Coverage for pyrdnap / rdnap2018.py: 93%
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2# -*- coding: utf-8 -*-
4u'''Main classes L{RDNAP2018v1} and L{RDNAP2018v2} follow C{variant 1} respectively C{variant 2} of
5the U{RDNAPTRANS(tm)2018_v220627<https://formulieren.kadaster.nl/aanvragen_rdnaptrans>} specification.
6Each provide a C{forward} method to convert geodetic lat-/longitudes and heights to C{RD} coodinates
7and C{NAP} heights and a C{reverse} method for converting the other way.
9The L{RDNAP2018v1.forward} and C{.reverse} results are within the C{RDNAPTRANS(tm)2018_v220627}
10self-validation requirements of C{0.000000010 degrees} respectively C{0.0010 meter} for points inside
11the C{RD} region, see B{C{Note below}}. Class L{RDNAP2018v2} does not.
13@note: L{RDNAP2018v1}, C{PyRDNAP} and C{pyrdnap} have B{not been formally validated} and are
14 B{not certified} to carry the trademark C{RDNAPTRANS(tm)}.
15'''
16# make sure int/int division yields float quotient, see .basics
17from __future__ import division as _; del _ # noqa: E702 ;
19from pyrdnap.rd0 import _RD, _RD0 as A0, RDNAP7Tuple
20from pyrdnap.v_grids import RDNAPError, _V_grid, _v_gridz_import
21from pyrdnap.__pygeodesy import (_0_0, _0_5, _1_0, _2_0,
22 _isNAN, _isNAN0, _earth_datum,
23 _ALL_DOCS, _ALL_OTHER, _FOR_DOCS,
24 _NamedBase, notOverloaded)
25from pygeodesy import (map1, EPS0, EPS1, NAN, PI_2, PI, PI2, # "consterns"
26 Datum, Datums, Ellipsoid, # datums, ellipsoids
27 property_RO, property_ROnce, # props
28 Lamd, Phid, # units
29 sincos2, sincos2d) # utily
31from math import asin, atan, copysign, degrees, exp, \
32 fabs, floor, hypot, radians, sin, sqrt
34__all__ = ()
35__version__ = '26.05.23'
37_TOL_D = 1e-9 # degrees 2.3.3f+
38_TOL_M = 1e-6 # meter
39_TOL_R = radians(_TOL_D) # 2e-11
40_TRIPS = 16 # 5..6 sufficient
43class _RDNAPbase(_NamedBase):
44 '''(INTERNAL) L{RDNAP2018v1}C{/-v2} base class.
45 '''
46 _datum = None # forward, v1 reverse Datum, lazily ("_DETRS")
47 _EETRS = None # forward, v1 reverse Ellipsoid, lazily
48 _raiser = False
50 def __init__(self, a_ellipsoid=None, f=None, raiser=False, **name):
51 '''New C{RDNAP2018v1} or C{-v2} instance.
53 @kwarg a_ellipsoid: An ellipsoid (L{Ellipsoid}) or the ellipsoid's equatorial
54 radius (C{scalar}, conventionally in C{meter}), see B{C{f}}
55 or a datum (L{Datum}). Default C{Datums.GRS80}.
56 @kwarg f: The flattening of the ellipsoid (C{scalar}) if B{C{a_ellipsoid}} is
57 specified as C{scalar}, ignored otherwise.
58 @kwarg raiser: If C{True} raise an L{RDNAPError} for lat-/longitudes outside
59 the C{RD} region (C{bool}).
60 @kwarg name: Optional name (C{str}).
62 @raise RDNAPError: Ellipsoid (or datum) is not oblate (i.e. is spherical or
63 prolate) or the datum's C{transform} is not C{unity}.
64 '''
65 if a_ellipsoid is f is None:
66 self._datum = Datums.GRS80
67 else:
68 _earth_datum(a_ellipsoid, f, **name) # sets self._datum
69 E = self._datum.ellipsoid
70 if not E.isOblate:
71 raise RDNAPError('not oblate: %r' % (E,))
72 self._EETRS = E
73 if raiser: # PYCHOK no cover
74 T = self._datum.transform
75 if not T.isunity:
76 raise RDNAPError('not unity: %r' % (T,))
77 self._raiser = True
78 if name:
79 self.name = name
81 def forward(self, lat, lon, height=0, raiser=None, name='forward'):
82 '''Convert GRS80 (ETRS98) geodetic C{(B{lat}, B{lon})} and B{C{height}}
83 to local C{(RDx, RDy)} coordinates and C{NAPh} quasi-geoid-height.
85 @arg lat: Latitude (C{degrees} geodetic).
86 @arg lon: Longitude (C{degrees} geodetic).
87 @kwarg height: Height, optional (C{meter} above geoid) or C{NAN}
88 to ignore C{NAPh} interpolation.
89 @kwarg raiser: If C{True} raise an L{RDNAPError} if B{C{lat}} or
90 B{C{lon}} is outside the C{RD} region (C{bool}),
91 if C{False} don't, overriding property C{raiser}.
92 @kwarg name: Optional name (C{str}).
94 @return: An L{RDNAP7Tuple}C{(RDx, RDy, NAPh, lat, lon, height, datum)}
95 with local C{RDx}, C{RDy} coordinates and C{NAPh} height.
96 '''
97 lat0, lon0 = \
98 lat_, lon_ = self._forwardXform(lat, lon, raiser)
99 for _ in range(_TRIPS): # 2.3.3a-f, 1..2
100 latc, lonc = self._rdlatlon2(lat_, lon_, lat0, lon0)
101 if fabs(latc - lat_) < _TOL_D and \
102 fabs(lonc - lon_) < _TOL_D:
103 break
104 lat_, lon_ = latc, lonc
106 phiClamC = _ellipsoidal2spherical(latc, lonc)
107 RDx, RDy = _spherical2oblique(*phiClamC)
108 NAPh = NAN if _isNAN(height) else (height - self.rdNAPh(lat, lon)) # 2.5.2
109 return RDNAP7Tuple(RDx, RDy, NAPh,
110 lat, lon, height, self.forwardDatum, name=name)
112 @property_RO
113 def forwardDatum(self):
114 '''Get the C{forward} datum (L{Datum}, default GRS80).
115 '''
116 return self._datum
118 def _inside2(self, lat, lon, raiser):
119 # default and variant 2: no datum Xform
120 if (raiser or (raiser is None and self._raiser)) and \
121 not _RD.isinside(lat, lon):
122 raise self._outsidError(lat, lon)
123 return lat, lon
125 _forwardXform = _inside2 # no datum Xform
127 def isinside(self, lat, lon, eps=0):
128 '''Is C{(B{lat}, B{lon})} inside the C{RD} region (C{bool})?
130 @kwarg eps: Over-/undersize the C{RD} region (C{degrees}).
131 '''
132 return _RD.isinside(lat, lon, eps)
134 def _outsidError(self, *lat_lon):
135 # format an RDNAPError for C{lat_lon} outside C{RD} region
136 return RDNAPError('%r outside %s' % (lat_lon, self.region))
138 @property_RO
139 def _rdgrid(self):
140 raise notOverloaded(self)
142 def _rdlatlon2(self, lat, lon, lat0=None, lon0=None): # 2.3.2
143 # return the RD-corrected C{(lat, lon)}
144 if _RD.isinside(lat, lon):
145 c_f_N_f6 = _RD._c_f_N_f6(lat, lon)
146 lat_corr = _bilinear(self._rdgrid._lat_corr, *c_f_N_f6)
147 lon_corr = _bilinear(self._rdgrid._lon_corr, *c_f_N_f6)
149 if lat0 is lon0 is None: # reverse
150 lat += lat_corr
151 lon += lon_corr
152 else: # forward
153 lat = lat0 - lat_corr
154 lon = lon0 - lon_corr
155 return lat, lon # NAN, NAN?
157 def rdNAPh(self, lat, lon, raiser=False): # 2.5.1 and 3.5
158 '''Interpolate the C{NAPh} quasi-geoid-height I{within} the C{RD} region.
160 @arg lat: Latitude (C{degrees} GRS80 (ETRS89), geodetic).
161 @arg lon: Longitude (C{degrees} GRS80 (ETRS89), geodetic).
162 @kwarg raiser: If C{True} raise an L{RDNAPError} if B{C{lat}} or
163 B{C{lon}} is outside the C{RD} region (C{bool}),
164 otherwise don't and return C{NAN}.
166 @return: C{NAPh} (C{meter}) or C{NAN} if C{B{raiser} is False} and
167 B{C{lat}} or B{C{lon}} is outside the C{RD} region.
168 '''
169 if _RD.isinside(lat, lon):
170 c_f_N_f6 = _RD._c_f_N_f6(lat, lon)
171 return _bilinear(self._rdgrid._NAP_h, *c_f_N_f6)
172 elif raiser:
173 raise self._outsidError(lat, lon)
174 return NAN # c0 2.5.1e+
176 @property_RO
177 def region(self):
178 '''Get the C{RD} region as L{Bounds4Tuple}C{(latS, lonW, latN, lonE)}, all C{GRS80 (ETRS89) degrees}.
179 '''
180 return _RD.region
182 def _reverse(self, RDx, RDy, NAPh, raiser=None, name='reverse'):
183 '''(INTERNAL) Convert local C{(B{RDx}, B{RDy})} coordinates and
184 B{C{NAPh}} quasi-geoid-height to GRS80 (ETRS89) or Bessel1841
185 (RD-Bessel) geodetic C{lat}, C{lon} and C{height}.
186 '''
187 philCamC = _oblique2spherical(RDx, RDy)
188 lat, lon = _spherical2ellipsoidal(*philCamC)
190 lat, lon = self._rdlatlon2(lat, lon)
191 lat, lon = self._reverseXform(lat, lon, raiser)
192 h = NAN if _isNAN(NAPh) else (NAPh + self.rdNAPh(lat, lon))
193 return RDNAP7Tuple(RDx, RDy, NAPh,
194 lat, lon, h, self.reverseDatum, name=name)
196 @property_RO
197 def reverseDatum(self):
198 '''Get the C{reverse} datum (L{Datum}), GRS80 or Bessel1841.
199 '''
200 return {1: self._datum,
201 2: A0.D0}.get(self.variant)
203 _reverseXform = _inside2 # no datum Xform
205 def toStr(self, prec=9, **unused): # PYCHOK signature
206 '''Return this C{RDNAP20181v1} or C{-v2} instance as a string.
208 @kwarg prec: Precision, number of decimal digits (0..9).
210 @return: This C{RDNAP2018v1} or C{-v2} (C{str}).
211 '''
212 return self.attrs('name', 'variant', 'forwardDatum', prec=prec) # _ellipsoid_, _name__
214 @property_RO
215 def variant(self):
216 raise None
219class RDNAP2018v1(_RDNAPbase):
220 '''Transformer implementing C{variant 1} of U{RD NAP 2018 v220627
221 <https://formulieren.kadaster.nl/aanvragen_rdnaptrans>}.
223 @note: Method L{RDNAP2018v1.reverse} returns B{GRS80 (ETRS89)}
224 geodetic lat- and longitudes.
226 @note: L{RDNAP2018v1} has B{not been formally validated} and is
227 B{not certified} to carry the trademark C{RDNAPTRANS(tm)}.
228 '''
229 if _FOR_DOCS:
230 __init__ = _RDNAPbase.__init__
231 forward = _RDNAPbase.forward
233 def _forwardXform(self, lat, lon, raiser):
234 # transform C{(lat, lon)} from GRS80 (ETRS89) to RD-Bessel datum
235 x, y, z = _geodetic2cartesian(lat, lon, self._EETRS, A0.H0_ETRS)
236 x, y, z = _RD._xETRS2RD.transform(x, y, z)
237 lat, lon = _cartesian2geodetic(x, y, z, A0.E0)
238 return self._inside2(lat, lon, raiser)
240 @property_ROnce
241 def _rdgrid(self):
242 try:
243 from pyrdnap import v1grid
244 except (AttributeError, ImportError, RDNAPError):
245 v1grid = _v_gridz_import(self.variant)
246 return v1grid
248 def reverse(self, RDx, RDy, NAPh=0, **raiser_name): # RDNAP to GRS80 (ETRS89)
249 '''Convert a local C{(B{RDx}, B{RDy})} point and B{C{NAPh}} height to
250 B{GRS80 (ETRS89)} geodetic C{(lat, lon, height)}.
252 @arg RDx: Local C{RD} X (C{meter}, conventionally).
253 @arg RDy: Local C{RD} Y (C{meter}, conventionally).
254 @kwarg NAPh: C{NAP} quasi-geoid-height (C{meter}, conventionally)
255 or C{NAN} to ignore C{NAPh} interpolation.
256 @kwarg raiser_name: Like the C{forward} method, C{B{raiser}=None}
257 (C{bool}) and optional C{B{name}='reverse'} (C{str}).
259 @return: An L{RDNAP7Tuple}C{(RDx, RDy, NAPh, lat, lon, height, datum)}
260 with geodetic C{lat} and C{lon}, C{height} and C{datum}
261 B{GRS80 (ETRS89)}.
262 '''
263 return self._reverse(RDx, RDy, NAPh, **raiser_name)
265 def _reverseXform(self, lat, lon, raiser):
266 # transform C{(lat, lon)} from RD-Bessel to GRS80 (ETRS89) datum
267 x, y, z = _geodetic2cartesian(lat, lon, A0.E0, A0.H0)
268 x, y, z = _RD._xRD2ETRS.transform(x, y, z)
269 lat, lon = _cartesian2geodetic(x, y, z, self._EETRS)
270 return self._inside2(lat, lon, raiser)
272 def similarity(self, inverse=False):
273 '''Get the similarity transform (C{Similarity}).
275 @kwarg inverse: Use C{True} for the C{reverse} or C{False}
276 for the C{forward} transform (C{bool}).
277 '''
278 return _RD._xRD2ETRS if inverse else _RD._xETRS2RD
280 @property_ROnce
281 def variant(self):
282 '''Get this C{RDNAP2018}'s variant (C{int}).
283 '''
284 return 1
287class RDNAP2018v2(_RDNAPbase):
288 '''Transformer implementing C{variant 2} of U{RD NAP 2018 v220627
289 <https://formulieren.kadaster.nl/aanvragen_rdnaptrans>}.
291 @note: Method L{RDNAP2018v2.reverse} returns B{Bessel1841 (RD-Bessel)}
292 and B{not GRS80 (ETRS89)} geodetic lat- and longitudes.
293 '''
294 if _FOR_DOCS:
295 __init__ = _RDNAPbase.__init__
296 forward = _RDNAPbase.forward
298 @property_ROnce
299 def _rdgrid(self):
300 try:
301 from pyrdnap import v2grid
302 except (AttributeError, ImportError, RDNAPError):
303 v2grid = _v_gridz_import(self.variant)
304 return v2grid
306 def reverse(self, RDx, RDy, NAPh=0, **raiser_name): # RDNAP to RD-Bessel
307 '''Convert a local C{(B{RDx}, B{RDy})} point and B{C{NAPh}} height
308 to B{Bessel1841 (RD-Bessel)} geodetic C{(lat, lon, height)}.
310 @arg RDx: Local C{RD} X (C{meter}, conventionally).
311 @arg RDy: Local C{RD} Y (C{meter}, conventionally).
312 @kwarg NAPh: C{NAP} quasi-geoid-height (C{meter}, conventionally)
313 or C{NAN} to ignore C{NAPh} interpolation.
314 @kwarg raiser_name: Like the C{forward} method, C{B{raiser}=None}
315 (C{bool}) and optional C{B{name}='reverse'} (C{str}).
317 @return: An L{RDNAP7Tuple}C{(RDx, RDy, NAPh, lat, lon, height, datum)}
318 with geodetic C{lat} and C{lon}, C{height} and C{datum}
319 B{Bessel1841 (RD-Bessel)}.
320 '''
321 return self._reverse(RDx, RDy, NAPh, **raiser_name)
323 def similarity(self, *unused): # PYCHOK signature
324 '''Get the similarity transform, always C{None}.
325 '''
326 return None
328 @property_ROnce
329 def variant(self):
330 '''Get this C{RDNAP2018}'s variant (C{int}).
331 '''
332 return 2
335def _atan3(y, x, x0): # 2.2.3e and 3.1.1i
336 # equiv to math.atan2 iff x0 is y
337 if x > 0:
338 r = atan(y / x)
339 elif x < 0:
340 r = atan(y / x) + copysign(PI, x0)
341 else:
342 r = copysign(PI_2, x0) if x0 else _0_0
343 return r
346def _atan_exp(w): # 2.4.1c
347 return atan(exp(w)) * _2_0 - PI_2
350def _bilinear(v_grid, c_latI, f_latI, latN_f, # 2.3.1f and g
351 c_lonI, f_lonI, lonN_f):
352 # interpolate a lat_corr_, lon_corr_ or NAP_...
353 assert isinstance(v_grid, _V_grid), v_grid
354 ne = v_grid(c_latI, c_lonI)
355 nw = v_grid(c_latI, f_lonI)
356 se = v_grid(f_latI, c_lonI)
357 sw = v_grid(f_latI, f_lonI)
358 lonN_f1 = _1_0 - lonN_f # == 1 - (lonN - f_lonN)
359 return (ne * lonN_f + nw * lonN_f1) * latN_f + \
360 (se * lonN_f + sw * lonN_f1) * (_1_0 - latN_f)
363def _cartesian2geodetic(x, y, z, E): # 2.2.3 == EcefUPC.reverse?
364 # convert cartesian C{(x, y, z)} to C{E}-geodetic C{(lat, lon)}
365 r = hypot(x, y)
366 if r > _TOL_M:
367 a = E.a * E.e2
368 phi_ = atan(z / r)
369 for _ in range(_TRIPS): # 4..6
370 s = sin(phi_)
371 s *= a / sqrt(_1_0 - s**2 * E.e2)
372 phi = atan((z + s) / r)
373 if fabs(phi - phi_) < _TOL_R:
374 break
375 phi_ = phi
376 else:
377 phi = copysign(PI_2, z)
378 lam = _atan3(y, x, y)
379 return degrees(phi), degrees(lam)
382def _ellipsoidal2spherical(lat, lon): # 2.4.1
383 # convert geodetic C{(lat, lon)} to spherical C{(𝛷, 𝛬)}
384 phiC = phi = Phid(lat)
385 if PI_2 > phi > -PI_2: # 2.4.1c
386 q = A0.log_tan(phi) - A0.log_e_2(phi)
387 w = A0.N0 * q + A0.M0 # 2.4.1b
388 phiC = _atan_exp(w)
389 lamC = (Lamd(lon) - A0.LAM0) * A0.N0 + A0.LAM0C # 2.4.1d
390 return phiC, lamC # -Capital
393def _eq0(r, r0=_0_0):
394 return fabs(r - r0) < _TOL_R
397# def _eq0d(d, d0=_0_0):
398# return fabs(d - d0) < _TOL_D
401def _geodetic2cartesian(lat, lon, E, h0=0): # 2.2.1
402 # convert C{E}-geodetic C{(lat, lon)} to cartesian C{(x, y, z)}
403 y, x = sincos2d(lon)
404 z, c = sincos2d(lat)
405 n = E.a / sqrt(_1_0 - z**2 * E.e2)
406 H = _isNAN0(h0)
407 c *= n + H
408 x *= c
409 y *= c
410 z *= n * (_1_0 - E.e2) + H
411 return x, y, z
414def _ne0(r, r0=_0_0):
415 return fabs(r - r0) > _TOL_R
418# def _ne0d(d, d0=_0_0):
419# return fabs(d - d0) > _TOL_D
422def _oblique2spherical(x, y): # 3.1.1
423 # inverse oblique stereographic conformal projection
424 # from C{RD (x, y)} to spherical C{(𝛷, 𝛬)}
425 x -= A0.X0
426 y -= A0.Y0
427 r = hypot(x, y)
428 if r > _TOL_M: # x and y
429 s0, c0 = A0.sincos2PHI0C
430 sp, cp = sincos2(atan(r / A0.RK2) * _2_0) # psi
431 ca = sp * y / r
432 xN = cp * c0 - ca * s0
433 yN = sp * x / r
434 zN = cp * s0 + ca * c0
435 phiC = asin(zN)
436 else:
437 _, xN = A0.sincos2PHI0C
438 yN = _0_0
439 phiC = A0.PHI0C # asin(sin(PHI0C))
440 lamC = _atan3(yN, xN, x) + A0.LAM0C
441 return phiC, lamC # -Capital
444def _spherical2ellipsoidal(phiC, lamC): # 3.1.2
445 # inverse Gauss conformal projection from
446 # spherical C{(𝛷, 𝛬)} to geodetic C{(lat, lon)}
447 phi = phiC
448 if PI_2 > phi > -PI_2:
449 q = (A0.log_tan(phi) - A0.M0) / A0.N0
450# w = A0.log_tan(phi)
451 for _ in range(_TRIPS): # 3..6
452 phi_ = phi
453 phi = _atan_exp(A0.log_e_2(phi) + q)
454 if fabs(phi - phi_) < _TOL_R:
455 break
456 lam = (lamC - A0.LAM0C) / A0.N0 + A0.LAM0
457 lam = floor((PI - lam) / PI2) * PI2 + lam
458 return map1(degrees, phi, lam)
461def _spherical2oblique(phiC, lamC): # 2.4.2
462 # oblique stereographic conformal projection
463 # from spherical C{(𝛷, 𝛬)} to C{RD (x, y)}
464 x = A0.X0 # 2.4.2g
465 y = A0.Y0 # 2.4.2h
466 a = phiC - A0.PHI0C # 𝛷 - 𝛷0
467 b = lamC - A0.LAM0C # 𝛬 - 𝛬0
468 if (_ne0(a) or _ne0(b)) and (_ne0(phiC, -A0.PHI0C) or
469 _ne0(lamC, -A0.LAM0C + PI)):
470 s0, c0 = A0.sincos2PHI0C # sin(𝛷0), cos(𝛷0)
471 s, c = sincos2(phiC) # sin(𝛷), cos(𝛷)
472 sp_22 = sin(a * _0_5)**2 + \
473 sin(b * _0_5)**2 * c * c0 # sin(𝜓/2)**2
474 if EPS0 < sp_22 < EPS1:
475 # r = 2kR * tan(𝜓/2)
476 # q = r / (sin(𝜓/2) * cos(𝜓/2) * 2)
477 # = 2kR * sin(𝜓/2) / (sin(𝜓/2) * cos(𝜓/2)**2 * 2)
478 # = 2kR / (cos(𝜓/2)**2 * 2)
479 # = 2kR / ((1 - sin(𝜓/2)**2) * 2)
480 # = 2kR / (2 - sin(𝜓/2)**2 * 2)
481 t = sp_22 * _2_0 # 0 < t < 2
482 q = A0.RK2 / (_2_0 - t)
483 x += q * (c * sin(b))
484 y += q * (s - s0 + s0 * t) / c0
485 elif _eq0(a) and _eq0(b):
486 pass
487 else: # if _eq0(phiC, -A0.PHI0C) and _eq0(lamC, A0.LAM0C - PI):
488 x = y = NAN
489# else:
490# raise RDNAPError(str((phiC, lamC)))
491 return x, y
494__all__ += _ALL_DOCS(_RDNAPbase)
495__all__ += _ALL_OTHER(RDNAP2018v1, RDNAP2018v2, RDNAPError,
496 Datum, Datums, Ellipsoid) # passed along from PyGeodesy
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
505# the rights to use, copy, modify, merge, publish, distribute, sublicense,
506# and/or sell copies of the Software, and to permit persons to whom the
507# Software is furnished to do so, subject to the following conditions:
508#
509# The above copyright notice and this permission notice shall be included
510# in all copies or substantial portions of the Software.
511#
512# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
513# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
514# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
515# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
516# OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
517# ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
518# OTHER DEALINGS IN THE SOFTWARE.