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 2011-2016}
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, 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, _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, _xattrs
31from pygeodesy.props import deprecated_method, property_doc_, property_RO, \
32 _update_all
33# from pygeodesy.streprs import Fmt, _xattrs # 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__ = '24.06.06'
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 ellipsoid axes or radius).
130 @kwarg datum: Optional, spherical datum to use (L{Datum}, L{Ellipsoid},
131 L{Ellipsoid2}, L{a_f2Tuple}) or earth radius in C{meter},
132 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: If B{C{latlonh}} is not a C{LatLon} or B{C{datum}} not
138 spherical.
139 '''
140 LatLonBase.__init__(self, latlonh, lon=lon, height=height, wrap=wrap, **name)
141 if datum not in (None, self.datum):
142 self.datum = datum
144 def bearingTo2(self, other, wrap=False, raiser=False):
145 '''Return the initial and final bearing (forward and reverse
146 azimuth) from this to an other point.
148 @arg other: The other point (C{LatLon}).
149 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
150 B{C{other}} point (C{bool}).
152 @return: A L{Bearing2Tuple}C{(initial, final)}.
154 @raise TypeError: The B{C{other}} point is not spherical.
156 @see: Methods C{initialBearingTo} and C{finalBearingTo}.
157 '''
158 # .initialBearingTo is inside .-Nvector and .-Trigonometry
159 i = self.initialBearingTo(other, wrap=wrap, raiser=raiser) # PYCHOK .initialBearingTo
160 f = self.finalBearingTo( other, wrap=wrap, raiser=raiser)
161 return Bearing2Tuple(i, f, name=self.name)
163 @property_doc_(''' this point's datum (L{Datum}).''')
164 def datum(self):
165 '''Get this point's datum (L{Datum}).
166 '''
167 return self._datum
169 @datum.setter # PYCHOK setter!
170 def datum(self, datum):
171 '''Set this point's datum I{without conversion} (L{Datum}, L{Ellipsoid},
172 L{Ellipsoid2}, L{a_f2Tuple}) or C{scalar} spherical earth radius).
174 @raise TypeError: If B{C{datum}} invalid or not not spherical.
175 '''
176 d = _spherical_datum(datum, name=self.name, raiser=_datum_)
177 if self._datum != d:
178 _update_all(self)
179 self._datum = d
181 def finalBearingTo(self, other, wrap=False, raiser=False):
182 '''Return the final bearing (reverse azimuth) from this to
183 an other point.
185 @arg other: The other point (spherical C{LatLon}).
186 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll
187 the B{C{other}} point (C{bool}).
189 @return: Final bearing (compass C{degrees360}).
191 @raise TypeError: The B{C{other}} point is not spherical.
192 '''
193 p = self.others(other)
194 if wrap:
195 p = _unrollon(self, p, wrap=wrap)
196 # final bearing is the reverse of the other, initial one
197 b = p.initialBearingTo(self, wrap=False, raiser=raiser) + _180_0
198 return b if b < 360 else (b - _360_0)
200 def intersecant2(self, circle, point, other, radius=R_M, exact=False, # PYCHOK signature
201 height=None, wrap=False):
202 '''Compute the intersections of a circle and a (great circle) line
203 given as two points or as a point and bearing.
205 @arg circle: Radius of the circle centered at this location (C{meter},
206 same units as B{C{radius}}) or a point on the circle
207 (this C{LatLon}).
208 @arg point: A point on the (great circle) line (this C{LatLon}).
209 @arg other: An other point I{on} (this {LatLon}) or the bearing at
210 B{C{point}} I{of} the (great circle) line (compass
211 C{degrees}).
212 @kwarg radius: Mean earth radius (C{meter}, conventionally).
213 @kwarg exact: If C{True} use the I{exact} rhumb methods for azimuth,
214 destination and distance, if C{False} use the basic
215 rhumb methods (C{bool}) or if C{None} use the I{great
216 circle} methods.
217 @kwarg height: Optional height for the intersection points (C{meter},
218 conventionally) or C{None} for interpolated heights.
219 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the points
220 B{C{circle}}, B{C{point}} and/or B{C{other}} (C{bool}).
222 @return: 2-Tuple of the intersection points (representing a chord), each
223 an instance of the B{C{point}} class. Both points are the same
224 instance if the (great circle) line is tangent to the circle.
226 @raise IntersectionError: The circle and line do not intersect.
228 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}
229 or B{C{other}} invalid.
231 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{radius}},
232 B{C{exact}}, B{C{height}} or B{C{napieradius}}.
233 '''
234 p = self.others(point=point)
235 try:
236 return _intersecant2(self, circle, p, other, radius=radius, exact=exact,
237 height=height, wrap=wrap)
238 except (TypeError, ValueError) as x:
239 raise _xError(x, center=self, circle=circle, point=point, other=other,
240 radius=radius, exact=exact, height=height, wrap=wrap)
242 def maxLat(self, bearing):
243 '''Return the maximum latitude reached when travelling on a great circle
244 on given bearing from this point based on Clairaut's formula.
246 The maximum latitude is independent of longitude and the same for all
247 points on a given latitude.
249 Negate the result for the minimum latitude (on the Southern hemisphere).
251 @arg bearing: Initial bearing (compass C{degrees360}).
253 @return: Maximum latitude (C{degrees90}).
255 @raise ValueError: Invalid B{C{bearing}}.
256 '''
257 r = acos1(fabs(sin(Bearing_(bearing)) * cos(self.phi)))
258 return degrees90(r)
260 def minLat(self, bearing):
261 '''Return the minimum latitude reached when travelling on a great circle
262 on given bearing from this point.
264 @arg bearing: Initial bearing (compass C{degrees360}).
266 @return: Minimum latitude (C{degrees90}).
268 @see: Method L{maxLat} for more details.
270 @raise ValueError: Invalid B{C{bearing}}.
271 '''
272 return -self.maxLat(bearing)
274 def _mpr(self, radius=R_M, exact=None): # meter per radian
275 if exact and not _isRadius(radius): # see .rhumb.ekx.Rhumb._mpr
276 radius = _earth_ellipsoid(radius)._Lpr
277 return radius
279 @property_doc_(''' the I{Napier} radius to apply spherical trigonometry.''')
280 def napieradius(self):
281 '''Get the I{Napier} radius (C{meter}, conventionally).
282 '''
283 return self._napieradius
285 @napieradius.setter # PYCHOK setter!
286 def napieradius(self, radius):
287 '''Set this I{Napier} radius (C{meter}, conventionally) or C{0}.
289 In methods L{intersecant2} and L{rhumbIntersecant2}, I{Napier}'s
290 spherical trigonometry is applied if the circle radius exceeds
291 the I{Napier} radius, otherwise planar trigonometry is used.
293 @raise UnitError: Invalid B{C{radius}}.
294 '''
295 self._napieradius = Radius(napieradius=radius or 0)
297# def nearestTo(self, point, other, **radius_exact_height_wrap): # PYCHOK signature
298# p = self.others(point=point)
299# try:
300# p, q = _intersecant2(self, p, p, other, **radius_exact_height_wrap)
301# except (TypeError, ValueError) as x:
302# raise _xError(x, this=self, point=point, other=other, **radius_exact_height_wrap)
303# return p.midpointTo(q)
305 def parse(self, strllh, height=0, sep=_COMMA_, **name):
306 '''Parse a string representing a similar, spherical C{LatLon}
307 point, consisting of C{"lat, lon[, height]"}.
309 @arg strllh: Lat, lon and optional height (C{str}), see function
310 L{pygeodesy.parse3llh}.
311 @kwarg height: Optional, default height (C{meter}).
312 @kwarg sep: Optional separator (C{str}).
313 @kwarg name: Optional C{B{name}=NN} (C{str}), overriding this name.
315 @return: The similar point (spherical C{LatLon}).
317 @raise ParseError: Invalid B{C{strllh}}.
318 '''
319 llh = _MODS.dms.parse3llh(strllh, height=height, sep=sep)
320 return self.classof(*llh, **name)
322 @property_RO
323 def _radius(self):
324 '''(INTERNAL) Get this sphere's radius.
325 '''
326 return self.datum.ellipsoid.equatoradius
328 def _rhumbs3(self, other, wrap, r=False): # != .latlonBase._rhumbx3
329 '''(INTERNAL) Rhumb_ helper function.
331 @arg other: The other point (spherical C{LatLon}).
332 '''
333 p = self.others(other, up=2)
334 if wrap:
335 p = _unrollon(self, p, wrap=wrap)
336 a2, b2 = p.philam
337 a1, b1 = self.philam
338 # if |db| > 180 take shorter rhumb
339 # line across the anti-meridian
340 db = wrapPI(b2 - b1)
341 dp = _logPI_2_2(a2, a1)
342 da = a2 - a1
343 if r:
344 # on Mercator projection, longitude distances shrink
345 # by latitude; the 'stretch factor' q becomes ill-
346 # conditioned along E-W line (0/0); use an empirical
347 # tolerance to avoid it
348 q = (da / dp) if fabs(dp) > EPS else cos(a1)
349 da = hypot(da, q * db) # angular distance radians
350 return da, db, dp
352 def rhumbAzimuthTo(self, other, radius=R_M, exact=False, wrap=False, b360=False):
353 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between
354 this and an other (spherical) point.
356 @arg other: The other point (spherical C{LatLon}).
357 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
358 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
359 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),
360 default C{False} for backward compatibility.
361 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
362 B{C{other}} point (C{bool}).
363 @kwarg b360: If C{True}, return the azimuth in the bearing range.
365 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).
367 @raise TypeError: The B{C{other}} point is incompatible or
368 B{C{radius}} is invalid.
369 '''
370 if exact: # use series, always
371 z = LatLonBase.rhumbAzimuthTo(self, other, exact=False, # Krüger
372 radius=radius, wrap=wrap, b360=b360)
373 else:
374 _, db, dp = self._rhumbs3(other, wrap)
375 z = (atan2b if b360 else atan2d)(db, dp) # see .rhumbBase.RhumbBase.Inverse
376 return z
378 @deprecated_method
379 def rhumbBearingTo(self, other): # unwrapped
380 '''DEPRECATED, use method C{.rhumbAzimuthTo}.'''
381 return self.rhumbAzimuthTo(other, b360=True) # [0..360)
383 def rhumbDestination(self, distance, azimuth, radius=R_M, height=None,
384 exact=False, **name):
385 '''Return the destination point having travelled the given distance from
386 this point along a rhumb line (loxodrome) of the given azimuth.
388 @arg distance: Distance travelled (C{meter}, same units as B{C{radius}}),
389 may be negative if C{B{exact}=True}.
390 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).
391 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
392 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if
393 C{B{exact}=True}.
394 @kwarg height: Optional height, overriding the default height (C{meter}.
395 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),
396 default C{False} for backward compatibility.
397 @kwarg name: Optional C{B{name}=NN} (C{str}).
399 @return: The destination point (spherical C{LatLon}).
401 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}
402 or B{C{height}}.
403 '''
404 if exact: # use series, always
405 r = LatLonBase.rhumbDestination(self, distance, azimuth, exact=False, # Krüger
406 radius=radius, height=height, **name)
407 else: # radius=None from .rhumbMidpointTo
408 if radius in (None, self._radius):
409 d, r = self.datum, radius
410 else:
411 d = _spherical_datum(radius, raiser=_radius_) # spherical only
412 r = d.ellipsoid.equatoradius
413 r = _m2radians(distance, r, low=-EPS) # distance=0 from .rhumbMidpointTo
415 a1, b1 = self.philam
416 sb, cb = sincos2(Bearing_(azimuth)) # radians
418 da = r * cb
419 a2 = a1 + da
420 # normalize latitude if past pole
421 if fabs(a2) > PI_2:
422 a2 = _copysign(PI, a2) - a2
424 dp = _logPI_2_2(a2, a1)
425 # q becomes ill-conditioned on E-W course 0/0
426 q = cos(a1) if isnear0(dp) else (da / dp)
427 b2 = b1 if isnear0(q) else (b1 + r * sb / q)
429 h = self._heigHt(height)
430 r = self.classof(degrees90(a2), degrees180(b2), datum=d, height=h, **name)
431 return r
433 def rhumbDistanceTo(self, other, radius=R_M, exact=False, wrap=False):
434 '''Return the distance from this to an other point along
435 a rhumb line (loxodrome).
437 @arg other: The other point (spherical C{LatLon}).
438 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
439 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if
440 C{B{exact}=True}.
441 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),
442 default C{False} for backward compatibility.
443 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
444 B{C{other}} point (C{bool}).
446 @return: Distance (C{meter}, the same units as B{C{radius}}
447 or C{radians} if B{C{radius}} is C{None}).
449 @raise TypeError: The B{C{other}} point is incompatible.
451 @raise ValueError: Invalid B{C{radius}}.
452 '''
453 if exact: # use series, always
454 r = LatLonBase.rhumbDistanceTo(self, other, exact=False, # Krüger
455 radius=radius, wrap=wrap)
456 if radius is None: # angular distance in radians
457 r = r / self._radius # /= chokes PyChecker
458 else:
459 # see <https://www.EdWilliams.org/avform.htm#Rhumb>
460 r, _, _ = self._rhumbs3(other, wrap, r=True)
461 if radius is not None:
462 r *= Radius(radius)
463 return r
465 def rhumbIntersecant2(self, circle, point, other, radius=R_M, exact=True, # PYCHOK signature
466 height=None, wrap=False):
467 '''Compute the intersections of a circle and a rhumb line given as two
468 points and as a point and azimuth.
470 @arg circle: Radius of the circle centered at this location (C{meter},
471 same units as B{C{radius}}) or a point on the circle
472 (this C{LatLon}).
473 @arg point: The rhumb line's start point (this C{LatLon}).
474 @arg other: An other point (this I{on} C{LatLon}) or the azimuth I{of}
475 (compass C{degrees}) the rhumb line.
476 @kwarg radius: Mean earth radius (C{meter}, conventionally).
477 @kwarg exact: If C{True} use the I{exact} rhumb methods for azimuth,
478 destination and distance, if C{False} use the basic
479 rhumb methods (C{bool}) or if C{None} use the I{great
480 circle} methods.
481 @kwarg height: Optional height for the intersection points (C{meter},
482 conventionally) or C{None}.
483 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the points
484 B{C{circle}}, B{C{point}} and/or B{C{other}} (C{bool}).
486 @return: 2-Tuple of the intersection points (representing a chord),
487 each an instance of this class. For a tangent line, both
488 points are the same instance, wrapped or I{normalized}.
490 @raise IntersectionError: The circle and line do not intersect.
492 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}
493 or B{C{other}} invalid.
495 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{radius}},
496 B{C{exact}} or B{C{height}}.
497 '''
498 m = LatLonBase.rhumbIntersecant2 if exact else \
499 LatLonSphericalBase.intersecant2
500 return m(self, circle, point, other, radius=radius, exact=exact,
501 height=height, wrap=wrap)
503 def rhumbMidpointTo(self, other, height=None, radius=R_M, exact=False,
504 fraction=_0_5, **wrap_name):
505 '''Return the (loxodromic) midpoint on the rhumb line between
506 this and an other point.
508 @arg other: The other point (spherical LatLon).
509 @kwarg height: Optional height, overriding the mean height (C{meter}).
510 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
511 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
512 @kwarg exact: If C{True}, use I{Elliptic, Krüger} L{Rhumb} (C{bool}),
513 default C{False} for backward compatibility.
514 @kwarg fraction: Midpoint location from this point (C{scalar}), may
515 be negative if C{B{exact}=True}.
516 @kwarg wrap_name: Optional C{B{name}=NN} (C{str}) and optional keyword
517 argument C{B{wrap}=False}, if C{True}, wrap or I{normalize}
518 and unroll the B{C{other}} point (C{bool}).
520 @return: The (mid)point at the given B{C{fraction}} along the rhumb
521 line (spherical C{LatLon}).
523 @raise TypeError: The B{C{other}} point is incompatible.
525 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}
526 '''
527 if exact: # use series, always
528 r = LatLonBase.rhumbMidpointTo(self, other, exact=False, # Krüger
529 radius=radius, height=height,
530 fraction=fraction, **wrap_name)
531 elif fraction is not _0_5:
532 f = Scalar_(fraction=fraction) # low=_0_0
533 w, n = self._wrap_name2(**wrap_name)
534 r, db, dp = self._rhumbs3(other, w, r=True) # radians
535 z = atan2b(db, dp)
536 h = self._havg(other, f=f, h=height)
537 r = self.rhumbDestination(r * f, z, radius=None, height=h, name=n)
539 else: # for backward compatibility, unwrapped
540 _, n = self._wrap_name2(**wrap_name)
541 # see <https://MathForum.org/library/drmath/view/51822.html>
542 a1, b1 = self.philam
543 a2, b2 = self.others(other).philam
544 _, n = self._wrap_name2(**wrap_name)
546 if fabs(b2 - b1) > PI:
547 b1 += PI2 # crossing anti-meridian
549 a3 = favg(a1, a2)
550 b3 = favg(b1, b2)
552 f1 = tanPI_2_2(a1)
553 if isnon0(f1):
554 f2 = tanPI_2_2(a2)
555 f = f2 / f1
556 if isnon0(f):
557 f = log(f)
558 if isnon0(f):
559 f3 = tanPI_2_2(a3)
560 b3 = fdot(map1(log, f1, f2, f3),
561 -b2, b1, b2 - b1) / f
563 d = self.datum if radius in (None, self._radius) else \
564 _spherical_datum(radius, name=self.name, raiser=_radius_)
565 h = self._havg(other, h=height)
566 r = self.classof(degrees90(a3), degrees180(b3), datum=d, height=h, name=n)
567 return r
569 @property_RO
570 def sphericalLatLon(self):
571 '''Get this C{LatLon}'s spherical class.
572 '''
573 return type(self)
575 def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature
576 '''Convert this point to C{Nvector} components, I{including
577 height}.
579 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}}
580 keyword arguments, ignored if
581 C{B{Nvector} is None}.
583 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}
584 if B{C{Nvector}} is C{None}.
586 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.
587 '''
588 return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds)
591def _intersecant2(c, r, p, b, radius=R_M, exact=False, height=None, wrap=False):
592 # (INTERNAL) Intersect a circle and line, see L{intersecant2}
593 # above, separated to allow callers to embellish any exceptions
595 if wrap:
596 p = _unrollon(c, p, wrap=wrap)
597 nonexact = exact is None
599 if not isinstanceof(r, c.__class__, p.__class__):
600 r = Radius_(circle=r)
601 elif nonexact:
602 r = c.distanceTo(r, radius=radius, wrap=wrap)
603 elif isbool(exact):
604 r = c.rhumbDistanceTo(r, radius=radius, exact=exact, wrap=wrap)
605 else:
606 raise _ValueError(exact=exact)
608 if not isinstanceof(b, c.__class__, p.__class__):
609 b = Bearing(b)
610 elif nonexact:
611 b = p.initialBearingTo(b, wrap=wrap)
612 else:
613 b = p.rhumbAzimuthTo(b, radius=radius, exact=exact, wrap=wrap,
614 b360=True)
616 d = p.distanceTo(c, radius=radius) if nonexact else \
617 p.rhumbDistanceTo(c, radius=radius, exact=exact)
618 if d > EPS0:
619 n = _xattr(c, napieradius=0)
620 a = p.initialBearingTo(c) if nonexact else \
621 p.rhumbAzimuthTo(c, radius=radius, exact=exact, b360=True)
622 s, c = sincos2d(b - a) # Napier's sin(A), cos(A)
623 if r > n:
624 # Napier's right spherical triangle rules (R2) and (R1)
625 # <https://WikiPedia.org/wiki/Spherical_trigonometry>
626 m = p._mpr(radius=radius, exact=exact) # meter per radian
627 if fabs(c) > EPS0:
628 d = d / m # /= chokes PyChecker
629 a = asin1(sin(d) * fabs(s)) # Napier's a
630 c = _copysign(cos(a), c)
631 d = acos1(cos(d) / c) * m
632 a *= m # meter
633 else: # point and chord center coincident
634 a, d = d, 0
635 c = cos(a / m)
636 h = (acos1(cos(r / m) / c) * m) if a < r else 0
637 else: # distance from the chord center to ...
638 a = fabs(d * s) # ... the cicle center ...
639 d *= c # ... and to the point
640 h = sqrt_a(r, a) if a < r else 0 # half chord length
641 if a > r:
642 raise IntersectionError(_too_(Fmt.distant(a)))
643 else:
644 d, h = 0, r # point and circle center coincident
646 _intersecant1, kwds = (p.destination, {}) if nonexact else \
647 (p.rhumbDestination, dict(exact=exact))
648 kwds.update(radius=radius, height=height)
649 t = (_intersecant1(d + h, b, **kwds),)
650 if h:
651 t += (_intersecant1(d - h, b, **kwds),)
652 else: # same instance twice
653 t *= 2
654 return t
657def _logPI_2_2(a2, a1):
658 '''(INTERNAL) C{log} of C{tanPI_2_2}'s quotient.
659 '''
660 return log(_over(tanPI_2_2(a2), tanPI_2_2(a1)))
663def _m2radians(distance, radius, low=EPS): # PYCHOK in .spherical*
664 '''(INTERNAL) Distance in C{meter} to angular distance in C{radians}.
666 @raise UnitError: Invalid B{C{distance}} or B{C{radius}}.
667 '''
668 r = float(distance)
669 if radius:
670 r = r / Radius_(radius=radius) # /= chokes PyChecker
671 if low is not None:
672 # small near0 values from .rhumbDestination not exact OK
673 r = _0_0 if low < 0 and r < 0 else Radians_(r, low=low)
674 # _0_0 if low < 0 and low < r < 0 else Radians_(r, low=low)
675 return r
678def _radians2m(rad, radius):
679 '''(INTERNAL) Angular distance in C{radians} to distance in C{meter}.
680 '''
681 if radius is not None: # not in (None, _0_0)
682 rad *= R_M if radius is R_M else Radius(radius)
683 return rad
686def _rads3(rad1, rad2, radius): # in .sphericalTrigonometry
687 '''(INTERNAL) Convert radii to radians.
688 '''
689 r1 = Radius_(rad1=rad1)
690 r2 = Radius_(rad2=rad2)
691 if radius is not None: # convert radii to radians
692 r1 = _m2radians(r1, radius)
693 r2 = _m2radians(r2, radius)
695 x = r1 < r2
696 if x:
697 r1, r2 = r2, r1
698 if r1 > PI:
699 raise IntersectionError(rad1=rad1, rad2=rad2,
700 txt=_exceed_PI_radians_)
701 return r1, r2, x
704__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)
706# **) MIT License
707#
708# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
709#
710# Permission is hereby granted, free of charge, to any person obtaining a
711# copy of this software and associated documentation files (the "Software"),
712# to deal in the Software without restriction, including without limitation
713# the rights to use, copy, modify, merge, publish, distribute, sublicense,
714# and/or sell copies of the Software, and to permit persons to whom the
715# Software is furnished to do so, subject to the following conditions:
716#
717# The above copyright notice and this permission notice shall be included
718# in all copies or substantial portions of the Software.
719#
720# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
721# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
722# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
723# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
724# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
725# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
726# OTHER DEALINGS IN THE SOFTWARE.