Coverage for pygeodesy/sphericalBase.py: 96%
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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 2011-2016}
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, PI, PI2, PI_2, R_M, \
18 _umod_360, isnear0, isnon0, _over, \
19 _0_0, _0_5, _1_0, _180_0
20from pygeodesy.datums import Datums, _spherical_datum
21from pygeodesy.errors import IntersectionError, _ValueError, _xError
22from pygeodesy.fmath import favg, fdot, hypot
23from pygeodesy.interns import NN, _COMMA_, _concentric_, _datum_, \
24 _distant_, _exceed_PI_radians_, _name_, \
25 _near_, _radius_, _too_
26from pygeodesy.latlonBase import _intersecend2, LatLonBase, \
27 _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, _xattrs
31from pygeodesy.props import deprecated_method, property_doc_, \
32 property_RO, _update_all
33# from pygeodesy.streprs import Fmt, _xattrs # from .nvectorBase
34from pygeodesy.units import Bearing, Bearing_, Radians_, Radius, \
35 Radius_, Scalar_
36from pygeodesy.utily import acos1, atan2b, atan2d, degrees90, \
37 degrees180, sincos2, _unrollon, \
38 tanPI_2_2, wrap360, wrapPI
40from math import cos, fabs, log, sin, sqrt
42__all__ = _ALL_LAZY.sphericalBase
43__version__ = '23.10.08'
46def _angular(distance, radius, low=EPS): # PYCHOK in .spherical*
47 '''(INTERNAL) Return an angular distance in C{radians}.
49 @raise UnitError: Invalid B{C{distance}} or B{C{radius}}.
50 '''
51 r = float(distance)
52 if radius:
53 r = r / Radius_(radius=radius) # /= chokes PyChecker
54 if low is not None:
55 # small near0 values from .rhumbDestination not exact OK
56 r = _0_0 if low < 0 and low < r < 0 else Radians_(r, low=low)
57 return r
60def _logPI_2_2(a2, a1):
61 '''(INTERNAL) C{log} of C{tanPI_2_2}'s quotient.
62 '''
63 return log(_over(tanPI_2_2(a2), tanPI_2_2(a1)))
66def _rads3(rad1, rad2, radius): # in .sphericalTrigonometry
67 '''(INTERNAL) Convert radii to radians.
68 '''
69 r1 = Radius_(rad1=rad1)
70 r2 = Radius_(rad2=rad2)
71 if radius is not None: # convert radii to radians
72 r1 = _angular(r1, radius)
73 r2 = _angular(r2, radius)
75 x = r1 < r2
76 if x:
77 r1, r2 = r2, r1
78 if r1 > PI:
79 raise IntersectionError(rad1=rad1, rad2=rad2,
80 txt=_exceed_PI_radians_)
81 return r1, r2, x
84class CartesianSphericalBase(CartesianBase):
85 '''(INTERNAL) Base class for spherical C{Cartesian}s.
86 '''
87 _datum = Datums.Sphere # L{Datum}
89 def intersections2(self, rad1, other, rad2, radius=R_M):
90 '''Compute the intersection points of two circles each defined
91 by a center point and a radius.
93 @arg rad1: Radius of the this circle (C{meter} or C{radians},
94 see B{C{radius}}).
95 @arg other: Center of the other circle (C{Cartesian}).
96 @arg rad2: Radius of the other circle (C{meter} or C{radians},
97 see B{C{radius}}).
98 @kwarg radius: Mean earth radius (C{meter} or C{None} if both
99 B{C{rad1}} and B{C{rad2}} are given in C{radians}).
101 @return: 2-Tuple of the intersection points, each C{Cartesian}.
102 For abutting circles, the intersection points are the
103 same C{Cartesian} instance, aka the I{radical center}.
105 @raise IntersectionError: Concentric, antipodal, invalid or
106 non-intersecting circles.
108 @raise TypeError: If B{C{other}} is not C{Cartesian}.
110 @raise ValueError: Invalid B{C{rad1}}, B{C{rad2}} or B{C{radius}}.
112 @see: U{Calculating intersection of two Circles
113 <https://GIS.StackExchange.com/questions/48937/
114 calculating-intersection-of-two-circles>} and method
115 or function C{trilaterate3d2}.
116 '''
117 x1, x2 = self, self.others(other)
118 r1, r2, x = _rads3(rad1, rad2, radius)
119 if x:
120 x1, x2 = x2, x1
121 try:
122 n, q = x1.cross(x2), x1.dot(x2)
123 n2, q1 = n.length2, (_1_0 - q**2)
124 if n2 < EPS or isnear0(q1):
125 raise ValueError(_near_(_concentric_))
126 c1, c2 = cos(r1), cos(r2)
127 x0 = x1.times((c1 - q * c2) / q1).plus(
128 x2.times((c2 - q * c1) / q1))
129 n1 = _1_0 - x0.length2
130 if n1 < EPS:
131 raise ValueError(_too_(_distant_))
132 except ValueError as x:
133 raise IntersectionError(center=self, rad1=rad1,
134 other=other, rad2=rad2, cause=x)
135 n = n.times(sqrt(n1 / n2))
136 if n.length > EPS:
137 x1 = x0.plus(n)
138 x2 = x0.minus(n)
139 else: # abutting circles
140 x1 = x2 = x0
142 return (_xattrs(x1, self, _datum_, _name_),
143 _xattrs(x2, self, _datum_, _name_))
146class LatLonSphericalBase(LatLonBase):
147 '''(INTERNAL) Base class for spherical C{LatLon}s.
148 '''
149 _datum = Datums.Sphere # spherical L{Datum}
151 def __init__(self, latlonh, lon=None, height=0, datum=None, wrap=False, name=NN):
152 '''Create a spherical C{LatLon} point frome the given lat-, longitude and
153 height on the given datum.
155 @arg latlonh: Latitude (C{degrees} or DMS C{str} with N or S suffix) or
156 a previous C{LatLon} instance provided C{B{lon}=None}.
157 @kwarg lon: Longitude (C{degrees} or DMS C{str} with E or W suffix) or
158 C(None), indicating B{C{latlonh}} is a C{LatLon}.
159 @kwarg height: Optional height above (or below) the earth surface (C{meter},
160 same units as the datum's ellipsoid axes or radius).
161 @kwarg datum: Optional, spherical datum to use (L{Datum}, L{Ellipsoid},
162 L{Ellipsoid2}, L{a_f2Tuple}) or earth radius in C{meter},
163 conventionally).
164 @kwarg wrap: If C{True}, wrap or I{normalize} B{C{lat}} and B{C{lon}}
165 (C{bool}).
166 @kwarg name: Optional name (string).
168 @raise TypeError: If B{C{latlonh}} is not a C{LatLon} or B{C{datum}} not
169 spherical.
170 '''
171 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, name=name)
172 if datum not in (None, self.datum):
173 self.datum = datum
175 def bearingTo2(self, other, wrap=False, raiser=False):
176 '''Return the initial and final bearing (forward and reverse
177 azimuth) from this to an other point.
179 @arg other: The other point (C{LatLon}).
180 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
181 B{C{other}} point (C{bool}).
183 @return: A L{Bearing2Tuple}C{(initial, final)}.
185 @raise TypeError: The B{C{other}} point is not spherical.
187 @see: Methods C{initialBearingTo} and C{finalBearingTo}.
188 '''
189 # .initialBearingTo is inside .-Nvector and .-Trigonometry
190 i = self.initialBearingTo(other, wrap=wrap, raiser=raiser) # PYCHOK .initialBearingTo
191 f = self.finalBearingTo( other, wrap=wrap, raiser=raiser)
192 return Bearing2Tuple(i, f, name=self.name)
194 @property_doc_(''' this point's datum (L{Datum}).''')
195 def datum(self):
196 '''Get this point's datum (L{Datum}).
197 '''
198 return self._datum
200 @datum.setter # PYCHOK setter!
201 def datum(self, datum):
202 '''Set this point's datum I{without conversion} (L{Datum}, L{Ellipsoid},
203 L{Ellipsoid2}, L{a_f2Tuple}) or C{scalar} spherical earth radius).
205 @raise TypeError: If B{C{datum}} invalid or not not spherical.
206 '''
207 d = _spherical_datum(datum, name=self.name, raiser=_datum_)
208 if self._datum != d:
209 _update_all(self)
210 self._datum = d
212 def finalBearingTo(self, other, wrap=False, raiser=False):
213 '''Return the final bearing (reverse azimuth) from this to
214 an other point.
216 @arg other: The other point (spherical C{LatLon}).
217 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
218 the B{C{other}} point (C{bool}).
220 @return: Final bearing (compass C{degrees360}).
222 @raise TypeError: The B{C{other}} point is not spherical.
224 @example:
226 >>> p = LatLon(52.205, 0.119)
227 >>> q = LatLon(48.857, 2.351)
228 >>> b = p.finalBearingTo(q) # 157.9
229 '''
230 p = self.others(other)
231 if wrap:
232 p = _unrollon(self, p, wrap=wrap)
233 # final bearing is the reverse of the other, initial one;
234 # .initialBearingTo is inside .-Nvector and .-Trigonometry
235 b = p.initialBearingTo(self, wrap=False, raiser=raiser)
236 return _umod_360(b + _180_0)
238 def intersecant2(self, circle, point, bearing, radius=R_M, exact=False,
239 height=None, wrap=False): # was=True
240 '''Compute the intersections of a circle and a line given as a point
241 and bearing or as two points.
243 @arg circle: Radius of the circle centered at this location
244 (C{meter}, same units as B{C{radius}}) or a point
245 on the circle (this C{LatLon}).
246 @arg point: An other point in- or outside the circle on the line
247 (this C{LatLon}).
248 @arg bearing: Bearing at the B{C{point}} (compass C{degrees360})
249 or an other point on the line (this C{LatLon}).
250 @kwarg radius: Mean earth radius (C{meter}, conventionally).
251 @kwarg exact: If C{True} use the I{exact} rhumb methods for azimuth,
252 destination and distance, if C{False} use the basic
253 rhumb methods (C{bool}) or if C{None} use the I{great
254 circle} methods.
255 @kwarg height: Optional height for the intersection points (C{meter},
256 conventionally) or C{None}.
257 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
258 B{C{point}}, B{C{circle}} and/or B{C{bearing}} (C{bool}).
260 @return: 2-Tuple of the intersection points (representing a chord),
261 each an instance of this class. For a tangent line, both
262 points are the same instance, the B{C{point}} or wrapped
263 or I{normalized}.
265 @raise IntersectionError: The circle and line do not intersect.
267 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}
268 or B{C{bearing}} invalid.
270 @raise ValueError: Invalid B{C{circle}}, B{C{bearing}}, B{C{radius}},
271 B{C{exact}} or B{C{height}}.
272 '''
273 p = self.others(point=point)
274 try:
275 return _intersecant2(self, circle, p, bearing, radius=radius, exact=exact,
276 height=height, wrap=wrap)
277 except (TypeError, ValueError) as x:
278 raise _xError(x, center=self, circle=circle, point=point, bearing=bearing,
279 exact=exact, wrap=wrap)
281 def maxLat(self, bearing):
282 '''Return the maximum latitude reached when travelling
283 on a great circle on given bearing from this point
284 based on Clairaut's formula.
286 The maximum latitude is independent of longitude
287 and the same for all points on a given latitude.
289 Negate the result for the minimum latitude (on the
290 Southern hemisphere).
292 @arg bearing: Initial bearing (compass C{degrees360}).
294 @return: Maximum latitude (C{degrees90}).
296 @raise ValueError: Invalid B{C{bearing}}.
297 '''
298 m = acos1(fabs(sin(Bearing_(bearing)) * cos(self.phi)))
299 return degrees90(m)
301 def minLat(self, bearing):
302 '''Return the minimum latitude reached when travelling
303 on a great circle on given bearing from this point.
305 @arg bearing: Initial bearing (compass C{degrees360}).
307 @return: Minimum latitude (C{degrees90}).
309 @see: Method L{maxLat} for more details.
311 @raise ValueError: Invalid B{C{bearing}}.
312 '''
313 return -self.maxLat(bearing)
315 def parse(self, strllh, height=0, sep=_COMMA_, name=NN):
316 '''Parse a string representing a similar, spherical C{LatLon}
317 point, consisting of C{"lat, lon[, height]"}.
319 @arg strllh: Lat, lon and optional height (C{str}),
320 see function L{pygeodesy.parse3llh}.
321 @kwarg height: Optional, default height (C{meter}).
322 @kwarg sep: Optional separator (C{str}).
323 @kwarg name: Optional instance name (C{str}),
324 overriding this name.
326 @return: The similar point (spherical C{LatLon}).
328 @raise ParseError: Invalid B{C{strllh}}.
329 '''
330 t = _MODS.dms.parse3llh(strllh, height=height, sep=sep)
331 r = self.classof(*t)
332 if name:
333 r.rename(name)
334 return r
336 @property_RO
337 def _radius(self):
338 '''(INTERNAL) Get this sphere's radius.
339 '''
340 return self.datum.ellipsoid.equatoradius
342 def _rhumbs3(self, other, wrap, r=False): # != .latlonBase._rhumbx3
343 '''(INTERNAL) Rhumb_ helper function.
345 @arg other: The other point (spherical C{LatLon}).
346 '''
347 p = self.others(other, up=2)
348 if wrap:
349 p = _unrollon(self, p, wrap=wrap)
350 a2, b2 = p.philam
351 a1, b1 = self.philam
352 # if |db| > 180 take shorter rhumb
353 # line across the anti-meridian
354 db = wrapPI(b2 - b1)
355 dp = _logPI_2_2(a2, a1)
356 da = a2 - a1
357 if r:
358 # on Mercator projection, longitude distances shrink
359 # by latitude; the 'stretch factor' q becomes ill-
360 # conditioned along E-W line (0/0); use an empirical
361 # tolerance to avoid it
362 q = (da / dp) if fabs(dp) > EPS else cos(a1)
363 da = hypot(da, q * db) # angular distance radians
364 return da, db, dp
366 def rhumbAzimuthTo(self, other, radius=R_M, exact=False, wrap=False):
367 '''Return the azimuth (bearing) of a rhumb line (loxodrome)
368 between this and an other (spherical) point.
370 @arg other: The other point (spherical C{LatLon}).
371 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
372 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
373 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),
374 default C{False} for backward compatibility.
375 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
376 B{C{other}} point (C{bool}).
378 @return: Rhumb line azimuth (compass C{degrees180}).
380 @raise TypeError: The B{C{other}} point is incompatible or
381 B{C{radius}} is invalid.
383 @example:
385 >>> p = LatLon(51.127, 1.338)
386 >>> q = LatLon(50.964, 1.853)
387 >>> b = p.rhumbBearingTo(q) # 116.7
388 '''
389 if exact: # use series, always
390 z = LatLonBase.rhumbAzimuthTo(self, other, exact=False, # Krüger
391 radius=radius, wrap=wrap)
392 else:
393 _, db, dp = self._rhumbs3(other, wrap)
394 z = atan2d(db, dp) # see .rhumbx.Rhumb.Inverse
395 return z
397 @deprecated_method
398 def rhumbBearingTo(self, other): # unwrapped
399 '''DEPRECATED, use method C{.rhumbAzimuthTo}.'''
400 return wrap360(self.rhumbAzimuthTo(other)) # [0..360)
402 def rhumbDestination(self, distance, bearing, radius=R_M, height=None, exact=False):
403 '''Return the destination point having travelled the given distance
404 from this point along a rhumb line (loxodrome) at the given bearing.
406 @arg distance: Distance travelled (C{meter}, same units as B{C{radius}}),
407 may be negative if C{B{exact}=True}.
408 @arg bearing: Bearing (azimuth) at this point (compass C{degrees360}).
409 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
410 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if
411 C{B{exact}=True}.
412 @kwarg height: Optional height, overriding the default height
413 (C{meter}, same unit as B{C{radius}}).
414 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),
415 default C{False} for backward compatibility.
417 @return: The destination point (spherical C{LatLon}).
419 @raise ValueError: Invalid B{C{distance}}, B{C{bearing}},
420 B{C{radius}} or B{C{height}}.
422 @example:
424 >>> p = LatLon(51.127, 1.338)
425 >>> q = p.rhumbDestination(40300, 116.7) # 50.9642°N, 001.8530°E
426 '''
427 if exact: # use series, always
428 r = LatLonBase.rhumbDestination(self, distance, bearing, exact=False, # Krüger
429 radius=radius, height=height)
430 else: # radius=None from .rhumbMidpointTo
431 if radius in (None, self._radius):
432 d, r = self.datum, radius
433 else:
434 d = _spherical_datum(radius, raiser=_radius_) # spherical only
435 r = d.ellipsoid.equatoradius
436 r = _angular(distance, r, low=-EPS) # distance=0 from .rhumbMidpointTo
438 a1, b1 = self.philam
439 sb, cb = sincos2(Bearing_(bearing))
441 da = r * cb
442 a2 = a1 + da
443 # normalize latitude if past pole
444 if fabs(a2) > PI_2:
445 a2 = _copysign(PI, a2) - a2
447 dp = _logPI_2_2(a2, a1)
448 # q becomes ill-conditioned on E-W course 0/0
449 q = (da / dp) if fabs(dp) > EPS else cos(a1)
450 b2 = (b1 + r * sb / q) if fabs(q) > EPS else b1
452 h = self._heigHt(height)
453 r = self.classof(degrees90(a2), degrees180(b2), datum=d, height=h)
454 return r
456 def rhumbDistanceTo(self, other, radius=R_M, exact=False, wrap=False):
457 '''Return the distance from this to an other point along
458 a rhumb line (loxodrome).
460 @arg other: The other point (spherical C{LatLon}).
461 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
462 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if
463 C{B{exact}=True}.
464 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),
465 default C{False} for backward compatibility.
466 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
467 B{C{other}} point (C{bool}).
469 @return: Distance (C{meter}, the same units as B{C{radius}}
470 or C{radians} if B{C{radius}} is C{None}).
472 @raise TypeError: The B{C{other}} point is incompatible.
474 @raise ValueError: Invalid B{C{radius}}.
476 @example:
478 >>> p = LatLon(51.127, 1.338)
479 >>> q = LatLon(50.964, 1.853)
480 >>> d = p.rhumbDistanceTo(q) # 403100
481 '''
482 if exact: # use series, always
483 r = LatLonBase.rhumbDistanceTo(self, other, exact=False, # Krüger
484 radius=radius, wrap=wrap)
485 if radius is None: # angular distance in radians
486 r = r / self._radius # /= chokes PyChecker
487 else:
488 # see <https://www.EdWilliams.org/avform.htm#Rhumb>
489 r, _, _ = self._rhumbs3(other, wrap, r=True)
490 if radius is not None:
491 r *= Radius(radius)
492 return r
494 def rhumbMidpointTo(self, other, height=None, radius=R_M, exact=False,
495 fraction=_0_5, wrap=False):
496 '''Return the (loxodromic) midpoint on the rhumb line between
497 this and an other point.
499 @arg other: The other point (spherical LatLon).
500 @kwarg height: Optional height, overriding the mean height
501 (C{meter}).
502 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
503 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
504 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),
505 default C{False} for backward compatibility.
506 @kwarg fraction: Midpoint location from this point (C{scalar}),
507 may be negative if C{B{exact}=True}.
508 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
509 B{C{other}} point (C{bool}).
511 @return: The (mid)point at the given B{C{fraction}} along
512 the rhumb line (spherical C{LatLon}).
514 @raise TypeError: The B{C{other}} point is incompatible.
516 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}
518 @example:
520 >>> p = LatLon(51.127, 1.338)
521 >>> q = LatLon(50.964, 1.853)
522 >>> m = p.rhumb_midpointTo(q)
523 >>> m.toStr() # '51.0455°N, 001.5957°E'
524 '''
525 if exact: # use series, always
526 r = LatLonBase.rhumbMidpointTo(self, other, exact=False, # Krüger
527 radius=radius, height=height,
528 fraction=fraction, wrap=wrap)
529 elif fraction is not _0_5:
530 f = Scalar_(fraction=fraction) # low=_0_0
531 r, db, dp = self._rhumbs3(other, wrap, 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)
536 else: # for backward compatibility, unwrapped
537 # see <https://MathForum.org/library/drmath/view/51822.html>
538 a1, b1 = self.philam
539 a2, b2 = self.others(other).philam
541 if fabs(b2 - b1) > PI:
542 b1 += PI2 # crossing anti-meridian
544 a3 = favg(a1, a2)
545 b3 = favg(b1, b2)
547 f1 = tanPI_2_2(a1)
548 if isnon0(f1):
549 f2 = tanPI_2_2(a2)
550 f = f2 / f1
551 if isnon0(f):
552 f = log(f)
553 if isnon0(f):
554 f3 = tanPI_2_2(a3)
555 b3 = fdot(map1(log, f1, f2, f3),
556 -b2, b1, b2 - b1) / f
558 d = self.datum if radius in (None, self._radius) else \
559 _spherical_datum(radius, name=self.name, raiser=_radius_)
560 h = self._havg(other, h=height)
561 r = self.classof(degrees90(a3), degrees180(b3), datum=d, height=h)
562 return r
564 def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature
565 '''Convert this point to C{Nvector} components, I{including
566 height}.
568 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}}
569 keyword arguments, ignored if
570 C{B{Nvector} is None}.
572 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}
573 if B{C{Nvector}} is C{None}.
575 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.
576 '''
577 return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds)
580def _intersecant2(c, r, p, b, radius=R_M, exact=False,
581 height=None, wrap=False):
582 # (INTERNAL) Intersect a circle and bearing, see L{intersecant2}
583 # above, separated to allow callers to embellish any exceptions
585 if wrap:
586 p = _unrollon(c, p, wrap=wrap)
587 nonexact = exact is None
589 if not isinstanceof(r, c.__class__, p.__class__):
590 r = Radius_(circle=r)
591 elif nonexact:
592 r = c.distanceTo(r, radius=radius, wrap=wrap)
593 elif isbool(exact):
594 r = c.rhumbDistanceTo(r, radius=radius, exact=exact, wrap=wrap)
595 else:
596 raise _ValueError(exact=exact)
598 if not isinstanceof(b, c.__class__, p.__class__):
599 b = Bearing(b)
600 elif nonexact:
601 b = p.initialBearingTo(b, wrap=wrap)
602 else:
603 b = p.rhumbAzimuthTo(b, radius=radius, exact=exact, wrap=wrap)
605 d = p.distanceTo(c, radius=radius) if nonexact else \
606 p.rhumbDistanceTo(c, radius=radius, exact=exact)
607 a = 0 if d < EPS else (p.initialBearingTo(c) if nonexact else
608 wrap360(p.rhumbAzimuthTo(c, radius=radius, exact=exact)))
609 return _intersecend2(p, d, a, b, r, radius, height, exact)
612def _r2m(r, radius):
613 '''(INTERNAL) Angular distance in C{radians} to C{meter}.
614 '''
615 if radius is not None: # not in (None, _0_0)
616 r *= R_M if radius is R_M else Radius(radius)
617 return r
620__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)
622# **) MIT License
623#
624# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
625#
626# Permission is hereby granted, free of charge, to any person obtaining a
627# copy of this software and associated documentation files (the "Software"),
628# to deal in the Software without restriction, including without limitation
629# the rights to use, copy, modify, merge, publish, distribute, sublicense,
630# and/or sell copies of the Software, and to permit persons to whom the
631# Software is furnished to do so, subject to the following conditions:
632#
633# The above copyright notice and this permission notice shall be included
634# in all copies or substantial portions of the Software.
635#
636# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
637# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
638# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
639# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
640# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
641# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
642# OTHER DEALINGS IN THE SOFTWARE.