Coverage for pygeodesy/ellipsoidalBase.py: 94%
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Private ellipsoidal base classes C{CartesianEllipsoidalBase}
5and C{LatLonEllipsoidalBase}.
7A pure Python implementation of geodesy tools for ellipsoidal earth models,
8transcoded in part from JavaScript originals by I{(C) Chris Veness 2005-2016}
9and published under the same MIT Licence**, see for example U{latlon-ellipsoidal
10<https://www.Movable-Type.co.UK/scripts/geodesy/docs/latlon-ellipsoidal.js.html>}.
11'''
12# make sure int/int division yields float quotient, see .basics
13from __future__ import division as _; del _ # PYCHOK semicolon
15# from pygeodesy.basics import _xinstanceof # from .datums
16from pygeodesy.constants import EPS, EPS0, EPS1, _0_0, _0_5
17from pygeodesy.cartesianBase import CartesianBase # PYCHOK used!
18from pygeodesy.datums import Datum, Datums, _earth_ellipsoid, _ellipsoidal_datum, \
19 _WGS84, _EWGS84, _xinstanceof # _spherical_datum
20# from pygeodesy.ellipsoids import _EWGS84 # from .datums
21from pygeodesy.errors import _incompatible, _IsnotError, RangeError, _TypeError, \
22 _ValueError, _xattr, _xellipsoidal, _xError, _xkwds, \
23 _xkwds_get, _xkwds_not
24# from pygeodesy.fmath import favg # _MODS
25from pygeodesy.interns import NN, _COMMA_, _ellipsoidal_
26from pygeodesy.latlonBase import LatLonBase, _trilaterate5, fabs, _Wrap
27from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
28# from pygeodesy.lcc import toLcc # _MODS
29# from pygeodesy.named import notOverloaded # _MODS
30# from pygeodesy.namedTuples import Vector3Tuple # _MODS
31from pygeodesy.props import deprecated_method, deprecated_property_RO, \
32 Property_RO, property_doc_, property_RO, _update_all
33# from pygeodesy.trf import _eT0Ds4 # _MODS
34from pygeodesy.units import Epoch, _isDegrees, Radius_, _1mm as _TOL_M
35# from pygeodesy.utily import _Wrap # from .latlonBase
37# from math import fabs # from .latlonBase
39__all__ = _ALL_LAZY.ellipsoidalBase
40__version__ = '24.02.04'
43class CartesianEllipsoidalBase(CartesianBase):
44 '''(INTERNAL) Base class for ellipsoidal C{Cartesian}s.
45 '''
46 _datum = _WGS84 # L{Datum}
47 _epoch = None # overriding .reframe.epoch (C{float})
48 _reframe = None # reference frame (L{RefFrame})
50 def __init__(self, x_xyz, y=None, z=None, datum=None, reframe=None,
51 epoch=None, ll=None, name=NN):
52 '''New ellispoidal C{Cartesian...}.
54 @kwarg reframe: Optional reference frame (L{RefFrame}).
55 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}),
56 a non-zero, fractional calendar year; silently ignored
57 if C{B{reframe}=None}.
59 @raise TypeError: Non-scalar B{C{x_xyz}}, B{C{y}} or B{C{z}} coordinate
60 or B{C{x_xyz}} not a C{Cartesian} L{Ecef9Tuple},
61 L{Vector3Tuple} or L{Vector4Tuple} or B{C{datum}} is
62 not a L{Datum}, B{C{reframe}} is not a L{RefFrame} or
63 B{C{epoch}} is not C{scalar} non-zero.
65 @see: Super-class L{CartesianBase<CartesianBase.__init__>} for more details.
66 '''
67 CartesianBase.__init__(self, x_xyz, y=y, z=z, datum=datum, ll=ll, name=name)
68 if reframe:
69 self.reframe = reframe
70 self.epoch = epoch
72# def __matmul__(self, other): # PYCHOK Python 3.5+
73# '''Return C{NotImplemented} for C{c_ = c @ datum}, C{c_ = c @ reframe} and C{c_ = c @ Transform}.
74# '''
75# RefFrame = _MODS.trf.RefFrame
76# return NotImplemented if isinstance(other, (Datum, RefFrame, Transform)) else \
77# _NotImplemented(self, other)
79 @deprecated_method
80 def convertRefFrame(self, reframe2, reframe, epoch=None):
81 '''DEPRECATED, use method L{toRefFrame}.'''
82 return self.toRefFrame(reframe2, reframe=reframe, epoch=epoch)
84 @property_RO
85 def ellipsoidalCartesian(self):
86 '''Get this C{Cartesian}'s ellipsoidal class.
87 '''
88 return type(self)
90 @property_doc_(''' this cartesian's observed or C{reframe} epoch (C{float}).''')
91 def epoch(self):
92 '''Get this cartesian's observed or C{reframe} epoch (C{Epoch}) or C{None}.
93 '''
94 return self._epoch or (self.reframe.epoch if self.reframe else None)
96 @epoch.setter # PYCHOK setter!
97 def epoch(self, epoch):
98 '''Set or clear this cartesian's observed epoch, a fractional
99 calendar year (L{Epoch}, C{scalar} or C{str}) or C{None}.
101 @raise TRFError: Invalid B{C{epoch}}.
102 '''
103 self._epoch = None if epoch is None else Epoch(epoch)
105 def intersections2(self, radius, center2, radius2, sphere=True,
106 Vector=None, **Vector_kwds):
107 '''Compute the intersection of two spheres or circles, each defined by a
108 cartesian center point and a radius.
110 @arg radius: Radius of this sphere or circle (same units as this point's
111 coordinates).
112 @arg center2: Center of the second sphere or circle (C{Cartesian}, L{Vector3d},
113 C{Vector3Tuple} or C{Vector4Tuple}).
114 @arg radius2: Radius of the second sphere or circle (same units as this and
115 the B{C{other}} point's coordinates).
116 @kwarg sphere: If C{True} compute the center and radius of the intersection
117 of two I{spheres}. If C{False}, ignore the C{z}-component and
118 compute the intersection of two I{circles} (C{bool}).
119 @kwarg Vector: Class to return intersections (C{Cartesian}, L{Vector3d} or
120 C{Vector3Tuple}) or C{None} for an instance of this (sub-)class.
121 @kwarg Vector_kwds: Optional, additional B{C{Vector}} keyword arguments,
122 ignored if C{B{Vector} is None}.
124 @return: If B{C{sphere}} is C{True}, a 2-tuple of the C{center} and C{radius}
125 of the intersection of the I{spheres}. The C{radius} is C{0.0} for
126 abutting spheres (and the C{center} is aka the I{radical center}).
128 If B{C{sphere}} is C{False}, a 2-tuple with the two intersection
129 points of the I{circles}. For abutting circles, both points are
130 the same instance, aka the I{radical center}.
132 @raise IntersectionError: Concentric, invalid or non-intersecting spheres or circles.
134 @raise TypeError: Invalid B{C{center2}}.
136 @raise UnitError: Invalid B{C{radius}} or B{C{radius2}}.
138 @see: U{Sphere-Sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>},
139 U{Circle-Circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>}
140 Intersection and function L{pygeodesy.radical2}.
141 '''
142 try:
143 return _MODS.vector3d._intersects2(self, Radius_(radius=radius),
144 center2, Radius_(radius2=radius2),
145 sphere=sphere, clas=self.classof,
146 Vector=Vector, **Vector_kwds)
147 except (TypeError, ValueError) as x:
148 raise _xError(x, center=self, radius=radius, center2=center2, radius2=radius2)
150 @property_doc_(''' this cartesian's reference frame (L{RefFrame}).''')
151 def reframe(self):
152 '''Get this cartesian's reference frame (L{RefFrame}) or C{None}.
153 '''
154 return self._reframe
156 @reframe.setter # PYCHOK setter!
157 def reframe(self, reframe):
158 '''Set or clear this cartesian's reference frame (L{RefFrame}) or C{None}.
160 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
161 '''
162 _set_reframe(self, reframe)
164 def toLatLon(self, datum=None, height=None, **LatLon_and_kwds): # PYCHOK signature
165 '''Convert this cartesian to a I{geodetic} (lat-/longitude) point.
167 @see: Method L{toLatLon<cartesianBase.CartesianBase.toLatLon>}
168 for further details.
169 '''
170 kwds = LatLon_and_kwds
171 if kwds:
172 kwds = _xkwds(kwds, reframe=self.reframe, epoch=self.epoch)
173 return CartesianBase.toLatLon(self, datum=datum, height=height, **kwds)
175 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, name=NN):
176 '''Convert this point to an other reference frame and epoch.
178 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
179 @kwarg reframe: Optional reference frame (L{RefFrame}), overriding this
180 point's reference frame.
181 @kwarg epoch: Optional epoch (L{Epoch}, C{scalar} or C{str}), overriding
182 this point's epoch.
183 @kwarg epoch2: Optional epoch to observe I{to} (L{Epoch}, C{scalar} or
184 C{str}).
185 @kwarg name: Optional name (C{str}), iff converted.
187 @return: The converted point (ellipsoidal C{Cartesian}) or if conversion
188 is C{nil}, this point or a copy of this point if the B{C{name}}
189 is non-empty.
191 @raise TRFError: This point's C{reframe} is not defined, invalid B{C{epoch}}
192 or B{C{epoch2}} or conversion from this point's C{reframe}
193 to B{C{reframe2}} is not available.
195 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame}.
196 '''
197 e, t0, d, d2 = _MODS.trf._eT0Ds4(self, reframe, epoch, reframe2, epoch2)
198 if t0:
199 r = self.toDatum(d).toTransforms_(t0).toDatum(d2).toDatum(self.datum)
200 r.reframe, r.epoch = reframe2, e
201 if name:
202 r.rename(name)
203 else:
204 r = self.copy(name=name) if name else self
205 return r
207 def toTransforms_(self, *transforms, **datum):
208 '''Apply none, one or several Helmert transforms to this point.
210 @arg transforms: Transforms to apply, in order (L{Transform}s).
211 @kwarg datum: Datum for the transformed point (L{Datum}), overriding
212 this point's datum.
214 @return: The transformed point (C{Cartesian}) or this point if the
215 B{C{transforms}} produce the same point.
216 '''
217 r = self
218 if transforms:
219 xyz = r.xyz
220 for t in transforms:
221 xyz = t.transform(*xyz)
222 d = _xkwds_get(datum, datum=r.datum)
223 if d != r.datum or xyz != r.xyz:
224 r = r.classof(xyz, datum=d)
225 return r
228class LatLonEllipsoidalBase(LatLonBase):
229 '''(INTERNAL) Base class for ellipsoidal C{LatLon}s.
230 '''
231 _datum = _WGS84 # L{Datum}
232 _elevation2to = None # _elevation2 timeout (C{secs})
233 _epoch = None # overriding .reframe.epoch (C{float})
234 _gamma = None # UTM/UPS meridian convergence (C{degrees})
235 _geoidHeight2to = None # _geoidHeight2 timeout (C{secs})
236 _reframe = None # reference frame (L{RefFrame})
237 _scale = None # UTM/UPS scale factor (C{float})
238 _toLLEB_args = () # Etm/Utm/Ups._toLLEB arguments
240 def __init__(self, latlonh, lon=None, height=0, datum=None, reframe=None,
241 epoch=None, wrap=False, name=NN):
242 '''Create an ellipsoidal C{LatLon} point from the givenlat-, longitude
243 and height on the given datum, reference frame and epoch.
245 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
246 a previous C{LatLon} instance provided C{B{lon}=None}.
247 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
248 C(None), indicating B{C{latlonh}} is a C{LatLon}.
249 @kwarg height: Optional height above (or below) the earth surface
250 (C{meter}, same units as the datum's ellipsoid axes).
251 @kwarg datum: Optional, ellipsoidal datum to use (L{Datum}, L{Ellipsoid},
252 L{Ellipsoid2} or L{a_f2Tuple}).
253 @kwarg reframe: Optional reference frame (L{RefFrame}).
254 @kwarg epoch: Optional epoch to observe for B{C{reframe}} (C{scalar}),
255 a non-zero, fractional calendar year; silently ignored
256 if C{B{reframe}=None}.
257 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
258 (C{bool}).
259 @kwarg name: Optional name (C{str}).
261 @raise RangeError: Value of C{lat} or B{C{lon}} outside the valid
262 range and L{rangerrors} set to C{True}.
264 @raise TypeError: If B{C{latlonh}} is not a C{LatLon}, B{C{datum}} is
265 not a L{Datum}, B{C{reframe}} is not a L{RefFrame}
266 or B{C{epoch}} is not C{scalar} non-zero.
268 @raise UnitError: Invalid B{C{lat}}, B{C{lon}} or B{C{height}}.
269 '''
270 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, name=name)
271 if datum not in (None, self._datum, _EWGS84):
272 self.datum = _ellipsoidal_datum(datum, name=name)
273 if reframe:
274 self.reframe = reframe
275 self.epoch = epoch
277# def __matmul__(self, other): # PYCHOK Python 3.5+
278# '''Return C{NotImplemented} for C{ll_ = ll @ datum} and C{ll_ = ll @ reframe}.
279# '''
280# RefFrame = _MODS.trf.RefFrame
281# return NotImplemented if isinstance(other, (Datum, RefFrame)) else \
282# _NotImplemented(self, other)
284 def antipode(self, height=None):
285 '''Return the antipode, the point diametrically opposite
286 to this point.
288 @kwarg height: Optional height of the antipode, height
289 of this point otherwise (C{meter}).
291 @return: The antipodal point (C{LatLon}).
292 '''
293 lla = LatLonBase.antipode(self, height=height)
294 if lla.datum != self.datum:
295 lla.datum = self.datum
296 return lla
298 @deprecated_property_RO
299 def convergence(self):
300 '''DEPRECATED, use property C{gamma}.'''
301 return self.gamma
303 @deprecated_method
304 def convertDatum(self, datum2):
305 '''DEPRECATED, use method L{toDatum}.'''
306 return self.toDatum(datum2)
308 @deprecated_method
309 def convertRefFrame(self, reframe2):
310 '''DEPRECATED, use method L{toRefFrame}.'''
311 return self.toRefFrame(reframe2)
313 @Property_RO
314 def _css(self):
315 '''(INTERNAL) Get this C{LatLon} point as a Cassini-Soldner location (L{Css}).
316 '''
317 css = _MODS.css
318 return css.toCss(self, height=self.height, Css=css.Css, name=self.name)
320 @property_doc_(''' this points's datum (L{Datum}).''')
321 def datum(self):
322 '''Get this point's datum (L{Datum}).
323 '''
324 return self._datum
326 @datum.setter # PYCHOK setter!
327 def datum(self, datum):
328 '''Set this point's datum I{without conversion} (L{Datum}).
330 @raise TypeError: The B{C{datum}} is not a L{Datum}
331 or not ellipsoidal.
332 '''
333 _xinstanceof(Datum, datum=datum)
334 if not datum.isEllipsoidal:
335 raise _IsnotError(_ellipsoidal_, datum=datum)
336 if self._datum != datum:
337 _update_all(self)
338 self._datum = datum
340 def distanceTo2(self, other, wrap=False):
341 '''I{Approximate} the distance and (initial) bearing between this
342 and an other (ellipsoidal) point based on the radii of curvature.
344 I{Suitable only for short distances up to a few hundred Km
345 or Miles and only between points not near-polar}.
347 @arg other: The other point (C{LatLon}).
348 @kwarg wrap: If C{True}, wrap or I{normalize} the B{C{other}}
349 point (C{bool}).
351 @return: An L{Distance2Tuple}C{(distance, initial)}.
353 @raise TypeError: The B{C{other}} point is not C{LatLon}.
355 @raise ValueError: Incompatible datum ellipsoids.
357 @see: Method L{Ellipsoid.distance2} and U{Local, flat earth
358 approximation<https://www.EdWilliams.org/avform.htm#flat>}
359 aka U{Hubeny<https://www.OVG.AT/de/vgi/files/pdf/3781/>}
360 formula.
361 '''
362 p = self.others(other)
363 if wrap:
364 p = _Wrap.point(p)
365 E = self.ellipsoids(other)
366 return E.distance2(*(self.latlon + p.latlon))
368 @Property_RO
369 def _elevation2(self):
370 '''(INTERNAL) Get elevation and data source.
371 '''
372 return _MODS.elevations.elevation2(self.lat, self.lon,
373 timeout=self._elevation2to)
375 def elevation2(self, adjust=True, datum=None, timeout=2):
376 '''Return elevation of this point for its or the given datum, ellipsoid
377 or sphere.
379 @kwarg adjust: Adjust the elevation for a B{C{datum}} other than
380 C{NAD83} (C{bool}).
381 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
382 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
383 radius).
384 @kwarg timeout: Optional query timeout (C{seconds}).
386 @return: An L{Elevation2Tuple}C{(elevation, data_source)} or
387 C{(None, error)} in case of errors.
389 @note: The adjustment applied is the difference in geocentric earth
390 radius between the B{C{datum}} and C{NAV83} upon which the
391 L{elevations.elevation2} is based.
393 @note: NED elevation is only available for locations within the
394 U{Conterminous US (CONUS)
395 <https://WikiPedia.org/wiki/Contiguous_United_States>}.
397 @see: Function L{elevations.elevation2} and method C{Ellipsoid.Rgeocentric}
398 for further details and possible C{error}s.
399 '''
400 if self._elevation2to != timeout:
401 self._elevation2to = timeout
402 LatLonEllipsoidalBase._elevation2._update(self)
403 return self._Radjust2(adjust, datum, self._elevation2)
405 def ellipsoid(self, datum=_WGS84):
406 '''Return the ellipsoid of this point's datum or the given datum.
408 @kwarg datum: Default datum (L{Datum}).
410 @return: The ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
411 '''
412 return _xattr(self, datum=datum).ellipsoid
414 @property_RO
415 def ellipsoidalLatLon(self):
416 '''Get this C{LatLon}'s ellipsoidal class.
417 '''
418 return type(self)
420 def ellipsoids(self, other):
421 '''Check the type and ellipsoid of this and an other point's datum.
423 @arg other: The other point (C{LatLon}).
425 @return: This point's datum ellipsoid (L{Ellipsoid} or L{Ellipsoid2}).
427 @raise TypeError: The B{C{other}} point is not C{LatLon}.
429 @raise ValueError: Incompatible datum ellipsoids.
430 '''
431 self.others(other, up=2) # ellipsoids' caller
433 E = self.ellipsoid()
434 try: # other may be Sphere, etc.
435 e = other.ellipsoid()
436 except AttributeError:
437 try: # no ellipsoid method, try datum
438 e = other.datum.ellipsoid
439 except AttributeError:
440 e = E # no datum, XXX assume equivalent?
441 if e != E:
442 raise _ValueError(e.named2, txt=_incompatible(E.named2))
443 return E
445 @property_doc_(''' this point's observed or C{reframe} epoch (C{float}).''')
446 def epoch(self):
447 '''Get this point's observed or C{reframe} epoch (L{Epoch}) or C{None}.
448 '''
449 return self._epoch or (self.reframe.epoch if self.reframe else None)
451 @epoch.setter # PYCHOK setter!
452 def epoch(self, epoch):
453 '''Set or clear this point's observed epoch, a fractional
454 calendar year (L{Epoch}, C{scalar} or C{str}) or C{None}.
456 @raise TRFError: Invalid B{C{epoch}}.
457 '''
458 self._epoch = None if epoch is None else Epoch(epoch)
460 @Property_RO
461 def Equidistant(self):
462 '''Get the prefered azimuthal equidistant projection I{class} (L{EquidistantKarney} or L{EquidistantExact}).
463 '''
464 try:
465 _ = self.datum.ellipsoid.geodesic
466 return _MODS.azimuthal.EquidistantKarney
467 except ImportError: # no geographiclib
468 return _MODS.azimuthal.EquidistantExact # XXX no longer L{azimuthal.Equidistant}
470 @Property_RO
471 def _etm(self):
472 '''(INTERNAL) Get this C{LatLon} point as an ETM coordinate (L{pygeodesy.toEtm8}).
473 '''
474 etm = _MODS.etm
475 return etm.toEtm8(self, datum=self.datum, Etm=etm.Etm)
477 @property_RO
478 def gamma(self):
479 '''Get this point's UTM or UPS meridian convergence (C{degrees}) or
480 C{None} if not available or not converted from L{Utm} or L{Ups}.
481 '''
482 return self._gamma
484 @Property_RO
485 def _geoidHeight2(self):
486 '''(INTERNAL) Get geoid height and model.
487 '''
488 return _MODS.elevations.geoidHeight2(self.lat, self.lon, model=0,
489 timeout=self._geoidHeight2to)
491 def geoidHeight2(self, adjust=False, datum=None, timeout=2):
492 '''Return geoid height of this point for its or the given datum, ellipsoid
493 or sphere.
495 @kwarg adjust: Adjust the geoid height for a B{C{datum}} other than
496 C{NAD83/NADV88} (C{bool}).
497 @kwarg datum: Optional datum overriding this point's datum (L{Datum},
498 L{Ellipsoid}, L{Ellipsoid2}, L{a_f2Tuple} or C{scalar}
499 radius).
500 @kwarg timeout: Optional query timeout (C{seconds}).
502 @return: A L{GeoidHeight2Tuple}C{(height, model_name)} or
503 C{(None, error)} in case of errors.
505 @note: The adjustment applied is the difference in geocentric earth
506 radius between the B{C{datum}} and C{NAV83/NADV88} upon which
507 the L{elevations.geoidHeight2} is based.
509 @note: The geoid height is only available for locations within the
510 U{Conterminous US (CONUS)
511 <https://WikiPedia.org/wiki/Contiguous_United_States>}.
513 @see: Function L{elevations.geoidHeight2} and method C{Ellipsoid.Rgeocentric}
514 for further details and possible C{error}s.
515 '''
516 if self._geoidHeight2to != timeout:
517 self._geoidHeight2to = timeout
518 LatLonEllipsoidalBase._geoidHeight2._update(self)
519 return self._Radjust2(adjust, datum, self._geoidHeight2)
521 def intermediateTo(self, other, fraction, height=None, wrap=False): # PYCHOK no cover
522 '''I{Must be overloaded}.'''
523 _MODS.named.notOverloaded(self, other, fraction, height=height, wrap=wrap)
525 def intersection3(self, end1, other, end2, height=None, wrap=False, # was=True
526 equidistant=None, tol=_TOL_M):
527 '''I{Iteratively} compute the intersection point of two lines, each
528 defined by two points or a start point and bearing from North.
530 @arg end1: End point of this line (C{LatLon}) or the initial
531 bearing at this point (compass C{degrees360}).
532 @arg other: Start point of the other line (C{LatLon}).
533 @arg end2: End point of the other line (C{LatLon}) or the initial
534 bearing at the other point (compass C{degrees360}).
535 @kwarg height: Optional height at the intersection (C{meter},
536 conventionally) or C{None} for the mean height.
537 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
538 B{C{other}} and B{C{end*}} points (C{bool}).
539 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
540 function L{pygeodesy.equidistant}), or C{None}
541 for this point's preferred C{.Equidistant}.
542 @kwarg tol: Tolerance for convergence and skew line distance and
543 length (C{meter}, conventionally).
545 @return: An L{Intersection3Tuple}C{(point, outside1, outside2)}
546 with C{point} a C{LatLon} instance.
548 @raise ImportError: Package U{geographiclib
549 <https://PyPI.org/project/geographiclib>}
550 not installed or not found, but only if
551 C{B{equidistant}=}L{EquidistantKarney}.
553 @raise IntersectionError: Skew, colinear, parallel or otherwise
554 non-intersecting lines or no convergence
555 for the given B{C{tol}}.
557 @raise TypeError: If B{C{end1}}, B{C{other}} or B{C{end2}} point
558 is not C{LatLon}.
560 @note: For each line specified with an initial bearing, a pseudo-end
561 point is computed as the C{destination} along that bearing at
562 about 1.5 times the distance from the start point to an initial
563 gu-/estimate of the intersection point (and between 1/8 and 3/8
564 of the authalic earth perimeter).
566 @see: I{Karney's} U{intersect.cpp<https://SourceForge.net/p/geographiclib/
567 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https://
568 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>}
569 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section
570 B{14. MARITIME BOUNDARIES} for more details about the iteration algorithm.
571 '''
572 try:
573 s2 = self.others(other)
574 return _MODS.ellipsoidalBaseDI._intersect3(self, end1,
575 s2, end2,
576 height=height, wrap=wrap,
577 equidistant=equidistant, tol=tol,
578 LatLon=self.classof, datum=self.datum)
579 except (TypeError, ValueError) as x:
580 raise _xError(x, start1=self, end1=end1, other=other, end2=end2,
581 height=height, wrap=wrap, tol=tol)
583 def intersections2(self, radius1, other, radius2, height=None, wrap=False, # was=True
584 equidistant=None, tol=_TOL_M):
585 '''I{Iteratively} compute the intersection points of two circles,
586 each defined by a center point and a radius.
588 @arg radius1: Radius of this circle (C{meter}, conventionally).
589 @arg other: Center of the other circle (C{LatLon}).
590 @arg radius2: Radius of the other circle (C{meter}, same units as
591 B{C{radius1}}).
592 @kwarg height: Optional height for the intersection points (C{meter},
593 conventionally) or C{None} for the I{"radical height"}
594 at the I{radical line} between both centers.
595 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the B{C{other}}
596 center (C{bool}).
597 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
598 function L{pygeodesy.equidistant}) or C{None}
599 for this point's preferred C{.Equidistant}.
600 @kwarg tol: Convergence tolerance (C{meter}, same units as
601 B{C{radius1}} and B{C{radius2}}).
603 @return: 2-Tuple of the intersection points, each a C{LatLon}
604 instance. For abutting circles, both intersection
605 points are the same instance, aka the I{radical center}.
607 @raise ImportError: Package U{geographiclib
608 <https://PyPI.org/project/geographiclib>}
609 not installed or not found, but only if
610 C{B{equidistant}=}L{EquidistantKarney}.
612 @raise IntersectionError: Concentric, antipodal, invalid or
613 non-intersecting circles or no
614 convergence for the given B{C{tol}}.
616 @raise TypeError: Invalid B{C{other}} or B{C{equidistant}}.
618 @raise UnitError: Invalid B{C{radius1}}, B{C{radius2}} or B{C{height}}.
620 @see: U{The B{ellipsoidal} case<https://GIS.StackExchange.com/questions/48937/
621 calculating-intersection-of-two-circles>}, U{Karney's paper
622 <https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section B{14. MARITIME BOUNDARIES},
623 U{circle-circle<https://MathWorld.Wolfram.com/Circle-CircleIntersection.html>} and
624 U{sphere-sphere<https://MathWorld.Wolfram.com/Sphere-SphereIntersection.html>}
625 intersections.
626 '''
627 try:
628 c2 = self.others(other)
629 return _MODS.ellipsoidalBaseDI._intersections2(self, radius1,
630 c2, radius2,
631 height=height, wrap=wrap,
632 equidistant=equidistant, tol=tol,
633 LatLon=self.classof, datum=self.datum)
634 except (AssertionError, TypeError, ValueError) as x:
635 raise _xError(x, center=self, radius1=radius1, other=other, radius2=radius2,
636 height=height, wrap=wrap, tol=tol)
638 def isenclosedBy(self, points, wrap=False):
639 '''Check whether a polygon or composite encloses this point.
641 @arg points: The polygon points or clips (C{LatLon}[],
642 L{BooleanFHP} or L{BooleanGH}).
643 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
644 B{C{points}} (C{bool}).
646 @return: C{True} if this point is inside the polygon or composite,
647 C{False} otherwise.
649 @raise PointsError: Insufficient number of B{C{points}}.
651 @raise TypeError: Some B{C{points}} are not C{LatLon}.
653 @raise ValueError: Invalid B{C{point}}, lat- or longitude.
655 @see: Functions L{pygeodesy.isconvex}, L{pygeodesy.isenclosedBy}
656 and L{pygeodesy.ispolar} especially if the B{C{points}} may
657 enclose a pole or wrap around the earth I{longitudinally}.
658 '''
659 return _MODS.points.isenclosedBy(self, points, wrap=wrap)
661 @property_RO
662 def iteration(self):
663 '''Get the most recent C{intersections2} or C{nearestOn} iteration
664 number (C{int}) or C{None} if not available/applicable.
665 '''
666 return self._iteration
668 @Property_RO
669 def _lcc(self):
670 '''(INTERNAL) Get this C{LatLon} point as a Lambert location (L{Lcc}).
671 '''
672 lcc = _MODS.lcc
673 return lcc.toLcc(self, height=self.height, Lcc=lcc.Lcc, name=self.name)
675 def midpointTo(self, other, height=None, fraction=_0_5, wrap=False):
676 '''Find the midpoint on a geodesic between this and an other point.
678 @arg other: The other point (C{LatLon}).
679 @kwarg height: Optional height for midpoint, overriding the
680 mean height (C{meter}).
681 @kwarg fraction: Midpoint location from this point (C{scalar}),
682 may be negative or greater than 1.0.
683 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
684 B{C{other}} point (C{bool}).
686 @return: Midpoint (C{LatLon}).
688 @raise TypeError: The B{C{other}} point is not C{LatLon}.
690 @raise ValueError: Invalid B{C{height}}.
692 @see: Methods C{intermediateTo} and C{rhumbMidpointTo}.
693 '''
694 return self.intermediateTo(other, fraction, height=height, wrap=wrap)
696 def nearestOn(self, point1, point2, within=True, height=None, wrap=False, # was=True
697 equidistant=None, tol=_TOL_M):
698 '''I{Iteratively} locate the closest point on the geodesic between
699 two other (ellipsoidal) points.
701 @arg point1: Start point (C{LatLon}).
702 @arg point2: End point (C{LatLon}).
703 @kwarg within: If C{True} return the closest point I{between}
704 B{C{point1}} and B{C{point2}}, otherwise the
705 closest point elsewhere on the geodesic (C{bool}).
706 @kwarg height: Optional height for the closest point (C{meter},
707 conventionally) or C{None} or C{False} for the
708 interpolated height. If C{False}, the closest
709 takes the heights of the points into account.
710 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll both
711 B{C{point1}} and B{C{point2}} (C{bool}).
712 @kwarg equidistant: An azimuthal equidistant projection (I{class} or
713 function L{pygeodesy.equidistant}) or C{None}
714 for this point's preferred C{.Equidistant}.
715 @kwarg tol: Convergence tolerance (C{meter}, conventionally).
717 @return: Closest point (C{LatLon}).
719 @raise ImportError: Package U{geographiclib
720 <https://PyPI.org/project/geographiclib>}
721 not installed or not found, but only if
722 C{B{equidistant}=}L{EquidistantKarney}.
724 @raise TypeError: Invalid B{C{point1}}, B{C{point2}} or
725 B{C{equidistant}}.
727 @raise ValueError: Datum or ellipsoid of B{C{point1}} or B{C{point2}} is
728 incompatible or no convergence for the given B{C{tol}}.
730 @see: I{Karney}'s U{intercept.cpp<https://SourceForge.net/p/geographiclib/
731 discussion/1026621/thread/21aaff9f/>}, U{The B{ellipsoidal} case<https://
732 GIS.StackExchange.com/questions/48937/calculating-intersection-of-two-circles>}
733 and U{Karney's paper<https://ArXiv.org/pdf/1102.1215.pdf>}, pp 20-21, section
734 B{14. MARITIME BOUNDARIES} for details about the iteration algorithm.
735 '''
736 try:
737 t = _MODS.ellipsoidalBaseDI._nearestOn2(self, point1, point2, within=within,
738 height=height, wrap=wrap,
739 equidistant=equidistant,
740 tol=tol, LatLon=self.classof)
741 except (TypeError, ValueError) as x:
742 raise _xError(x, point=self, point1=point1, point2=point2, within=within,
743 height=height, wrap=wrap, tol=tol)
744 return t.closest
746 @Property_RO
747 def _osgr(self):
748 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr}),
749 based on the OS recommendation.
750 '''
751 return _MODS.osgr.toOsgr(self, kTM=False, name=self.name) # datum=self.datum
753 @Property_RO
754 def _osgrTM(self):
755 '''(INTERNAL) Get this C{LatLon} point as an OSGR coordinate (L{Osgr})
756 based on I{Karney}'s Krüger implementation.
757 '''
758 return _MODS.osgr.toOsgr(self, kTM=True, name=self.name) # datum=self.datum
760 def parse(self, strllh, height=0, datum=None, epoch=None, reframe=None,
761 sep=_COMMA_, wrap=False, name=NN):
762 '''Parse a string consisting of C{"lat, lon[, height]"},
763 representing a similar, ellipsoidal C{LatLon} point.
765 @arg strllh: Lat, lon and optional height (C{str}),
766 see function L{pygeodesy.parse3llh}.
767 @kwarg height: Optional, default height (C{meter} or
768 C{None}).
769 @kwarg datum: Optional datum (L{Datum}), overriding this
770 datum I{without conversion}.
771 @kwarg epoch: Optional datum (L{Epoch}), overriding this
772 epoch I{without conversion}.
773 @kwarg reframe: Optional datum (L{RefFrame}), overriding
774 this reframe I{without conversion}.
775 @kwarg sep: Optional separator (C{str}).
776 @kwarg wrap: If C{True}, wrap or I{normalize} the lat-
777 and longitude (C{bool}).
778 @kwarg name: Optional instance name (C{str}), overriding
779 this name.
781 @return: The similar point (ellipsoidal C{LatLon}).
783 @raise ParseError: Invalid B{C{strllh}}.
784 '''
785 a, b, h = _MODS.dms.parse3llh(strllh, height=height, sep=sep, wrap=wrap)
786 r = self.classof(a, b, height=h, datum=self.datum)
787 if datum not in (None, self.datum):
788 r.datum = datum
789 if epoch not in (None, self.epoch):
790 r.epoch = epoch
791 if reframe not in (None, self.reframe):
792 r.reframe = reframe
793 return self._xnamed(r, name=name, force=True) if name else r
795 def _Radjust2(self, adjust, datum, meter_text2):
796 '''(INTERNAL) Adjust an C{elevation} or C{geoidHeight} with
797 difference in Gaussian radii of curvature of the given
798 datum and NAD83 ellipsoids at this point's latitude.
800 @note: This is an arbitrary, possibly incorrect adjustment.
801 '''
802 if adjust: # Elevation2Tuple or GeoidHeight2Tuple
803 m, t = meter_text2
804 if isinstance(m, float) and fabs(m) > EPS:
805 n = Datums.NAD83.ellipsoid.rocGauss(self.lat)
806 if n > EPS0:
807 # use ratio, datum and NAD83 units may differ
808 E = self.ellipsoid() if datum in (None, self.datum) else \
809 _earth_ellipsoid(datum)
810 r = E.rocGauss(self.lat)
811 if r > EPS0 and fabs(r - n) > EPS: # EPS1
812 m *= r / n
813 meter_text2 = meter_text2.classof(m, t)
814 return self._xnamed(meter_text2)
816 @property_doc_(''' this point's reference frame (L{RefFrame}).''')
817 def reframe(self):
818 '''Get this point's reference frame (L{RefFrame}) or C{None}.
819 '''
820 return self._reframe
822 @reframe.setter # PYCHOK setter!
823 def reframe(self, reframe):
824 '''Set or clear this point's reference frame (L{RefFrame}) or C{None}.
826 @raise TypeError: The B{C{reframe}} is not a L{RefFrame}.
827 '''
828 _set_reframe(self, reframe)
830 @Property_RO
831 def scale(self):
832 '''Get this point's UTM grid or UPS point scale factor (C{float})
833 or C{None} if not converted from L{Utm} or L{Ups}.
834 '''
835 return self._scale
837 def toCartesian(self, height=None, **Cartesian_and_kwds): # PYCHOK signature
838 '''Convert this point to cartesian, I{geocentric} coordinates,
839 also known as I{Earth-Centered, Earth-Fixed} (ECEF).
841 @see: Method L{toCartesian<latlonBase.LatLonBase.toCartesian>}
842 for further details.
843 '''
844 kwds = Cartesian_and_kwds
845 if kwds:
846 kwds = _xkwds(kwds, reframe=self.reframe, epoch=self.epoch)
847 return LatLonBase.toCartesian(self, height=height, **kwds)
849 def toCss(self, **toCss_kwds):
850 '''Convert this C{LatLon} point to a Cassini-Soldner location.
852 @kwarg toCss_kwds: Optional L{pygeodesy.toCss} keyword arguments.
854 @return: The Cassini-Soldner location (L{Css}).
856 @see: Function L{pygeodesy.toCss}.
857 '''
858 return self._css if not toCss_kwds else _MODS.css.toCss(
859 self, **_xkwds(toCss_kwds, name=self.name))
861 def toDatum(self, datum2, height=None, name=NN):
862 '''Convert this point to an other datum.
864 @arg datum2: Datum to convert I{to} (L{Datum}).
865 @kwarg height: Optional height, overriding the
866 converted height (C{meter}).
867 @kwarg name: Optional name (C{str}), iff converted.
869 @return: The converted point (ellipsoidal C{LatLon})
870 or a copy of this point if B{C{datum2}}
871 matches this point's C{datum}.
873 @raise TypeError: Invalid B{C{datum2}}.
874 '''
875 n = name or self.name
876 d2 = _ellipsoidal_datum(datum2, name=n)
877 if self.datum == d2:
878 r = self.copy(name=name)
879 else:
880 kwds = _xkwds_not(None, LatLon=self.classof, name=n,
881 epoch=self.epoch, reframe=self.reframe)
882 c = self.toCartesian().toDatum(d2)
883 r = c.toLatLon(datum=d2, height=height, **kwds)
884 return r
886 def toEtm(self, **toEtm8_kwds):
887 '''Convert this C{LatLon} point to an ETM coordinate.
889 @kwarg toEtm8_kwds: Optional L{pygeodesy.toEtm8} keyword arguments.
891 @return: The ETM coordinate (L{Etm}).
893 @see: Function L{pygeodesy.toEtm8}.
894 '''
895 return self._etm if not toEtm8_kwds else _MODS.etm.toEtm8(
896 self, **_xkwds(toEtm8_kwds, name=self.name))
898 def toLcc(self, **toLcc_kwds):
899 '''Convert this C{LatLon} point to a Lambert location.
901 @kwarg toLcc_kwds: Optional L{pygeodesy.toLcc} keyword arguments.
903 @return: The Lambert location (L{Lcc}).
905 @see: Function L{pygeodesy.toLcc}.
906 '''
907 return self._lcc if not toLcc_kwds else _MODS.lcc.toLcc(
908 self, **_xkwds(toLcc_kwds, name=self.name))
910 def toMgrs(self, center=False, pole=NN):
911 '''Convert this C{LatLon} point to an MGRS coordinate.
913 @kwarg center: If C{True}, try to I{un}-center MGRS
914 to its C{lowerleft} (C{bool}) or by
915 C{B{center} meter} (C{scalar}).
916 @kwarg pole: Optional top/center for the MGRS UPS
917 projection (C{str}, 'N[orth]' or 'S[outh]').
919 @return: The MGRS coordinate (L{Mgrs}).
921 @see: Method L{toUtmUps} and L{Mgrs.toLatLon}.
922 '''
923 return self.toUtmUps(center=center, pole=pole).toMgrs(center=False)
925 def toOsgr(self, kTM=False, **toOsgr_kwds):
926 '''Convert this C{LatLon} point to an OSGR coordinate.
928 @kwarg kTM: If C{True} use I{Karney}'s Krüger method from module
929 L{ktm}, otherwise I{Ordinance Survery}'s recommended
930 formulation (C{bool}).
931 @kwarg toOsgr_kwds: Optional L{pygeodesy.toOsgr} keyword arguments.
933 @return: The OSGR coordinate (L{Osgr}).
935 @see: Function L{pygeodesy.toOsgr}.
936 '''
937 if toOsgr_kwds:
938 r = _MODS.osgr.toOsgr(self, kTM=kTM, **_xkwds(toOsgr_kwds, name=self.name))
939 else:
940 r = self._osgrTM if kTM else self._osgr
941 return r
943 def toRefFrame(self, reframe2, reframe=None, epoch=None, epoch2=None, height=None, name=NN):
944 '''Convert this point to an other reference frame and epoch.
946 @arg reframe2: Reference frame to convert I{to} (L{RefFrame}).
947 @kwarg reframe: Optional reference frame (L{RefFrame}), overriding this
948 point's reference frame.
949 @kwarg epoch: Optional epoch (L{Epoch}, C{scalar} or C{str}), overriding
950 this point's epoch.
951 @kwarg epoch2: Optional epoch to observe for the converted point (L{Epoch},
952 C{scalar} or C{str}).
953 @kwarg height: Optional height, overriding the converted height (C{meter}).
954 @kwarg name: Optional name (C{str}), iff converted.
956 @return: The converted point (ellipsoidal C{LatLon}) or if conversion is
957 C{nil}, this point or a copy of this point if the B{C{name}} is
958 non-empty.
960 @raise TRFError: This point's C{reframe} is not defined, invalid B{C{epoch}}
961 or B{C{epoch2}} or conversion from this point's C{reframe}
962 to B{C{reframe2}} is not available.
964 @raise TypeError: B{C{reframe2}} or B{C{reframe}} not a L{RefFrame}.
965 '''
966 e, t0, d, d2 = _MODS.trf._eT0Ds4(self, reframe, epoch, reframe2, epoch2)
967 if t0:
968 c = self.toCartesian().toDatum(d).toTransforms_(t0).toDatum(d2)
969 n = name or self.name
970 ll = c.toLatLon(datum=self.datum, epoch=e, height=height,
971 LatLon=self.classof, name=n, reframe=reframe2)
972 else:
973 ll = self.copy(name=name) if name else self
974 return ll
976 def toUps(self, pole=NN, falsed=True, center=False):
977 '''Convert this C{LatLon} point to a UPS coordinate.
979 @kwarg pole: Optional top/center of (stereographic)
980 projection (C{str}, 'N[orth]' or 'S[outh]').
981 @kwarg falsed: False easting and northing (C{bool}).
982 @kwarg center: If C{True}, I{un}-center the UPS
983 to its C{lowerleft} (C{bool}) or
984 by C{B{center} meter} (C{scalar}).
986 @return: The UPS coordinate (L{Ups}).
988 @see: Function L{pygeodesy.toUps8}.
989 '''
990 if self._upsOK(pole, falsed):
991 u = self._ups
992 else:
993 ups = _MODS.ups
994 u = ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
995 pole=pole, falsed=falsed)
996 return _lowerleft(u, center)
998 def toUtm(self, center=False):
999 '''Convert this C{LatLon} point to a UTM coordinate.
1001 @kwarg center: If C{True}, I{un}-center the UTM
1002 to its C{lowerleft} (C{bool}) or
1003 by C{B{center} meter} (C{scalar}).
1005 @return: The UTM coordinate (L{Utm}).
1007 @see: Method L{Mgrs.toUtm} and function L{pygeodesy.toUtm8}.
1008 '''
1009 return _lowerleft(self._utm, center)
1011 def toUtmUps(self, pole=NN, center=False):
1012 '''Convert this C{LatLon} point to a UTM or UPS coordinate.
1014 @kwarg pole: Optional top/center of UPS (stereographic)
1015 projection (C{str}, 'N[orth]' or 'S[outh]').
1016 @kwarg center: If C{True}, I{un}-center the UTM or UPS to
1017 its C{lowerleft} (C{bool}) or by C{B{center}
1018 meter} (C{scalar}).
1020 @return: The UTM or UPS coordinate (L{Utm} or L{Ups}).
1022 @see: Function L{pygeodesy.toUtmUps8}.
1023 '''
1024 if self._utmOK():
1025 u = self._utm
1026 elif self._upsOK(pole):
1027 u = self._ups
1028 else: # no cover
1029 utmups = _MODS.utmups
1030 u = utmups.toUtmUps8(self, datum=self.datum, pole=pole, name=self.name,
1031 Utm=utmups.Utm, Ups=utmups.Ups)
1032 if isinstance(u, utmups.Utm):
1033 self._update(False, _utm=u) # PYCHOK kwds
1034 elif isinstance(u, utmups.Ups):
1035 self._update(False, _ups=u) # PYCHOK kwds
1036 else:
1037 _xinstanceof(utmups.Utm, utmups.Ups, toUtmUps8=u)
1038 return _lowerleft(u, center)
1040 @deprecated_method
1041 def to3xyz(self): # PYCHOK no cover
1042 '''DEPRECATED, use method C{toEcef}.
1044 @return: A L{Vector3Tuple}C{(x, y, z)}.
1046 @note: Overloads C{LatLonBase.to3xyz}
1047 '''
1048 r = self.toEcef()
1049 return _MODS.namedTuples.Vector3Tuple(r.x, r.y, r.z, name=self.name)
1051 def triangulate(self, bearing1, other, bearing2, **height_wrap_tol):
1052 '''I{Iteratively} locate a point given this, an other point and the (initial)
1053 bearing at this and at the other point.
1055 @arg bearing1: Bearing at this point (compass C{degrees360}).
1056 @arg other: Start point of the other line (C{LatLon}).
1057 @arg bearing2: Bearing at the other point (compass C{degrees360}).
1058 @kwarg height_wrap_tol: Optional keyword arguments C{B{height}=None},
1059 C{B{wrap}=False} and C{B{tol}}, see method L{intersection3}.
1061 @return: Triangulated point (C{LatLon}).
1063 @see: Method L{intersection3} for further details.
1064 '''
1065 if _isDegrees(bearing1) and _isDegrees(bearing2):
1066 r = self.intersection3(bearing1, other, bearing2, **height_wrap_tol)
1067 return r.point
1068 raise _TypeError(bearing1=bearing1, bearing2=bearing2 **height_wrap_tol)
1070 def trilaterate5(self, distance1, point2, distance2, point3, distance3,
1071 area=True, eps=EPS1, wrap=False):
1072 '''Trilaterate three points by I{area overlap} or I{perimeter
1073 intersection} of three intersecting circles.
1075 @arg distance1: Distance to this point (C{meter}), same units
1076 as B{C{eps}}).
1077 @arg point2: Second center point (C{LatLon}).
1078 @arg distance2: Distance to point2 (C{meter}, same units as
1079 B{C{eps}}).
1080 @arg point3: Third center point (C{LatLon}).
1081 @arg distance3: Distance to point3 (C{meter}, same units as
1082 B{C{eps}}).
1083 @kwarg area: If C{True} compute the area overlap, otherwise the
1084 perimeter intersection of the circles (C{bool}).
1085 @kwarg eps: The required I{minimal overlap} for C{B{area}=True}
1086 or the I{intersection margin} for C{B{area}=False}
1087 (C{meter}, conventionally).
1088 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
1089 B{C{point2}} and B{C{point3}} (C{bool}).
1091 @return: A L{Trilaterate5Tuple}C{(min, minPoint, max, maxPoint, n)}
1092 with C{min} and C{max} in C{meter}, same units as B{C{eps}},
1093 the corresponding trilaterated points C{minPoint} and
1094 C{maxPoint} as I{ellipsoidal} C{LatLon} and C{n}, the number
1095 of trilatered points found for the given B{C{eps}}.
1097 If only a single trilaterated point is found, C{min I{is}
1098 max}, C{minPoint I{is} maxPoint} and C{n = 1}.
1100 For C{B{area}=True}, C{min} and C{max} are the smallest
1101 respectively largest I{radial} overlap found.
1103 For C{B{area}=False}, C{min} and C{max} represent the
1104 nearest respectively farthest intersection margin.
1106 If C{B{area}=True} and all 3 circles are concentric, C{n=0}
1107 and C{minPoint} and C{maxPoint} are the B{C{point#}} with
1108 the smallest B{C{distance#}} C{min} respectively C{max} the
1109 largest B{C{distance#}}.
1111 @raise IntersectionError: Trilateration failed for the given B{C{eps}},
1112 insufficient overlap for C{B{area}=True}, no
1113 circle intersections for C{B{area}=False} or
1114 all circles are (near-)concentric.
1116 @raise TypeError: Invalid B{C{point2}} or B{C{point3}}.
1118 @raise ValueError: Coincident B{C{points}} or invalid B{C{distance1}},
1119 B{C{distance2}} or B{C{distance3}}.
1121 @note: Ellipsoidal trilateration invokes methods C{LatLon.intersections2}
1122 and C{LatLon.nearestOn} based on I{Karney}'s Python U{geographiclib
1123 <https://PyPI.org/project/geographiclib>} if installed, otherwise
1124 the accurate (but slower) C{ellipsoidalExact.LatLon} methods.
1125 '''
1126 return _trilaterate5(self, distance1,
1127 self.others(point2=point2), distance2,
1128 self.others(point3=point3), distance3,
1129 area=area, eps=eps, wrap=wrap)
1131 @Property_RO
1132 def _ups(self): # __dict__ value overwritten by method C{toUtmUps}
1133 '''(INTERNAL) Get this C{LatLon} point as UPS coordinate (L{Ups}),
1134 see L{pygeodesy.toUps8}.
1135 '''
1136 ups = _MODS.ups
1137 return ups.toUps8(self, datum=self.datum, Ups=ups.Ups,
1138 pole=NN, falsed=True, name=self.name)
1140 def _upsOK(self, pole=NN, falsed=True):
1141 '''(INTERNAL) Check matching C{Ups}.
1142 '''
1143 try:
1144 u = self._ups
1145 except RangeError:
1146 return False
1147 return falsed and (u.pole == pole[:1].upper() or not pole)
1149 @Property_RO
1150 def _utm(self): # __dict__ value overwritten by method C{toUtmUps}
1151 '''(INTERNAL) Get this C{LatLon} point as UTM coordinate (L{Utm}),
1152 see L{pygeodesy.toUtm8}.
1153 '''
1154 utm = _MODS.utm
1155 return utm.toUtm8(self, datum=self.datum, Utm=utm.Utm, name=self.name)
1157 def _utmOK(self):
1158 '''(INTERNAL) Check C{Utm}.
1159 '''
1160 try:
1161 _ = self._utm
1162 except RangeError:
1163 return False
1164 return True
1167def _lowerleft(utmups, center):
1168 '''(INTERNAL) Optionally I{un}-center C{utmups}.
1169 '''
1170 if center in (False, 0, _0_0):
1171 u = utmups
1172 elif center in (True,):
1173 u = utmups._lowerleft
1174 else:
1175 u = _MODS.utmupsBase._lowerleft(utmups, center)
1176 return u
1179def _nearestOn(point, point1, point2, within=True, height=None, wrap=False, # was=True
1180 equidistant=None, tol=_TOL_M, **LatLon_and_kwds):
1181 '''(INTERNAL) Get closest point, imported by .ellipsoidalExact,
1182 -GeodSolve, -Karney and -Vincenty to embellish exceptions.
1183 '''
1184 try:
1185 p = _xellipsoidal(point=point)
1186 t = _MODS.ellipsoidalBaseDI._nearestOn2(p, point1, point2, within=within,
1187 height=height, wrap=wrap,
1188 equidistant=equidistant,
1189 tol=tol, **LatLon_and_kwds)
1190 except (TypeError, ValueError) as x:
1191 raise _xError(x, point=point, point1=point1, point2=point2)
1192 return t.closest
1195def _set_reframe(inst, reframe):
1196 '''(INTERNAL) Set or clear an instance's reference frame.
1197 '''
1198 if reframe is not None:
1199 _xinstanceof(_MODS.trf.RefFrame, reframe=reframe)
1200 inst._reframe = reframe
1201 elif inst.reframe is not None:
1202 inst._reframe = None
1205__all__ += _ALL_DOCS(CartesianEllipsoidalBase, LatLonEllipsoidalBase)
1207# **) MIT License
1208#
1209# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1210#
1211# Permission is hereby granted, free of charge, to any person obtaining a
1212# copy of this software and associated documentation files (the "Software"),
1213# to deal in the Software without restriction, including without limitation
1214# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1215# and/or sell copies of the Software, and to permit persons to whom the
1216# Software is furnished to do so, subject to the following conditions:
1217#
1218# The above copyright notice and this permission notice shall be included
1219# in all copies or substantial portions of the Software.
1220#
1221# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1222# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
1223# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
1224# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
1225# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1226# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
1227# OTHER DEALINGS IN THE SOFTWARE.