Coverage for pygeodesy/ltp.py: 95%
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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_, \
37 property_ROver, _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__ = '24.07.25'
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 C{B{Vector} is 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}), required if
423 B{C{latlonh0}} is C{scalar}, 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, like B{C{lon0}}.
427 @kwarg ecef: An ECEF converter (L{EcefKarney} I{only}), like B{C{lon0}}.
428 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and keyword argument
429 C{B{lon00}=B{lon0}} for the arbitrary I{polar} longitude
430 (C{degrees}), see method C{reverse} and property C{lon00}
431 for further details.
433 @raise LocalError: If B{C{latlonh0}} not C{LatLon}, L{LatLon4Tuple}, L{Ltp},
434 L{LocalCartesian} or L{Ecef9Tuple} or B{C{latlonh0}},
435 B{C{lon0}}, B{C{height0}} or B{C{lon00}} invalid.
437 @raise TypeError: Invalid B{C{ecef}} or not L{EcefKarney}.
439 @note: If BC{latlonh0} is an L{Ltp} or L{LocalCartesian}, only C{lat0}, C{lon0},
440 C{height0} and I{polar} C{lon00} are copied, I{not} the ECEF converter.
441 '''
442 self.reset(latlonh0, lon0=lon0, height0=height0, ecef=ecef, **lon00_name)
444 def __eq__(self, other):
445 '''Compare this and an other instance.
447 @arg other: The other ellipsoid (L{LocalCartesian} or L{Ltp}).
449 @return: C{True} if equal, C{False} otherwise.
450 '''
451 return other is self or (isinstance(other, self.__class__) and
452 other.ecef == self.ecef and
453 other._t0 == self._t0)
455 @Property_RO
456 def datum(self):
457 '''Get the ECEF converter's datum (L{Datum}).
458 '''
459 return self.ecef.datum
461 @Property_RO
462 def ecef(self):
463 '''Get the ECEF converter (L{EcefKarney}).
464 '''
465 return self._ecef
467 def _ecef2local(self, ecef, Xyz, name_Xyz_kwds):
468 '''(INTERNAL) Convert geocentric/geodetic to local, like I{forward}.
470 @arg ecef: Geocentric (and geodetic) (L{Ecef9Tuple}).
471 @arg Xyz: An L{XyzLocal}, L{Enu} or L{Ned} I{class} or C{None}.
472 @arg name_Xyz_kwds: Optional C{B{name}=NN} (C{str}) and optional,
473 additional B{C{Xyz}} keyword arguments, ignored if
474 C{B{Xyz} is None}.
476 @return: An C{B{Xyz}(x, y, z, ltp, **B{name_Xyz_kwds}} instance or
477 if C{B{Xyz} is None}, a L{Local9Tuple}C{(x, y, z, lat, lon,
478 height, ltp, ecef, M)} with this C{ltp}, B{C{ecef}}
479 (L{Ecef9Tuple}) converted to this C{datum} and C{M=None},
480 always.
482 @raise TypeError: Invalid B{C{Xyz}} or B{C{name_Xyz_kwds}}.
483 '''
484 _xinstanceof(Ecef9Tuple, ecef=ecef)
485 ltp = self
486 if ecef.datum != ltp.datum:
487 ecef = ecef.toDatum(ltp.datum)
488 n, kwds = _name2__(name_Xyz_kwds, _or_nameof=ecef)
489 x, y, z = self.M.rotate(ecef.xyz, *ltp._t0_xyz)
490 r = Local9Tuple(x, y, z, ecef.lat, ecef.lon, ecef.height,
491 ltp, ecef, None, name=n)
492 if Xyz:
493 _xsubclassof(*_XyzLocals4, Xyz=Xyz) # Vector3d
494 r = r.toXyz(Xyz=Xyz, name=n, **kwds)
495 return r
497 @Property_RO
498 def ellipsoid(self):
499 '''Get the ECEF converter's ellipsoid (L{Ellipsoid}).
500 '''
501 return self.ecef.datum.ellipsoid
503 def forward(self, latlonh, lon=None, height=0, M=False, **name):
504 '''Convert I{geodetic} C{(lat, lon, height)} to I{local} cartesian
505 C{(x, y, z)}.
507 @arg latlonh: Either a C{LatLon}, L{Ltp}, L{Ecef9Tuple} or C{scalar}
508 (geodetic) latitude (C{degrees}).
509 @kwarg lon: Optional C{scalar} (geodetic) longitude for C{scalar}
510 B{C{latlonh}} (C{degrees}).
511 @kwarg height: Optional height (C{meter}, conventionally) perpendicular
512 to and above (or below) the ellipsoid's surface.
513 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix},
514 iff available (C{bool}).
515 @kwarg name: Optional C{B{name}=NN} (C{str}).
517 @return: A L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)}
518 with I{local} C{x}, C{y}, C{z}, I{geodetic} C{(lat}, C{lon},
519 C{height}, this C{ltp}, C{ecef} (L{Ecef9Tuple}) with
520 I{geocentric} C{x}, C{y}, C{z} (and I{geodetic} C{lat},
521 C{lon}, C{height}) and the I{concatenated} rotation matrix
522 C{M} (L{EcefMatrix}) if requested.
524 @raise LocalError: If B{C{latlonh}} not C{scalar}, C{LatLon}, L{Ltp},
525 L{Ecef9Tuple} or invalid or if B{C{lon}} not
526 C{scalar} for C{scalar} B{C{latlonh}} or invalid
527 or if B{C{height}} invalid.
528 '''
529 lat, lon, h, n = _llhn4(latlonh, lon, height, Error=LocalError, **name)
530 t = self.ecef._forward(lat, lon, h, n, M=M)
531 x, y, z = self.M.rotate(t.xyz, *self._t0_xyz)
532 m = self.M.multiply(t.M) if M else None
533 return self._9Tuple(x, y, z, lat, lon, h, self, t, m, name=n or self.name)
535 @Property_RO
536 def height0(self):
537 '''Get the origin's height (C{meter}).
538 '''
539 return self._t0.height
541 @Property_RO
542 def lat0(self):
543 '''Get the origin's latitude (C{degrees}).
544 '''
545 return self._t0.lat
547 @Property_RO
548 def latlonheight0(self):
549 '''Get the origin's lat-, longitude and height (L{LatLon3Tuple}C{(lat, lon, height)}).
550 '''
551 return LatLon3Tuple(self.lat0, self.lon0, self.height0, name=self.name)
553 def _local2ecef(self, local, nine=False, M=False):
554 '''(INTERNAL) Convert I{local} to geocentric/geodetic, like I{.reverse}.
556 @arg local: Local (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer} or L{Local9Tuple}).
557 @kwarg nine: If C{True}, return a 9-, otherwise a 3-tuple (C{bool}).
558 @kwarg M: Include the rotation matrix (C{bool}).
560 @return: A I{geocentric} 3-tuple C{(x, y, z)} or if C{B{nine}=True},
561 an L{Ecef9Tuple}C{(x, y, z, lat, lon, height, C, M, datum)},
562 optionally including rotation matrix C{M} otherwise C{None}.
563 '''
564 _xinstanceof(*_XyzLocals5, local=local)
565 t = self.M.unrotate(local.xyz, *self._t0_xyz)
566 if nine:
567 t = self.ecef.reverse(*t, M=M)
568 return t
570 @Property_RO
571 def lon0(self):
572 '''Get the origin's longitude (C{degrees}).
573 '''
574 return self._t0.lon
576 @Property
577 def lon00(self):
578 '''Get the arbitrary, I{polar} longitude (C{degrees}).
579 '''
580 return self._lon00
582 @lon00.setter # PYCHOK setter!
583 def lon00(self, lon00):
584 '''Set the arbitrary, I{polar} longitude (C{degrees}).
585 '''
586 # lon00 <https://GitHub.com/mrJean1/PyGeodesy/issues/77>
587 self._lon00 = Degrees(lon00=lon00)
589 @Property_RO
590 def M(self):
591 '''Get the rotation matrix (C{EcefMatrix}).
592 '''
593 return self._t0.M
595 def reset(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, **lon00_name):
596 '''Reset this converter, see L{LocalCartesian.__init__} for more details.
597 '''
598 _, name = _xkwds_pop2(lon00_name, lon00=None) # PYCHOK get **name
599 if isinstance(latlonh0, LocalCartesian):
600 if self._t0:
601 _update_all(self)
602 self._ecef = latlonh0.ecef
603 self._lon00 = latlonh0.lon00
604 self._t0 = latlonh0._t0
605 n = _name__(name, _or_nameof=latlonh0)
606 else:
607 n = _name__(name, _or_nameof=self)
608 lat0, lon0, height0, n = _llhn4(latlonh0, lon0, height0, suffix=_0_,
609 Error=LocalError, name=n)
610 if ecef: # PYCHOK no cover
611 _xinstanceof(self._Ecef, ecef=ecef)
612 _update_all(self)
613 self._ecef = ecef
614 elif self._t0:
615 _update_all(self)
616 self._t0 = self.ecef._forward(lat0, lon0, height0, n, M=True)
617 self.lon00 = _xattr(latlonh0, lon00=_xkwds_get(lon00_name, lon00=lon0))
618 if n:
619 self.rename(n)
621 def reverse(self, xyz, y=None, z=None, M=False, **lon00_name):
622 '''Convert I{local} C{(x, y, z)} to I{geodetic} C{(lat, lon, height)}.
624 @arg xyz: A I{local} (L{XyzLocal}, L{Enu}, L{Ned}, L{Aer}, L{Local9Tuple}) or
625 local C{x} coordinate (C{scalar}).
626 @kwarg y: Local C{y} coordinate for C{scalar} B{C{xyz}} and B{C{z}} (C{meter}).
627 @kwarg z: Local C{z} coordinate for C{scalar} B{C{xyz}} and B{C{y}} (C{meter}).
628 @kwarg M: Optionally, return the I{concatenated} rotation L{EcefMatrix}, iff
629 available (C{bool}).
630 @kwarg lon00_name: Optional C{B{name}=NN} (C{str}) and keyword argument
631 C{B{lon00}=B{lon0}} for the arbitrary I{polar} longitude
632 (C{degrees}), overriding see the property C{B{lon00}=B{lon0}}
633 value. The I{polar} longitude (C{degrees}) is returned with
634 I{polar} latitudes C{abs(B{lat0}) == 90} for local C{B{x}=0}
635 and C{B{y}=0} locations.
637 @return: An L{Local9Tuple}C{(x, y, z, lat, lon, height, ltp, ecef, M)} with
638 I{local} C{x}, C{y}, C{z}, I{geodetic} C{lat}, C{lon}, C{height},
639 this C{ltp}, an C{ecef} (L{Ecef9Tuple}) with the I{geocentric} C{x},
640 C{y}, C{z} (and I{geodetic} C{lat}, C{lon}, C{height}) and the
641 I{concatenated} rotation matrix C{M} (L{EcefMatrix}) if requested.
643 @raise LocalError: Invalid B{C{xyz}} or C{scalar} C{x} or B{C{y}} and/or B{C{z}}
644 not C{scalar} for C{scalar} B{C{xyz}}.
645 '''
646 lon00, name =_xkwds_pop2(lon00_name, lon00=self.lon00)
647 x, y, z, n = _xyzn4(xyz, y, z, _XyzLocals5, Error=LocalError, name=name)
648 c = self.M.unrotate((x, y, z), *self._t0_xyz)
649 t = self.ecef.reverse(*c, M=M, lon00=lon00)
650 m = self.M.multiply(t.M) if M else None
651 return self._9Tuple(x, y, z, t.lat, t.lon, t.height, self, t, m, name=n or self.name)
653 @Property_RO
654 def _t0_xyz(self):
655 '''(INTERNAL) Get C{(x0, y0, z0)} as L{Vector3Tuple}.
656 '''
657 return self._t0.xyz
659 def toStr(self, prec=9, **unused): # PYCHOK signature
660 '''Return this L{LocalCartesian} as a string.
662 @kwarg prec: Precision, number of (decimal) digits (0..9).
664 @return: This L{LocalCartesian} representation (C{str}).
665 '''
666 return self.attrs(_lat0_, _lon0_, _height0_, _M_, _ecef_, _name_, prec=prec)
669class Ltp(LocalCartesian):
670 '''A I{local tangent plan} (LTP), a sub-class of C{LocalCartesian} with
671 (re-)configurable ECEF converter.
672 '''
673 _Ecef = _EcefBase
675 def __init__(self, latlonh0=INT0, lon0=INT0, height0=INT0, ecef=None, **lon00_name):
676 '''New C{Ltp}, see L{LocalCartesian.__init__} for more details.
678 @kwarg ecef: Optional ECEF converter (L{EcefKarney}, L{EcefFarrell21},
679 L{EcefFarrell22}, L{EcefSudano}, L{EcefVeness} or
680 L{EcefYou} I{instance}), overriding the default
681 L{EcefKarney}C{(datum=Datums.WGS84)} for C{scalar}.
683 @see: Class L{LocalCartesian<LocalCartesian.__init__>} for further details.
685 @raise TypeError: Invalid B{C{ecef}}.
686 '''
687 LocalCartesian.reset(self, latlonh0, lon0=lon0, height0=height0,
688 ecef=ecef, **lon00_name)
690 @Property
691 def ecef(self):
692 '''Get this LTP's ECEF converter (C{Ecef...} I{instance}).
693 '''
694 return self._ecef
696 @ecef.setter # PYCHOK setter!
697 def ecef(self, ecef):
698 '''Set this LTP's ECEF converter (C{Ecef...} I{instance}).
700 @raise TypeError: Invalid B{C{ecef}}.
701 '''
702 _xinstanceof(_EcefBase, ecef=ecef)
703 if self._ecef != ecef: # PYCHOK no cover
704 self.reset(self._t0)
705 self._ecef = ecef
708class _ChLV(object):
709 '''(INTERNAL) Base class for C{ChLV*} classes.
710 '''
711 _03_falsing = ChLVyx2Tuple(0.6e6, 0.2e6)
712# _92_falsing = ChLVYX2Tuple(2.0e6, 1.0e6) # _95_ - _03_
713 _95_falsing = ChLVEN2Tuple(2.6e6, 1.2e6)
715 def _ChLV9Tuple(self, fw, M, name, *Y_X_h_lat_lon_h):
716 '''(INTERNAL) Helper for C{ChLVa/e.forward} and C{.reverse}.
717 '''
718 if bool(M): # PYCHOK no cover
719 m = self.forward if fw else self.reverse # PYCHOK attr
720 n = _DOT_(self.__class__.__name__, m.__name__)
721 raise _NotImplementedError(unstr(n, M=M), txt=None)
722 t = Y_X_h_lat_lon_h + (self, self._t0, None) # PYCHOK _t0
723 return ChLV9Tuple(t, name=name)
725 @property_ROver
726 def _enh_n_h(self):
727 '''(INTERNAL) Get C{ChLV*.reverse} args[1:4] names, I{once}.
728 '''
729 t = _args_kwds_names(_ChLV.reverse)[1:4]
730 # assert _args_kwds_names( ChLV.reverse)[1:4] == t
731 # assert _args_kwds_names(ChLVa.reverse)[1:4] == t
732 # assert _args_kwds_names(ChLVe.reverse)[1:4] == t
733 return t # overwrite property_ROver
735 def forward(self, latlonh, lon=None, height=0, M=None, **name): # PYCHOK no cover
736 '''Convert WGS84 geodetic to I{Swiss} projection coordinates. I{Must be overloaded}.
738 @arg latlonh: Either a C{LatLon}, L{Ltp} or C{scalar} (geodetic) latitude (C{degrees}).
739 @kwarg lon: Optional, C{scalar} (geodetic) longitude for C{scalar} B{C{latlonh}} (C{degrees}).
740 @kwarg height: Optional, height, vertically above (or below) the surface of the ellipsoid
741 (C{meter}) for C{scalar} B{C{latlonh}} and B{C{lon}}.
742 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
743 for C{ChLV} only, C{None} otherwise (C{bool}).
744 @kwarg name: Optional C{B{name}=NN} (C{str}).
746 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
747 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
748 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
749 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},
750 C{ChLVa} or C{ChLVe} instance.
752 @raise LocalError: Invalid or non-C{scalar} B{C{latlonh}}, B{C{lon}} or B{C{height}}.
753 '''
754 notOverloaded(self, latlonh, lon=lon, height=height, M=M, **name)
756 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK no cover
757 '''Convert I{Swiss} projection to WGS84 geodetic coordinates.
759 @arg enh_: A Swiss projection (L{ChLV9Tuple}) or the C{scalar}, falsed I{Swiss E_LV95}
760 or I{y_LV03} easting (C{meter}).
761 @kwarg n: Falsed I{Swiss N_LV85} or I{x_LV03} northing for C{scalar} B{C{enh_}} and
762 B{C{h_}} (C{meter}).
763 @kwarg h_: I{Swiss h'} height for C{scalar} B{C{enh_}} and B{C{n}} (C{meter}).
764 @kwarg M: If C{True}, return the I{concatenated} rotation L{EcefMatrix} iff available
765 for C{ChLV} only, C{None} otherwise (C{bool}).
766 @kwarg name: Optional C{B{name}=NN} (C{str}).
768 @return: A L{ChLV9Tuple}C{(Y, X, h_, lat, lon, height, ltp, ecef, M)} with the unfalsed
769 I{Swiss Y, X} coordinates, I{Swiss h_} height, the given I{geodetic} C{lat},
770 C{lon} and C{height}, this C{ChLV*} instance and C{ecef} (L{Ecef9Tuple}) at
771 I{Bern, Ch} and rotation matrix C{M}. The returned C{ltp} is this C{ChLV},
772 C{ChLVa} or C{ChLVe} instance.
774 @raise LocalError: Invalid or non-C{scalar} B{C{enh_}}, B{C{n}} or B{C{h_}}.
775 '''
776 notOverloaded(self, enh_, n=n, h_=h_, M=M, **name)
778 @staticmethod
779 def _falsing2(LV95):
780 '''(INTERNAL) Get the C{LV95} or C{LV03} falsing.
781 '''
782 return _ChLV._95_falsing if LV95 in (True, 95) else (
783 _ChLV._03_falsing if LV95 in (False, 3) else ChLVYX2Tuple(0, 0))
785 @staticmethod
786 def _llh2abh_3(lat, lon, h):
787 '''(INTERNAL) Helper for C{ChLVa/e.forward}.
788 '''
789 def _deg2ab(deg, sLL):
790 # convert degrees to arc-seconds
791 def _dms(ds, p, q, swap):
792 d = _floor(ds)
793 t = (ds - d) * p
794 m = _floor(t)
795 s = (t - m) * p
796 if swap:
797 d, s = s, d
798 return d + (m + s * q) * q
800 s = _dms(deg, _60_0, _0_01, False) # deg2sexag
801 s = _dms( s, _100_0, _60_0, True) # sexag2asec
802 return (s - sLL) / ChLV._s_ab
804 a = _deg2ab(lat, ChLV._sLat) # phi', lat_aux
805 b = _deg2ab(lon, ChLV._sLon) # lam', lng_aux
806 h_ = fsumf_(h, -ChLV.Bern.height, 2.73 * b, 6.94 * a)
807 return a, b, h_
809 @staticmethod
810 def _YXh_2abh3(Y, X, h_):
811 '''(INTERNAL) Helper for C{ChLVa/e.reverse}.
812 '''
813 def _YX2ab(YX):
814 return YX * ChLV._ab_m
816 a, b = map1(_YX2ab, Y, X)
817 h = fsumf_(h_, ChLV.Bern.height, -12.6 * a, -22.64 * b)
818 return a, b, h
820 def _YXh_n4(self, enh_, n, h_, **name):
821 '''(INTERNAL) Helper for C{ChLV*.reverse}.
822 '''
823 Y, X, h_, name = _xyzn4(enh_, n, h_, ChLV9Tuple,
824 _xyz_y_z_names=self._enh_n_h, **name)
825 if isinstance(enh_, ChLV9Tuple):
826 Y, X = enh_.Y, enh_.X
827 else: # isscalar(enh_)
828 Y, X = ChLV.unfalse2(Y, X) # PYCHOK ChLVYX2Tuple
829 return Y, X, h_, name
832class ChLV(_ChLV, Ltp):
833 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates using
834 L{pygeodesy.EcefKarney}'s Earth-Centered, Earth-Fixed (ECEF) methods.
836 @see: U{Swiss projection formulas<https://www.SwissTopo.admin.CH/en/maps-data-online/
837 calculation-services.html>}, page 7ff, U{NAVREF<https://www.SwissTopo.admin.CH/en/
838 maps-data-online/calculation-services/navref.html>}, U{REFRAME<https://www.SwissTopo.admin.CH/
839 en/maps-data-online/calculation-services/reframe.html>} and U{SwissTopo Scripts GPS WGS84
840 <-> LV03<https://GitHub.com/ValentinMinder/Swisstopo-WGS84-LV03>}.
841 '''
842 _9Tuple = ChLV9Tuple
844 _ab_d = 0.36 # a, b units per degree, ...
845 _ab_m = 1.0e-6 # ... per meter and ...
846 _ab_M = _1_0 # ... per 1,000 Km or 1 Mm
847 _s_d = _3600_0 # arc-seconds per degree ...
848 _s_ab = _s_d / _ab_d # ... and per a, b unit
849 _sLat = 169028.66 # Bern, Ch in ...
850 _sLon = 26782.5 # ... arc-seconds ...
851 # lat, lon, height == 46°57'08.66", 7°26'22.50", 49.55m ("new" 46°57'07.89", 7°26'22.335")
852 Bern = LatLon4Tuple(_sLat / _s_d, _sLon / _s_d, 49.55, _WGS84, name='Bern')
854 def __init__(self, latlonh0=Bern, **other_Ltp_kwds):
855 '''New ECEF-based I{WGS84-Swiss} L{ChLV} converter, centered at I{Bern, Ch}.
857 @kwarg latlonh0: The I{geodetic} origin and height, overriding C{Bern, Ch}.
858 @kwarg other_Ltp_kwds: Optional, other L{Ltp.__init__} keyword arguments.
860 @see: L{Ltp.__init__} for more information.
861 '''
862 Ltp.__init__(self, latlonh0, **_xkwds(other_Ltp_kwds, ecef=None, name=ChLV.Bern.name))
864 def forward(self, latlonh, lon=None, height=0, M=None, **name): # PYCHOK unused M
865 # overloaded for the _ChLV.forward.__doc__
866 return Ltp.forward(self, latlonh, lon=lon, height=height, M=M, **name)
868 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature
869 # overloaded for the _ChLV.reverse.__doc__
870 Y, X, h_, n = self._YXh_n4(enh_, n, h_, **name)
871 return Ltp.reverse(self, Y, X, h_, M=M, name=n)
873 @staticmethod
874 def false2(Y, X, LV95=True, **name):
875 '''Add the I{Swiss LV95} or I{LV03} falsing.
877 @arg Y: Unfalsed I{Swiss Y} easting (C{meter}).
878 @arg X: Unfalsed I{Swiss X} northing (C{meter}).
879 @kwarg LV95: If C{True} add C{LV95} falsing, if C{False} add
880 C{LV03} falsing, otherwise leave unfalsed.
881 @kwarg name: Optional C{B{name}=NN} (C{str}).
883 @return: A L{ChLVEN2Tuple}C{(E_LV95, N_LV95)} or a
884 L{ChLVyx2Tuple}C{(y_LV03, x_LV03)} with falsed B{C{Y}}
885 and B{C{X}}, otherwise a L{ChLVYX2Tuple}C{(Y, X)}
886 with B{C{Y}} and B{C{X}} as-is.
887 '''
888 e, n = t = _ChLV._falsing2(LV95)
889 return t.classof(e + Y, n + X, **name)
891 @staticmethod
892 def isLV03(e, n):
893 '''Is C{(B{e}, B{n})} a valid I{Swiss LV03} projection?
895 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
896 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
898 @return: C{True} if C{(B{e}, B{n})} is a valid, falsed I{Swiss
899 LV03}, projection C{False} otherwise.
900 '''
901 # @see: U{Map<https://www.SwissTopo.admin.CH/en/knowledge-facts/
902 # surveying-geodesy/reference-frames/local/lv95.html>}
903 return 400.0e3 < e < 900.0e3 and 40.0e3 < n < 400.0e3
905 @staticmethod
906 def isLV95(e, n, raiser=True):
907 '''Is C{(B{e}, B{n})} a valid I{Swiss LV95} or I{LV03} projection?
909 @arg e: Falsed (or unfalsed) I{Swiss} easting (C{meter}).
910 @arg n: Falsed (or unfalsed) I{Swiss} northing (C{meter}).
911 @kwarg raiser: If C{True}, throw a L{LocalError} if B{C{e}} and
912 B{C{n}} are invalid I{Swiss LV95} nor I{LV03}.
914 @return: C{True} or C{False} if C{(B{e}, B{n})} is a valid I{Swiss
915 LV95} respectively I{LV03} projection, C{None} otherwise.
916 '''
917 if ChLV.isLV03(e, n):
918 return False
919 elif ChLV.isLV03(e - 2.0e6, n - 1.0e6): # _92_falsing = _95_ - _03_
920 return True
921 elif raiser: # PYCHOK no cover
922 raise LocalError(unstr(ChLV.isLV95, e=e, n=n))
923 return None
925 @staticmethod
926 def unfalse2(e, n, LV95=None, **name):
927 '''Remove the I{Swiss LV95} or I{LV03} falsing.
929 @arg e: Falsed I{Swiss E_LV95} or I{y_LV03} easting (C{meter}).
930 @arg n: Falsed I{Swiss N_LV95} or I{x_LV03} northing (C{meter}).
931 @kwarg LV95: If C{True} remove I{LV95} falsing, if C{False} remove
932 I{LV03} falsing, otherwise use method C{isLV95(B{e},
933 B{n})}.
934 @kwarg name: Optional C{B{name}=NN} (C{str}).
936 @return: A L{ChLVYX2Tuple}C{(Y, X)} with the unfalsed B{C{e}}
937 respectively B{C{n}}.
938 '''
939 Y, X = _ChLV._falsing2(ChLV.isLV95(e, n) if LV95 is None else LV95)
940 return ChLVYX2Tuple(e - Y, n - X, **name)
943class ChLVa(_ChLV, LocalCartesian):
944 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
945 using the U{Approximate<https://www.SwissTopo.admin.CH/en/maps-data-online/
946 calculation-services.html>} formulas, page 13.
948 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
949 '''
950 def __init__(self, name=ChLV.Bern.name):
951 '''New I{Approximate WGS84-Swiss} L{ChLVa} converter, centered at I{Bern, Ch}.
953 @kwarg name: Optional C{B{name}=Bern.name} (C{str}).
954 '''
955 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)
957 def forward(self, latlonh, lon=None, height=0, M=None, **name):
958 # overloaded for the _ChLV.forward.__doc__
959 lat, lon, h, n = _llhn4(latlonh, lon, height, **name)
960 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)
961 a2, b2 = a**2, b**2
963 Y = fsumf_( 72.37, 211455.93 * b,
964 -10938.51 * b * a,
965 -0.36 * b * a2,
966 -44.54 * b * b2) # + 600_000
967 X = fsumf_(147.07, 308807.95 * a,
968 3745.25 * b2,
969 76.63 * a2,
970 -194.56 * b2 * a,
971 119.79 * a2 * a) # + 200_000
972 return self._ChLV9Tuple(True, M, n, Y, X, h_, lat, lon, h)
974 def reverse(self, enh_, n=None, h_=0, M=None, **name): # PYCHOK signature
975 # overloaded for the _ChLV.reverse.__doc__
976 Y, X, h_, n = self._YXh_n4(enh_, n, h_, **name)
977 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)
978 ab_d, a2, b2 = ChLV._ab_d, a**2, b**2
980 lat = _Fsumf_(16.9023892, 3.238272 * b,
981 -0.270978 * a2,
982 -0.002528 * b2,
983 -0.0447 * a2 * b,
984 -0.014 * b2 * b).fover(ab_d)
985 lon = _Fsumf_( 2.6779094, 4.728982 * a,
986 0.791484 * a * b,
987 0.1306 * a * b2,
988 -0.0436 * a * a2).fover(ab_d)
989 return self._ChLV9Tuple(False, M, n, Y, X, h_, lat, lon, h)
992class ChLVe(_ChLV, LocalCartesian):
993 '''Conversion between I{WGS84 geodetic} and I{Swiss} projection coordinates
994 using the U{Ellipsoidal approximate<https://www.SwissTopo.admin.CH/en/
995 maps-data-online/calculation-services.html>} formulas, pp 10-11 and U{Bolliger,
996 J.<https://eMuseum.GGGS.CH/literatur-lv/liste-Dateien/1967_Bolliger_a.pdf>}
997 pp 148-151 (also U{GGGS<https://eMuseum.GGGS.CH/literatur-lv/liste.htm>}).
999 @note: Methods L{ChLVe.forward} and L{ChLVe.reverse} have an additional keyword
1000 argument C{B{gamma}=False} to approximate the I{meridian convergence}.
1001 If C{B{gamma}=True} a 2-tuple C{(t, gamma)} is returned with C{t} the
1002 usual result (C{ChLV9Tuple}) and C{gamma}, the I{meridian convergence}
1003 (decimal C{degrees}). To convert C{gamma} to C{grades} or C{gons},
1004 use function L{pygeodesy.degrees2grades}.
1006 @see: Older U{references<https://GitHub.com/alphasldiallo/Swisstopo-WGS84-LV03>}.
1007 '''
1008 def __init__(self, name=ChLV.Bern.name):
1009 '''New I{Approximate WGS84-Swiss} L{ChLVe} converter, centered at I{Bern, Ch}.
1011 @kwarg name: Optional C{B{name}=Bern.name} (C{str}).
1012 '''
1013 LocalCartesian.__init__(self, latlonh0=ChLV.Bern, name=name)
1015 def forward(self, latlonh, lon=None, height=0, M=None, gamma=False, **name): # PYCHOK gamma
1016 # overloaded for the _ChLV.forward.__doc__
1017 lat, lon, h, n = _llhn4(latlonh, lon, height, **name)
1018 a, b, h_ = _ChLV._llh2abh_3(lat, lon, h)
1019 ab_M, z, _H = ChLV._ab_M, 0, Fhorner
1021 B1 = _H(a, 211428.533991, -10939.608605, -2.658213, -8.539078, -0.00345, -0.007992)
1022 B3 = _H(a, -44.232717, 4.291740, -0.309883, 0.013924)
1023 B5 = _H(a, 0.019784, -0.004277)
1024 Y = _H(b, z, B1, z, B3, z, B5).fover(ab_M) # 1,000 Km!
1026 B0 = _H(a, z, 308770.746371, 75.028131, 120.435227, 0.009488, 0.070332, -0.00001)
1027 B2 = _H(a, 3745.408911, -193.792705, 4.340858, -0.376174, 0.004053)
1028 B4 = _H(a, -0.734684, 0.144466, -0.011842)
1029 B6 = 0.000488
1030 X = _H(b, B0, z, B2, z, B4, z, B6).fover(ab_M) # 1,000 Km!
1032 t = self._ChLV9Tuple(True, M, n, Y, X, h_, lat, lon, h)
1033 if gamma:
1034 U1 = _H(a, 2255515.207166, 2642.456961, 1.284180, 2.577486, 0.001165)
1035 U3 = _H(a, -412.991934, 64.106344, -2.679566, 0.123833)
1036 U5 = _H(a, 0.204129, -0.037725)
1037 g = _H(b, z, U1, z, U3, z, U5).fover(ChLV._ab_m) # * ChLV._ab_d degrees?
1038 t = t, g
1039 return t
1041 def reverse(self, enh_, n=None, h_=0, M=None, gamma=False, **name): # PYCHOK gamma
1042 # overloaded for the _ChLV.reverse.__doc__
1043 Y, X, h_, n = self._YXh_n4(enh_, n, h_, **name)
1044 a, b, h = _ChLV._YXh_2abh3(Y, X, h_)
1045 s_d, _H, z = ChLV._s_d, Fhorner, 0
1047 A0 = _H(b, ChLV._sLat, 32386.4877666, -25.486822, -132.457771, 0.48747, 0.81305, -0.0069)
1048 A2 = _H(b, -2713.537919, -450.442705, -75.53194, -14.63049, -2.7604)
1049 A4 = _H(b, 24.42786, 13.20703, 4.7476)
1050 A6 = -0.4249
1051 lat = _H(a, A0, z, A2, z, A4, z, A6).fover(s_d)
1053 A1 = _H(b, 47297.3056722, 7925.714783, 1328.129667, 255.02202, 48.17474, 9.0243)
1054 A3 = _H(b, -442.709889, -255.02202, -96.34947, -30.0808)
1055 A5 = _H(b, 9.63495, 9.0243)
1056 lon = _H(a, ChLV._sLon, A1, z, A3, z, A5).fover(s_d)
1057 # == (ChLV._sLon + a * (A1 + a**2 * (A3 + a**2 * A5))) / s_d
1059 t = self._ChLV9Tuple(False, M, n, Y, X, h_, lat, lon, h)
1060 if gamma:
1061 U1 = _H(b, 106679.792202, 17876.57022, 4306.5241, 794.87772, 148.1545, 27.8725)
1062 U3 = _H(b, -1435.508, -794.8777, -296.309, -92.908)
1063 U5 = _H(b, 29.631, 27.873)
1064 g = _H(a, z, U1, z, U3, z, U5).fover(ChLV._s_ab) # degrees
1065 t = t, g
1066 return t
1069def _fov_2(**fov):
1070 # Half a field-of-view angle in C{degrees}.
1071 f = Degrees(Error=LocalError, **fov) * _0_5
1072 if EPS < f < _90_0:
1073 return f
1074 t = _invalid_ if f < 0 else _too_(_wide_ if f > EPS else _narrow_)
1075 raise LocalError(txt=t, **fov)
1078def _toLocal(inst, ltp, Xyz, Xyz_kwds):
1079 '''(INTENRAL) Helper for C{CartesianBase.toLocal} and C{latLonBase.toLocal}.
1080 '''
1081 return _xLtp(ltp, inst._Ltp)._ecef2local(inst._ecef9, Xyz, Xyz_kwds)
1084def _toLtp(inst, Ecef, ecef9, name):
1085 '''(INTENRAL) Helper for C{CartesianBase.toLtp} and C{latLonBase.toLtp}.
1086 '''
1087 return inst._Ltp if Ecef in (None, inst.Ecef) and not name else \
1088 Ltp(ecef9, ecef=Ecef(inst.datum), name=inst._name__(name))
1091def tyr3d(tilt=INT0, yaw=INT0, roll=INT0, Vector=Vector3d, **name_Vector_kwds):
1092 '''Convert an attitude pose into a (3-D) direction vector.
1094 @kwarg tilt: Pitch, elevation from horizontal (C{degrees}), negative down
1095 (clockwise rotation along and around the x-axis).
1096 @kwarg yaw: Bearing, heading (compass C{degrees360}), clockwise from North
1097 (counter-clockwise rotation along and around the z-axis).
1098 @kwarg roll: Roll, bank (C{degrees}), positive to the right and down
1099 (clockwise rotation along and around the y-axis).
1100 @kwarg Vector: Class to return the direction vector (C{Cartesian},
1101 L{Vector3d} or C{Vector3Tuple}) or C{None}.
1102 @kwarg name_Vector_kwds: Optional C{B{name}=NN} (C{str}) and optional,
1103 additional B{C{Vector}} keyword arguments, ignored if
1104 C{B{Vector} is None}.
1106 @return: A named B{C{Vector}} instance or if C{B{Vector} is None},
1107 a named L{Vector3Tuple}C{(x, y, z)}.
1109 @raise AttitudeError: Invalid B{C{tilt}}, B{C{yaw}} or B{C{roll}}.
1111 @raise TypeError: Invalid B{C{Vector}} or B{C{name_Vector_kwds}}.
1113 @see: U{Yaw, pitch, and roll rotations<http://MSL.CS.UIUC.edu/planning/node102.html>}
1114 and function L{pygeodesy.hartzell} argument C{los}, Line-Of-Sight.
1115 '''
1116 v = Attitude4Tuple(_0_0, tilt, yaw, roll).tyr3d
1117 if Vector is not type(v):
1118 n, kwds = _name2__(name_Vector_kwds, name__=tyr3d)
1119 v = Vector3Tuple(v.x, v.y, v.z, name=n) if Vector is None else \
1120 Vector(v.x, v.y, v.z, name=n, **kwds)
1121 elif name_Vector_kwds:
1122 n, _ = _name2__(name_Vector_kwds)
1123 if n:
1124 v = v.copy(name=n)
1125 return v
1128def _xLtp(ltp, *dflt):
1129 '''(INTERNAL) Validate B{C{ltp}} or ist B{C{dflt}}.
1130 '''
1131 if dflt and ltp is None:
1132 ltp = dflt[0]
1133 _xinstanceof(Ltp, LocalCartesian, ltp=ltp)
1134 return ltp
1136# **) MIT License
1137#
1138# Copyright (C) 2016-2024 -- mrJean1 at Gmail -- All Rights Reserved.
1139#
1140# Permission is hereby granted, free of charge, to any person obtaining a
1141# copy of this software and associated documentation files (the "Software"),
1142# to deal in the Software without restriction, including without limitation
1143# the rights to use, copy, modify, merge, publish, distribute, sublicense,
1144# and/or sell copies of the Software, and to permit persons to whom the
1145# Software is furnished to do so, subject to the following conditions:
1146#
1147# The above copyright notice and this permission notice shall be included
1148# in all copies or substantial portions of the Software.
1149#
1150# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
1151# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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1154# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
1155# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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