C{scalar}), like B{C{y}}.
59 @kwarg h: Optional height above surface (C{meter}).
60 @kwarg datum: Optional, I{pass-thru} datum (L{Datum}).
61 @kwarg ll_name: Optional C{B{name}=NN} (C{str}) and optional, original
62 latlon C{B{ll}=None} (C{LatLon}).
64 @raise TypeError: Non-scalar B{C{x}}, B{C{y}} or B{C{z}} coordinate or
65 B{C{x_xyz}} not an C{Nvector}, L{Vector3Tuple} or
66 L{Vector4Tuple} or invalid B{C{datum}}.
67 '''
68 h, d, ll, n = _xyzhdlln4(x_xyz, h, datum, **ll_name)
69 Vector3d.__init__(self, x_xyz, y=y, z=z, ll=ll, name=n)
70 if h:
71 self.h = h
72 if d is not None:
73 self._datum = _spherical_datum(d, name=n) # pass-thru
75 @Property_RO
76 def datum(self):
77 '''Get the I{pass-thru} datum (C{Datum}) or C{None}.
78 '''
79 return self._datum
81 @property_RO
82 def Ecef(self):
83 '''Get the ECEF I{class} (L{EcefKarney}), I{once}.
84 '''
85 NvectorBase.Ecef = E = _MODS.ecef.EcefKarney # overwrite property_RO
86 return E
88 @property_RO
89 def ellipsoidalNvector(self):
90 '''Get the C{Nvector type} iff ellipsoidal, overloaded in L{pygeodesy.ellipsoidalNvector.Nvector}.
91 '''
92 return False
94 @property_doc_(''' the height above surface (C{meter}).''')
95 def h(self):
96 '''Get the height above surface (C{meter}).
97 '''
98 return self._h
100 @h.setter # PYCHOK setter!
101 def h(self, h):
102 '''Set the height above surface (C{meter}).
104 @raise TypeError: If B{C{h}} invalid.
106 @raise VectorError: If B{C{h}} invalid.
107 '''
108 h = Height(h=h, Error=VectorError)
109 if self._h != h:
110 _update_all(self)
111 self._h = h
113 @property_doc_(''' the height prefix (C{str}).''')
114 def H(self):
115 '''Get the height prefix (C{str}).
116 '''
117 return self._H
119 @H.setter # PYCHOK setter!
120 def H(self, H):
121 '''Set the height prefix (C{str}).
122 '''
123 self._H = str(H) if H else NN
125 def hStr(self, prec=-2, m=NN):
126 '''Return a string for the height B{C{h}}.
128 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
129 @kwarg m: Optional unit of the height (C{str}).
131 @see: Function L{pygeodesy.hstr}.
132 '''
133 return NN(self.H, hstr(self.h, prec=prec, m=m))
135 @Property_RO
136 def isEllipsoidal(self):
137 '''Check whether this n-vector is ellipsoidal (C{bool} or C{None} if unknown).
138 '''
139 return self.datum.isEllipsoidal if self.datum else None
141 @Property_RO
142 def isSpherical(self):
143 '''Check whether this n-vector is spherical (C{bool} or C{None} if unknown).
144 '''
145 return self.datum.isSpherical if self.datum else None
147 @Property_RO
148 def lam(self):
149 '''Get the (geodetic) longitude in C{radians} (C{float}).
150 '''
151 return self.philam.lam
153 @Property_RO
154 def lat(self):
155 '''Get the (geodetic) latitude in C{degrees} (C{float}).
156 '''
157 return self.latlon.lat
159 @Property_RO
160 def latlon(self):
161 '''Get the (geodetic) lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
162 '''
163 return n_xyz2latlon(self.x, self.y, self.z, name=self.name)
165 @Property_RO
166 def latlonheight(self):
167 '''Get the (geodetic) lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
168 '''
169 return self.latlon.to3Tuple(self.h)
171 @Property_RO
172 def latlonheightdatum(self):
173 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
174 '''
175 return self.latlonheight.to4Tuple(self.datum)
177 @Property_RO
178 def lon(self):
179 '''Get the (geodetic) longitude in C{degrees} (C{float}).
180 '''
181 return self.latlon.lon
183 @Property_RO
184 def phi(self):
185 '''Get the (geodetic) latitude in C{radians} (C{float}).
186 '''
187 return self.philam.phi
189 @Property_RO
190 def philam(self):
191 '''Get the (geodetic) lat-, longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
192 '''
193 return n_xyz2philam(self.x, self.y, self.z, name=self.name)
195 @Property_RO
196 def philamheight(self):
197 '''Get the (geodetic) lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
198 '''
199 return self.philam.to3Tuple(self.h)
201 @Property_RO
202 def philamheightdatum(self):
203 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLam4Tuple}C{(phi, lam, height, datum)}).
204 '''
205 return self.philamheight.to4Tuple(self.datum)
207 @property_RO
208 def sphericalNvector(self):
209 '''Get the C{Nvector type} iff spherical, overloaded in L{pygeodesy.sphericalNvector.Nvector}.
210 '''
211 return False
213 @deprecated_method
214 def to2ab(self): # PYCHOK no cover
215 '''DEPRECATED, use property L{philam}.
217 @return: A L{PhiLam2Tuple}C{(phi, lam)}.
218 '''
219 return self.philam
221 @deprecated_method
222 def to3abh(self, height=None): # PYCHOK no cover
223 '''DEPRECATED, use property L{philamheight} or C{philam.to3Tuple(B{height})}.
225 @kwarg height: Optional height, overriding this
226 n-vector's height (C{meter}).
228 @return: A L{PhiLam3Tuple}C{(phi, lam, height)}.
230 @raise ValueError: Invalid B{C{height}}.
231 '''
232 return self.philamheight if height in (None, self.h) else \
233 self.philam.to3Tuple(height)
235 def toCartesian(self, h=None, Cartesian=None, datum=None, **Cartesian_kwds):
236 '''Convert this n-vector to C{Nvector}-based cartesian (ECEF) coordinates.
238 @kwarg h: Optional height, overriding this n-vector's height (C{meter}).
239 @kwarg Cartesian: Optional class to return the (ECEF) coordinates
240 (C{Cartesian}).
241 @kwarg datum: Optional datum (C{Datum}), overriding this datum.
242 @kwarg Cartesian_kwds: Optional, additional B{C{Cartesian}} keyword
243 arguments, ignored if C{B{Cartesian} is None}.
245 @return: The cartesian (ECEF) coordinates (B{C{Cartesian}}) or
246 if C{B{Cartesian} is None}, an L{Ecef9Tuple}C{(x, y, z,
247 lat, lon, height, C, M, datum)} with C{C} and C{M} if
248 available.
250 @raise TypeError: Invalid B{C{Cartesian}} or B{C{Cartesian_kwds}}
251 argument.
253 @raise ValueError: Invalid B{C{h}}.
254 '''
255 D = _spherical_datum(datum or self.datum, name=self.name)
256 E = D.ellipsoid
257 h = self.h if h is None else Height(h)
259 x, y, z = self.x, self.y, self.z
260 # Kenneth Gade eqn 22
261 n = E.b / hypot_(x * E.a_b, y * E.a_b, z)
262 r = h + n * E.a2_b2
264 x *= r
265 y *= r
266 z *= h + n
268 if Cartesian is None:
269 r = self.Ecef(D).reverse(x, y, z, M=True)
270 else:
271 kwds = _xkwds(Cartesian_kwds, datum=D) # h=0
272 r = Cartesian(x, y, z, **kwds)
273 return self._xnamed(r)
275 @deprecated_method
276 def to2ll(self): # PYCHOK no cover
277 '''DEPRECATED, use property L{latlon}.
279 @return: A L{LatLon2Tuple}C{(lat, lon)}.
280 '''
281 return self.latlon
283 @deprecated_method
284 def to3llh(self, height=None): # PYCHOK no cover
285 '''DEPRECATED, use property C{latlonheight} or C{latlon.to3Tuple(B{height})}.
287 @kwarg height: Optional height, overriding this
288 n-vector's height (C{meter}).
290 @return: A L{LatLon3Tuple}C{(lat, lon, height)}.
292 @raise ValueError: Invalid B{C{height}}.
293 '''
294 return self.latlonheight if height in (None, self.h) else \
295 self.latlon.to3Tuple(height)
297 def toLatLon(self, height=None, LatLon=None, datum=None, **LatLon_kwds):
298 '''Convert this n-vector to an C{Nvector}-based geodetic point.
300 @kwarg height: Optional height, overriding this n-vector's
301 height (C{meter}).
302 @kwarg LatLon: Optional class to return the geodetic point
303 (C{LatLon}) or C{None}.
304 @kwarg datum: Optional, spherical datum (C{Datum}).
305 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
306 arguments, ignored if C{B{LatLon} is None}.
308 @return: The geodetic point (C{LatLon}) or if C{B{LatLon} is None},
309 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M,
310 datum)} with C{C} and C{M} if available.
312 @raise TypeError: Invalid B{C{LatLon}} or B{C{LatLon_kwds}}
313 argument.
315 @raise ValueError: Invalid B{C{height}}.
316 '''
317 d = _spherical_datum(datum or self.datum, name=self.name)
318 h = self.h if height is None else Height(height)
319 # use self.Cartesian(Cartesian=None) for better accuracy of the height
320 # than self.Ecef(d).forward(self.lat, self.lon, height=h, M=True)
321 if LatLon is None:
322 r = self.toCartesian(h=h, Cartesian=None, datum=d)
323 else:
324 kwds = _xkwds(LatLon_kwds, height=h, datum=d)
325 r = LatLon(self.lat, self.lon, **self._name1__(kwds))
326 return r
328 def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected
329 '''Return a string representation of this n-vector.
331 Height component is only included if non-zero.
333 @kwarg prec: Number of (decimal) digits, unstripped (C{int}).
334 @kwarg fmt: Enclosing backets format (C{str}).
335 @kwarg sep: Optional separator between components (C{str}).
337 @return: Comma-separated C{"(x, y, z [, h])"} enclosed in
338 B{C{fmt}} brackets (C{str}).
339 '''
340 t = Vector3d.toStr(self, prec=prec, fmt=NN, sep=sep)
341 if self.h:
342 t = sep.join((t, self.hStr()))
343 return (fmt % (t,)) if fmt else t
345 def toVector3d(self, norm=True):
346 '''Convert this n-vector to a 3-D vector, I{ignoring height}.
348 @kwarg norm: If C{True}, normalize the 3-D vector (C{bool}).
350 @return: The (normalized) vector (L{Vector3d}).
351 '''
352 v = Vector3d.unit(self) if norm else self
353 return Vector3d(v.x, v.y, v.z, name=self.name)
355 @deprecated_method
356 def to4xyzh(self, h=None): # PYCHOK no cover
357 '''DEPRECATED, use property L{xyzh} or C{xyz.to4Tuple(B{h})}.'''
358 return self.xyzh if h in (None, self.h) else Vector4Tuple(
359 self.x, self.y, self.z, h, name=self.name)
361 def unit(self, ll=None):
362 '''Normalize this n-vector to unit length.
364 @kwarg ll: Optional, original latlon (C{LatLon}).
366 @return: Normalized vector (C{Nvector}).
367 '''
368 return _xattrs(Vector3d.unit(self, ll=ll), self, _under(_h_))
370 @Property_RO
371 def xyzh(self):
372 '''Get this n-vector's components (L{Vector4Tuple}C{(x, y, z, h)})
373 '''
374 return self.xyz.to4Tuple(self.h)
377NorthPole = NvectorBase(0, 0, +1, name='NorthPole') # North pole (C{Nvector})
378SouthPole = NvectorBase(0, 0, -1, name='SouthPole') # South pole (C{Nvector})
381class _N_vector_(NvectorBase):
382 '''(INTERNAL) Minimal, low-overhead C{n-vector}.
383 '''
384 def __init__(self, x, y, z, h=0, **name):
385 self._x, self._y, self._z = x, y, z
386 if h:
387 self._h = h
388 if name:
389 self.name = name
392class LatLonNvectorBase(LatLonBase):
393 '''(INTERNAL) Base class for n-vector-based ellipsoidal and
394 spherical C{LatLon} classes.
395 '''
397 def _update(self, updated, *attrs, **setters): # PYCHOK _Nv=None
398 '''(INTERNAL) Zap cached attributes if updated.
400 @see: C{ellipsoidalNvector.LatLon} and C{sphericalNvector.LatLon}
401 for the special case of B{C{_Nv}}.
402 '''
403 if updated:
404 _Nv, setters = _xkwds_pop2(setters, _Nv=None)
405 if _Nv is not None:
406 if _Nv._fromll is not None:
407 _Nv._fromll = None
408 self._Nv = None
409 LatLonBase._update(self, updated, *attrs, **setters)
411# def distanceTo(self, other, **kwds): # PYCHOK no cover
412# '''I{Must be overloaded}.'''
413# self._notOverloaded(other, **kwds)
415 def intersections2(self, radius1, other, radius2, **kwds): # PYCHOK expected
416 '''B{Not implemented}, throws a C{NotImplementedError} always.'''
417 self._notImplemented(radius1, other, radius2, **kwds)
419 def others(self, *other, **name_other_up):
420 '''Refined class comparison.
422 @arg other: The other instance (C{LatLonNvectorBase}).
423 @kwarg name_other_up: Overriding C{name=other} and C{up=1}
424 keyword arguments.
426 @return: The B{C{other}} if compatible.
428 @raise TypeError: Incompatible B{C{other}} C{type}.
429 '''
430 if other:
431 other0 = other[0]
432 if isinstance(other0, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase?
433 return other0
435 other, name, up = _xother3(self, other, **name_other_up)
436 if not isinstance(other, (self.__class__, LatLonNvectorBase)): # XXX NvectorBase?
437 LatLonBase.others(self, other, name=name, up=up + 1)
438 return other
440 def toNvector(self, **Nvector_and_kwds): # PYCHOK signature
441 '''Convert this point to C{Nvector} components, I{including height}.
443 @kwarg Nvector_and_kwds: Optional C{Nvector} class and C{Nvector} keyword arguments,
444 Specify C{B{Nvector}=...} to override this C{Nvector} class
445 or use C{B{Nvector}=None}.
447 @return: An C{Nvector} or if C{Nvector is None}, a L{Vector4Tuple}C{(x, y, z, h)}.
449 @raise TypeError: Invalid C{Nvector} or other B{C{Nvector_and_kwds}} item.
450 '''
451 return LatLonBase.toNvector(self, **_xkwds(Nvector_and_kwds, Nvector=NvectorBase))
453 def triangulate(self, bearing1, other, bearing2, height=None, wrap=False): # PYCHOK signature
454 '''Locate a point given this, an other point and the (initial) bearing
455 from this and the other point.
457 @arg bearing1: Bearing at this point (compass C{degrees360}).
458 @arg other: The other point (C{LatLon}).
459 @arg bearing2: Bearing at the other point (compass C{degrees360}).
460 @kwarg height: Optional height at the triangulated point, overriding
461 the mean height (C{meter}).
462 @kwarg wrap: If C{True}, use this and the B{C{other}} point
463 I{normalized} (C{bool}).
465 @return: Triangulated point (C{LatLon}).
467 @raise TypeError: Invalid B{C{other}} point.
469 @raise Valuerror: Points coincide.
470 '''
471 return _triangulate(self, bearing1, self.others(other), bearing2,
472 height=height, wrap=wrap, LatLon=self.classof)
474 def trilaterate(self, distance1, point2, distance2, point3, distance3,
475 radius=R_M, height=None, useZ=False, wrap=False):
476 '''Locate a point at given distances from this and two other points.
478 @arg distance1: Distance to this point (C{meter}, same units
479 as B{C{radius}}).
480 @arg point2: Second reference point (C{LatLon}).
481 @arg distance2: Distance to point2 (C{meter}, same units as
482 B{C{radius}}).
483 @arg point3: Third reference point (C{LatLon}).
484 @arg distance3: Distance to point3 (C{meter}, same units as
485 B{C{radius}}).
486 @kwarg radius: Mean earth radius (C{meter}).
487 @kwarg height: Optional height at trilaterated point, overriding
488 the mean height (C{meter}, same units as B{C{radius}}).
489 @kwarg useZ: Include Z component iff non-NaN, non-zero (C{bool}).
490 @kwarg wrap: If C{True}, use this, B{C{point2}} and B{C{point3}}
491 I{normalized} (C{bool}).
493 @return: Trilaterated point (C{LatLon}).
495 @raise IntersectionError: No intersection, trilateration failed.
497 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
499 @raise ValueError: Some B{C{points}} coincide or invalid B{C{distance1}},
500 B{C{distance2}}, B{C{distance3}} or B{C{radius}}.
502 @see: U{Trilateration<https://WikiPedia.org/wiki/Trilateration>},
503 Veness' JavaScript U{Trilateration<https://www.Movable-Type.co.UK/
504 scripts/latlong-vectors.html>} and method C{LatLon.trilaterate5}
505 of other, non-C{Nvector LatLon} classes.
506 '''
507 return _trilaterate(self, distance1, self.others(point2=point2), distance2,
508 self.others(point3=point3), distance3,
509 radius=radius, height=height, useZ=useZ,
510 wrap=wrap, LatLon=self.classof)
512 def trilaterate5(self, distance1, point2, distance2, point3, distance3, # PYCHOK signature
513 area=False, eps=EPS1, radius=R_M, wrap=False):
514 '''B{Not implemented} for C{B{area}=True} and falls back to method
515 C{trilaterate} otherwise.
517 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}
518 with a single trilaterated intersection C{minPoint I{is}
519 maxPoint}, C{min I{is} max} the nearest intersection
520 margin and count C{n = 1}.
522 @raise NotImplementedError: Keyword argument C{B{area}=True} not
523 (yet) supported.
525 @see: Method L{trilaterate} for other and more details.
526 '''
527 if area:
528 self._notImplemented(area=area)
530 t = _trilaterate(self, distance1, self.others(point2=point2), distance2,
531 self.others(point3=point3), distance3,
532 radius=radius, useZ=True, wrap=wrap,
533 LatLon=self.classof)
534 # ... and handle B{C{eps}} and C{IntersectionError}
535 # like function C{.latlonBase._trilaterate5}
536 d = self.distanceTo(t, radius=radius, wrap=wrap) # PYCHOK distanceTo
537 d = min(fabs(distance1 - d), fabs(distance2 - d), fabs(distance3 - d))
538 if d < eps: # min is max, minPoint is maxPoint
539 return Trilaterate5Tuple(d, t, d, t, 1) # n = 1
540 t = _SPACE_(_no_(_intersection_), Fmt.PAREN(min.__name__, Fmt.f(d, prec=3)))
541 raise IntersectionError(area=area, eps=eps, radius=radius, wrap=wrap, txt=t)
544def _nsumOf(nvs, h_None, Vector, Vector_kwds): # .sphericalNvector, .vector3d
545 '''(INTERNAL) Separated to allow callers to embellish exceptions.
546 '''
547 X, Y, Z, n = Fsum(), Fsum(), Fsum(), 0
548 H = Fsum() if h_None is None else n
549 for n, v in enumerate(nvs or ()): # one pass
550 X += v.x
551 Y += v.y
552 Z += v.z
553 H += v.h
554 if n < 1:
555 raise ValueError(_SPACE_(Fmt.PARENSPACED(len=n), _insufficient_))
557 x, y, z = map1(float, X, Y, Z)
558 h = H.fover(n) if h_None is None else h_None
559 return Vector3Tuple(x, y, z).to4Tuple(h) if Vector is None else \
560 Vector(x, y, z, **_xkwds(Vector_kwds, h=h))
563def sumOf(nvectors, Vector=None, h=None, **Vector_kwds):
564 '''Return the I{vectorial} sum of two or more n-vectors.
566 @arg nvectors: Vectors to be added (C{Nvector}[]).
567 @kwarg Vector: Optional class for the vectorial sum (C{Nvector})
568 or C{None}.
569 @kwarg h: Optional height, overriding the mean height (C{meter}).
570 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword
571 arguments, ignored if C{B{Vector} is None}.
573 @return: Vectorial sum (B{C{Vector}}) or a L{Vector4Tuple}C{(x, y,
574 z, h)} if C{B{Vector} is None}.
576 @raise VectorError: No B{C{nvectors}}.
577 '''
578 try:
579 return _nsumOf(nvectors, h, Vector, Vector_kwds)
580 except (TypeError, ValueError) as x:
581 raise VectorError(nvectors=nvectors, Vector=Vector, cause=x)
584def _triangulate(point1, bearing1, point2, bearing2, height=None,
585 wrap=False, **LatLon_and_kwds):
586 # (INTERNAL) Locate a point given two known points and initial
587 # bearings from those points, see C{LatLon.triangulate} above
589 def _gc(p, b, _i_):
590 n = p.toNvector()
591 de = NorthPole.cross(n, raiser=_pole_).unit() # east vector @ n
592 dn = n.cross(de) # north vector @ n
593 s, c = sincos2d(Bearing(b, name=_bearing_ + _i_))
594 dest = de.times(s)
595 dnct = dn.times(c)
596 d = dnct.plus(dest) # direction vector @ n
597 return n.cross(d) # great circle point + bearing
599 if wrap:
600 point2 = _unrollon(point1, point2, wrap=wrap)
601 if _isequalTo(point1, point2, eps=EPS):
602 raise _ValueError(points=point2, wrap=wrap, txt=_coincident_)
604 gc1 = _gc(point1, bearing1, _1_) # great circle p1 + b1
605 gc2 = _gc(point2, bearing2, _2_) # great circle p2 + b2
607 n = gc1.cross(gc2, raiser=_point_) # n-vector of intersection point
608 h = point1._havg(point2, h=height)
609 kwds = _xkwds(LatLon_and_kwds, height=h)
610 return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
613def _trilaterate(point1, distance1, point2, distance2, point3, distance3,
614 radius=R_M, height=None, useZ=False,
615 wrap=False, **LatLon_and_kwds):
616 # (INTERNAL) Locate a point at given distances from
617 # three other points, see LatLon.triangulate above
619 def _nr2(p, d, r, _i_, *qs): # .toNvector and angular distance squared
620 for q in qs:
621 if _isequalTo(p, q, eps=EPS):
622 raise _ValueError(points=p, txt=_coincident_)
623 return p.toNvector(), (Scalar(d, name=_distance_ + _i_) / r)**2
625 p1, r = point1, Radius_(radius)
626 p2, p3, _ = _unrollon3(p1, point2, point3, wrap)
628 n1, r12 = _nr2(p1, distance1, r, _1_)
629 n2, r22 = _nr2(p2, distance2, r, _2_, p1)
630 n3, r32 = _nr2(p3, distance3, r, _3_, p1, p2)
632 # the following uses x,y coordinate system with origin at n1, x axis n1->n2
633 y = n3.minus(n1)
634 x = n2.minus(n1)
635 z = None
637 d = x.length # distance n1->n2
638 if d > EPS_2: # and y.length > EPS_2:
639 X = x.unit() # unit vector in x direction n1->n2
640 i = X.dot(y) # signed magnitude of x component of n1->n3
641 Y = y.minus(X.times(i)).unit() # unit vector in y direction
642 j = Y.dot(y) # signed magnitude of y component of n1->n3
643 if fabs(j) > EPS_2:
644 # courtesy of U{Carlos Freitas<https://GitHub.com/mrJean1/PyGeodesy/issues/33>}
645 x = fsumf_(r12, -r22, d**2) / (d * _2_0) # n1->intersection x- and ...
646 y = fsumf_(r12, -r32, i**2, j**2, x * i * _N_2_0) / (j * _2_0) # ... y-component
647 # courtesy of U{AleixDev<https://GitHub.com/mrJean1/PyGeodesy/issues/43>}
648 z = fsumf_(max(r12, r22, r32), -(x**2), -(y**2)) # XXX not just r12!
649 if z > EPS:
650 n = n1.plus(X.times(x)).plus(Y.times(y))
651 if useZ: # include Z component
652 Z = X.cross(Y) # unit vector perpendicular to plane
653 n = n.plus(Z.times(sqrt(z)))
654 if height is None:
655 h = fidw((point1.height, point2.height, point3.height),
656 map1(fabs, distance1, distance2, distance3))
657 else:
658 h = Height(height)
659 kwds = _xkwds(LatLon_and_kwds, height=h)
660 return n.toLatLon(**kwds) # Nvector(n.x, n.y, n.z).toLatLon(...)
662 # no intersection, d < EPS_2 or fabs(j) < EPS_2 or z < EPS
663 t = _SPACE_(_no_, _intersection_, NN)
664 raise IntersectionError(point1=point1, distance1=distance1,
665 point2=point2, distance2=distance2,
666 point3=point3, distance3=distance3,
667 txt=unstr(t, z=z, useZ=useZ, wrap=wrap))
670__all__ += _ALL_DOCS(LatLonNvectorBase, NvectorBase, sumOf) # classes
672# **) MIT License
673#
674# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
675#
676# Permission is hereby granted, free of charge, to any person obtaining a
677# copy of this software and associated documentation files (the "Software"),
678# to deal in the Software without restriction, including without limitation
679# the rights to use, copy, modify, merge, publish, distribute, sublicense,
680# and/or sell copies of the Software, and to permit persons to whom the
681# Software is furnished to do so, subject to the following conditions:
682#
683# The above copyright notice and this permission notice shall be included
684# in all copies or substantial portions of the Software.
685#
686# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
687# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
688# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
689# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
690# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
691# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
692# OTHER DEALINGS IN THE SOFTWARE.