Coverage for pygeodesy/ltp.py: 95%
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« prev ^ index » next coverage.py v7.2.2, created at 2024-06-10 14:08 -0400
2# -*- coding: utf-8 -*-
4u'''I{Local Tangent Plane} (LTP) and I{local} cartesian coordinates.
6I{Local cartesian} and I{local tangent plane} classes L{LocalCartesian}, approximations L{ChLVa}
7and L{ChLVe} and L{Ltp}, L{ChLV}, L{LocalError}, L{Attitude} and L{Frustum}.
9@see: U{Local tangent plane coordinates<https://WikiPedia.org/wiki/Local_tangent_plane_coordinates>}
10 and class L{LocalCartesian}, transcoded from I{Charles Karney}'s C++ classU{LocalCartesian
11 <https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1LocalCartesian.html>}.
12'''
13# make sure int/int division yields float quotient, see .basics
14from __future__ import division as _; del _ # PYCHOK semicolon
16from pygeodesy.basics import _args_kwds_names, map1, map2, _xinstanceof, \
17 _xsubclassof # .datums
18from pygeodesy.constants import EPS, INT0, _umod_360, _0_0, _0_01, _0_5, _1_0, \
19 _2_0, _60_0, _90_0, _100_0, _180_0, _3600_0, \
20 _N_1_0 # PYCHOK used!
21# from pygeodesy.datums import _WGS84 # from .ecef
22from pygeodesy.ecef import _EcefBase, EcefKarney, Ecef9Tuple, _llhn4, \
23 _xyzn4, _WGS84
24from pygeodesy.errors import _NotImplementedError, _ValueError, _xattr, \
25 _xkwds, _xkwds_get, _xkwds_pop2
26from pygeodesy.fmath import fabs, fdot, Fhorner
27from pygeodesy.fsums import _floor, _Fsumf_, fsumf_, fsum1f_
28from pygeodesy.interns import _0_, _COMMASPACE_, _DOT_, _ecef_, _height_, _M_, \
29 _invalid_, _lat0_, _lon0_, _name_, _too_
30# from pygeodesy.lazily import _ALL_LAZY # from vector3d
31from pygeodesy.ltpTuples import Attitude4Tuple, ChLVEN2Tuple, ChLV9Tuple, \
32 ChLVYX2Tuple, Footprint5Tuple, Local9Tuple, \
33 ChLVyx2Tuple, _XyzLocals4, _XyzLocals5, Xyz4Tuple
34from pygeodesy.named import _name__, _name2__, _NamedBase, notOverloaded
35from pygeodesy.namedTuples import LatLon3Tuple, LatLon4Tuple, Vector3Tuple
36from pygeodesy.props import Property, Property_RO, property_doc_, property_RO, \
37 _update_all
38from pygeodesy.streprs import Fmt, strs, unstr
39from pygeodesy.units import Bearing, Degrees, _isHeight, Meter
40from pygeodesy.utily import cotd, _loneg, sincos2d, sincos2d_, tand, tand_, \
41 wrap180, wrap360
42from pygeodesy.vector3d import _ALL_LAZY, Vector3d
44# from math import fabs, floor as _floor # from .fmath, .fsums
46__all__ = _ALL_LAZY.ltp
47__version__ = '24.06.07'
49_height0_ = _height_ + _0_
50_narrow_ = 'narrow'
51_wide_ = 'wide'
54class Attitude(_NamedBase):
55 '''The pose of a plane or camera in space.
56 '''
57 _alt = Meter( alt =_0_0)
58 _roll = Degrees(roll=_0_0)
59 _tilt = Degrees(tilt=_0_0)
60 _yaw = Bearing(yaw =_0_0)
62 def __init__(self, alt_attitude=INT0, tilt=INT0, yaw=INT0, roll=INT0, **name):
63 '''New L{Attitude}.
65 @kwarg alt_attitude: Altitude (C{meter}) above earth or previous attitude
66 (L{Attitude} or L{Attitude4Tuple}) with the C{B{alt}itude},
67 B{C{tilt}}, B{C{yaw}} and B{C{roll}}.
68 @kwarg tilt: Pitch, elevation from horizontal (C{degrees180}), negative down
69 (clockwise rotation along and around the x- or East axis).
70 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
71 (counter-clockwise rotation along and around the z- or Up axis).
72 @kwarg roll: Roll, bank (C{degrees180}), positive to the right and down
73 (clockwise rotation along and around the y- or North axis).
74 @kwarg name: Optional C{B{name}=NN} C{str}).
76 @raise AttitudeError: Invalid B{C{alt_attitude}}, B{C{tilt}}, B{C{yaw}} or
77 B{C{roll}}.
79 @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>} and
80 U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
81 '''
82 if _isHeight(alt_attitude):
83 t = Attitude4Tuple(alt_attitude, tilt, yaw, roll)
84 else:
85 try:
86 t = alt_attitude.atyr
87 except AttributeError:
88 raise AttitudeError(alt=alt_attitude, tilt=tilt, yaw=yaw, rol=roll)
89 for n, v in t.items():
90 if v:
91 setattr(self, n, v)
92 n = _name__(name, _or_nameof=t)
93 if n:
94 self.name = n
96 @property_doc_(' altitude above earth in C{meter}.')
97 def alt(self):
98 return self._alt
100 @alt.setter # PYCHOK setter!
101 def alt(self, alt): # PYCHOK no cover
102 a = Meter(alt=alt, Error=AttitudeError)
103 if self._alt != a:
104 _update_all(self)
105 self._alt = a
107 altitude = alt
109 @Property_RO
110 def atyr(self):
111 '''Return this attitude's alt[itude], tilt, yaw and roll as an L{Attitude4Tuple}.
112 '''
113 return Attitude4Tuple(self.alt, self.tilt, self.yaw, self.roll, name=self.name)
115 @Property_RO
116 def matrix(self):
117 '''Get the 3x3 rotation matrix C{R(yaw)·R(tilt)·R(roll)}, aka I{ZYX} (C{float}, row-order).
119 @see: Matrix M of case 10 in U{Appendix A
120 <https://ntrs.NASA.gov/api/citations/19770019231/downloads/19770019231.pdf>}.
121 '''
122 _f = fsum1f_
123 # to follow the definitions of rotation angles alpha, beta and gamma:
124 # negate yaw since yaw is counter-clockwise around the z-axis, swap
125 # tilt and roll since tilt is around the x- and roll around the y-axis
126 sa, ca, sb, cb, sg, cg = sincos2d_(-self.yaw, self.roll, self.tilt)
127 return ((ca * cb, _f(ca * sb * sg, -sa * cg), _f(ca * sb * cg, sa * sg)),
128 (sa * cb, _f(sa * sb * sg, ca * cg), _f(sa * sb * cg, -ca * sg)),
129 ( -sb, cb * sg, cb * cg))
131 @property_doc_(' roll/bank in C{degrees180}, positive to the right and down.')
132 def roll(self):
133 return self._roll
135 @roll.setter # PYCHOK setter!
136 def roll(self, roll):
137 r = Degrees(roll=roll, wrap=wrap180, Error=AttitudeError)
138 if self._roll != r:
139 _update_all(self)
140 self._roll = r
142 bank = roll
144 def rotate(self, x_xyz, y=None, z=None, Vector=None, **name_Vector_kwds):
145 '''Transform a (local) cartesian by this attitude's matrix.
147 @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector (C{Cartesian},
148 L{Vector3d} or L{Vector3Tuple}).
149 @kwarg y: Y component of vector (C{scalar}), same units as B{C{x}}.
150 @kwarg z: Z component of vector (C{scalar}), same units as B{C{x}}.
151 @kwarg Vector: Class to return transformed point (C{Cartesian}, L{Vector3d}
152 or C{Vector3Tuple}) or C{None}.
153 @kwarg name_Vector_kwds: Optional C{B{name}=NN} (C{str}) and optional,
154 additional B{C{Vector}} keyword arguments, ignored if
155 C{B{Vector} is None}.
157 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None},
158 a named L{Vector3Tuple}C{(x, y, z)}.
160 @raise AttitudeError: Invalid B{C{x_xyz}}, B{C{y}} or B{C{z}}.
162 @raise TypeError: Invalid B{C{Vector}} or B{C{name_Vector_kwds}}.
164 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
165 '''
166 try:
167 try:
168 xyz = map2(float, x_xyz.xyz)
169 except AttributeError:
170 xyz = map1(float, x_xyz, y, z)
171 except (TypeError, ValueError) as x:
172 raise AttitudeError(x_xyz=x_xyz, y=y, z=z, cause=x)
174 x, y, z = (fdot(r, *xyz) for r in self.matrix)
175 n, kwds = _name2__(name_Vector_kwds, _or_nameof=self)
176 return Vector3Tuple(x, y, z, name=n) if Vector is None else \
177 Vector(x, y, z, name=n, **kwds)
179 @property_doc_(' tilt/pitch/elevation from horizontal in C{degrees180}, negative down.')
180 def tilt(self):
181 return self._tilt
183 @tilt.setter # PYCHOK setter!
184 def tilt(self, tilt):
185 t = Degrees(tilt=tilt, wrap=wrap180, Error=AttitudeError)
186 if self._tilt != t:
187 _update_all(self)
188 self._tilt = t
190 elevation = pitch = tilt
192 def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature
193 '''Format this attitude as string.
195 @kwarg prec: The C{float} precision, number of decimal digits (0..9).
196 Trailing zero decimals are stripped for B{C{prec}} values
197 of 1 and above, but kept for negative B{C{prec}} values.
198 @kwarg sep: Separator to join (C{str}).
200 @return: This attitude (C{str}).
201 '''
202 return self.atyr.toStr(prec=prec, sep=sep)
204 @Property_RO
205 def tyr3d(self):
206 '''Get this attitude's (3-D) directional vector (L{Vector3d}).
208 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}.
209 '''
210 def _r2d(r):
211 return fsumf_(_N_1_0, *r)
213 return Vector3d(*map(_r2d, self.matrix), name__=tyr3d)
215 @property_doc_(' yaw/bearing/heading in compass C{degrees360}, clockwise from North.')
216 def yaw(self):
217 return self._yaw
219 @yaw.setter # PYCHOK setter!
220 def yaw(self, yaw):
221 y = Bearing(yaw=yaw, Error=AttitudeError)
222 if self._yaw != y:
223 _update_all(self)
224 self._yaw = y
226 bearing = heading = yaw
229class AttitudeError(_ValueError):
230 '''An L{Attitude} or L{Attitude4Tuple} issue.
231 '''
232 pass
235class Frustum(_NamedBase):
236 '''A rectangular pyramid, typically representing a camera's I{field-of-view}
237 (fov) and the intersection with (or projection to) a I{local tangent plane}.
239 @see: U{Viewing frustum<https://WikiPedia.org/wiki/Viewing_frustum>}.
240 '''
241 _h_2 = _0_0 # half hfov in degrees
242 _ltp = None # local tangent plane
243 _tan_h_2 = _0_0 # tan(_h_2)
244 _v_2 = _0_0 # half vfov in degrees
246 def __init__(self, hfov, vfov, ltp=None, **name):
247 '''New L{Frustum}.
249 @arg hfov: Horizontal field-of-view (C{degrees180}).
250 @arg vfov: Vertical field-of-view (C{degrees180}).
251 @kwarg ltp: Optional I{local tangent plane} (L{Ltp}).
252 @kwarg name: Optional C{B{name}=NN} (C{str}).
254 @raise LocalError: Invalid B{C{hfov}} or B{C{vfov}}.
255 '''
256 self._h_2 = h = _fov_2(hfov=hfov)
257 self._v_2 = _fov_2(vfov=vfov)
259 self._tan_h_2 = tand(h, hfov_2=h)
261 if ltp:
262 self._ltp = _xLtp(ltp)
263 if name:
264 self.name # PYCHOK effect
266 def footprint5(self, alt_attitude, tilt=0, yaw=0, roll=0, z=_0_0, ltp=None, **name): # MCCABE 15
267 '''Compute the center and corners of the intersection with (or projection
268 to) the I{local tangent plane} (LTP).
270 @arg alt_attitude: An altitude (C{meter}) above I{local tangent plane} or
271 an attitude (L{Attitude} or L{Attitude4Tuple}) with the
272 C{B{alt}itude}, B{C{tilt}}, B{C{yaw}} and B{C{roll}}.
273 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
274 (clockwise rotation along and around the x- or East axis).
275 @kwarg yaw: Bearing, heading (compass C{degrees}), clockwise from North
276 (counter-clockwise rotation along and around the z- or Up axis).
277 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
278 (clockwise rotation along and around the y- or North axis).
279 @kwarg z: Optional height of the footprint (C{meter}) above I{local tangent plane}.
280 @kwarg ltp: The I{local tangent plane} (L{Ltp}), overriding this
281 frustum's C{ltp}.
282 @kwarg name: Optional C{B{name}=NN} (C{str}).
284 @return: A L{Footprint5Tuple}C{(center, upperleft, upperight, loweright,
285 lowerleft)} with the C{center} and 4 corners, each an L{Xyz4Tuple}.
287 @raise TypeError: Invalid B{C{ltp}}.
289 @raise UnitError: Invalid B{C{altitude}}, B{C{tilt}}, B{C{roll}} or B{C{z}}.
291 @raise ValueError: If B{C{altitude}} too low, B{C{z}} too high or B{C{tilt}}
292 or B{C{roll}} -including B{C{vfov}} respectively B{C{hfov}}-
293 over the horizon.
295 @see: U{Principal axes<https://WikiPedia.org/wiki/Aircraft_principal_axes>}.
296 '''
297 def _xy2(a, e, h_2, tan_h_2, r):
298 # left and right corners, or swapped
299 if r < EPS: # no roll
300 r = a * tan_h_2
301 l = -r # PYCHOK l is ell
302 else: # roll
303 r, l = tand_(r - h_2, r + h_2, roll_hfov=r) # PYCHOK l is ell
304 r *= -a # negate right positive
305 l *= -a # PYCHOK l is ell
306 y = a * cotd(e, tilt_vfov=e)
307 return (l, y), (r, y)
309 def _xyz5(b, xy5, z, ltp):
310 # rotate (x, y)'s by bearing, clockwise
311 s, c = sincos2d(b)
312 _f = fsum1f_
313 for x, y in xy5:
314 yield Xyz4Tuple(_f(x * c, y * s),
315 _f(y * c, -x * s), z, ltp)
317 try:
318 a, t, y, r = alt_attitude.atyr
319 except AttributeError:
320 a, t, y, r = alt_attitude, tilt, yaw, roll
322 a = Meter(altitude=a)
323 if a < EPS: # too low
324 raise _ValueError(altitude=a)
325 if z: # PYCHOK no cover
326 z = Meter(z=z)
327 a -= z
328 if a < EPS: # z above a
329 raise _ValueError(altitude_z=a)
330 else:
331 z = _0_0
333 b = Degrees(yaw=y, wrap=wrap360) # bearing
334 e = -Degrees(tilt=t, wrap=wrap180) # elevation, pitch
335 if not EPS < e < _180_0:
336 raise _ValueError(tilt=t)
337 if e > _90_0:
338 e = _loneg(e)
339 b = _umod_360(b + _180_0)
341 r = Degrees(roll=r, wrap=wrap180) # roll center
342 x = (-a * tand(r, roll=r)) if r else _0_0
343 y = a * cotd(e, tilt=t) # ground range
344 if fabs(y) < EPS:
345 y = _0_0
347 v, h, t = self._v_2, self._h_2, self._tan_h_2
348 # center and corners, clockwise from upperleft, rolled
349 xy5 = ((x, y),) + _xy2(a, e - v, h, t, r) \
350 + _xy2(a, e + v, -h, -t, r) # swapped
351 # turn center and corners by yaw, clockwise
352 p = self.ltp if ltp is None else ltp # None OK
353 return Footprint5Tuple(_xyz5(b, xy5, z, p), **name) # *_xyz5
355 @Property_RO
356 def hfov(self):
357 '''Get the horizontal C{fov} (C{degrees}).
358 '''
359 return Degrees(hfov=self._h_2 * _2_0)
361 @Property_RO
362 def ltp(self):
363 '''Get the I{local tangent plane} (L{Ltp}) or C{None}.
364 '''
365 return self._ltp
367 def toStr(self, prec=3, fmt=Fmt.F, sep=_COMMASPACE_): # PYCHOK signature
368 '''Convert this frustum to a "hfov, vfov, ltp" string.
370 @kwarg prec: Number of (decimal) digits, unstripped (0..8 or C{None}).
371 @kwarg fmt: Optional, C{float} format (C{letter}).
372 @kwarg sep: Separator to join (C{str}).
374 @return: Frustum in the specified form (C{str}).
375 '''
376 t = self.hfov, self.vfov
377 if self.ltp:
378 t += self.ltp,
379 t = strs(t, prec=prec, fmt=fmt)
380 return sep.join(t) if sep else t
382 @Property_RO
383 def vfov(self):
384 '''Get the vertical C{fov} (C{degrees}).
385 '''
386 return Degrees(vfov=self._v_2 * _2_0)
389class LocalError(_ValueError):
390 '''A L{LocalCartesian} or L{Ltp} related issue.
391 '''
392 pass
395class LocalCartesian(_NamedBase):
396 '''Conversion between geodetic C{(lat, lon, height)} and I{local
397 cartesian} C{(x, y, z)} coordinates with I{geodetic} origin
398 C{(lat0, lon0, height0)}, transcoded from I{Karney}'s C++ class
399 U{LocalCartesian<https://GeographicLib.SourceForge.io/C++/doc/
400 classGeographicLib_1_1LocalCartesian.html>}.
402 The C{z} axis is normal to the ellipsoid, the C{y} axis points due
403 North. The plane C{z = -height0} is tangent to the ellipsoid.
405 The conversions all take place via geocentric coordinates using a
406 geocentric L{EcefKarney}, by default the WGS84 datum/ellipsoid.
408 @see: Class L{Ltp}.
409 '''
410 _ecef = EcefKarney(_WGS84)
411 _Ecef = EcefKarney
412 _lon00 = INT0 # self.lon0
413 _t0 = None # origin (..., lat0, lon0, height0, ...) L{Ecef9Tuple}
414 _9Tuple = Local9Tuple
416 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, **lon00_name):
417 '''New L{LocalCartesian} converter.
419 @kwarg latlonh0: The (geodetic) origin (C{LatLon}, L{LatLon4Tuple}, L{Ltp}
420 L{LocalCartesian} or L{Ecef9Tuple}) or the C{scalar}
421 latitude of the (goedetic) origin (C{degrees}).
422 @kwarg lon0: Longitude of the (goedetic) origin (C{degrees}) for C{scalar}
423 B{C{latlonh0}}, ignored otherwise.
424 @kwarg height0: Optional height (C{meter}, conventionally) at the (goedetic)
425 origin perpendicular to and above (or below) the ellipsoid's
426 surface and for C{scalar} B{C{latlonh0}}, ignored otherwise.
427 @kwarg ecef: An ECEF converter (L{EcefKarney} I{only}) for C{scalar}
428 B{C{latlonh0}}, ignored otherwise.
429 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and keyword argument
430 C{B{lon00}=B{lon0}} for the arbitrary I{polar} longitude
431 (C{degrees}), see method C{reverse} and property C{lon00}
432 for further details.
434 @raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{LatLon4Tuple}, L{Ltp},
435 L{LocalCartesian} or L{Ecef9Tuple} or B{C{latlonh0}},
436 B{C{lon0}}, B{C{height0}} or B{C{lon00}} invalid.
438 @raise TypeError: Invalid B{C{ecef}} or not L{EcefKarney}.
440 @note: If BC{latlonh0} is an L{Ltp} or L{LocalCartesian}, only C{lat0}, C{lon0},
441 C{height0} and I{polar} C{lon00} are copied, I{not} the ECEF converter.
442 '''
443 self.reset(latlonh0, lon0=lon0, height0=height0, ecef=ecef, **lon00_name)
445 def __eq__(self, other):
446 '''Compare this and an other instance.
448 @arg other: The other ellipsoid (L{LocalCartesian} or L{Ltp}).
450 @return: C{True} if equal, C{False} otherwise.
451 '''
452 return other is self or (isinstance(other, self.__class__) and
453 other.ecef == self.ecef and
454 other._t0 == self._t0)
456 @Property_RO
457 def datum(self):
458 '''Get the ECEF converter's datum (L{Datum}).
459 '''
460 return self.ecef.datum
462 @Property_RO
463 def ecef(self):
464 '''Get the ECEF converter (L{EcefKarney}).
465 '''
466 return self._ecef
468 def _ecef2local(self, ecef, Xyz, name_Xyz_kwds):
469 '''(INTERNAL) Convert geocentric/geodetic to local, like I{forward}.
471 @arg ecef: Geocentric (and geodetic) (L{Ecef9Tuple}).
472 @arg Xyz: An L{XyzLocal}, L{Enu} or L{Ned} I{class} or C{None}.
473 @arg name_Xyz_kwds: Optional C{B{name}=NN} (C{str}) and optional,
474 additional B{C{Xyz}} keyword arguments, ignored if
475 C{B{Xyz} is None}.
477 @return: An C{B{Xyz}(x, y, z, ltp, **B{name_Xyz_kwds}} instance or
478 if C{B{Xyz} is None}, a L{Local9Tuple}C{(x, y, z, lat, lon,
479 height, ltp, ecef, M)} with this C{ltp}, B{C{ecef}}
480 (L{Ecef9Tuple}) converted to this C{datum} and C{M=None},
481 always.
483 @raise TypeError: Invalid B{C{Xyz}} or B{C{name_Xyz_kwds}}.
484 '''
485 _xinstanceof(Ecef9Tuple, ecef=ecef)
486 ltp = self
487 if ecef.datum != ltp.datum:
488 ecef = ecef.toDatum(ltp.datum)
489 n, kwds = _name2__(name_Xyz_kwds, _or_nameof=ecef)
490 x, y, z = self.M.rotate(ecef.xyz, *ltp._t0_xyz)
491 r = Local9Tuple(x, y, z, ecef.lat, ecef.lon, ecef.height,
492 ltp, ecef, None, name=n)
493 if Xyz:
494 _xsubclassof(*_XyzLocals4, Xyz=Xyz) # Vector3d
495 r = r.toXyz(Xyz=Xyz, name=n, **kwds)
496 return r
498 @Property_RO
499 def ellipsoid(self):
500 '''Get the ECEF converter's ellipsoid (L{Ellipsoid}).
501 '''
502 return self.ecef.datum.ellipsoid
504 def forward(self, latlonh, lon=None, height=0, M=False, **name):
505 '''Convert I{geodetic} C{(lat, lon, height)} to I{local} cartesian
506 C{(x, y, z)}.
508 @arg latlonh: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or C{scalar}
509 (geodetic) latitude (C{degrees}).
510 @kwarg lon: Optional C{scalar} (geodetic) longitude for C{scalar}
511 B{C{latlonh}} (C{degrees}).
512 @kwarg height: Optional height (C{meter}, conventionally) perpendicular
513 to and above (or below) the ellipsoid's surface.
514 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix},
515 iff available (C{bool}).
516 @kwarg name: Optional C{B{name}=NN} (C{str}).
518 @return: A L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)}
519 with I{local} C{x}, C{y}, C{z}, I{geodetic} C{(lat}, C{lon},
520 C{height}, this C{ltp}, C{ecef} (L{Ecef9Tuple}) with
521 I{geocentric} C{x}, C{y}, C{z} (and I{geodetic} C{lat},
522 C{lon}, C{height}) and the I{concatenated} rotation matrix
523 C{M} (L{EcefMatrix}) if requested.
525 @raise LocalError: If B{C{latlonh}} not C{scalar}, C{LatLon}, L{Ltp},
526 L{Ecef9Tuple} or invalid or if B{C{lon}} not
527 C{scalar} for C{scalar} B{C{latlonh}} or invalid
528 or if B{C{height}} invalid.
529 '''
530 lat, lon, h, n = _llhn4(latlonh, lon, height, Error=LocalError, **name)
531 t = self.ecef._forward(lat, lon, h, n, M=M)
532 x, y, z = self.M.rotate(t.xyz, *self._t0_xyz)
533 m = self.M.multiply(t.M) if M else None
534 return self._9Tuple(x, y, z, lat, lon, h, self, t, m, name=n or self.name)
536 @Property_RO
537 def height0(self):
538 '''Get the origin's height (C{meter}).
539 '''
540 return self._t0.height
542 @Property_RO
543 def lat0(self):
544 '''Get the origin's latitude (C{degrees}).
545 '''
546 return self._t0.lat
548 @Property_RO
549 def latlonheight0(self):
550 '''Get the origin's lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
551 '''
552 return LatLon3Tuple(self.lat0, self.lon0, self.height0, name=self.name)
554 def _local2ecef(self, local, nine=False, M=False):
555 '''(INTERNAL) Convert I{local} to geocentric/geodetic, like I{.reverse}.
557 @arg local: Local (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer} or L{Local9Tuple}).
558 @kwarg nine: If C{True}, return a 9-, otherwise a 3-tuple (C{bool}).
559 @kwarg M: Include the rotation matrix (C{bool}).
561 @return: A I{geocentric} 3-tuple C{(x, y, z)} or if C{B{nine}=True},
562 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)},
563 optionally including rotation matrix C{M} otherwise C{None}.
564 '''
565 _xinstanceof(*_XyzLocals5, local=local)
566 t = self.M.unrotate(local.xyz, *self._t0_xyz)
567 if nine:
568 t = self.ecef.reverse(*t, M=M)
569 return t
571 @Property_RO
572 def lon0(self):
573 '''Get the origin's longitude (C{degrees}).
574 '''
575 return self._t0.lon
577 @Property
578 def lon00(self):
579 '''Get the arbitrary, I{polar} longitude (C{degrees}).
580 '''
581 return self._lon00
583 @lon00.setter # PYCHOK setter!
584 def lon00(self, lon00):
585 '''Set the arbitrary, I{polar} longitude (C{degrees}).
586 '''
587 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
588 self._lon00 = Degrees(lon00=lon00)
590 @Property_RO
591 def M(self):
592 '''Get the rotation matrix (C{EcefMatrix}).
593 '''
594 return self._t0.M
596 def reset(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, **lon00_name):
597 '''Reset this converter, see L{LocalCartesian.__init__} for more details.
598 '''
599 _, name = _xkwds_pop2(lon00_name, lon00=None) # PYCHOK get **name
600 if isinstance(latlonh0, LocalCartesian):
601 if self._t0:
602 _update_all(self)
603 self._ecef = latlonh0.ecef
604 self._lon00 = latlonh0.lon00
605 self._t0 = latlonh0._t0
606 n = _name__(name, _or_nameof=latlonh0)
607 else:
608 n = _name__(name, _or_nameof=self)
609 lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, suffix=_0_,
610 Error=LocalError, name=n)
611 if ecef: # PYCHOK no cover
612 _xinstanceof(self._Ecef, ecef=ecef)
613 _update_all(self)
614 self._ecef = ecef
615 elif self._t0:
616 _update_all(self)
617 self._t0 = self.ecef._forward(lat0, lon0, height0, n, M=True)
618 self.lon00 = _xattr(latlonh0, lon00=_xkwds_get(lon00_name, lon00=lon0))
619 if n:
620 self.rename(n)
622 def reverse(self, xyz, y=None, z=None, M=False, **lon00_name):
623 '''Convert I{local} C{(x, y, z)} to I{geodetic} C{(lat, lon, height)}.
625 @arg xyz: A I{local} (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer}, L{Local9Tuple}) or
626 local C{x} coordinate (C{scalar}).
627 @kwarg y: Local C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
628 @kwarg z: Local C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
629 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix}, iff
630 available (C{bool}).
631 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and keyword argument
632 C{B{lon00}=B{lon0}} for the arbitrary I{polar} longitude
633 (C{degrees}), overriding see the property C{B{lon00}=B{lon0}}
634 value. The I{polar} longitude (C{degrees}) is returned with
635 I{polar} latitudes C{abs(B{lat0}) == 90} for local C{B{x}=0}
636 and C{B{y}=0} locations.
638 @return: An L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with
639 I{local} C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height},
640 this C{ltp}, an C{ecef} (L{Ecef9Tuple}) with the I{geocentric} C{x},
641 C{y}, C{z} (and I{geodetic} C{lat}, C{lon}, C{height}) and the
642 I{concatenated} rotation matrix C{M} (L{EcefMatrix}) if requested.
644 @raise LocalError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
645 not C{scalar} for C{scalar} B{C{xyz}}.
646 '''
647 lon00, name =_xkwds_pop2(lon00_name, lon00=self.lon00)
648 x, y, z, n = _xyzn4(xyz, y, z, _XyzLocals5, Error=LocalError, name=name)
649 c = self.M.unrotate((x, y, z), *self._t0_xyz)
650 t = self.ecef.reverse(*c, M=M, lon00=lon00)
651 m = self.M.multiply(t.M) if M else None
652 return self._9Tuple(x, y, z, t.lat, t.lon, t.height, self, t, m, name=n or self.name)
654 @Property_RO
655 def _t0_xyz(self):
656 '''(INTERNAL) Get C{(x0, y0, z0)} as L{Vector3Tuple}.
657 '''
658 return self._t0.xyz
660 def toStr(self, prec=9, **unused): # PYCHOK signature
661 '''Return this L{LocalCartesian} as a string.
663 @kwarg prec: Precision, number of (decimal) digits (0..9).
665 @return: This L{LocalCartesian} representation (C{str}).
666 '''
667 return self.attrs(_lat0_, _lon0_, _height0_, _M_, _ecef_, _name_, prec=prec)
670class Ltp(LocalCartesian):
671 '''A I{local tangent plan} (LTP), a sub-class of C{LocalCartesian} with
672 (re-)configurable ECEF converter.
673 '''
674 _Ecef = _EcefBase
676 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, **lon00_name):
677 '''New C{Ltp}, see L{LocalCartesian.__init__} for more details.
679 @kwarg ecef: Optional ECEF converter (L{EcefKarney}, L{EcefFarrell21},
680 L{EcefFarrell22}, L{EcefSudano}, L{EcefVeness} or
681 L{EcefYou} I{instance}), overriding the default
682 L{EcefKarney}C{(datum=Datums.WGS84)} for C{scalar}.
684 @see: Class L{LocalCartesian<LocalCartesian.__init__>} for further details.
686 @raise TypeError: Invalid B{C{ecef}}.
687 '''
688 LocalCartesian.reset(self, latlonh0, lon0=lon0, height0=height0,
689 ecef=ecef, **lon00_name)
691 @Property
692 def ecef(self):
693 '''Get this LTP's ECEF converter (C{Ecef...} I{instance}).
694 '''
695 return self._ecef
697 @ecef.setter # PYCHOK setter!
698 def ecef(self, ecef):
699 '''Set this LTP's ECEF converter (C{Ecef...} I{instance}).
701 @raise TypeError: Invalid B{C{ecef}}.
702 '''
703 _xinstanceof(_EcefBase, ecef=ecef)
704 if self._ecef != ecef: # PYCHOK no cover
705 self.reset(self._t0)
706 self._ecef = ecef
709class _ChLV(object):
710 '''(INTERNAL) Base class for C{ChLV*} classes.
711 '''
712 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)
713# _92_falsing = ChLVYX2Tuple(2.0e6, 1.0e6) # _95_ - _03_
714 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)
716 def _ChLV9Tuple(self, fw, M, name, *Y_X_h_lat_lon_h):
717 '''(INTERNAL) Helper for C{ChLVa/e.forward} and C{.reverse}.
718 '''
719 if bool(M): # PYCHOK no cover
720 m = self.forward if fw else self.reverse # PYCHOK attr
721 n = _DOT_(self.__class__.__name__, m.__name__)
722 raise _NotImplementedError(unstr(n, M=M), txt=None)
723 t = Y_X_h_lat_lon_h + (self, self._t0, None) # PYCHOK _t0
724 return ChLV9Tuple(t, name=name)
726 @property_RO
727 def _enh_n_h(self):
728 '''(INTERNAL) Get C{ChLV*.reverse} args[1:4] names, I{once}.
729 '''
730 _ChLV._enh_n_h = t = _args_kwds_names(_ChLV.reverse)[1:4] # overwrite property_RO
731 # assert _args_kwds_names( ChLV.reverse)[1:4] == t
732 # assert _args_kwds_names(ChLVa.reverse)[1:4] == t
733 # assert _args_kwds_names(ChLVe.reverse)[1:4] == t
734 return t
736 def forward(self, latlonh, lon=None, height=0, M=None, **name): # PYCHOK no cover
737 '''Convert WGS84 geodetic to I{Swiss} projection coordinates. I{Must be overloaded}.
739 @arg latlonh: Either a C{LatLon}, L{Ltp} or C{scalar} (geodetic) latitude (C{degrees}).
740 @kwarg lon: Optional, C{scalar} (geodetic) longitude for C{scalar} B{C{latlonh}} (C{degrees}).
741 @kwarg height: Optional, height, vertically above (or below) the surface of the ellipsoid
742 (C{meter}) for C{scalar} B{C{latlonh}} and B{C{lon}}.
743 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
744 for C{ChLV} only, C{None} otherwise (C{bool}).
745 @kwarg name: Optional C{B{name}=NN} (C{str}).
747 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
748 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
749 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
750 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},
751 C{ChLVa} or C{ChLVe} instance.
753 @raise LocalError: Invalid or non-C{scalar} B{C{latlonh}}, B{C{lon}} or B{C{height}}.
754 '''
755 notOverloaded(self, latlonh, lon=lon, height=height, M=M, **name)
757 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK no cover
758 '''Convert I{Swiss} projection to WGS84 geodetic coordinates.
760 @arg enh_: A Swiss projection (L{ChLV9Tuple}) or the C{scalar}, falsed I{Swiss E_LV95}
761 or I{y_LV03} easting (C{meter}).
762 @kwarg n: Falsed I{Swiss N_LV85} or I{x_LV03} northing for C{scalar} B{C{enh_}} and
763 B{C{h_}} (C{meter}).
764 @kwarg h_: I{Swiss h'} height for C{scalar} B{C{enh_}} and B{C{n}} (C{meter}).
765 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
766 for C{ChLV} only, C{None} otherwise (C{bool}).
767 @kwarg name: Optional C{B{name}=NN} (C{str}).
769 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
770 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
771 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
772 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},
773 C{ChLVa} or C{ChLVe} instance.
775 @raise LocalError: Invalid or non-C{scalar} B{C{enh_}}, B{C{n}} or B{C{h_}}.
776 '''
777 notOverloaded(self, enh_, n=n, h_=h_, M=M, **name)
779 @staticmethod
780 def _falsing2(LV95):
781 '''(INTERNAL) Get the C{LV95} or C{LV03} falsing.
782 '''
783 return _ChLV._95_falsing if LV95 in (True, 95) else (
784 _ChLV._03_falsing if LV95 in (False, 3) else ChLVYX2Tuple(0, 0))
786 @staticmethod
787 def _llh2abh_3(lat, lon, h):
788 '''(INTERNAL) Helper for C{ChLVa/e.forward}.
789 '''
790 def _deg2ab(deg, sLL):
791 # convert degrees to arc-seconds
792 def _dms(ds, p, q, swap):
793 d = _floor(ds)
794 t = (ds - d) * p
795 m = _floor(t)
796 s = (t - m) * p
797 if swap:
798 d, s = s, d
799 return d + (m + s * q) * q
801 s = _dms(deg, _60_0, _0_01, False) # deg2sexag
802 s = _dms( s, _100_0, _60_0, True) # sexag2asec
803 return (s - sLL) / ChLV._s_ab
805 a = _deg2ab(lat, ChLV._sLat) # phi', lat_aux
806 b = _deg2ab(lon, ChLV._sLon) # lam', lng_aux
807 h_ = fsumf_(h, -ChLV.Bern.height, 2.73 * b, 6.94 * a)
808 return a, b, h_
810 @staticmethod
811 def _YXh_2abh3(Y, X, h_):
812 '''(INTERNAL) Helper for C{ChLVa/e.reverse}.
813 '''
814 def _YX2ab(YX):
815 return YX * ChLV._ab_m
817 a, b = map1(_YX2ab, Y, X)
818 h = fsumf_(h_, ChLV.Bern.height, -12.6 * a, -22.64 * b)
819 return a, b, h
821 def _YXh_n4(self, enh_, n, h_, **name):
822 '''(INTERNAL) Helper for C{ChLV*.reverse}.
823 '''
824 Y, X, h_, name = _xyzn4(enh_, n, h_, ChLV9Tuple,
825 _xyz_y_z_names=self._enh_n_h, **name)
826 if isinstance(enh_, ChLV9Tuple):
827 Y, X = enh_.Y, enh_.X
828 else: # isscalar(enh_)
829 Y, X = ChLV.unfalse2(Y, X) # PYCHOK ChLVYX2Tuple
830 return Y, X, h_, name
833class ChLV(_ChLV, Ltp):
834 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates using
835 L{pygeodesy.EcefKarney}'s Earth-Centered, Earth-Fixed (ECEF) methods.
837 @see: U{Swiss projection formulas<https://www.SwissTopo.admin.CH/en/maps-data-online/
838 calculation-services.html>}, page 7ff, U{NAVREF<https://www.SwissTopo.admin.CH/en/
839 maps-data-online/calculation-services/navref.html>}, U{REFRAME<https://www.SwissTopo.admin.CH/
840 en/maps-data-online/calculation-services/reframe.html>} and U{SwissTopo Scripts GPS WGS84
841 <-> LV03<https://GitHub.com/ValentinMinder/Swisstopo-WGS84-LV03>}.
842 '''
843 _9Tuple = ChLV9Tuple
845 _ab_d = 0.36 # a, b units per degree, ...
846 _ab_m = 1.0e-6 # ... per meter and ...
847 _ab_M = _1_0 # ... per 1,000 Km or 1 Mm
848 _s_d = _3600_0 # arc-seconds per degree ...
849 _s_ab = _s_d / _ab_d # ... and per a, b unit
850 _sLat = 169028.66 # Bern, Ch in ...
851 _sLon = 26782.5 # ... arc-seconds ...
852 # lat, lon, height == 46°57'08.66", 7°26'22.50", 49.55m ("new" 46°57'07.89", 7°26'22.335")
853 Bern = LatLon4Tuple(_sLat / _s_d, _sLon / _s_d, 49.55, _WGS84, name='Bern')
855 def __init__(self, latlonh0=Bern, **other_Ltp_kwds):
856 '''New ECEF-based I{WGS84-Swiss} L{ChLV} converter, centered at I{Bern, Ch}.
858 @kwarg latlonh0: The I{geodetic} origin and height, overriding C{Bern, Ch}.
859 @kwarg other_Ltp_kwds: Optional, other L{Ltp.__init__} keyword arguments.
861 @see: L{Ltp.__init__} for more information.
862 '''
863 Ltp.__init__(self, latlonh0, **_xkwds(other_Ltp_kwds, ecef=None, name=ChLV.Bern.name))
865 def forward(self, latlonh, lon=None, height=0, M=None, **name): # PYCHOK unused M
866 # overloaded for the _ChLV.forward.__doc__
867 return Ltp.forward(self, latlonh, lon=lon, height=height, M=M, **name)
869 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature
870 # overloaded for the _ChLV.reverse.__doc__
871 Y, X, h_, n = self._YXh_n4(enh_, n, h_, **name)
872 return Ltp.reverse(self, Y, X, h_, M=M, name=n)
874 @staticmethod
875 def false2(Y, X, LV95=True, **name):
876 '''Add the I{Swiss LV95} or I{LV03} falsing.
878 @arg Y: Unfalsed I{Swiss Y} easting (C{meter}).
879 @arg X: Unfalsed I{Swiss X} northing (C{meter}).
880 @kwarg LV95: If C{True} add C{LV95} falsing, if C{False} add
881 C{LV03} falsing, otherwise leave unfalsed.
882 @kwarg name: Optional C{B{name}=NN} (C{str}).
884 @return: A L{ChLVEN2Tuple}C{(E_LV95, N_LV95)} or a
885 L{ChLVyx2Tuple}C{(y_LV03, x_LV03)} with falsed B{C{Y}}
886 and B{C{X}}, otherwise a L{ChLVYX2Tuple}C{(Y, X)}
887 with B{C{Y}} and B{C{X}} as-is.
888 '''
889 e, n = t = _ChLV._falsing2(LV95)
890 return t.classof(e + Y, n + X, **name)
892 @staticmethod
893 def isLV03(e, n):
894 '''Is C{(B{e}, B{n})} a valid I{Swiss LV03} projection?
896 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
897 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
899 @return: C{True} if C{(B{e}, B{n})} is a valid, falsed I{Swiss
900 LV03}, projection C{False} otherwise.
901 '''
902 # @see: U{Map<https://www.SwissTopo.admin.CH/en/knowledge-facts/
903 # surveying-geodesy/reference-frames/local/lv95.html>}
904 return 400.0e3 < e < 900.0e3 and 40.0e3 < n < 400.0e3
906 @staticmethod
907 def isLV95(e, n, raiser=True):
908 '''Is C{(B{e}, B{n})} a valid I{Swiss LV95} or I{LV03} projection?
910 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
911 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
912 @kwarg raiser: If C{True}, throw a L{LocalError} if B{C{e}} and
913 B{C{n}} are invalid I{Swiss LV95} nor I{LV03}.
915 @return: C{True} or C{False} if C{(B{e}, B{n})} is a valid I{Swiss
916 LV95} respectively I{LV03} projection, C{None} otherwise.
917 '''
918 if ChLV.isLV03(e, n):
919 return False
920 elif ChLV.isLV03(e - 2.0e6, n - 1.0e6): # _92_falsing = _95_ - _03_
921 return True
922 elif raiser: # PYCHOK no cover
923 raise LocalError(unstr(ChLV.isLV95, e=e, n=n))
924 return None
926 @staticmethod
927 def unfalse2(e, n, LV95=None, **name):
928 '''Remove the I{Swiss LV95} or I{LV03} falsing.
930 @arg e: Falsed I{Swiss E_LV95} or I{y_LV03} easting (C{meter}).
931 @arg n: Falsed I{Swiss N_LV95} or I{x_LV03} northing (C{meter}).
932 @kwarg LV95: If C{True} remove I{LV95} falsing, if C{False} remove
933 I{LV03} falsing, otherwise use method C{isLV95(B{e},
934 B{n})}.
935 @kwarg name: Optional C{B{name}=NN} (C{str}).
937 @return: A L{ChLVYX2Tuple}C{(Y, X)} with the unfalsed B{C{e}}
938 respectively B{C{n}}.
939 '''
940 Y, X = _ChLV._falsing2(ChLV.isLV95(e, n) if LV95 is None else LV95)
941 return ChLVYX2Tuple(e - Y, n - X, **name)
944class ChLVa(_ChLV, LocalCartesian):
945 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
946 using the U{Approximate<https://www.SwissTopo.admin.CH/en/maps-data-online/
947 calculation-services.html>} formulas, page 13.
949 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
950 '''
951 def __init__(self, name=ChLV.Bern.name):
952 '''New I{Approximate WGS84-Swiss} L{ChLVa} converter, centered at I{Bern, Ch}.
954 @kwarg name: Optional C{B{name}=Bern.name} (C{str}).
955 '''
956 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)
958 def forward(self, latlonh, lon=None, height=0, M=None, **name):
959 # overloaded for the _ChLV.forward.__doc__
960 lat, lon, h, n = _llhn4(latlonh, lon, height, **name)
961 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)
962 a2, b2 = a**2, b**2
964 Y = fsumf_( 72.37, 211455.93 * b,
965 -10938.51 * b * a,
966 -0.36 * b * a2,
967 -44.54 * b * b2) # + 600_000
968 X = fsumf_(147.07, 308807.95 * a,
969 3745.25 * b2,
970 76.63 * a2,
971 -194.56 * b2 * a,
972 119.79 * a2 * a) # + 200_000
973 return self._ChLV9Tuple(True, M, n, Y, X, h_, lat, lon, h)
975 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature
976 # overloaded for the _ChLV.reverse.__doc__
977 Y, X, h_, n = self._YXh_n4(enh_, n, h_, **name)
978 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)
979 ab_d, a2, b2 = ChLV._ab_d, a**2, b**2
981 lat = _Fsumf_(16.9023892, 3.238272 * b,
982 -0.270978 * a2,
983 -0.002528 * b2,
984 -0.0447 * a2 * b,
985 -0.014 * b2 * b).fover(ab_d)
986 lon = _Fsumf_( 2.6779094, 4.728982 * a,
987 0.791484 * a * b,
988 0.1306 * a * b2,
989 -0.0436 * a * a2).fover(ab_d)
990 return self._ChLV9Tuple(False, M, n, Y, X, h_, lat, lon, h)
993class ChLVe(_ChLV, LocalCartesian):
994 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
995 using the U{Ellipsoidal approximate<https://www.SwissTopo.admin.CH/en/
996 maps-data-online/calculation-services.html>} formulas, pp 10-11 and U{Bolliger,
997 J.<https://eMuseum.GGGS.CH/literatur-lv/liste-Dateien/1967_Bolliger_a.pdf>}
998 pp 148-151 (also U{GGGS<https://eMuseum.GGGS.CH/literatur-lv/liste.htm>}).
1000 @note: Methods L{ChLVe.forward} and L{ChLVe.reverse} have an additional keyword
1001 argument C{B{gamma}=False} to approximate the I{meridian convergence}.
1002 If C{B{gamma}=True} a 2-tuple C{(t, gamma)} is returned with C{t} the
1003 usual result (C{ChLV9Tuple}) and C{gamma}, the I{meridian convergence}
1004 (decimal C{degrees}). To convert C{gamma} to C{grades} or C{gons},
1005 use function L{pygeodesy.degrees2grades}.
1007 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
1008 '''
1009 def __init__(self, name=ChLV.Bern.name):
1010 '''New I{Approximate WGS84-Swiss} L{ChLVe} converter, centered at I{Bern, Ch}.
1012 @kwarg name: Optional C{B{name}=Bern.name} (C{str}).
1013 '''
1014 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)
1016 def forward(self, latlonh, lon=None, height=0, M=None, gamma=False, **name): # PYCHOK gamma
1017 # overloaded for the _ChLV.forward.__doc__
1018 lat, lon, h, n = _llhn4(latlonh, lon, height, **name)
1019 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)
1020 ab_M, z, _H = ChLV._ab_M, 0, Fhorner
1022 B1 = _H(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)
1023 B3 = _H(a, -44.232717, 4.291740, -0.309883, 0.013924)
1024 B5 = _H(a, 0.019784, -0.004277)
1025 Y = _H(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km!
1027 B0 = _H(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)
1028 B2 = _H(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053)
1029 B4 = _H(a, -0.734684, 0.144466, -0.011842)
1030 B6 = 0.000488
1031 X = _H(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km!
1033 t = self._ChLV9Tuple(True, M, n, Y, X, h_, lat, lon, h)
1034 if gamma:
1035 U1 = _H(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165)
1036 U3 = _H(a, -412.991934, 64.106344, -2.679566, 0.123833)
1037 U5 = _H(a, 0.204129, -0.037725)
1038 g = _H(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees?
1039 t = t, g
1040 return t
1042 def reverse(self, enh_, n=None, h_=0, M=None, gamma=False, **name): # PYCHOK gamma
1043 # overloaded for the _ChLV.reverse.__doc__
1044 Y, X, h_, n = self._YXh_n4(enh_, n, h_, **name)
1045 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)
1046 s_d, _H, z = ChLV._s_d, Fhorner, 0
1048 A0 = _H(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)
1049 A2 = _H(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604)
1050 A4 = _H(b, 24.42786, 13.20703, 4.7476)
1051 A6 = -0.4249
1052 lat = _H(a, A0, z, A2, z, A4, z, A6).fover(s_d)
1054 A1 = _H(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)
1055 A3 = _H(b, -442.709889, -255.02202, -96.34947, -30.0808)
1056 A5 = _H(b, 9.63495, 9.0243)
1057 lon = _H(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)
1058 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d
1060 t = self._ChLV9Tuple(False, M, n, Y, X, h_, lat, lon, h)
1061 if gamma:
1062 U1 = _H(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)
1063 U3 = _H(b, -1435.508, -794.8777, -296.309, -92.908)
1064 U5 = _H(b, 29.631, 27.873)
1065 g = _H(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees
1066 t = t, g
1067 return t
1070def _fov_2(**fov):
1071 # Half a field-of-view angle in C{degrees}.
1072 f = Degrees(Error=LocalError, **fov) * _0_5
1073 if EPS < f < _90_0:
1074 return f
1075 t = _invalid_ if f < 0 else _too_(_wide_ if f > EPS else _narrow_)
1076 raise LocalError(txt=t, **fov)
1079def _toLocal(inst, ltp, Xyz, Xyz_kwds):
1080 '''(INTENRAL) Helper for C{CartesianBase.toLocal} and C{latLonBase.toLocal}.
1081 '''
1082 return _xLtp(ltp, inst._Ltp)._ecef2local(inst._ecef9, Xyz, Xyz_kwds)
1085def _toLtp(inst, Ecef, ecef9, name):
1086 '''(INTENRAL) Helper for C{CartesianBase.toLtp} and C{latLonBase.toLtp}.
1087 '''
1088 return inst._Ltp if Ecef in (None, inst.Ecef) and not name else \
1089 Ltp(ecef9, ecef=Ecef(inst.datum), name=inst._name__(name))
1092def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **name_Vector_kwds):
1093 '''Convert an attitude pose into a (3-D) direction vector.
1095 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
1096 (clockwise rotation along and around the x-axis).
1097 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
1098 (counter-clockwise rotation along and around the z-axis).
1099 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
1100 (clockwise rotation along and around the y-axis).
1101 @kwarg Vector: Class to return the direction vector (C{Cartesian},
1102 L{Vector3d} or C{Vector3Tuple}) or C{None}.
1103 @kwarg name_Vector_kwds: Optional C{B{name}=NN} (C{str}) and optional,
1104 additional B{C{Vector}} keyword arguments, ignored if
1105 C{B{Vector} is None}.
1107 @return: A named B{C{Vector}} instance or if B{C{Vector}} is C{None},
1108 a named L{Vector3Tuple}C{(x, y, z)}.
1110 @raise AttitudeError: Invalid B{C{tilt}}, B{C{yaw}} or B{C{roll}}.
1112 @raise TypeError: Invalid B{C{Vector}} or B{C{name_Vector_kwds}}.
1114 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}
1115 and function L{pygeodesy.hartzell} argument C{los}, Line-Of-Sight.
1116 '''
1117 v = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d
1118 if Vector is not type(v):
1119 n, kwds = _name2__(name_Vector_kwds, name__=tyr3d)
1120 v = Vector3Tuple(v.x, v.y, v.z, name=n) if Vector is None else \
1121 Vector(v.x, v.y, v.z, name=n, **kwds)
1122 elif name_Vector_kwds:
1123 n, _ = _name2__(name_Vector_kwds)
1124 if n:
1125 v = v.copy(name=n)
1126 return v
1129def _xLtp(ltp, *dflt):
1130 '''(INTERNAL) Validate B{C{ltp}} or ist B{C{dflt}}.
1131 '''
1132 if dflt and ltp is None:
1133 ltp = dflt[0]
1134 _xinstanceof(Ltp, LocalCartesian, ltp=ltp)
1135 return ltp
1137# **) MIT License
1138#
1139# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1140#
1141# Permission is hereby granted, free of charge, to any person obtaining a
1142# copy of this software and associated documentation files (the "Software"),
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1146# Software is furnished to do so, subject to the following conditions:
1147#
1148# The above copyright notice and this permission notice shall be included
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