GeographicLib  2.1.1
LambertConformalConic.cpp
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1 /**
2  * \file LambertConformalConic.cpp
3  * \brief Implementation for GeographicLib::LambertConformalConic class
4  *
5  * Copyright (c) Charles Karney (2010-2022) <charles@karney.com> and licensed
6  * under the MIT/X11 License. For more information, see
7  * https://geographiclib.sourceforge.io/
8  **********************************************************************/
9 
11 
12 #if defined(_MSC_VER)
13 // Squelch warnings about enum-float expressions
14 # pragma warning (disable: 5055)
15 #endif
16 
17 namespace GeographicLib {
18 
19  using namespace std;
20 
22  real stdlat, real k0)
23  : eps_(numeric_limits<real>::epsilon())
24  , epsx_(Math::sq(eps_))
25  , ahypover_(Math::digits() * log(real(numeric_limits<real>::radix)) + 2)
26  , _a(a)
27  , _f(f)
28  , _fm(1 - _f)
29  , _e2(_f * (2 - _f))
30  , _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
31  {
32  if (!(isfinite(_a) && _a > 0))
33  throw GeographicErr("Equatorial radius is not positive");
34  if (!(isfinite(_f) && _f < 1))
35  throw GeographicErr("Polar semi-axis is not positive");
36  if (!(isfinite(k0) && k0 > 0))
37  throw GeographicErr("Scale is not positive");
38  if (!(fabs(stdlat) <= Math::qd))
39  throw GeographicErr("Standard latitude not in [-" + to_string(Math::qd)
40  + "d, " + to_string(Math::qd) + "d]");
41  real sphi, cphi;
42  Math::sincosd(stdlat, sphi, cphi);
43  Init(sphi, cphi, sphi, cphi, k0);
44  }
45 
47  real stdlat1, real stdlat2,
48  real k1)
49  : eps_(numeric_limits<real>::epsilon())
50  , epsx_(Math::sq(eps_))
51  , ahypover_(Math::digits() * log(real(numeric_limits<real>::radix)) + 2)
52  , _a(a)
53  , _f(f)
54  , _fm(1 - _f)
55  , _e2(_f * (2 - _f))
56  , _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
57  {
58  if (!(isfinite(_a) && _a > 0))
59  throw GeographicErr("Equatorial radius is not positive");
60  if (!(isfinite(_f) && _f < 1))
61  throw GeographicErr("Polar semi-axis is not positive");
62  if (!(isfinite(k1) && k1 > 0))
63  throw GeographicErr("Scale is not positive");
64  if (!(fabs(stdlat1) <= Math::qd))
65  throw GeographicErr("Standard latitude 1 not in [-"
66  + to_string(Math::qd) + "d, "
67  + to_string(Math::qd) + "d]");
68  if (!(fabs(stdlat2) <= Math::qd))
69  throw GeographicErr("Standard latitude 2 not in [-"
70  + to_string(Math::qd) + "d, "
71  + to_string(Math::qd) + "d]");
72  real sphi1, cphi1, sphi2, cphi2;
73  Math::sincosd(stdlat1, sphi1, cphi1);
74  Math::sincosd(stdlat2, sphi2, cphi2);
75  Init(sphi1, cphi1, sphi2, cphi2, k1);
76  }
77 
79  real sinlat1, real coslat1,
80  real sinlat2, real coslat2,
81  real k1)
82  : eps_(numeric_limits<real>::epsilon())
83  , epsx_(Math::sq(eps_))
84  , ahypover_(Math::digits() * log(real(numeric_limits<real>::radix)) + 2)
85  , _a(a)
86  , _f(f)
87  , _fm(1 - _f)
88  , _e2(_f * (2 - _f))
89  , _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
90  {
91  if (!(isfinite(_a) && _a > 0))
92  throw GeographicErr("Equatorial radius is not positive");
93  if (!(isfinite(_f) && _f < 1))
94  throw GeographicErr("Polar semi-axis is not positive");
95  if (!(isfinite(k1) && k1 > 0))
96  throw GeographicErr("Scale is not positive");
97  if (signbit(coslat1))
98  throw GeographicErr("Standard latitude 1 not in [-"
99  + to_string(Math::qd) + "d, "
100  + to_string(Math::qd) + "d]");
101  if (signbit(coslat2))
102  throw GeographicErr("Standard latitude 2 not in [-"
103  + to_string(Math::qd) + "d, "
104  + to_string(Math::qd) + "d]");
105  if (!(fabs(sinlat1) <= 1 && coslat1 <= 1) || (coslat1 == 0 && sinlat1 == 0))
106  throw GeographicErr("Bad sine/cosine of standard latitude 1");
107  if (!(fabs(sinlat2) <= 1 && coslat2 <= 1) || (coslat2 == 0 && sinlat2 == 0))
108  throw GeographicErr("Bad sine/cosine of standard latitude 2");
109  if (coslat1 == 0 || coslat2 == 0)
110  if (!(coslat1 == coslat2 && sinlat1 == sinlat2))
111  throw GeographicErr
112  ("Standard latitudes must be equal is either is a pole");
113  Init(sinlat1, coslat1, sinlat2, coslat2, k1);
114  }
115 
116  void LambertConformalConic::Init(real sphi1, real cphi1,
117  real sphi2, real cphi2, real k1) {
118  {
119  real r;
120  r = hypot(sphi1, cphi1);
121  sphi1 /= r; cphi1 /= r;
122  r = hypot(sphi2, cphi2);
123  sphi2 /= r; cphi2 /= r;
124  }
125  bool polar = (cphi1 == 0);
126  cphi1 = fmax(epsx_, cphi1); // Avoid singularities at poles
127  cphi2 = fmax(epsx_, cphi2);
128  // Determine hemisphere of tangent latitude
129  _sign = sphi1 + sphi2 >= 0 ? 1 : -1;
130  // Internally work with tangent latitude positive
131  sphi1 *= _sign; sphi2 *= _sign;
132  if (sphi1 > sphi2) {
133  swap(sphi1, sphi2); swap(cphi1, cphi2); // Make phi1 < phi2
134  }
135  real
136  tphi1 = sphi1/cphi1, tphi2 = sphi2/cphi2, tphi0;
137  //
138  // Snyder: 15-8: n = (log(m1) - log(m2))/(log(t1)-log(t2))
139  //
140  // m = cos(bet) = 1/sec(bet) = 1/sqrt(1+tan(bet)^2)
141  // bet = parametric lat, tan(bet) = (1-f)*tan(phi)
142  //
143  // t = tan(pi/4-chi/2) = 1/(sec(chi) + tan(chi)) = sec(chi) - tan(chi)
144  // log(t) = -asinh(tan(chi)) = -psi
145  // chi = conformal lat
146  // tan(chi) = tan(phi)*cosh(xi) - sinh(xi)*sec(phi)
147  // xi = eatanhe(sin(phi)), eatanhe(x) = e * atanh(e*x)
148  //
149  // n = (log(sec(bet2))-log(sec(bet1)))/(asinh(tan(chi2))-asinh(tan(chi1)))
150  //
151  // Let log(sec(bet)) = b(tphi), asinh(tan(chi)) = c(tphi)
152  // Then n = Db(tphi2, tphi1)/Dc(tphi2, tphi1)
153  // In limit tphi2 -> tphi1, n -> sphi1
154  //
155  real
156  tbet1 = _fm * tphi1, scbet1 = hyp(tbet1),
157  tbet2 = _fm * tphi2, scbet2 = hyp(tbet2);
158  real
159  scphi1 = 1/cphi1,
160  xi1 = Math::eatanhe(sphi1, _es), shxi1 = sinh(xi1), chxi1 = hyp(shxi1),
161  tchi1 = chxi1 * tphi1 - shxi1 * scphi1, scchi1 = hyp(tchi1),
162  scphi2 = 1/cphi2,
163  xi2 = Math::eatanhe(sphi2, _es), shxi2 = sinh(xi2), chxi2 = hyp(shxi2),
164  tchi2 = chxi2 * tphi2 - shxi2 * scphi2, scchi2 = hyp(tchi2),
165  psi1 = asinh(tchi1);
166  if (tphi2 - tphi1 != 0) {
167  // Db(tphi2, tphi1)
168  real num = Dlog1p(Math::sq(tbet2)/(1 + scbet2),
169  Math::sq(tbet1)/(1 + scbet1))
170  * Dhyp(tbet2, tbet1, scbet2, scbet1) * _fm;
171  // Dc(tphi2, tphi1)
172  real den = Dasinh(tphi2, tphi1, scphi2, scphi1)
173  - Deatanhe(sphi2, sphi1) * Dsn(tphi2, tphi1, sphi2, sphi1);
174  _n = num/den;
175 
176  if (_n < 1/real(4))
177  _nc = sqrt((1 - _n) * (1 + _n));
178  else {
179  // Compute nc = cos(phi0) = sqrt((1 - n) * (1 + n)), evaluating 1 - n
180  // carefully. First write
181  //
182  // Dc(tphi2, tphi1) * (tphi2 - tphi1)
183  // = log(tchi2 + scchi2) - log(tchi1 + scchi1)
184  //
185  // then den * (1 - n) =
186  // (log((tchi2 + scchi2)/(2*scbet2)) -
187  // log((tchi1 + scchi1)/(2*scbet1))) / (tphi2 - tphi1)
188  // = Dlog1p(a2, a1) * (tchi2+scchi2 + tchi1+scchi1)/(4*scbet1*scbet2)
189  // * fm * Q
190  //
191  // where
192  // a1 = ( (tchi1 - scbet1) + (scchi1 - scbet1) ) / (2 * scbet1)
193  // Q = ((scbet2 + scbet1)/fm)/((scchi2 + scchi1)/D(tchi2, tchi1))
194  // - (tbet2 + tbet1)/(scbet2 + scbet1)
195  real t;
196  {
197  real
198  // s1 = (scbet1 - scchi1) * (scbet1 + scchi1)
199  s1 = (tphi1 * (2 * shxi1 * chxi1 * scphi1 - _e2 * tphi1) -
200  Math::sq(shxi1) * (1 + 2 * Math::sq(tphi1))),
201  s2 = (tphi2 * (2 * shxi2 * chxi2 * scphi2 - _e2 * tphi2) -
202  Math::sq(shxi2) * (1 + 2 * Math::sq(tphi2))),
203  // t1 = scbet1 - tchi1
204  t1 = tchi1 < 0 ? scbet1 - tchi1 : (s1 + 1)/(scbet1 + tchi1),
205  t2 = tchi2 < 0 ? scbet2 - tchi2 : (s2 + 1)/(scbet2 + tchi2),
206  a2 = -(s2 / (scbet2 + scchi2) + t2) / (2 * scbet2),
207  a1 = -(s1 / (scbet1 + scchi1) + t1) / (2 * scbet1);
208  t = Dlog1p(a2, a1) / den;
209  }
210  // multiply by (tchi2 + scchi2 + tchi1 + scchi1)/(4*scbet1*scbet2) * fm
211  t *= ( ( (tchi2 >= 0 ? scchi2 + tchi2 : 1/(scchi2 - tchi2)) +
212  (tchi1 >= 0 ? scchi1 + tchi1 : 1/(scchi1 - tchi1)) ) /
213  (4 * scbet1 * scbet2) ) * _fm;
214 
215  // Rewrite
216  // Q = (1 - (tbet2 + tbet1)/(scbet2 + scbet1)) -
217  // (1 - ((scbet2 + scbet1)/fm)/((scchi2 + scchi1)/D(tchi2, tchi1)))
218  // = tbm - tam
219  // where
220  real tbm = ( ((tbet1 > 0 ? 1/(scbet1+tbet1) : scbet1 - tbet1) +
221  (tbet2 > 0 ? 1/(scbet2+tbet2) : scbet2 - tbet2)) /
222  (scbet1+scbet2) );
223 
224  // tam = (1 - ((scbet2+scbet1)/fm)/((scchi2+scchi1)/D(tchi2, tchi1)))
225  //
226  // Let
227  // (scbet2 + scbet1)/fm = scphi2 + scphi1 + dbet
228  // (scchi2 + scchi1)/D(tchi2, tchi1) = scphi2 + scphi1 + dchi
229  // then
230  // tam = D(tchi2, tchi1) * (dchi - dbet) / (scchi1 + scchi2)
231  real
232  // D(tchi2, tchi1)
233  dtchi = den / Dasinh(tchi2, tchi1, scchi2, scchi1),
234  // (scbet2 + scbet1)/fm - (scphi2 + scphi1)
235  dbet = (_e2/_fm) * ( 1 / (scbet2 + _fm * scphi2) +
236  1 / (scbet1 + _fm * scphi1) );
237 
238  // dchi = (scchi2 + scchi1)/D(tchi2, tchi1) - (scphi2 + scphi1)
239  // Let
240  // tzet = chxiZ * tphi - shxiZ * scphi
241  // tchi = tzet + nu
242  // scchi = sczet + mu
243  // where
244  // xiZ = eatanhe(1), shxiZ = sinh(xiZ), chxiZ = cosh(xiZ)
245  // nu = scphi * (shxiZ - shxi) - tphi * (chxiZ - chxi)
246  // mu = - scphi * (chxiZ - chxi) + tphi * (shxiZ - shxi)
247  // then
248  // dchi = ((mu2 + mu1) - D(nu2, nu1) * (scphi2 + scphi1)) /
249  // D(tchi2, tchi1)
250  real
251  xiZ = Math::eatanhe(real(1), _es),
252  shxiZ = sinh(xiZ), chxiZ = hyp(shxiZ),
253  // These are differences not divided differences
254  // dxiZ1 = xiZ - xi1; dshxiZ1 = shxiZ - shxi; dchxiZ1 = chxiZ - chxi
255  dxiZ1 = Deatanhe(real(1), sphi1)/(scphi1*(tphi1+scphi1)),
256  dxiZ2 = Deatanhe(real(1), sphi2)/(scphi2*(tphi2+scphi2)),
257  dshxiZ1 = Dsinh(xiZ, xi1, shxiZ, shxi1, chxiZ, chxi1) * dxiZ1,
258  dshxiZ2 = Dsinh(xiZ, xi2, shxiZ, shxi2, chxiZ, chxi2) * dxiZ2,
259  dchxiZ1 = Dhyp(shxiZ, shxi1, chxiZ, chxi1) * dshxiZ1,
260  dchxiZ2 = Dhyp(shxiZ, shxi2, chxiZ, chxi2) * dshxiZ2,
261  // mu1 + mu2
262  amu12 = (- scphi1 * dchxiZ1 + tphi1 * dshxiZ1
263  - scphi2 * dchxiZ2 + tphi2 * dshxiZ2),
264  // D(xi2, xi1)
265  dxi = Deatanhe(sphi1, sphi2) * Dsn(tphi2, tphi1, sphi2, sphi1),
266  // D(nu2, nu1)
267  dnu12 =
268  ( (_f * 4 * scphi2 * dshxiZ2 > _f * scphi1 * dshxiZ1 ?
269  // Use divided differences
270  (dshxiZ1 + dshxiZ2)/2 * Dhyp(tphi1, tphi2, scphi1, scphi2)
271  - ( (scphi1 + scphi2)/2
272  * Dsinh(xi1, xi2, shxi1, shxi2, chxi1, chxi2) * dxi ) :
273  // Use ratio of differences
274  (scphi2 * dshxiZ2 - scphi1 * dshxiZ1)/(tphi2 - tphi1))
275  + ( (tphi1 + tphi2)/2 * Dhyp(shxi1, shxi2, chxi1, chxi2)
276  * Dsinh(xi1, xi2, shxi1, shxi2, chxi1, chxi2) * dxi )
277  - (dchxiZ1 + dchxiZ2)/2 ),
278  // dtchi * dchi
279  dchia = (amu12 - dnu12 * (scphi2 + scphi1)),
280  tam = (dchia - dtchi * dbet) / (scchi1 + scchi2);
281  t *= tbm - tam;
282  _nc = sqrt(fmax(real(0), t) * (1 + _n));
283  }
284  {
285  real r = hypot(_n, _nc);
286  _n /= r;
287  _nc /= r;
288  }
289  tphi0 = _n / _nc;
290  } else {
291  tphi0 = tphi1;
292  _nc = 1/hyp(tphi0);
293  _n = tphi0 * _nc;
294  if (polar)
295  _nc = 0;
296  }
297 
298  _scbet0 = hyp(_fm * tphi0);
299  real shxi0 = sinh(Math::eatanhe(_n, _es));
300  _tchi0 = tphi0 * hyp(shxi0) - shxi0 * hyp(tphi0); _scchi0 = hyp(_tchi0);
301  _psi0 = asinh(_tchi0);
302 
303  _lat0 = atan(_sign * tphi0) / Math::degree();
304  _t0nm1 = expm1(- _n * _psi0); // Snyder's t0^n - 1
305  // a * k1 * m1/t1^n = a * k1 * m2/t2^n = a * k1 * n * (Snyder's F)
306  // = a * k1 / (scbet1 * exp(-n * psi1))
307  _scale = _a * k1 / scbet1 *
308  // exp(n * psi1) = exp(- (1 - n) * psi1) * exp(psi1)
309  // with (1-n) = nc^2/(1+n) and exp(-psi1) = scchi1 + tchi1
310  exp( - (Math::sq(_nc)/(1 + _n)) * psi1 )
311  * (tchi1 >= 0 ? scchi1 + tchi1 : 1 / (scchi1 - tchi1));
312  // Scale at phi0 = k0 = k1 * (scbet0*exp(-n*psi0))/(scbet1*exp(-n*psi1))
313  // = k1 * scbet0/scbet1 * exp(n * (psi1 - psi0))
314  // psi1 - psi0 = Dasinh(tchi1, tchi0) * (tchi1 - tchi0)
315  _k0 = k1 * (_scbet0/scbet1) *
316  exp( - (Math::sq(_nc)/(1 + _n)) *
317  Dasinh(tchi1, _tchi0, scchi1, _scchi0) * (tchi1 - _tchi0))
318  * (tchi1 >= 0 ? scchi1 + tchi1 : 1 / (scchi1 - tchi1)) /
319  (_scchi0 + _tchi0);
320  _nrho0 = polar ? 0 : _a * _k0 / _scbet0;
321  {
322  // Figure _drhomax using code at beginning of Forward with lat = -90
323  real
324  sphi = -1, cphi = epsx_,
325  tphi = sphi/cphi,
326  scphi = 1/cphi, shxi = sinh(Math::eatanhe(sphi, _es)),
327  tchi = hyp(shxi) * tphi - shxi * scphi, scchi = hyp(tchi),
328  psi = asinh(tchi),
329  dpsi = Dasinh(tchi, _tchi0, scchi, _scchi0) * (tchi - _tchi0);
330  _drhomax = - _scale * (2 * _nc < 1 && dpsi != 0 ?
331  (exp(Math::sq(_nc)/(1 + _n) * psi ) *
332  (tchi > 0 ? 1/(scchi + tchi) : (scchi - tchi))
333  - (_t0nm1 + 1))/(-_n) :
334  Dexp(-_n * psi, -_n * _psi0) * dpsi);
335  }
336  }
337 
339  static const LambertConformalConic mercator(Constants::WGS84_a(),
341  real(0), real(1));
342  return mercator;
343  }
344 
345  void LambertConformalConic::Forward(real lon0, real lat, real lon,
346  real& x, real& y,
347  real& gamma, real& k) const {
348  lon = Math::AngDiff(lon0, lon);
349  // From Snyder, we have
350  //
351  // theta = n * lambda
352  // x = rho * sin(theta)
353  // = (nrho0 + n * drho) * sin(theta)/n
354  // y = rho0 - rho * cos(theta)
355  // = nrho0 * (1-cos(theta))/n - drho * cos(theta)
356  //
357  // where nrho0 = n * rho0, drho = rho - rho0
358  // and drho is evaluated with divided differences
359  real sphi, cphi;
360  Math::sincosd(Math::LatFix(lat) * _sign, sphi, cphi);
361  cphi = fmax(epsx_, cphi);
362  real
363  lam = lon * Math::degree(),
364  tphi = sphi/cphi, scbet = hyp(_fm * tphi),
365  scphi = 1/cphi, shxi = sinh(Math::eatanhe(sphi, _es)),
366  tchi = hyp(shxi) * tphi - shxi * scphi, scchi = hyp(tchi),
367  psi = asinh(tchi),
368  theta = _n * lam, stheta = sin(theta), ctheta = cos(theta),
369  dpsi = Dasinh(tchi, _tchi0, scchi, _scchi0) * (tchi - _tchi0),
370  drho = - _scale * (2 * _nc < 1 && dpsi != 0 ?
371  (exp(Math::sq(_nc)/(1 + _n) * psi ) *
372  (tchi > 0 ? 1/(scchi + tchi) : (scchi - tchi))
373  - (_t0nm1 + 1))/(-_n) :
374  Dexp(-_n * psi, -_n * _psi0) * dpsi);
375  x = (_nrho0 + _n * drho) * (_n != 0 ? stheta / _n : lam);
376  y = _nrho0 *
377  (_n != 0 ?
378  (ctheta < 0 ? 1 - ctheta : Math::sq(stheta)/(1 + ctheta)) / _n : 0)
379  - drho * ctheta;
380  k = _k0 * (scbet/_scbet0) /
381  (exp( - (Math::sq(_nc)/(1 + _n)) * dpsi )
382  * (tchi >= 0 ? scchi + tchi : 1 / (scchi - tchi)) / (_scchi0 + _tchi0));
383  y *= _sign;
384  gamma = _sign * theta / Math::degree();
385  }
386 
387  void LambertConformalConic::Reverse(real lon0, real x, real y,
388  real& lat, real& lon,
389  real& gamma, real& k) const {
390  // From Snyder, we have
391  //
392  // x = rho * sin(theta)
393  // rho0 - y = rho * cos(theta)
394  //
395  // rho = hypot(x, rho0 - y)
396  // drho = (n*x^2 - 2*y*nrho0 + n*y^2)/(hypot(n*x, nrho0-n*y) + nrho0)
397  // theta = atan2(n*x, nrho0-n*y)
398  //
399  // From drho, obtain t^n-1
400  // psi = -log(t), so
401  // dpsi = - Dlog1p(t^n-1, t0^n-1) * drho / scale
402  y *= _sign;
403  real
404  // Guard against 0 * inf in computation of ny
405  nx = _n * x, ny = _n != 0 ? _n * y : 0, y1 = _nrho0 - ny,
406  den = hypot(nx, y1) + _nrho0, // 0 implies origin with polar aspect
407  // isfinite test is to avoid inf/inf
408  drho = ((den != 0 && isfinite(den))
409  ? (x*nx + y * (ny - 2*_nrho0)) / den
410  : den);
411  drho = fmin(drho, _drhomax);
412  if (_n == 0)
413  drho = fmax(drho, -_drhomax);
414  real
415  tnm1 = _t0nm1 + _n * drho/_scale,
416  dpsi = (den == 0 ? 0 :
417  (tnm1 + 1 != 0 ? - Dlog1p(tnm1, _t0nm1) * drho / _scale :
418  ahypover_));
419  real tchi;
420  if (2 * _n <= 1) {
421  // tchi = sinh(psi)
422  real
423  psi = _psi0 + dpsi, tchia = sinh(psi), scchi = hyp(tchia),
424  dtchi = Dsinh(psi, _psi0, tchia, _tchi0, scchi, _scchi0) * dpsi;
425  tchi = _tchi0 + dtchi; // Update tchi using divided difference
426  } else {
427  // tchi = sinh(-1/n * log(tn))
428  // = sinh((1-1/n) * log(tn) - log(tn))
429  // = + sinh((1-1/n) * log(tn)) * cosh(log(tn))
430  // - cosh((1-1/n) * log(tn)) * sinh(log(tn))
431  // (1-1/n) = - nc^2/(n*(1+n))
432  // cosh(log(tn)) = (tn + 1/tn)/2; sinh(log(tn)) = (tn - 1/tn)/2
433  real
434  tn = tnm1 + 1 == 0 ? epsx_ : tnm1 + 1,
435  sh = sinh( -Math::sq(_nc)/(_n * (1 + _n)) *
436  (2 * tn > 1 ? log1p(tnm1) : log(tn)) );
437  tchi = sh * (tn + 1/tn)/2 - hyp(sh) * (tnm1 * (tn + 1)/tn)/2;
438  }
439 
440  // log(t) = -asinh(tan(chi)) = -psi
441  gamma = atan2(nx, y1);
442  real
443  tphi = Math::tauf(tchi, _es),
444  scbet = hyp(_fm * tphi), scchi = hyp(tchi),
445  lam = _n != 0 ? gamma / _n : x / y1;
446  lat = Math::atand(_sign * tphi);
447  lon = lam / Math::degree();
448  lon = Math::AngNormalize(lon + Math::AngNormalize(lon0));
449  k = _k0 * (scbet/_scbet0) /
450  (exp(_nc != 0 ? - (Math::sq(_nc)/(1 + _n)) * dpsi : 0)
451  * (tchi >= 0 ? scchi + tchi : 1 / (scchi - tchi)) / (_scchi0 + _tchi0));
452  gamma /= _sign * Math::degree();
453  }
454 
455  void LambertConformalConic::SetScale(real lat, real k) {
456  if (!(isfinite(k) && k > 0))
457  throw GeographicErr("Scale is not positive");
458  if (!(fabs(lat) <= Math::qd))
459  throw GeographicErr("Latitude for SetScale not in [-"
460  + to_string(Math::qd) + "d, "
461  + to_string(Math::qd) + "d]");
462  if (fabs(lat) == Math::qd && !(_nc == 0 && lat * _n > 0))
463  throw GeographicErr("Incompatible polar latitude in SetScale");
464  real x, y, gamma, kold;
465  Forward(0, lat, 0, x, y, gamma, kold);
466  k /= kold;
467  _scale *= k;
468  _k0 *= k;
469  }
470 
471 } // namespace GeographicLib
GeographicLib::Math::real real
Definition: GeodSolve.cpp:31
Header for GeographicLib::LambertConformalConic class.
Exception handling for GeographicLib.
Definition: Constants.hpp:316
Lambert conformal conic projection.
LambertConformalConic(real a, real f, real stdlat, real k0)
void Reverse(real lon0, real x, real y, real &lat, real &lon, real &gamma, real &k) const
void Forward(real lon0, real lat, real lon, real &x, real &y, real &gamma, real &k) const
void SetScale(real lat, real k=real(1))
static const LambertConformalConic & Mercator()
Mathematical functions needed by GeographicLib.
Definition: Math.hpp:76
static T degree()
Definition: Math.hpp:200
static T LatFix(T x)
Definition: Math.hpp:300
static void sincosd(T x, T &sinx, T &cosx)
Definition: Math.cpp:106
static T sq(T x)
Definition: Math.hpp:212
static T tauf(T taup, T es)
Definition: Math.cpp:219
static T AngNormalize(T x)
Definition: Math.cpp:71
static T atand(T x)
Definition: Math.cpp:202
static T AngDiff(T x, T y, T &e)
Definition: Math.cpp:82
static T eatanhe(T x, T es)
Definition: Math.cpp:205
@ qd
degrees per quarter turn
Definition: Math.hpp:141
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)