GeographicLib  1.46
LambertConformalConic.cpp
Go to the documentation of this file.
1 /**
2  * \file LambertConformalConic.cpp
3  * \brief Implementation for GeographicLib::LambertConformalConic class
4  *
7  * http://geographiclib.sourceforge.net/
8  **********************************************************************/
9
11
12 namespace GeographicLib {
13
14  using namespace std;
15
17  real stdlat, real k0)
18  : eps_(numeric_limits<real>::epsilon())
19  , epsx_(Math::sq(eps_))
20  , ahypover_(Math::digits() * log(real(numeric_limits<real>::radix)) + 2)
21  , _a(a)
22  , _f(f)
23  , _fm(1 - _f)
24  , _e2(_f * (2 - _f))
25  , _es((_f < 0 ? -1 : 1) * sqrt(abs(_e2)))
26  {
27  if (!(Math::isfinite(_a) && _a > 0))
28  throw GeographicErr("Major radius is not positive");
29  if (!(Math::isfinite(_f) && _f < 1))
30  throw GeographicErr("Minor radius is not positive");
31  if (!(Math::isfinite(k0) && k0 > 0))
32  throw GeographicErr("Scale is not positive");
33  if (!(abs(stdlat) <= 90))
34  throw GeographicErr("Standard latitude not in [-90d, 90d]");
35  real sphi, cphi;
36  Math::sincosd(stdlat, sphi, cphi);
37  Init(sphi, cphi, sphi, cphi, k0);
38  }
39
41  real stdlat1, real stdlat2,
42  real k1)
43  : eps_(numeric_limits<real>::epsilon())
44  , epsx_(Math::sq(eps_))
45  , ahypover_(Math::digits() * log(real(numeric_limits<real>::radix)) + 2)
46  , _a(a)
47  , _f(f)
48  , _fm(1 - _f)
49  , _e2(_f * (2 - _f))
50  , _es((_f < 0 ? -1 : 1) * sqrt(abs(_e2)))
51  {
52  if (!(Math::isfinite(_a) && _a > 0))
53  throw GeographicErr("Major radius is not positive");
54  if (!(Math::isfinite(_f) && _f < 1))
55  throw GeographicErr("Minor radius is not positive");
56  if (!(Math::isfinite(k1) && k1 > 0))
57  throw GeographicErr("Scale is not positive");
58  if (!(abs(stdlat1) <= 90))
59  throw GeographicErr("Standard latitude 1 not in [-90d, 90d]");
60  if (!(abs(stdlat2) <= 90))
61  throw GeographicErr("Standard latitude 2 not in [-90d, 90d]");
62  real sphi1, cphi1, sphi2, cphi2;
63  Math::sincosd(stdlat1, sphi1, cphi1);
64  Math::sincosd(stdlat2, sphi2, cphi2);
65  Init(sphi1, cphi1, sphi2, cphi2, k1);
66  }
67
69  real sinlat1, real coslat1,
70  real sinlat2, real coslat2,
71  real k1)
72  : eps_(numeric_limits<real>::epsilon())
73  , epsx_(Math::sq(eps_))
74  , ahypover_(Math::digits() * log(real(numeric_limits<real>::radix)) + 2)
75  , _a(a)
76  , _f(f)
77  , _fm(1 - _f)
78  , _e2(_f * (2 - _f))
79  , _es((_f < 0 ? -1 : 1) * sqrt(abs(_e2)))
80  {
81  if (!(Math::isfinite(_a) && _a > 0))
82  throw GeographicErr("Major radius is not positive");
83  if (!(Math::isfinite(_f) && _f < 1))
84  throw GeographicErr("Minor radius is not positive");
85  if (!(Math::isfinite(k1) && k1 > 0))
86  throw GeographicErr("Scale is not positive");
87  if (!(coslat1 >= 0))
88  throw GeographicErr("Standard latitude 1 not in [-90d, 90d]");
89  if (!(coslat2 >= 0))
90  throw GeographicErr("Standard latitude 2 not in [-90d, 90d]");
91  if (!(abs(sinlat1) <= 1 && coslat1 <= 1) || (coslat1 == 0 && sinlat1 == 0))
92  throw GeographicErr("Bad sine/cosine of standard latitude 1");
93  if (!(abs(sinlat2) <= 1 && coslat2 <= 1) || (coslat2 == 0 && sinlat2 == 0))
94  throw GeographicErr("Bad sine/cosine of standard latitude 2");
95  if (coslat1 == 0 || coslat2 == 0)
96  if (!(coslat1 == coslat2 && sinlat1 == sinlat2))
97  throw GeographicErr
98  ("Standard latitudes must be equal is either is a pole");
99  Init(sinlat1, coslat1, sinlat2, coslat2, k1);
100  }
101
102  void LambertConformalConic::Init(real sphi1, real cphi1,
103  real sphi2, real cphi2, real k1) {
104  {
105  real r;
106  r = Math::hypot(sphi1, cphi1);
107  sphi1 /= r; cphi1 /= r;
108  r = Math::hypot(sphi2, cphi2);
109  sphi2 /= r; cphi2 /= r;
110  }
111  bool polar = (cphi1 == 0);
112  cphi1 = max(epsx_, cphi1); // Avoid singularities at poles
113  cphi2 = max(epsx_, cphi2);
114  // Determine hemisphere of tangent latitude
115  _sign = sphi1 + sphi2 >= 0 ? 1 : -1;
116  // Internally work with tangent latitude positive
117  sphi1 *= _sign; sphi2 *= _sign;
118  if (sphi1 > sphi2) {
119  swap(sphi1, sphi2); swap(cphi1, cphi2); // Make phi1 < phi2
120  }
121  real
122  tphi1 = sphi1/cphi1, tphi2 = sphi2/cphi2, tphi0;
123  //
124  // Snyder: 15-8: n = (log(m1) - log(m2))/(log(t1)-log(t2))
125  //
126  // m = cos(bet) = 1/sec(bet) = 1/sqrt(1+tan(bet)^2)
127  // bet = parametric lat, tan(bet) = (1-f)*tan(phi)
128  //
129  // t = tan(pi/4-chi/2) = 1/(sec(chi) + tan(chi)) = sec(chi) - tan(chi)
130  // log(t) = -asinh(tan(chi)) = -psi
131  // chi = conformal lat
132  // tan(chi) = tan(phi)*cosh(xi) - sinh(xi)*sec(phi)
133  // xi = eatanhe(sin(phi)), eatanhe(x) = e * atanh(e*x)
134  //
135  // n = (log(sec(bet2))-log(sec(bet1)))/(asinh(tan(chi2))-asinh(tan(chi1)))
136  //
137  // Let log(sec(bet)) = b(tphi), asinh(tan(chi)) = c(tphi)
138  // Then n = Db(tphi2, tphi1)/Dc(tphi2, tphi1)
139  // In limit tphi2 -> tphi1, n -> sphi1
140  //
141  real
142  tbet1 = _fm * tphi1, scbet1 = hyp(tbet1),
143  tbet2 = _fm * tphi2, scbet2 = hyp(tbet2);
144  real
145  scphi1 = 1/cphi1,
146  xi1 = Math::eatanhe(sphi1, _es), shxi1 = sinh(xi1), chxi1 = hyp(shxi1),
147  tchi1 = chxi1 * tphi1 - shxi1 * scphi1, scchi1 = hyp(tchi1),
148  scphi2 = 1/cphi2,
149  xi2 = Math::eatanhe(sphi2, _es), shxi2 = sinh(xi2), chxi2 = hyp(shxi2),
150  tchi2 = chxi2 * tphi2 - shxi2 * scphi2, scchi2 = hyp(tchi2),
151  psi1 = Math::asinh(tchi1);
152  if (tphi2 - tphi1 != 0) {
153  // Db(tphi2, tphi1)
154  real num = Dlog1p(Math::sq(tbet2)/(1 + scbet2),
155  Math::sq(tbet1)/(1 + scbet1))
156  * Dhyp(tbet2, tbet1, scbet2, scbet1) * _fm;
157  // Dc(tphi2, tphi1)
158  real den = Dasinh(tphi2, tphi1, scphi2, scphi1)
159  - Deatanhe(sphi2, sphi1) * Dsn(tphi2, tphi1, sphi2, sphi1);
160  _n = num/den;
161
162  if (_n < 0.25)
163  _nc = sqrt((1 - _n) * (1 + _n));
164  else {
165  // Compute nc = cos(phi0) = sqrt((1 - n) * (1 + n)), evaluating 1 - n
166  // carefully. First write
167  //
168  // Dc(tphi2, tphi1) * (tphi2 - tphi1)
169  // = log(tchi2 + scchi2) - log(tchi1 + scchi1)
170  //
171  // then den * (1 - n) =
172  // (log((tchi2 + scchi2)/(2*scbet2)) - log((tchi1 + scchi1)/(2*scbet1)))
173  // / (tphi2 - tphi1)
174  // = Dlog1p(a2, a1) * (tchi2+scchi2 + tchi1+scchi1)/(4*scbet1*scbet2)
175  // * fm * Q
176  //
177  // where
178  // a1 = ( (tchi1 - scbet1) + (scchi1 - scbet1) ) / (2 * scbet1)
179  // Q = ((scbet2 + scbet1)/fm)/((scchi2 + scchi1)/D(tchi2, tchi1))
180  // - (tbet2 + tbet1)/(scbet2 + scbet1)
181  real t;
182  {
183  real
184  // s1 = (scbet1 - scchi1) * (scbet1 + scchi1)
185  s1 = (tphi1 * (2 * shxi1 * chxi1 * scphi1 - _e2 * tphi1) -
186  Math::sq(shxi1) * (1 + 2 * Math::sq(tphi1))),
187  s2 = (tphi2 * (2 * shxi2 * chxi2 * scphi2 - _e2 * tphi2) -
188  Math::sq(shxi2) * (1 + 2 * Math::sq(tphi2))),
189  // t1 = scbet1 - tchi1
190  t1 = tchi1 < 0 ? scbet1 - tchi1 : (s1 + 1)/(scbet1 + tchi1),
191  t2 = tchi2 < 0 ? scbet2 - tchi2 : (s2 + 1)/(scbet2 + tchi2),
192  a2 = -(s2 / (scbet2 + scchi2) + t2) / (2 * scbet2),
193  a1 = -(s1 / (scbet1 + scchi1) + t1) / (2 * scbet1);
194  t = Dlog1p(a2, a1) / den;
195  }
196  // multiply by (tchi2 + scchi2 + tchi1 + scchi1)/(4*scbet1*scbet2) * fm
197  t *= ( ( (tchi2 >= 0 ? scchi2 + tchi2 : 1/(scchi2 - tchi2)) +
198  (tchi1 >= 0 ? scchi1 + tchi1 : 1/(scchi1 - tchi1)) ) /
199  (4 * scbet1 * scbet2) ) * _fm;
200
201  // Rewrite
202  // Q = (1 - (tbet2 + tbet1)/(scbet2 + scbet1)) -
203  // (1 - ((scbet2 + scbet1)/fm)/((scchi2 + scchi1)/D(tchi2, tchi1)))
204  // = tbm - tam
205  // where
206  real tbm = ( ((tbet1 > 0 ? 1/(scbet1+tbet1) : scbet1 - tbet1) +
207  (tbet2 > 0 ? 1/(scbet2+tbet2) : scbet2 - tbet2)) /
208  (scbet1+scbet2) );
209
210  // tam = (1 - ((scbet2+scbet1)/fm)/((scchi2+scchi1)/D(tchi2, tchi1)))
211  //
212  // Let
213  // (scbet2 + scbet1)/fm = scphi2 + scphi1 + dbet
214  // (scchi2 + scchi1)/D(tchi2, tchi1) = scphi2 + scphi1 + dchi
215  // then
216  // tam = D(tchi2, tchi1) * (dchi - dbet) / (scchi1 + scchi2)
217  real
218  // D(tchi2, tchi1)
219  dtchi = den / Dasinh(tchi2, tchi1, scchi2, scchi1),
220  // (scbet2 + scbet1)/fm - (scphi2 + scphi1)
221  dbet = (_e2/_fm) * ( 1 / (scbet2 + _fm * scphi2) +
222  1 / (scbet1 + _fm * scphi1) );
223
224  // dchi = (scchi2 + scchi1)/D(tchi2, tchi1) - (scphi2 + scphi1)
225  // Let
226  // tzet = chxiZ * tphi - shxiZ * scphi
227  // tchi = tzet + nu
228  // scchi = sczet + mu
229  // where
230  // xiZ = eatanhe(1), shxiZ = sinh(xiZ), chxiZ = cosh(xiZ)
231  // nu = scphi * (shxiZ - shxi) - tphi * (chxiZ - chxi)
232  // mu = - scphi * (chxiZ - chxi) + tphi * (shxiZ - shxi)
233  // then
234  // dchi = ((mu2 + mu1) - D(nu2, nu1) * (scphi2 + scphi1)) /
235  // D(tchi2, tchi1)
236  real
237  xiZ = Math::eatanhe(real(1), _es),
238  shxiZ = sinh(xiZ), chxiZ = hyp(shxiZ),
239  // These are differences not divided differences
240  // dxiZ1 = xiZ - xi1; dshxiZ1 = shxiZ - shxi; dchxiZ1 = chxiZ - chxi
241  dxiZ1 = Deatanhe(real(1), sphi1)/(scphi1*(tphi1+scphi1)),
242  dxiZ2 = Deatanhe(real(1), sphi2)/(scphi2*(tphi2+scphi2)),
243  dshxiZ1 = Dsinh(xiZ, xi1, shxiZ, shxi1, chxiZ, chxi1) * dxiZ1,
244  dshxiZ2 = Dsinh(xiZ, xi2, shxiZ, shxi2, chxiZ, chxi2) * dxiZ2,
245  dchxiZ1 = Dhyp(shxiZ, shxi1, chxiZ, chxi1) * dshxiZ1,
246  dchxiZ2 = Dhyp(shxiZ, shxi2, chxiZ, chxi2) * dshxiZ2,
247  // mu1 + mu2
248  amu12 = (- scphi1 * dchxiZ1 + tphi1 * dshxiZ1
249  - scphi2 * dchxiZ2 + tphi2 * dshxiZ2),
250  // D(xi2, xi1)
251  dxi = Deatanhe(sphi1, sphi2) * Dsn(tphi2, tphi1, sphi2, sphi1),
252  // D(nu2, nu1)
253  dnu12 =
254  ( (_f * 4 * scphi2 * dshxiZ2 > _f * scphi1 * dshxiZ1 ?
255  // Use divided differences
256  (dshxiZ1 + dshxiZ2)/2 * Dhyp(tphi1, tphi2, scphi1, scphi2)
257  - ( (scphi1 + scphi2)/2
258  * Dsinh(xi1, xi2, shxi1, shxi2, chxi1, chxi2) * dxi ) :
259  // Use ratio of differences
260  (scphi2 * dshxiZ2 - scphi1 * dshxiZ1)/(tphi2 - tphi1))
261  + ( (tphi1 + tphi2)/2 * Dhyp(shxi1, shxi2, chxi1, chxi2)
262  * Dsinh(xi1, xi2, shxi1, shxi2, chxi1, chxi2) * dxi )
263  - (dchxiZ1 + dchxiZ2)/2 ),
264  // dtchi * dchi
265  dchia = (amu12 - dnu12 * (scphi2 + scphi1)),
266  tam = (dchia - dtchi * dbet) / (scchi1 + scchi2);
267  t *= tbm - tam;
268  _nc = sqrt(max(real(0), t) * (1 + _n));
269  }
270  {
271  real r = Math::hypot(_n, _nc);
272  _n /= r;
273  _nc /= r;
274  }
275  tphi0 = _n / _nc;
276  } else {
277  tphi0 = tphi1;
278  _nc = 1/hyp(tphi0);
279  _n = tphi0 * _nc;
280  if (polar)
281  _nc = 0;
282  }
283
284  _scbet0 = hyp(_fm * tphi0);
285  real shxi0 = sinh(Math::eatanhe(_n, _es));
286  _tchi0 = tphi0 * hyp(shxi0) - shxi0 * hyp(tphi0); _scchi0 = hyp(_tchi0);
287  _psi0 = Math::asinh(_tchi0);
288
289  _lat0 = atan(_sign * tphi0) / Math::degree();
290  _t0nm1 = Math::expm1(- _n * _psi0); // Snyder's t0^n - 1
291  // a * k1 * m1/t1^n = a * k1 * m2/t2^n = a * k1 * n * (Snyder's F)
292  // = a * k1 / (scbet1 * exp(-n * psi1))
293  _scale = _a * k1 / scbet1 *
294  // exp(n * psi1) = exp(- (1 - n) * psi1) * exp(psi1)
295  // with (1-n) = nc^2/(1+n) and exp(-psi1) = scchi1 + tchi1
296  exp( - (Math::sq(_nc)/(1 + _n)) * psi1 )
297  * (tchi1 >= 0 ? scchi1 + tchi1 : 1 / (scchi1 - tchi1));
298  // Scale at phi0 = k0 = k1 * (scbet0*exp(-n*psi0))/(scbet1*exp(-n*psi1))
299  // = k1 * scbet0/scbet1 * exp(n * (psi1 - psi0))
300  // psi1 - psi0 = Dasinh(tchi1, tchi0) * (tchi1 - tchi0)
301  _k0 = k1 * (_scbet0/scbet1) *
302  exp( - (Math::sq(_nc)/(1 + _n)) *
303  Dasinh(tchi1, _tchi0, scchi1, _scchi0) * (tchi1 - _tchi0))
304  * (tchi1 >= 0 ? scchi1 + tchi1 : 1 / (scchi1 - tchi1)) /
305  (_scchi0 + _tchi0);
306  _nrho0 = polar ? 0 : _a * _k0 / _scbet0;
307  {
308  // Figure _drhomax using code at beginning of Forward with lat = -90
309  real
310  sphi = -1, cphi = epsx_,
311  tphi = sphi/cphi,
312  scphi = 1/cphi, shxi = sinh(Math::eatanhe(sphi, _es)),
313  tchi = hyp(shxi) * tphi - shxi * scphi, scchi = hyp(tchi),
314  psi = Math::asinh(tchi),
315  dpsi = Dasinh(tchi, _tchi0, scchi, _scchi0) * (tchi - _tchi0);
316  _drhomax = - _scale * (2 * _nc < 1 && dpsi != 0 ?
317  (exp(Math::sq(_nc)/(1 + _n) * psi ) *
318  (tchi > 0 ? 1/(scchi + tchi) : (scchi - tchi))
319  - (_t0nm1 + 1))/(-_n) :
320  Dexp(-_n * psi, -_n * _psi0) * dpsi);
321  }
322  }
323
325  static const LambertConformalConic mercator(Constants::WGS84_a(),
327  real(0), real(1));
328  return mercator;
329  }
330
331  void LambertConformalConic::Forward(real lon0, real lat, real lon,
332  real& x, real& y, real& gamma, real& k)
333  const {
334  lon = Math::AngDiff(lon0, lon);
335  // From Snyder, we have
336  //
337  // theta = n * lambda
338  // x = rho * sin(theta)
339  // = (nrho0 + n * drho) * sin(theta)/n
340  // y = rho0 - rho * cos(theta)
341  // = nrho0 * (1-cos(theta))/n - drho * cos(theta)
342  //
343  // where nrho0 = n * rho0, drho = rho - rho0
344  // and drho is evaluated with divided differences
345  real sphi, cphi;
346  Math::sincosd(Math::LatFix(lat) * _sign, sphi, cphi);
347  cphi = max(epsx_, cphi);
348  real
349  lam = lon * Math::degree(),
350  tphi = sphi/cphi, scbet = hyp(_fm * tphi),
351  scphi = 1/cphi, shxi = sinh(Math::eatanhe(sphi, _es)),
352  tchi = hyp(shxi) * tphi - shxi * scphi, scchi = hyp(tchi),
353  psi = Math::asinh(tchi),
354  theta = _n * lam, stheta = sin(theta), ctheta = cos(theta),
355  dpsi = Dasinh(tchi, _tchi0, scchi, _scchi0) * (tchi - _tchi0),
356  drho = - _scale * (2 * _nc < 1 && dpsi != 0 ?
357  (exp(Math::sq(_nc)/(1 + _n) * psi ) *
358  (tchi > 0 ? 1/(scchi + tchi) : (scchi - tchi))
359  - (_t0nm1 + 1))/(-_n) :
360  Dexp(-_n * psi, -_n * _psi0) * dpsi);
361  x = (_nrho0 + _n * drho) * (_n ? stheta / _n : lam);
362  y = _nrho0 *
363  (_n ?
364  (ctheta < 0 ? 1 - ctheta : Math::sq(stheta)/(1 + ctheta)) / _n : 0)
365  - drho * ctheta;
366  k = _k0 * (scbet/_scbet0) /
367  (exp( - (Math::sq(_nc)/(1 + _n)) * dpsi )
368  * (tchi >= 0 ? scchi + tchi : 1 / (scchi - tchi)) / (_scchi0 + _tchi0));
369  y *= _sign;
370  gamma = _sign * theta / Math::degree();
371  }
372
373  void LambertConformalConic::Reverse(real lon0, real x, real y,
374  real& lat, real& lon,
375  real& gamma, real& k)
376  const {
377  // From Snyder, we have
378  //
379  // x = rho * sin(theta)
380  // rho0 - y = rho * cos(theta)
381  //
382  // rho = hypot(x, rho0 - y)
383  // drho = (n*x^2 - 2*y*nrho0 + n*y^2)/(hypot(n*x, nrho0-n*y) + nrho0)
384  // theta = atan2(n*x, nrho0-n*y)
385  //
386  // From drho, obtain t^n-1
387  // psi = -log(t), so
388  // dpsi = - Dlog1p(t^n-1, t0^n-1) * drho / scale
389  y *= _sign;
390  real
391  // Guard against 0 * inf in computation of ny
392  nx = _n * x, ny = _n ? _n * y : 0, y1 = _nrho0 - ny,
393  den = Math::hypot(nx, y1) + _nrho0, // 0 implies origin with polar aspect
394  // isfinite test is to avoid inf/inf
395  drho = ((den != 0 && Math::isfinite(den))
396  ? (x*nx + y * (ny - 2*_nrho0)) / den
397  : den);
398  drho = min(drho, _drhomax);
399  if (_n == 0)
400  drho = max(drho, -_drhomax);
401  real
402  tnm1 = _t0nm1 + _n * drho/_scale,
403  dpsi = (den == 0 ? 0 :
404  (tnm1 + 1 != 0 ? - Dlog1p(tnm1, _t0nm1) * drho / _scale :
405  ahypover_));
406  real tchi;
407  if (2 * _n <= 1) {
408  // tchi = sinh(psi)
409  real
410  psi = _psi0 + dpsi, tchia = sinh(psi), scchi = hyp(tchia),
411  dtchi = Dsinh(psi, _psi0, tchia, _tchi0, scchi, _scchi0) * dpsi;
412  tchi = _tchi0 + dtchi; // Update tchi using divided difference
413  } else {
414  // tchi = sinh(-1/n * log(tn))
415  // = sinh((1-1/n) * log(tn) - log(tn))
416  // = + sinh((1-1/n) * log(tn)) * cosh(log(tn))
417  // - cosh((1-1/n) * log(tn)) * sinh(log(tn))
418  // (1-1/n) = - nc^2/(n*(1+n))
419  // cosh(log(tn)) = (tn + 1/tn)/2; sinh(log(tn)) = (tn - 1/tn)/2
420  real
421  tn = tnm1 + 1 == 0 ? epsx_ : tnm1 + 1,
422  sh = sinh( -Math::sq(_nc)/(_n * (1 + _n)) *
423  (2 * tn > 1 ? Math::log1p(tnm1) : log(tn)) );
424  tchi = sh * (tn + 1/tn)/2 - hyp(sh) * (tnm1 * (tn + 1)/tn)/2;
425  }
426
427  // log(t) = -asinh(tan(chi)) = -psi
428  gamma = atan2(nx, y1);
429  real
430  tphi = Math::tauf(tchi, _es),
431  scbet = hyp(_fm * tphi), scchi = hyp(tchi),
432  lam = _n ? gamma / _n : x / y1;
433  lat = Math::atand(_sign * tphi);
434  lon = lam / Math::degree();
435  lon = Math::AngNormalize(lon + Math::AngNormalize(lon0));
436  k = _k0 * (scbet/_scbet0) /
437  (exp(_nc ? - (Math::sq(_nc)/(1 + _n)) * dpsi : 0)
438  * (tchi >= 0 ? scchi + tchi : 1 / (scchi - tchi)) / (_scchi0 + _tchi0));
439  gamma /= _sign * Math::degree();
440  }
441
442  void LambertConformalConic::SetScale(real lat, real k) {
443  if (!(Math::isfinite(k) && k > 0))
444  throw GeographicErr("Scale is not positive");
445  if (!(abs(lat) <= 90))
446  throw GeographicErr("Latitude for SetScale not in [-90d, 90d]");
447  if (abs(lat) == 90 && !(_nc == 0 && lat * _n > 0))
448  throw GeographicErr("Incompatible polar latitude in SetScale");
449  real x, y, gamma, kold;
450  Forward(0, lat, 0, x, y, gamma, kold);
451  k /= kold;
452  _scale *= k;
453  _k0 *= k;
454  }
455
456 } // namespace GeographicLib
static T AngNormalize(T x)
Definition: Math.hpp:437
void Forward(real lon0, real lat, real lon, real &x, real &y, real &gamma, real &k) const
LambertConformalConic(real a, real f, real stdlat, real k0)
static T atand(T x)
Definition: Math.hpp:703
GeographicLib::Math::real real
Definition: GeodSolve.cpp:31
static bool isfinite(T x)
Definition: Math.hpp:781
Lambert conformal conic projection.
static T LatFix(T x)
Definition: Math.hpp:456
Mathematical functions needed by GeographicLib.
Definition: Math.hpp:102
static void sincosd(T x, T &sinx, T &cosx)
Definition: Math.hpp:545
static T AngDiff(T x, T y, T &e)
Definition: Math.hpp:475
static T expm1(T x)
Definition: Math.hpp:265
void SetScale(real lat, real k=real(1))
static T asinh(T x)
Definition: Math.hpp:311
static T hypot(T x, T y)
Definition: Math.hpp:243
static T sq(T x)
Definition: Math.hpp:232
static const LambertConformalConic & Mercator()
Namespace for GeographicLib.
Definition: Accumulator.cpp:12
static T degree()
Definition: Math.hpp:216
static T log1p(T x)
Definition: Math.hpp:288
Exception handling for GeographicLib.
Definition: Constants.hpp:373
void Reverse(real lon0, real x, real y, real &lat, real &lon, real &gamma, real &k) const
static T tauf(T taup, T es)
Definition: Math.cpp:31
static T eatanhe(T x, T es)
Definition: Math.cpp:21