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, isscalar, 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 NN, _COMMA_, _concentric_, _datum_, \
25 _distant_, _exceed_PI_radians_, _name_, \
26 _near_, _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_, \
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_, _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__ = '23.10.24'
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=NN):
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 name (string).
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=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.
193 @example:
195 >>> p = LatLon(52.205, 0.119)
196 >>> q = LatLon(48.857, 2.351)
197 >>> b = p.finalBearingTo(q) # 157.9
198 '''
199 p = self.others(other)
200 if wrap:
201 p = _unrollon(self, p, wrap=wrap)
202 # final bearing is the reverse of the other, initial one
203 b = p.initialBearingTo(self, wrap=False, raiser=raiser) + _180_0
204 return b if b < 360 else (b - _360_0)
206 def intersecant2(self, circle, point, other, radius=R_M, exact=False, # PYCHOK signature
207 height=None, wrap=False):
208 '''Compute the intersections of a circle and a (great circle) line
209 given as two points or as a point and bearing.
211 @arg circle: Radius of the circle centered at this location (C{meter},
212 same units as B{C{radius}}) or a point on the circle
213 (this C{LatLon}).
214 @arg point: A point on the (great circle) line (this C{LatLon}).
215 @arg other: An other point I{on} (this {LatLon}) or the bearing at
216 B{C{point}} I{of} the (great circle) line (compass
217 C{degrees}).
218 @kwarg radius: Mean earth radius (C{meter}, conventionally).
219 @kwarg exact: If C{True} use the I{exact} rhumb methods for azimuth,
220 destination and distance, if C{False} use the basic
221 rhumb methods (C{bool}) or if C{None} use the I{great
222 circle} methods.
223 @kwarg height: Optional height for the intersection points (C{meter},
224 conventionally) or C{None} for interpolated heights.
225 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the points
226 B{C{circle}}, B{C{point}} and/or B{C{other}} (C{bool}).
228 @return: 2-Tuple of the intersection points (representing a chord), each
229 an instance of the B{C{point}} class. Both points are the same
230 instance if the (great circle) line is tangent to the circle.
232 @raise IntersectionError: The circle and line do not intersect.
234 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}
235 or B{C{other}} invalid.
237 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{radius}},
238 B{C{exact}}, B{C{height}} or B{C{napieradius}}.
239 '''
240 p = self.others(point=point)
241 try:
242 return _intersecant2(self, circle, p, other, radius=radius, exact=exact,
243 height=height, wrap=wrap)
244 except (TypeError, ValueError) as x:
245 raise _xError(x, center=self, circle=circle, point=point, other=other,
246 radius=radius, exact=exact, height=height, wrap=wrap)
248 def maxLat(self, bearing):
249 '''Return the maximum latitude reached when travelling
250 on a great circle on given bearing from this point
251 based on Clairaut's formula.
253 The maximum latitude is independent of longitude
254 and the same for all points on a given latitude.
256 Negate the result for the minimum latitude (on the
257 Southern hemisphere).
259 @arg bearing: Initial bearing (compass C{degrees360}).
261 @return: Maximum latitude (C{degrees90}).
263 @raise ValueError: Invalid B{C{bearing}}.
264 '''
265 m = acos1(fabs(sin(Bearing_(bearing)) * cos(self.phi)))
266 return degrees90(m)
268 def minLat(self, bearing):
269 '''Return the minimum latitude reached when travelling
270 on a great circle on given bearing from this point.
272 @arg bearing: Initial bearing (compass C{degrees360}).
274 @return: Minimum latitude (C{degrees90}).
276 @see: Method L{maxLat} for more details.
278 @raise ValueError: Invalid B{C{bearing}}.
279 '''
280 return -self.maxLat(bearing)
282 def _mpr(self, radius=R_M, exact=None): # meter per radian
283 if exact and not isscalar(radius): # see .rhumbx.Rhumb._mpr
284 radius = _earth_ellipsoid(radius)._Lpr
285 return radius
287 @property_doc_(''' the I{Napier} radius to apply spherical trigonometry.''')
288 def napieradius(self):
289 '''Get the I{Napier} radius (C{meter}, conventionally).
290 '''
291 return self._napieradius
293 @napieradius.setter # PYCHOK setter!
294 def napieradius(self, radius):
295 '''Set this I{Napier} radius (C{meter}, conventionally) or C{0}.
297 In methods L{intersecant2} and L{rhumbIntersecant2}, I{Napier}'s
298 spherical trigonometry is applied if the circle radius exceeds
299 the I{Napier} radius, otherwise planar trigonometry is used.
301 @raise UnitError: Invalid B{C{radius}}.
302 '''
303 self._napieradius = Radius(napieradius=radius or 0)
305# def nearestTo(self, point, other, **radius_exact_height_wrap): # PYCHOK signature
306# p = self.others(point=point)
307# try:
308# p, q = _intersecant2(self, p, p, other, **radius_exact_height_wrap)
309# except (TypeError, ValueError) as x:
310# raise _xError(x, this=self, point=point, other=other, **radius_exact_height_wrap)
311# return p.midpointTo(q)
313 def parse(self, strllh, height=0, sep=_COMMA_, name=NN):
314 '''Parse a string representing a similar, spherical C{LatLon}
315 point, consisting of C{"lat, lon[, height]"}.
317 @arg strllh: Lat, lon and optional height (C{str}),
318 see function L{pygeodesy.parse3llh}.
319 @kwarg height: Optional, default height (C{meter}).
320 @kwarg sep: Optional separator (C{str}).
321 @kwarg name: Optional instance name (C{str}),
322 overriding this name.
324 @return: The similar point (spherical C{LatLon}).
326 @raise ParseError: Invalid B{C{strllh}}.
327 '''
328 t = _MODS.dms.parse3llh(strllh, height=height, sep=sep)
329 r = self.classof(*t)
330 if name:
331 r.rename(name)
332 return r
334 @property_RO
335 def _radius(self):
336 '''(INTERNAL) Get this sphere's radius.
337 '''
338 return self.datum.ellipsoid.equatoradius
340 def _rhumbs3(self, other, wrap, r=False): # != .latlonBase._rhumbx3
341 '''(INTERNAL) Rhumb_ helper function.
343 @arg other: The other point (spherical C{LatLon}).
344 '''
345 p = self.others(other, up=2)
346 if wrap:
347 p = _unrollon(self, p, wrap=wrap)
348 a2, b2 = p.philam
349 a1, b1 = self.philam
350 # if |db| > 180 take shorter rhumb
351 # line across the anti-meridian
352 db = wrapPI(b2 - b1)
353 dp = _logPI_2_2(a2, a1)
354 da = a2 - a1
355 if r:
356 # on Mercator projection, longitude distances shrink
357 # by latitude; the 'stretch factor' q becomes ill-
358 # conditioned along E-W line (0/0); use an empirical
359 # tolerance to avoid it
360 q = (da / dp) if fabs(dp) > EPS else cos(a1)
361 da = hypot(da, q * db) # angular distance radians
362 return da, db, dp
364 def rhumbAzimuthTo(self, other, radius=R_M, exact=False, wrap=False, b360=False):
365 '''Return the azimuth (bearing) of a rhumb line (loxodrome) between
366 this and an other (spherical) point.
368 @arg other: The other point (spherical C{LatLon}).
369 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
370 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
371 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),
372 default C{False} for backward compatibility.
373 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
374 B{C{other}} point (C{bool}).
375 @kwarg b360: If C{True}, return the azimuth in the bearing range.
377 @return: Rhumb azimuth (compass C{degrees180} or C{degrees360}).
379 @raise TypeError: The B{C{other}} point is incompatible or
380 B{C{radius}} is invalid.
382 @example:
384 >>> p = LatLon(51.127, 1.338)
385 >>> q = LatLon(50.964, 1.853)
386 >>> b = p.rhumbBearingTo(q) # 116.7
387 '''
388 if exact: # use series, always
389 z = LatLonBase.rhumbAzimuthTo(self, other, exact=False, # Krüger
390 radius=radius, wrap=wrap, b360=b360)
391 else:
392 _, db, dp = self._rhumbs3(other, wrap)
393 z = (atan2b if b360 else atan2d)(db, dp) # see .rhumbBase.RhumbBase.Inverse
394 return z
396 @deprecated_method
397 def rhumbBearingTo(self, other): # unwrapped
398 '''DEPRECATED, use method C{.rhumbAzimuthTo}.'''
399 return self.rhumbAzimuthTo(other, b360=True) # [0..360)
401 def rhumbDestination(self, distance, azimuth, radius=R_M, height=None, exact=False):
402 '''Return the destination point having travelled the given distance from
403 this point along a rhumb line (loxodrome) of the given azimuth.
405 @arg distance: Distance travelled (C{meter}, same units as B{C{radius}}),
406 may be negative if C{B{exact}=True}.
407 @arg azimuth: Azimuth (bearing) of the rhumb line (compass C{degrees}).
408 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
409 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if
410 C{B{exact}=True}.
411 @kwarg height: Optional height, overriding the default height (C{meter}.
412 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}), default
413 C{False} for backward compatibility.
415 @return: The destination point (spherical C{LatLon}).
417 @raise ValueError: Invalid B{C{distance}}, B{C{azimuth}}, B{C{radius}}
418 or B{C{height}}.
420 @example:
422 >>> p = LatLon(51.127, 1.338)
423 >>> q = p.rhumbDestination(40300, 116.7) # 50.9642°N, 001.8530°E
424 '''
425 if exact: # use series, always
426 r = LatLonBase.rhumbDestination(self, distance, azimuth, exact=False, # Krüger
427 radius=radius, height=height)
428 else: # radius=None from .rhumbMidpointTo
429 if radius in (None, self._radius):
430 d, r = self.datum, radius
431 else:
432 d = _spherical_datum(radius, raiser=_radius_) # spherical only
433 r = d.ellipsoid.equatoradius
434 r = _m2radians(distance, r, low=-EPS) # distance=0 from .rhumbMidpointTo
436 a1, b1 = self.philam
437 sb, cb = sincos2(Bearing_(azimuth)) # radians
439 da = r * cb
440 a2 = a1 + da
441 # normalize latitude if past pole
442 if fabs(a2) > PI_2:
443 a2 = _copysign(PI, a2) - a2
445 dp = _logPI_2_2(a2, a1)
446 # q becomes ill-conditioned on E-W course 0/0
447 q = cos(a1) if isnear0(dp) else (da / dp)
448 b2 = b1 if isnear0(q) else (b1 + r * sb / q)
450 h = self._heigHt(height)
451 r = self.classof(degrees90(a2), degrees180(b2), datum=d, height=h)
452 return r
454 def rhumbDistanceTo(self, other, radius=R_M, exact=False, wrap=False):
455 '''Return the distance from this to an other point along
456 a rhumb line (loxodrome).
458 @arg other: The other point (spherical C{LatLon}).
459 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
460 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}) if
461 C{B{exact}=True}.
462 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),
463 default C{False} for backward compatibility.
464 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
465 B{C{other}} point (C{bool}).
467 @return: Distance (C{meter}, the same units as B{C{radius}}
468 or C{radians} if B{C{radius}} is C{None}).
470 @raise TypeError: The B{C{other}} point is incompatible.
472 @raise ValueError: Invalid B{C{radius}}.
474 @example:
476 >>> p = LatLon(51.127, 1.338)
477 >>> q = LatLon(50.964, 1.853)
478 >>> d = p.rhumbDistanceTo(q) # 403100
479 '''
480 if exact: # use series, always
481 r = LatLonBase.rhumbDistanceTo(self, other, exact=False, # Krüger
482 radius=radius, wrap=wrap)
483 if radius is None: # angular distance in radians
484 r = r / self._radius # /= chokes PyChecker
485 else:
486 # see <https://www.EdWilliams.org/avform.htm#Rhumb>
487 r, _, _ = self._rhumbs3(other, wrap, r=True)
488 if radius is not None:
489 r *= Radius(radius)
490 return r
492 def rhumbIntersecant2(self, circle, point, other, radius=R_M, exact=True, # PYCHOK signature
493 height=None, wrap=False):
494 '''Compute the intersections of a circle and a rhumb line given as two
495 points and as a point and azimuth.
497 @arg circle: Radius of the circle centered at this location (C{meter},
498 same units as B{C{radius}}) or a point on the circle
499 (this C{LatLon}).
500 @arg point: The rhumb line's start point (this C{LatLon}).
501 @arg other: An other point (this I{on} C{LatLon}) or the azimuth I{of}
502 (compass C{degrees}) the rhumb line.
503 @kwarg radius: Mean earth radius (C{meter}, conventionally).
504 @kwarg exact: If C{True} use the I{exact} rhumb methods for azimuth,
505 destination and distance, if C{False} use the basic
506 rhumb methods (C{bool}) or if C{None} use the I{great
507 circle} methods.
508 @kwarg height: Optional height for the intersection points (C{meter},
509 conventionally) or C{None}.
510 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the points
511 B{C{circle}}, B{C{point}} and/or B{C{other}} (C{bool}).
513 @return: 2-Tuple of the intersection points (representing a chord),
514 each an instance of this class. For a tangent line, both
515 points are the same instance, wrapped or I{normalized}.
517 @raise IntersectionError: The circle and line do not intersect.
519 @raise TypeError: If B{C{point}} is not this C{LatLon} or B{C{circle}}
520 or B{C{other}} invalid.
522 @raise UnitError: Invalid B{C{circle}}, B{C{other}}, B{C{radius}},
523 B{C{exact}} or B{C{height}}.
524 '''
525 m = LatLonBase.rhumbIntersecant2 if exact else \
526 LatLonSphericalBase.intersecant2
527 return m(self, circle, point, other, radius=radius, exact=exact,
528 height=height, wrap=wrap)
530 def rhumbMidpointTo(self, other, height=None, radius=R_M, exact=False,
531 fraction=_0_5, wrap=False):
532 '''Return the (loxodromic) midpoint on the rhumb line between
533 this and an other point.
535 @arg other: The other point (spherical LatLon).
536 @kwarg height: Optional height, overriding the mean height
537 (C{meter}).
538 @kwarg radius: Earth radius (C{meter}) or earth model (L{Datum},
539 L{Ellipsoid}, L{Ellipsoid2} or L{a_f2Tuple}).
540 @kwarg exact: If C{True}, use I{Krüger} L{rhumbx} (C{bool}),
541 default C{False} for backward compatibility.
542 @kwarg fraction: Midpoint location from this point (C{scalar}),
543 may be negative if C{B{exact}=True}.
544 @kwarg wrap: If C{True}, wrap or I{normalize} and unroll the
545 B{C{other}} point (C{bool}).
547 @return: The (mid)point at the given B{C{fraction}} along
548 the rhumb line (spherical C{LatLon}).
550 @raise TypeError: The B{C{other}} point is incompatible.
552 @raise ValueError: Invalid B{C{height}} or B{C{fraction}}
554 @example:
556 >>> p = LatLon(51.127, 1.338)
557 >>> q = LatLon(50.964, 1.853)
558 >>> m = p.rhumb_midpointTo(q)
559 >>> m.toStr() # '51.0455°N, 001.5957°E'
560 '''
561 if exact: # use series, always
562 r = LatLonBase.rhumbMidpointTo(self, other, exact=False, # Krüger
563 radius=radius, height=height,
564 fraction=fraction, wrap=wrap)
565 elif fraction is not _0_5:
566 f = Scalar_(fraction=fraction) # low=_0_0
567 r, db, dp = self._rhumbs3(other, wrap, r=True) # radians
568 z = atan2b(db, dp)
569 h = self._havg(other, f=f, h=height)
570 r = self.rhumbDestination(r * f, z, radius=None, height=h)
572 else: # for backward compatibility, unwrapped
573 # see <https://MathForum.org/library/drmath/view/51822.html>
574 a1, b1 = self.philam
575 a2, b2 = self.others(other).philam
577 if fabs(b2 - b1) > PI:
578 b1 += PI2 # crossing anti-meridian
580 a3 = favg(a1, a2)
581 b3 = favg(b1, b2)
583 f1 = tanPI_2_2(a1)
584 if isnon0(f1):
585 f2 = tanPI_2_2(a2)
586 f = f2 / f1
587 if isnon0(f):
588 f = log(f)
589 if isnon0(f):
590 f3 = tanPI_2_2(a3)
591 b3 = fdot(map1(log, f1, f2, f3),
592 -b2, b1, b2 - b1) / f
594 d = self.datum if radius in (None, self._radius) else \
595 _spherical_datum(radius, name=self.name, raiser=_radius_)
596 h = self._havg(other, h=height)
597 r = self.classof(degrees90(a3), degrees180(b3), datum=d, height=h)
598 return r
600 @property_RO
601 def sphericalLatLon(self):
602 '''Get this C{LatLon}'s spherical class.
603 '''
604 return type(self)
606 def toNvector(self, Nvector=NvectorBase, **Nvector_kwds): # PYCHOK signature
607 '''Convert this point to C{Nvector} components, I{including
608 height}.
610 @kwarg Nvector_kwds: Optional, additional B{C{Nvector}}
611 keyword arguments, ignored if
612 C{B{Nvector} is None}.
614 @return: An B{C{Nvector}} or a L{Vector4Tuple}C{(x, y, z, h)}
615 if B{C{Nvector}} is C{None}.
617 @raise TypeError: Invalid B{C{Nvector}} or B{C{Nvector_kwds}}.
618 '''
619 return LatLonBase.toNvector(self, Nvector=Nvector, **Nvector_kwds)
622def _intersecant2(c, r, p, b, radius=R_M, exact=False, height=None, wrap=False):
623 # (INTERNAL) Intersect a circle and line, see L{intersecant2}
624 # above, separated to allow callers to embellish any exceptions
626 if wrap:
627 p = _unrollon(c, p, wrap=wrap)
628 nonexact = exact is None
630 if not isinstanceof(r, c.__class__, p.__class__):
631 r = Radius_(circle=r)
632 elif nonexact:
633 r = c.distanceTo(r, radius=radius, wrap=wrap)
634 elif isbool(exact):
635 r = c.rhumbDistanceTo(r, radius=radius, exact=exact, wrap=wrap)
636 else:
637 raise _ValueError(exact=exact)
639 if not isinstanceof(b, c.__class__, p.__class__):
640 b = Bearing(b)
641 elif nonexact:
642 b = p.initialBearingTo(b, wrap=wrap)
643 else:
644 b = p.rhumbAzimuthTo(b, radius=radius, exact=exact, wrap=wrap,
645 b360=True)
647 d = p.distanceTo(c, radius=radius) if nonexact else \
648 p.rhumbDistanceTo(c, radius=radius, exact=exact)
649 if d > EPS0:
650 n = _xattr(c, napieradius=0)
651 a = p.initialBearingTo(c) if nonexact else \
652 p.rhumbAzimuthTo(c, radius=radius, exact=exact, b360=True)
653 s, c = sincos2d(b - a) # Napier's sin(A), cos(A)
654 if r > n:
655 # Napier's right spherical triangle rules (R2) and (R1)
656 # <https://WikiPedia.org/wiki/Spherical_trigonometry>
657 m = p._mpr(radius=radius, exact=exact) # meter per radian
658 if fabs(c) > EPS0:
659 d = d / m # /= chokes PyChecker
660 a = asin1(sin(d) * fabs(s)) # Napier's a
661 c = _copysign(cos(a), c)
662 d = acos1(cos(d) / c) * m
663 a *= m # meter
664 else: # point and chord center coincident
665 a, d = d, 0
666 c = cos(a / m)
667 h = (acos1(cos(r / m) / c) * m) if a < r else 0
668 else: # distance from the chord center to ...
669 a = fabs(d * s) # ... the cicle center ...
670 d *= c # ... and to the point
671 h = sqrt_a(r, a) if a < r else 0 # half chord length
672 if a > r:
673 raise IntersectionError(_too_(Fmt.distant(a)))
674 else:
675 d, h = 0, r # point and circle center coincident
677 _intersecant1, kwds = (p.destination, {}) if nonexact else \
678 (p.rhumbDestination, dict(exact=exact))
679 kwds.update(radius=radius, height=height)
680 t = (_intersecant1(d + h, b, **kwds),)
681 if h:
682 t += (_intersecant1(d - h, b, **kwds),)
683 else: # same instance twice
684 t *= 2
685 return t
688def _logPI_2_2(a2, a1):
689 '''(INTERNAL) C{log} of C{tanPI_2_2}'s quotient.
690 '''
691 return log(_over(tanPI_2_2(a2), tanPI_2_2(a1)))
694def _m2radians(distance, radius, low=EPS): # PYCHOK in .spherical*
695 '''(INTERNAL) Distance in C{meter} to angular distance in C{radians}.
697 @raise UnitError: Invalid B{C{distance}} or B{C{radius}}.
698 '''
699 r = float(distance)
700 if radius:
701 r = r / Radius_(radius=radius) # /= chokes PyChecker
702 if low is not None:
703 # small near0 values from .rhumbDestination not exact OK
704 r = _0_0 if low < 0 and r < 0 else Radians_(r, low=low)
705 # _0_0 if low < 0 and low < r < 0 else Radians_(r, low=low)
706 return r
709def _radians2m(rad, radius):
710 '''(INTERNAL) Angular distance in C{radians} to distance in C{meter}.
711 '''
712 if radius is not None: # not in (None, _0_0)
713 rad *= R_M if radius is R_M else Radius(radius)
714 return rad
717def _rads3(rad1, rad2, radius): # in .sphericalTrigonometry
718 '''(INTERNAL) Convert radii to radians.
719 '''
720 r1 = Radius_(rad1=rad1)
721 r2 = Radius_(rad2=rad2)
722 if radius is not None: # convert radii to radians
723 r1 = _m2radians(r1, radius)
724 r2 = _m2radians(r2, radius)
726 x = r1 < r2
727 if x:
728 r1, r2 = r2, r1
729 if r1 > PI:
730 raise IntersectionError(rad1=rad1, rad2=rad2,
731 txt=_exceed_PI_radians_)
732 return r1, r2, x
735__all__ += _ALL_DOCS(CartesianSphericalBase, LatLonSphericalBase)
737# **) MIT License
738#
739# Copyright (C) 2016-2023 -- mrJean1 at Gmail -- All Rights Reserved.
740#
741# Permission is hereby granted, free of charge, to any person obtaining a
742# copy of this software and associated documentation files (the "Software"),
743# to deal in the Software without restriction, including without limitation
744# the rights to use, copy, modify, merge, publish, distribute, sublicense,
745# and/or sell copies of the Software, and to permit persons to whom the
746# Software is furnished to do so, subject to the following conditions:
747#
748# The above copyright notice and this permission notice shall be included
749# in all copies or substantial portions of the Software.
750#
751# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
752# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
753# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
754# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
755# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
756# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
757# OTHER DEALINGS IN THE SOFTWARE.