Coverage for pygeodesy/sphericalBase.py: 94%
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2# -*- coding: utf-8 -*-
4u'''(INTERNAL) Private spherical base classes C{CartesianSphericalBase} and
5C{LatLonSphericalBase} for L{sphericalNvector} and L{sphericalTrigonometry}.
7A pure Python implementation of geodetic (lat-/longitude) functions,
8transcoded in part from JavaScript originals by I{(C) Chris Veness 2011-2024}
9and published under the same MIT Licence**, see
10U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>}.
11'''
12# make sure int/int division yields float quotient, see .basics
13from __future__ import division as _; del _ # PYCHOK semicolon
15from pygeodesy.basics import _copysign, isbool, isinstanceof, map1
16from pygeodesy.cartesianBase import CartesianBase, Bearing2Tuple
17from pygeodesy.constants import EPS, EPS0, PI, PI2, PI_2, R_M, \
18 _0_0, _0_5, _1_0, _180_0, _360_0, \
19 _over, isnear0, isnon0
20from pygeodesy.datums import Datums, _earth_ellipsoid, _spherical_datum
21from pygeodesy.errors import IntersectionError, _ValueError, \
22 _xattr, _xattrs, _xError
23from pygeodesy.fmath import favg, fdot, hypot, sqrt_a
24from pygeodesy.interns import _COMMA_, _concentric_, _datum_, _distant_, \
25 _exceed_PI_radians_, _name_, _near_, \
26 _radius_, _too_
27from pygeodesy.latlonBase import LatLonBase, _trilaterate5 # PYCHOK passed
28from pygeodesy.lazily import _ALL_DOCS, _ALL_LAZY, _ALL_MODS as _MODS
29# from pygeodesy.namedTuples import Bearing2Tuple # from .cartesianBase
30from pygeodesy.nvectorBase import NvectorBase, Fmt
31from pygeodesy.props import deprecated_method, property_doc_, property_RO, \
32 _update_all
33# from pygeodesy.streprs import Fmt # from .nvectorBase
34from pygeodesy.units import Bearing, Bearing_, _isRadius, Radians_, Radius, \
35 Radius_, Scalar_, _100km
36from pygeodesy.utily import acos1, asin1, atan2b, atan2d, degrees90, \
37 degrees180, sincos2, sincos2d, _unrollon, \
38 tanPI_2_2, wrapPI
40from math import cos, fabs, log, sin, sqrt
42__all__ = _ALL_LAZY.sphericalBase
43__version__ = '24.10.19'
46class CartesianSphericalBase(CartesianBase):
47 '''(INTERNAL) Base class for spherical C{Cartesian}s.
48 '''
49 _datum = Datums.Sphere # L{Datum}
51 def intersections2(self, rad1, other, rad2, radius=R_M):
52 '''Compute the intersection points of two circles each defined
53 by a center point and a radius.
55 @arg rad1: Radius of the this circle (C{meter} or C{radians},
56 see B{C{radius}}).
57 @arg other: Center of the other circle (C{Cartesian}).
58 @arg rad2: Radius of the other circle (C{meter} or C{radians},
59 see B{C{radius}}).
60 @kwarg radius: Mean earth radius (C{meter} or C{None} if both
61 B{C{rad1}} and B{C{rad2}} are given in C{radians}).
63 @return: 2-Tuple of the intersection points, each C{Cartesian}.
64 For abutting circles, the intersection points are the
65 same C{Cartesian} instance, aka the I{radical center}.
67 @raise IntersectionError: Concentric, antipodal, invalid or
68 non-intersecting circles.
70 @raise TypeError: If B{C{other}} is not C{Cartesian}.
72 @raise ValueError: Invalid B{C{rad1}}, B{C{rad2}} or B{C{radius}}.
74 @see: U{Calculating intersection of two Circles
75 <https://GIS.StackExchange.com/questions/48937/
76 calculating-intersection-of-two-circles>} and method
77 or function C{trilaterate3d2}.
78 '''
79 x1, x2 = self, self.others(other)
80 r1, r2, x = _rads3(rad1, rad2, radius)
81 if x:
82 x1, x2 = x2, x1
83 try:
84 n, q = x1.cross(x2), x1.dot(x2)
85 n2, q1 = n.length2, (_1_0 - q**2)
86 if n2 < EPS or isnear0(q1):
87 raise ValueError(_near_(_concentric_))
88 c1, c2 = cos(r1), cos(r2)
89 x0 = x1.times((c1 - q * c2) / q1).plus(
90 x2.times((c2 - q * c1) / q1))
91 n1 = _1_0 - x0.length2
92 if n1 < EPS:
93 raise ValueError(_too_(_distant_))
94 except ValueError as x:
95 raise IntersectionError(center=self, rad1=rad1,
96 other=other, rad2=rad2, cause=x)
97 n = n.times(sqrt(n1 / n2))
98 if n.length > EPS:
99 x1 = x0.plus(n)
100 x2 = x0.minus(n)
101 else: # abutting circles
102 x1 = x2 = x0
104 return (_xattrs(x1, self, _datum_, _name_),
105 _xattrs(x2, self, _datum_, _name_))
107 @property_RO
108 def sphericalCartesian(self):
109 '''Get this C{Cartesian}'s spherical class.
110 '''
111 return type(self)
114class LatLonSphericalBase(LatLonBase):
115 '''(INTERNAL) Base class for spherical C{LatLon}s.
116 '''
117 _datum = Datums.Sphere # spherical L{Datum}
118 _napieradius = _100km
120 def __init__(self, latlonh, lon=None, height=0, datum=None, wrap=False, **name):
121 '''Create a spherical C{LatLon} point frome the given lat-, longitude and
122 height on the given datum.
124 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
125 a previous C{LatLon} instance provided C{B{lon}=None}.
126 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
127 C(None), indicating B{C{latlonh}} is a C{LatLon}.
128 @kwarg height: Optional height above (or below) the earth surface (C{meter},
129 same units as the datum's radius or axes).
130 @kwarg datum: Optional, spherical datum to use (L{Datum}, L{Ellipsoid},
131 L{Ellipsoid2}, L{a_f2Tuple}) or the mean earth radius
132 (C{meter}, conventionally).
133 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
134 (C{bool}).
135 @kwarg name: Optional C{B{name}=NN} (C{str}).
137 @raise TypeError: Invalid B{C{latlonh}} or B{C{datum}} not spherical.
138 '''
139 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, **name)
140 if datum not in (None, self.datum):
141 self.datum = datum
143 def bearingTo2(self, other, wrap=False, raiser=False):
144 '''Return the initial and final bearing (forward and reverse azimuth)
145 from this to an other point.
147 @arg other: The other point (C{LatLon}).
148 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
149 B{C{other}} point (C{bool}).
151 @return: A L{Bearing2Tuple}C{(initial, final)}.
153 @raise TypeError: The B{C{other}} point is not spherical.
155 @see: Methods C{initialBearingTo} and C{finalBearingTo}.
156 '''
157 # .initialBearingTo is inside .-Nvector and .-Trigonometry
158 i = self.initialBearingTo(other, wrap=wrap, raiser=raiser) # PYCHOK .initialBearingTo
159 f = self.finalBearingTo( other, wrap=wrap, raiser=raiser)
160 return Bearing2Tuple(i, f, name=self.name)
162 @property_doc_(''' this point's datum (L{Datum}).''')
163 def datum(self):
164 '''Get this point's datum (L{Datum}).
165 '''
166 return self._datum
168 @datum.setter # PYCHOK setter!
169 def datum(self, datum):
170 '''Set this point's datum I{without conversion} (L{Datum}, L{Ellipsoid},
171 L{Ellipsoid2}, L{a_f2Tuple}) or C{scalar} spherical earth radius).
173 @raise TypeError: If B{C{datum}} invalid or not not spherical.
174 '''
175 d = _spherical_datum(datum, name=self.name, raiser=_datum_)
176 if self._datum != d:
177 _update_all(self)
178 self._datum = d
180 def finalBearingTo(self, other, wrap=False, raiser=False):
181 '''Return the final bearing (reverse azimuth) from this to
182 an other point.
184 @arg other: The other point (spherical C{LatLon}).
185 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
186 the B{C{other}} point (C{bool}).
188 @return: Final bearing (compass C{degrees360}).
190 @raise TypeError: The B{C{other}} point is not spherical.
191 '''
192 p = self.others(other)
193 if wrap:
194 p = _unrollon(self, p, wrap=wrap)
195 # final bearing is the reverse of the other, initial one
196 b = p.initialBearingTo(self, wrap=False, raiser=raiser) + _180_0
197 return b if b < 360 else (b - _360_0)
199 def intersecant2(self, circle, point, other, radius=R_M, exact=False, # PYCHOK signature
200 height=None, wrap=False):
201 '''Compute the intersections of a circle and a (great circle) line
202 given as two points or as a point and bearing.
204 @arg circle: Radius of the circle centered at this location (C{meter},
205 same units as B{C{radius}}) or a point on the circle
206 (same C{LatLon} class).
207 @arg point: A point on the (great circle) line (same C{LatLon} class).
208 @arg other: An other point I{on} (same C{LatLon} class) or the bearing
209 at B{C{point}} I{of} the (great circle) line (compass
210 C{degrees}).
211 @kwarg radius: Mean earth radius (C{meter}, conventionally).
212 @kwarg exact: If C{True}, use the I{exact} rhumb methods for azimuth,
213 destination and distance, if C{False} use the basic
214 rhumb methods (C{bool}) or if C{None} use the I{great
215 circle} methods.
216 @kwarg height: Optional height for the intersection points (C{meter},
217 conventionally) or C{None} for interpolated heights.
218 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll B{C{circle}},
219 B{C{point}} and B{C{other}} iff points (C{bool}).
221 @return: 2-Tuple of the intersection points (representing a chord), each
222 an instance of the B{C{point}} class. Both points are the same
223 instance if the (great circle) line is tangent to the circle.
225 @raise IntersectionError: The circle and line do not intersect.
227 @raise TypeError: Invalid B{C{point}}, B{C{circle}} or B{C{other}}.
229 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{radius}},
230 B{C{exact}}, B{C{height}} or B{C{napieradius}}.
231 '''
232 p = self.others(point=point)
233 try:
234 return _intersecant2(self, circle, p, other, radius=radius, exact=exact,
235 height=height, wrap=wrap)
236 except (TypeError, ValueError) as x:
237 raise _xError(x, center=self, circle=circle, point=point, other=other,
238 radius=radius, exact=exact, height=height, wrap=wrap)
240 def maxLat(self, bearing):
241 '''Return the maximum latitude reached when travelling on a great circle
242 on given bearing from this point based on Clairaut's formula.
244 The maximum latitude is independent of longitude and the same for all
245 points on a given latitude.
247 Negate the result for the minimum latitude (on the Southern hemisphere).
249 @arg bearing: Initial bearing (compass C{degrees360}).
251 @return: Maximum latitude (C{degrees90}).
253 @raise ValueError: Invalid B{C{bearing}}.
254 '''
255 r = acos1(fabs(sin(Bearing_(bearing)) * cos(self.phi)))
256 return degrees90(r)
258 def minLat(self, bearing):
259 '''Return the minimum latitude reached when travelling on a great circle
260 on given bearing from this point.
262 @arg bearing: Initial bearing (compass C{degrees360}).
264 @return: Minimum latitude (C{degrees90}).
266 @see: Method L{maxLat} for more details.
268 @raise ValueError: Invalid B{C{bearing}}.
269 '''
270 return -self.maxLat(bearing)
272 def _mpr(self, radius=R_M, exact=None): # meter per radian
273 if exact and not _isRadius(radius): # see .rhumb.ekx.Rhumb._mpr
274 radius = _earth_ellipsoid(radius)._Lpr
275 return radius
277 @property_doc_(''' the I{Napier} radius to apply spherical trigonometry.''')
278 def napieradius(self):
279 '''Get the I{Napier} radius (C{meter}, conventionally).
280 '''
281 return self._napieradius
283 @napieradius.setter # PYCHOK setter!
284 def napieradius(self, radius):
285 '''Set this I{Napier} radius (C{meter}, conventionally) or C{0}.
287 In methods L{intersecant2} and L{rhumbIntersecant2}, I{Napier}'s
288 spherical trigonometry is applied if the circle radius exceeds
289 the I{Napier} radius, otherwise planar trigonometry is used.
291 @raise UnitError: Invalid B{C{radius}}.
292 '''
293 self._napieradius = Radius(napieradius=radius or 0)
295# def nearestTo(self, point, other, **radius_exact_height_wrap): # PYCHOK signature
296# p = self.others(point=point)
297# try:
298# p, q = _intersecant2(self, p, p, other, **radius_exact_height_wrap)
299# except (TypeError, ValueError) as x:
300# raise _xError(x, this=self, point=point, other=other, **radius_exact_height_wrap)
301# return p.midpointTo(q)
303 def parse(self, strllh, height=0, sep=_COMMA_, **name):
304 '''Parse a string representing a similar, spherical C{LatLon}
305 point, consisting of C{"lat, lon[, height]"}.
307 @arg strllh: Lat, lon and optional height (C{str}), see function
308 L{pygeodesy.parse3llh}.
309 @kwarg height: Optional, default height (C{meter}).
310 @kwarg sep: Optional separator (C{str}).
311 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
313 @return: The similar point (spherical C{LatLon}).
315 @raise ParseError: Invalid B{C{strllh}}.
316 '''
317 llh = _MODS.dms.parse3llh(strllh, height=height, sep=sep)
318 return self.classof(*llh, **name)
320 @property_RO
321 def _radius(self):
322 '''(INTERNAL) Get this sphere's radius.
323 '''
324 return self.datum.ellipsoid.equatoradius
326 def _rhumbs3(self, other, wrap, r=False): # != .latlonBase._rhumbx3
327 '''(INTERNAL) Rhumb_ helper function.
329 @arg other: The other point (spherical C{LatLon}).
330 '''
331 p = self.others(other, up=2)
332 if wrap:
333 p = _unrollon(self, p, wrap=wrap)
334 a2, b2 = p.philam
335 a1, b1 = self.philam
336 # if |db| > 180 take shorter rhumb
337 # line across the anti-meridian
338 db = wrapPI(b2 - b1)
339 dp = _logPI_2_2(a2, a1)
340 da = a2 - a1
341 if r:
342 # on Mercator projection, longitude distances shrink
343 # by latitude; the 'stretch factor' q becomes ill-
344 # conditioned along E-W line (0/0); use an empirical
345 # tolerance to avoid it
346 q = (da / dp) if fabs(dp) > EPS else cos(a1)
347 da = hypot(da, q * db) # angular distance radians
348 return da, db, dp
350 def rhumbAzimuthTo(self, other, radius=R_M, exact=False, wrap=False, b360=False):
351 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between
352 this and an other (spherical) point.
354 @arg other: The other point (spherical C{LatLon}).
355 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
356 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
357 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),
358 default C{False} for backward compatibility.
359 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
360 B{C{other}} point (C{bool}).
361 @kwarg b360: If C{True}, return the azimuth in the bearing range.
363 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).
365 @raise TypeError: The B{C{other}} point is incompatible or
366 B{C{radius}} is invalid.
367 '''
368 if exact: # use series, always
369 z = LatLonBase.rhumbAzimuthTo(self, other, exact=False, # Krüger
370 radius=radius, wrap=wrap, b360=b360)
371 else:
372 _, db, dp = self._rhumbs3(other, wrap)
373 z = (atan2b if b360 else atan2d)(db, dp) # see .rhumbBase.RhumbBase.Inverse
374 return z
376 @deprecated_method
377 def rhumbBearingTo(self, other): # unwrapped
378 '''DEPRECATED, use method C{.rhumbAzimuthTo}.'''
379 return self.rhumbAzimuthTo(other, b360=True) # [0..360)
381 def rhumbDestination(self, distance, azimuth, radius=R_M, height=None,
382 exact=False, **name):
383 '''Return the destination point having travelled the given distance from
384 this point along a rhumb line (loxodrome) of the given azimuth.
386 @arg distance: Distance travelled (C{meter}, same units as B{C{radius}}),
387 may be negative if C{B{exact}=True}.
388 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).
389 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
390 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if
391 C{B{exact}=True}.
392 @kwarg height: Optional height, overriding the default height (C{meter}.
393 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),
394 default C{False} for backward compatibility.
395 @kwarg name: Optional C{B{name}=NN} (C{str}).
397 @return: The destination point (spherical C{LatLon}).
399 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}
400 or B{C{height}}.
401 '''
402 if exact: # use series, always
403 r = LatLonBase.rhumbDestination(self, distance, azimuth, exact=False, # Krüger
404 radius=radius, height=height, **name)
405 else: # radius=None from .rhumbMidpointTo
406 if radius in (None, self._radius):
407 d, r = self.datum, radius
408 else:
409 d = _spherical_datum(radius, raiser=_radius_) # spherical only
410 r = d.ellipsoid.equatoradius
411 r = _m2radians(distance, r, low=-EPS) # distance=0 from .rhumbMidpointTo
413 a1, b1 = self.philam
414 sb, cb = sincos2(Bearing_(azimuth)) # radians
416 da = r * cb
417 a2 = a1 + da
418 # normalize latitude if past pole
419 if fabs(a2) > PI_2:
420 a2 = _copysign(PI, a2) - a2
422 dp = _logPI_2_2(a2, a1)
423 # q becomes ill-conditioned on E-W course 0/0
424 q = cos(a1) if isnear0(dp) else (da / dp)
425 b2 = b1 if isnear0(q) else (b1 + r * sb / q)
427 h = self._heigHt(height)
428 r = self.classof(degrees90(a2), degrees180(b2), datum=d, height=h, **name)
429 return r
431 def rhumbDistanceTo(self, other, radius=R_M, exact=False, wrap=False):
432 '''Return the distance from this to an other point along
433 a rhumb line (loxodrome).
435 @arg other: The other point (spherical C{LatLon}).
436 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
437 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if
438 C{B{exact}=True}.
439 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),
440 default C{False} for backward compatibility.
441 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
442 B{C{other}} point (C{bool}).
444 @return: Distance (C{meter}, the same units as B{C{radius}} or
445 C{radians} if C{B{radius} is None}).
447 @raise TypeError: The B{C{other}} point is incompatible.
449 @raise ValueError: Invalid B{C{radius}}.
450 '''
451 if exact: # use series, always
452 r = LatLonBase.rhumbDistanceTo(self, other, exact=False, # Krüger
453 radius=radius, wrap=wrap)
454 if radius is None: # angular distance in radians
455 r = r / self._radius # /= chokes PyChecker
456 else:
457 # see <https://www.EdWilliams.org/avform.htm#Rhumb>
458 r, _, _ = self._rhumbs3(other, wrap, r=True)
459 if radius is not None:
460 r *= Radius(radius)
461 return r
463 def rhumbIntersecant2(self, circle, point, other, radius=R_M, exact=True, # PYCHOK signature
464 height=None, wrap=False):
465 '''Compute the intersections of a circle and a rhumb line given as two
466 points and as a point and azimuth.
468 @arg circle: Radius of the circle centered at this location (C{meter},
469 same units as B{C{radius}}) or a point on the circle
470 (same C{LatLon} class).
471 @arg point: The rhumb line's start point (same C{LatLon} class).
472 @arg other: An other point (this I{on} C{LatLon}) or the azimuth I{of}
473 (compass C{degrees}) the rhumb line.
474 @kwarg radius: Mean earth radius (C{meter}, conventionally).
475 @kwarg exact: If C{True}, use the I{exact} rhumb methods for azimuth,
476 destination and distance, if C{False} use the basic
477 rhumb methods (C{bool}) or if C{None} use the I{great
478 circle} methods.
479 @kwarg height: Optional height for the intersection points (C{meter},
480 conventionally) or C{None}.
481 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the points
482 B{C{circle}}, B{C{point}} and/or B{C{other}} (C{bool}).
484 @return: 2-Tuple of the intersection points (representing a chord),
485 each an instance of this class. For a tangent line, both
486 points are the same instance, wrapped or I{normalized}.
488 @raise IntersectionError: The circle and line do not intersect.
490 @raise TypeError: Invalid B{C{point}}, B{C{circle}} or B{C{other}}.
492 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{radius}},
493 B{C{exact}} or B{C{height}}.
494 '''
495 m = LatLonBase.rhumbIntersecant2 if exact else \
496 LatLonSphericalBase.intersecant2
497 return m(self, circle, point, other, radius=radius, exact=exact,
498 height=height, wrap=wrap)
500 def rhumbMidpointTo(self, other, height=None, radius=R_M, exact=False,
501 fraction=_0_5, **wrap_name):
502 '''Return the (loxodromic) midpoint on the rhumb line between this
503 and an other point.
505 @arg other: The other point (spherical LatLon).
506 @kwarg height: Optional height, overriding the mean height (C{meter}).
507 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
508 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
509 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),
510 default C{False} for backward compatibility.
511 @kwarg fraction: Midpoint location from this point (C{scalar}), may
512 be negative if C{B{exact}=True}.
513 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword
514 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
515 and unroll the B{C{other}} point (C{bool}).
517 @return: The (mid)point at the given B{C{fraction}} along the rhumb
518 line (spherical C{LatLon}).
520 @raise TypeError: The B{C{other}} point is incompatible.
522 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}
523 '''
524 if exact: # use series, always
525 r = LatLonBase.rhumbMidpointTo(self, other, exact=False, # Krüger
526 radius=radius, height=height,
527 fraction=fraction, **wrap_name)
528 elif fraction is not _0_5:
529 f = Scalar_(fraction=fraction) # low=_0_0
530 w, n = self._wrap_name2(**wrap_name)
531 r, db, dp = self._rhumbs3(other, w, r=True) # radians
532 z = atan2b(db, dp)
533 h = self._havg(other, f=f, h=height)
534 r = self.rhumbDestination(r * f, z, radius=None, height=h, name=n)
536 else: # for backward compatibility, unwrapped
537 _, n = self._wrap_name2(**wrap_name)
538 # see <https://MathForum.org/library/drmath/view/51822.html>
539 a1, b1 = self.philam
540 a2, b2 = self.others(other).philam
541 _, n = self._wrap_name2(**wrap_name)
543 if fabs(b2 - b1) > PI:
544 b1 += PI2 # crossing anti-meridian
546 a3 = favg(a1, a2)
547 b3 = favg(b1, b2)
549 f1 = tanPI_2_2(a1)
550 if isnon0(f1):
551 f2 = tanPI_2_2(a2)
552 f = f2 / f1
553 if isnon0(f):
554 f = log(f)
555 if isnon0(f):
556 f3 = tanPI_2_2(a3)
557 b3 = fdot(map1(log, f1, f2, f3),
558 -b2, b1, b2 - b1) / f
560 d = self.datum if radius in (None, self._radius) else \
561 _spherical_datum(radius, name=self.name, raiser=_radius_)
562 h = self._havg(other, h=height)
563 r = self.classof(degrees90(a3), degrees180(b3), datum=d, height=h, name=n)
564 return r
566 @property_RO
567 def sphericalLatLon(self):
568 '''Get this C{LatLon}'s spherical class.
569 '''
570 return type(self)
572 def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature
573 '''Convert this point to C{Nvector} components, I{including
574 height}.
576 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}} keyword
577 arguments, ignored if C{B{Nvector} is None}.
579 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)} if
580 B{C{Nvector} is None}.
582 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.
583 '''
584 return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds)
587def _intersecant2(c, r, p, b, radius=R_M, exact=False, height=None, wrap=False):
588 # (INTERNAL) Intersect a circle and line, see L{intersecant2}
589 # above, separated to allow callers to embellish any exceptions
591 if wrap:
592 p = _unrollon(c, p, wrap=wrap)
593 nonexact = exact is None
595 if not isinstanceof(r, c.__class__, p.__class__):
596 r = Radius_(circle=r)
597 elif nonexact:
598 r = c.distanceTo(r, radius=radius, wrap=wrap)
599 elif isbool(exact):
600 r = c.rhumbDistanceTo(r, radius=radius, exact=exact, wrap=wrap)
601 else:
602 raise _ValueError(exact=exact)
604 if not isinstanceof(b, c.__class__, p.__class__):
605 b = Bearing(b)
606 elif nonexact:
607 b = p.initialBearingTo(b, wrap=wrap)
608 else:
609 b = p.rhumbAzimuthTo(b, radius=radius, exact=exact, wrap=wrap,
610 b360=True)
612 d = p.distanceTo(c, radius=radius) if nonexact else \
613 p.rhumbDistanceTo(c, radius=radius, exact=exact)
614 if d > EPS0:
615 n = _xattr(c, napieradius=0)
616 a = p.initialBearingTo(c) if nonexact else \
617 p.rhumbAzimuthTo(c, radius=radius, exact=exact, b360=True)
618 s, c = sincos2d(b - a) # Napier's sin(A), cos(A)
619 if r > n:
620 # Napier's right spherical triangle rules (R2) and (R1)
621 # <https://WikiPedia.org/wiki/Spherical_trigonometry>
622 m = p._mpr(radius=radius, exact=exact) # meter per radian
623 if fabs(c) > EPS0:
624 d = d / m # /= chokes PyChecker
625 a = asin1(sin(d) * fabs(s)) # Napier's a
626 c = _copysign(cos(a), c)
627 d = acos1(cos(d) / c) * m
628 a *= m # meter
629 else: # point and chord center coincident
630 a, d = d, 0
631 c = cos(a / m)
632 h = (acos1(cos(r / m) / c) * m) if a < r else 0
633 else: # distance from the chord center to ...
634 a = fabs(d * s) # ... the cicle center ...
635 d *= c # ... and to the point
636 h = sqrt_a(r, a) if a < r else 0 # half chord length
637 if a > r:
638 raise IntersectionError(_too_(Fmt.distant(a)))
639 else:
640 d, h = 0, r # point and circle center coincident
642 _intersecant1, kwds = (p.destination, {}) if nonexact else \
643 (p.rhumbDestination, dict(exact=exact))
644 kwds.update(radius=radius, height=height)
645 t = (_intersecant1(d + h, b, **kwds),)
646 if h:
647 t += (_intersecant1(d - h, b, **kwds),)
648 else: # same instance twice
649 t *= 2
650 return t
653def _logPI_2_2(a2, a1):
654 '''(INTERNAL) C{log} of C{tanPI_2_2}'s quotient.
655 '''
656 return log(_over(tanPI_2_2(a2), tanPI_2_2(a1)))
659def _m2radians(distance, radius, low=EPS): # PYCHOK in .spherical*
660 '''(INTERNAL) Distance in C{meter} to angular distance in C{radians}.
662 @raise UnitError: Invalid B{C{distance}} or B{C{radius}}.
663 '''
664 r = float(distance)
665 if radius:
666 r = r / Radius_(radius=radius) # /= chokes PyChecker
667 if low is not None:
668 # small near0 values from .rhumbDestination not exact OK
669 r = _0_0 if low < 0 and r < 0 else Radians_(r, low=low)
670 # _0_0 if low < 0 and low < r < 0 else Radians_(r, low=low)
671 return r
674def _radians2m(rad, radius):
675 '''(INTERNAL) Angular distance in C{radians} to distance in C{meter}.
676 '''
677 if radius is not None: # not in (None, _0_0)
678 rad *= R_M if radius is R_M else Radius(radius)
679 return rad
682def _rads3(rad1, rad2, radius): # in .sphericalTrigonometry
683 '''(INTERNAL) Convert radii to radians.
684 '''
685 r1 = Radius_(rad1=rad1)
686 r2 = Radius_(rad2=rad2)
687 if radius is not None: # convert radii to radians
688 r1 = _m2radians(r1, radius)
689 r2 = _m2radians(r2, radius)
691 x = r1 < r2
692 if x:
693 r1, r2 = r2, r1
694 if r1 > PI:
695 raise IntersectionError(rad1=rad1, rad2=rad2,
696 txt=_exceed_PI_radians_)
697 return r1, r2, x
700__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)
702# **) MIT License
703#
704# Copyright (C) 2016-2025 -- mrJean1 at Gmail -- All Rights Reserved.
705#
706# Permission is hereby granted, free of charge, to any person obtaining a
707# copy of this software and associated documentation files (the "Software"),
708# to deal in the Software without restriction, including without limitation
709# the rights to use, copy, modify, merge, publish, distribute, sublicense,
710# and/or sell copies of the Software, and to permit persons to whom the
711# Software is furnished to do so, subject to the following conditions:
712#
713# The above copyright notice and this permission notice shall be included
714# in all copies or substantial portions of the Software.
715#
716# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
717# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
718# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
719# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
720# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
721# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
722# OTHER DEALINGS IN THE SOFTWARE.