Coverage for pyrdnap / rd0.py: 99%
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« prev ^ index » next coverage.py v7.14.0, created at 2026-06-26 11:46 -0400
2# -*- coding: utf-8 -*-
4u'''(INTERNAL) RijksDriehoeksmeting C{_RD} and reference C{_RD0}
5constants and classes C{RDNAP7Tuple} and C{LqRD}.
6'''
7# make sure int/int division yields float quotient, see .basics
8from __future__ import division as _; del _ # noqa: E702 ;
10from pyrdnap.v_grids import _v_assert
11from pyrdnap.__pygeodesy import (_0_5, _1_0, _2_0, # PYCHOK used!
12 _isNAN, _isNAN0, _xinstanceof, _xsubclassof,
13 _LLEB, _xkwds,
14 _COMMASPACE_, _datum_, _lat_, _lon_, _height_,
15 _all_OTHER, _FOR_DOCS, _Pass, _NamedTuple)
16from pygeodesy import (map1, map2, NAN, NN, # basics, "consterns"
17 Datum, Datums, Similarity, # datums
18 Ellipsoid, Ellipsoids, LqRD as _LqRD, # ellipsoids, ltp
19 Bounds4Tuple, LatLon2Tuple, LatLon3Tuple, LatLon4Tuple, # namedTuples
20 PhiLam2Tuple, PhiLam3Tuple, PhiLam4Tuple, Vector2Tuple, Vector3Tuple,
21 Property_RO, property_ROnce, pairs, # props, streprs
22 Height, Lam, Lamd, Lat, Lon, Meter, Phi, Phid, # units
23 sincos2, tanPI_2_2) # utily
25from math import atan2, ceil, fabs, floor, log, sin, sqrt
27__all__ = ()
28__version__ = '26.06.18'
30_LQRD0 = _LqRD() # get Amersfoort, region4, etc. (deleted below)
33def _c_f_N_f3(*deg_SW_D):
34 # return int(ceil) and int(floor) of Normalized
35 # and (Normalized less floor) of C{deg} degrees
36 N = _degN(*deg_SW_D)
37 # assert N >= 0, N
38 f = floor(N)
39 return int(ceil(N)), int(f), (N - f)
42def _degN(deg, degSW, deg_D):
43 # return C{deg} Normalized
44 return (deg - degSW) * deg_D
47class _RDbase(object):
48 '''(INTERNAL) Base.
49 '''
50 def _preDict(self, _pred, **d):
51 # return updated dict C{d}
52 for n in self.__class__.__dict__.keys():
53 if _pred(n):
54 d[n] = getattr(self, n)
55 return d
57 def toStr(self, prec=9, **fmt_ints):
58 # return this C{_RDx} as string
59 d = self._toDict() # PYCHOK OK
60 t = pairs(d, prec=prec, **fmt_ints)
61 return _COMMASPACE_(*t)
64class _RD(_RDbase):
65 '''(INTERNAL) Bounds, constants for RDNAP2018 (ASCII.txt).
66 '''
67 lat_D = Lat(lat_D=80.0) # degrees, all
68 lon_D = Lon(lon_D=50.0)
70# latD = Lat(latD=1 / lat_D) # degrees, all
71# lonD = Lon(lonD=1 / lon_D)
73 def __init__(self):
74 S, W, N, E = self._region4RD
75 nlat = _degN(N, S, self.lat_D) + _1_0 # 2.3.2g n-phi
76 nlon = _degN(E, W, self.lon_D) + _1_0 # 2.3.2g n-lambda
77 _v_assert(map1(int, nlat, nlon))
79 def _c_f_N_f6(self, lat, lon):
80 # return (int(ceil), int(floor), Normalized less floor) of C{lat}) + \
81 # (int(ceil), int(floor), Normalized less floor) of C{lon})
82 S, W, _, _ = self._region4RD
83 return _c_f_N_f3(lat, S, self.lat_D) + \
84 _c_f_N_f3(lon, W, self.lon_D)
86 def isinside(self, lat, lon, asRD=True, eps=0): # eps=_TOL_D, 0 or -_TOLD_D
87 '''Is C{(lat, lon)} inside the C{RD} or C{ETRS} region, optionally
88 over-/undersized by positive respectively negative C{eps} degrees?
90 @return: C{True} if inside or on, otherwise C{False} (C{bool}).
91 '''
92 S, W, N, E = self._region4RD if asRD else self._region4ETRS
93 # XXX use "< N" and "< E" instead of "<="?
94 return ((S - lat) <= eps and (lat - N) <= eps and
95 (W - lon) <= eps and (lon - E) <= eps) if eps else \
96 (S <= lat <= N and W <= lon <= E)
98 @property_ROnce
99 def _RDNAPv0(self):
100 from pyrdnap.rdnap2018 import _RDNAPbase
101 return _RDNAPbase() # singleton, instance!
103 @property_ROnce
104 def _region4ETRS(self): # as ETRS L{Bounds4Tuple}
105 return self._RDNAPv0.region4(False)
107 _region4RD = _LQRD0.region4() # as RD-Bessel L{Bounds4Tuple}, in .rdnap2018
109 def _toDict(self):
110 def _p(n): # lambda
111 return n.endswith('D') or n.endswith('S')
113 return self._preDict(_p)
115 @property_ROnce
116 def _xETRS2RD(self): # transform ETRS (GRS80) to RD-Bessel
117 return Similarity(tx=-565.7346, ty=-50.4058, tz=-465.2895, s=-4.07242,
118 rx=-1.91513, ry=1.60365, rz=-9.09546, name='_xETRS2RD')
120 @property_ROnce
121 def _xRD2ETRS(self): # transform RD-Bessel to ETRS (GRS80)
122 return Similarity(tx=565.7381, ty=50.4018, tz=465.2904, s=4.07244,
123 rx=1.91514, ry=-1.60363, rz=9.09546, name='_xRD2ETRS')
125 # % python -c "import pyrdnap; print(pyrdnap.rd0._RD.toStr())"
126 # _region4ETRS=ETRS region (latS=49.999276, lonW=2.000032, latN=55.998561, lonE=7.999158),
127 # _region4RD=RD region (latS=50.0, lonW=2.0, latN=56.0, lonE=8.0),
128 # _xETRS2RD=Similarity(name='_xETRS2RD', tx=-565.73, ty=-50.406, tz=-465.29, s=-4.0724,
129 # rx=-1.9151, ry=1.6037, rz=-9.0955),
130 # _xRD2ETRS=Similarity(name='_xRD2ETRS', tx=565.74, ty=50.402, tz=465.29, s=4.0724,
131 # rx=1.9151, ry=-1.6036, rz=9.0955),
132 # lat_D=80.0, lon_D=50.0 # latD=0.0125, lonD=0.02
134_RD = _RD() # PYCHOK singleton, in .test/testRndTrips
137class _RD0(_RDbase):
138 '''(INTERNAL) C{RD} Amersfoort, NL / C{RD New} constants for RDNAP2018 (ASCII.txt).
140 @see: U{EPSG:9809<https://EPSG.io/9809-method>}, U{"Oblique Stereographic"
141 <https://PROJ.org/en/stable/operations/projections/sterea.html>} and
142 <http://geotiff.maptools.org/proj_list/oblique_stereographic.html>
143 '''
144 H0 = Meter(H0 =_LQRD0.height0) # Amersfoort.height0 0.0 m
145 H0_ETRS = Meter(H0_ETRS=_LQRD0.height0_ETRS) # 43.0 m
146 K0 = 0.9999079 # 2.4.1 scale factor
147 LAT0 = Lat(LAT0=_LQRD0.Amersfoort.lat) # '52 9 22.178N' == 52.156160555555+°
148 LON0 = Lon(LON0=_LQRD0.Amersfoort.lon) # ' 5 23 15.5E' == 5.387638888888+°
149 LAM0 = Lamd(LAM0=LON0) # 𝜆0, 0.094032038
150 LAM0C = Lam(LAM0C=LAM0) # 𝛬0 on sphere == 𝜆0
151 PHI0 = Phid(PHI0=LAT0) # 𝜑0 0.910296727, PHI0C 𝛷0 set below
152 X0 = Meter(X0=155000.0) # false Easting 155029.784?
153 Y0 = Meter(Y0=463000.0) # false Norting 463109.889?
155# @property_ROnce
156# def C0(self): # c, sphere
157# s, _ = self.sincos2PHI0
158# w = self._w1(s)
159# c = (w - _1_0) / (w + _1_0)
160# return (((self.N0 + s) * (_1_0 - c)) /
161# ((self.N0 - s) * (_1_0 + c)))
163# def chilam(self, lat, lon): # EPSG:9809
164# # return 2-tuple (chi, lam), conformal in radians
165# s, _ = sincos2d(lat)
166# w2 = self._w1(s) * self.C0
167# s = (w2 - _1_0) / (w2 + _1_0)
168# r = radians(lon - self.LON0) * self.N0
169# return asin(s), r
171 @property_ROnce
172 def D0(self): # lazily
173 return Datums.Bessel1841
175 @property_ROnce
176 def D80(self): # lazily
177 return Datums.GRS80
179 @property_ROnce
180 def E0(self): # lazily
181 return self.D0.ellipsoid
183 def log_e_2(self, phi):
184 e = self.E0.e
185 p = e * sin(phi)
186 return log((_1_0 + p) / (_1_0 - p)) * (e * _0_5)
188 def log_tan(self, phi):
189 return log(tanPI_2_2(phi)) # tan((phi + PI/2) / 2)
191 @property_ROnce
192 def M0(self): # 2.4.1 p 15 m
193 return self.W0 - self.N0 * self.Q0
195 @property_ROnce
196 def N0(self): # 2.4.1 p 15 n, sphere
197 E = self.E0
198 _, c = self.sincos2PHI0
199 return sqrt(c**4 * E.e2 / E.e21 + _1_0)
201 @property_ROnce
202 def PHI0C(self): # 2.4.1 p 15 𝛷0 on sphere
203 m, n = self.Rmn2
204 s, c = self.sincos2PHI0
205 return Phi(PHI0C=atan2(m * s, n * c)) # atan((m / n) * tan(PHI0))
207 @property_ROnce
208 def Q0(self): # 2.4.1 p 15 q0
209 return self.log_tan(self.PHI0) - self.log_e_2(self.PHI0)
211 @property_ROnce
212 def R(self): # 2.4.1 p 15 R, radius conformal sphere
213 m, n = self.Rmn2
214 return m * n
216 @property_ROnce
217 def RK2(self): # 2.4.2
218 return self.R * self.K0 * _2_0
220 @property_ROnce
221 def Rmn2(self): # 2.4.1 p 15 (sqrt(RsubM), sqrt(RsubN))
222 # RsubM, RsubN == RHO0, NU0 EPSG:9809
223 E = self.E0
224 s, _ = self.sincos2PHI0
225 s = _1_0 - s**2 * E.e2
226 # assert s > 0
227 N = E.a / sqrt(s)
228 # assert N > 0
229 M = E.e21 * N / s
230 # assert M > 0
231 return map1(sqrt, M, N) # sqrt!
233 @property_ROnce
234 def sincos2PHI0(self): # 𝜑0
235 return sincos2(self.PHI0)
237 @property_ROnce
238 def sincos2PHI0C(self): # 𝛷0
239 return sincos2(self.PHI0C)
241 def _toDict(self):
242 def _p(n): # lambda
243 return n.endswith('0') or n.startswith('R') or \
244 n.endswith('0C') # _0_
246 return self._preDict(_p, H0_ETRS=self.H0_ETRS)
248 @property_ROnce
249 def W0(self): # 2.4.1 p 15 w0
250 return self.log_tan(self.PHI0C) # 𝛷0
252# def _w1(self, sphi): # EPSG:9809
253# w1 = NAN
254# if _1_0 > sphi > _N_1_0:
255# e = self.E0.e
256# S = (_1_0 + sphi) / (_1_0 - sphi)
257# T = (_1_0 - sphi * e) / (_1_0 + sphi * e)
258# w1 = pow(pow(T, e) * S, self.N0)
259# return w1
261 # % python -c "import pyrdnap; print(pyrdnap.rd0._RD0.toStr())"
262 # D0=Datum(name='Bessel1841', ellipsoid=Ellipsoids.Bessel1841, transform=Transforms.Bessel1841),
263 # D80=Datum(name='GRS80', ellipsoid=Ellipsoids.GRS80, transform=Transforms.WGS84),
264 # E0=Ellipsoid(name='Bessel1841', a=6377397.155, f=0.00334277, f_=299.1528128, b=6356078.962818),
265 # H0=0.0, H0_ETRS=43.0, K0=0.9999079, LAM0=0.094032038, LAM0C=0.094032038,
266 # LAT0=52.156160556, LON0=5.387638889, M0=0.003773954, N0=1.000475857,
267 # PHI0=0.910296727, PHI0C=0.909684757, Q0=1.06531844,
268 # R=6382644.571035411, RK2=12764113.458940838, Rmn2=(2524.794785679199, 2527.9854850929623),
269 # sincos2PHI0=(0.7896858198001045, 0.6135114554811807),
270 # sincos2PHI0C=(0.7893102212553742, 0.6139946047171686),
271 # W0=1.069599332, X0=155000.0, Y0=463000.0
273_RD0 = _RD0() # PYCHOK singleton, in .test/testRndTrips
276class RDNAP7Tuple(_NamedTuple): # in .v_self
277 '''7-Tuple C{(RDx, RDy, NAPh, lat, lon, height, datum)} with I{local} C{RDx},
278 C{RDy} and C{NAPh} quasi-geoid_height, geodetic C{lat}, C{lon}, C{height}
279 and C{datum} with C{lat} and C{lon} in C{degrees} and with C{RDx}, C{RDy},
280 C{NAPh} and C{height} in C{meter}, conventionally.
282 @note: I{By default} C{lat}, C{lon} and C{datum} are B{GRS80 (ETRS89)} when
283 returned from L{RDNAP2018v1.reverse} but B{Bessel1841 (RD-Bessel)}
284 from L{RDNAP2018v2.reverse}.
285 '''
286 _Names_ = ('RDx', 'RDy', 'NAPh', _lat_, _lon_, _height_, _datum_)
287 _Units_ = ( Meter, Meter, Meter, Lat, Lon, Height, _Pass)
289 def diff(self, other, datum=None, **name):
290 '''Return the difference between this and an C{other} C{RDNAP7Tuple}.
292 @kwarg datum: Datum C{diff} (C{Datum}, None or NAN).
293 @kwarg name: Optional name (C{str}).
295 @return: An L{RDNAP7Tuple} with the C{fabs(diff)} for each item,
296 except C{datum} as B{C{datum}}.
297 '''
298 def _diff(a, b):
299 try:
300 return fabs(a - b)
301 except TypeError:
302 return datum
304 _xinstanceof(RDNAP7Tuple, other=other)
305 t = map2(_diff, self, other)
306 return RDNAP7Tuple(t, **name)
308 @Property_RO
309 def lam(self):
310 '''Get the longitude (B{C{radians}}).
311 '''
312 return Lamd(self.lon) # PYCHOK lon
314 @Property_RO
315 def latlon(self):
316 '''Get the lat-, longitude in C{degrees} (L{LatLon2Tuple}C{(lat, lon)}).
317 '''
318 return LatLon2Tuple(self.lat, self.lon, name=self.name)
320 @Property_RO
321 def latlonheight(self):
322 '''Get the lat-, longitude in C{degrees} and height (L{LatLon3Tuple}C{(lat, lon, height)}).
323 '''
324 return self.latlon.to3Tuple(self.height)
326 @Property_RO
327 def latlonheightdatum(self):
328 '''Get the lat-, longitude in C{degrees} with height and datum (L{LatLon4Tuple}C{(lat, lon, height, datum)}).
329 '''
330 return self.latlonheight.to4Tuple(self.datum)
332 @Property_RO
333 def phi(self):
334 '''Get the latitude (B{C{radians}}).
335 '''
336 return Phid(self.lat) # PYCHOK lat
338 @Property_RO
339 def philam(self):
340 '''Get the lat- and longitude in C{radians} (L{PhiLam2Tuple}C{(phi, lam)}).
341 '''
342 return PhiLam2Tuple(self.phi, self.lam, name=self.name) # PYCHOK lam, phi
344 @Property_RO
345 def philamheight(self):
346 '''Get the lat-, longitude in C{radians} and height (L{PhiLam3Tuple}C{(phi, lam, height)}).
347 '''
348 return self.philam.to3Tuple(self.height) # PYCHOK height
350 @Property_RO
351 def philamheightdatum(self):
352 '''Get the lat-, longitude in C{radians} with height and datum (L{PhiLamn4Tuple}C{(phi, lam, height, datum)}).
353 '''
354 return self.philamheight.to4Tuple(self.datum)
356 def toDatum(self, datum2, name=NN):
357 '''Convert this C{lat}, C{lon} and C{height} to B{C{datum2}}.
359 @arg datum2: Datum to convert I{to} (L{Datum}).
360 @kwarg name: Optional name (C{str}), overriding this name.
362 @return: An L{RDNAP7Tuple} with transformed C{lat}, C{lon} and C{height}
363 or this L{RDNAP7Tuple} if this.datum is B{C{datum2}}.
365 @note: This datum conversion is based on C{pygeodesy} which differs from
366 C{RDNAPTRANS(tm)2018_v220627}.
368 @see: Methods L{RDNAP7Tuple.asETRS} and L{RDNAP7Tuple.asRD}.
369 '''
370 _xinstanceof(Datum, datum2=datum2)
371 if self.datum is datum2 or self.datum == datum2: # PYCHOK datum
372 return self
373 g = self.toLatLon(_LLEB).toDatum(datum2)
374 h = NAN if _isNAN(self.height) else g.height # PYCHOK preserve height NAN
375 return self.dup(lat=g.lat, lon=g.lon, datum=g.datum, height=h,
376 name=name or self.name)
378 def toETRS(self, **name):
379 '''Copy this L{RDNAP7Tuple} with C{lat} and C{lon} C{reverse3} transformed
380 to ETRS89 (GRS80), provided this C{datum} is RD-Bessel (Bessel1841).
382 @kwarg name: Optional name (C{str}), overriding this name.
384 @see: Methods L{RDNAP7Tuple.toRD} and L{RDNAP7Tuple.toDatum}.
385 '''
386 return self._toX(_RD0.D0, _RD._RDNAPv0.reverse3, **name)
388 def toLatLon(self, LatLon, **LatLon_kwds):
389 '''Return this C{lat}, C{lon}, C{datum} and C{height} as B{C{LatLon}}.
391 @arg LatLon: An ellipsoidal C{LatLon} class (C{pygeodesy.ellipsoidal*}).
392 @kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword arguments.
394 @return: An B{C{LatLon}} instance.
396 @raise TypeError: B{C{LatLon}} not ellipsoidal or an other issue.
397 '''
398 _xsubclassof(_LLEB, LatLon=LatLon)
399 h = _isNAN0(self.height) # PYCHOK height
400 kwds = _xkwds(LatLon_kwds, name=self.name, height=h)
401 return LatLon(self.lat, self.lon, datum=self.datum, **kwds) # PYCHOK datum
403 def toRD(self, **name):
404 '''Copy this L{RDNAP7Tuple} with C{lat} and C{lon} C{forward3} transformed
405 to RD-Bessel (Bessel1841), provided this C{datum} is ETRS89 (GRS80).
407 @kwarg name: Optional name (C{str}), overriding this name.
409 @see: Methods L{RDNAP7Tuple.toETRS} and L{RDNAP7Tuple.toDatum}.
410 '''
411 return self._toX(_RD0.D80, _RD._RDNAPv0.forward3, **name)
413 def _toX(self, datum, _xform, name=NN):
414 # helper for C{toETRS} and C{toRD}
415 if self.datum is datum or self.datum == datum: # PYCHOK datum
416 lat, lon, d = _xform(*self.latlon)
417 return self.dup(lat=lat, lon=lon, datum=d, name=name or self.name)
418 return self
420 @Property_RO
421 def xy(self):
422 '''Get the I{local} C{(RDx, RDy)} coordinates (L{Vector2Tuple}C{(x, y)}).
423 '''
424 return Vector2Tuple(self.RDx, self.RDy, name=self.name)
426 @Property_RO
427 def xyz(self):
428 '''Get the I{local} C{(RDx, RDy, NAPh)} coordinates and height (L{Vector3Tuple}C{(x, y, z)}).
429 '''
430 return Vector3Tuple(self.RDx, self.RDy, self.NAPh, name=self.name)
433class LqRD(_LqRD):
434 '''Like U{pygeodesy.LqRD<https://mrJean1.GitHub.io/PyGeodesy/docs/pygeodesy.ltp.LqRD-class.html>}
435 but with methods C{forward} and C{reverse} returning an L{RDNAP7Tuple} with C{NAPh} replaced
436 by I{local} C{z}, the perpendicular distance to the local tangent plane (LTP).
438 This C{quasi-RD} transformer B{does not} implement any U{RD NAP<https://www.NSGI.NL/
439 coordinatenstelsels-en-transformaties/coordinatentransformaties/rdnap-etrs89-rdnaptrans>}
440 specification and B{does not} provide I{Netherlands}' C{B{N}ormaal B{A}msterdams B{P}eil
441 (NAP)} quasi-geodetic-height.
442 '''
443 if _FOR_DOCS:
444 __init__ = _LqRD.__init__
446 def forward(self, lat_latlonh, lon=None, height=0, **name): # PYCHOK signature
447 '''Convert I{geodetic} C{(lat, lon, height)} to I{local} C{quasi-RD (x, y, z)}.
449 @arg lat_latlonh: C{Scalar} (geodetic) latitude (C{degrees}) or a I{local}
450 C{quasi-RD} L{RDNAP7Tuple}.
451 @kwarg lon: C{Scalar} (geodetic) longitude (C{degrees}) iff B{C{lat_latlonh}}
452 is C{scalar}, ignored otherwise.
453 @kwarg height: Optional height (C{meter}, conventionally) perpendicular to and
454 above (or below) the ellipsoid's surface, iff B{C{lat_latlonh}}
455 is C{scalar}, ignored otherwise.
456 @kwarg name: Optional C{B{name}=NN} (C{str}).
458 @return: An L{RDNAP7Tuple}C{(RDx, RDy, NAPh, lat, lon, height, datum)} with
459 C{NAPh} set to I{local} C{z}.
461 @see: C{pygeodesy.LqRD.forward} for more information.
462 '''
463 t = _LqRD.forward(self, lat_latlonh, lon=lon, height=height)
464 return LqRD._l9t2r7t(t, **name)
466 def reverse(self, x_xyz, y=None, z=None, **name): # PYCHOK signature
467 '''Convert I{local} C{quasi-RD (x, y, z)} to I{geodetic} C{(lat, lon, height)}.
469 @arg x_xyz: Local C{quasi-RD x} coordinate (C{scalar}) or a I{local}
470 C{quasi-RD} L{RDNAP7Tuple}.
471 @kwarg y: Local C{quasi-RD y} coordinate (C{meter}) iff B{C{x_xyz}} is
472 C{scalar}, ignored otherwise.
473 @kwarg z: Local C{z} coordinate (C{meter}) iff B{C{x_xyz}} is C{scalar},
474 ignored otherwise.
475 @kwarg name: Optional C{B{name}=NN} (C{str}).
477 @return: An L{RDNAP7Tuple}C{(RDx, RDy, NAPh, lat, lon, height, datum)}
478 with C{NAPh} set to I{local} B{C{z}}.
480 @see: C{pygeodesy.LqRD.reverse} for more information.
481 '''
482 t = _LqRD.reverse(self, x_xyz, y=y, z=z)
483 return LqRD._l9t2r7t(t, **name)
485 @staticmethod
486 def _l9t2r7t(t, name=NN, **unused): # M=False
487 return RDNAP7Tuple(t.x, t.y, t.z, # NAPh = t.z
488 t.lat, t.lon, t.height, t.ecef.datum, name=name or t.name)
491__all__ += _all_OTHER(LqRD, RDNAP7Tuple, # passed along from PyGeodesy
492 Bounds4Tuple, Datum, Datums, Ellipsoid, Ellipsoids,
493 LatLon2Tuple, LatLon3Tuple, LatLon4Tuple,
494 PhiLam2Tuple, PhiLam3Tuple, PhiLam4Tuple,
495 Similarity, Vector2Tuple, Vector3Tuple)
496del _all_OTHER, _LQRD0
498# **) MIT License
499#
500# Copyright (C) 2026-2026 -- mrJean1 at Gmail -- All Rights Reserved.
501#
502# Permission is hereby granted, free of charge, to any person obtaining a
503# copy of this software and associated documentation files (the "Software"),
504# to deal in the Software without restriction, including without limitation
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