GeographicLib 2.7

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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) <karney@alum.mit.edu> and licensed
6 * under the MIT/X11 License. For more information, see
7 * https://geographiclib.sourceforge.io/
8 **********************************************************************/
9
10#include <GeographicLib/LambertConformalConic.hpp>
11
12 namespace GeographicLib {
13
14 using namespace std;
15
16 LambertConformalConic::LambertConformalConic(real a, real f,
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(fabs(_e2)))
26 {
27 if (!(isfinite(_a) && _a > 0))
28 throw GeographicErr("Equatorial radius is not positive");
29 if (!(isfinite(_f) && _f < 1))
30 throw GeographicErr("Polar semiaxis is not positive");
31 if (!(isfinite(k0) && k0 > 0))
32 throw GeographicErr("Scale is not positive");
33 if (!(fabs(stdlat) <= Math::qd))
34 throw GeographicErr("Standard latitude not in [-" + to_string(Math::qd)
35 + "d, " + to_string(Math::qd) + "d]");
36 real sphi, cphi;
37 Math::sincosd(stdlat, sphi, cphi);
38 Init(sphi, cphi, sphi, cphi, k0);
39 }
40
41 LambertConformalConic::LambertConformalConic(real a, real f,
42 real stdlat1, real stdlat2,
43 real k1)
44 : eps_(numeric_limits<real>::epsilon())
45 , epsx_(Math::sq(eps_))
46 , ahypover_(Math::digits() * log(real(numeric_limits<real>::radix)) + 2)
47 , _a(a)
48 , _f(f)
49 , _fm(1 - _f)
50 , _e2(_f * (2 - _f))
51 , _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
52 {
53 if (!(isfinite(_a) && _a > 0))
54 throw GeographicErr("Equatorial radius is not positive");
55 if (!(isfinite(_f) && _f < 1))
56 throw GeographicErr("Polar semiaxis is not positive");
57 if (!(isfinite(k1) && k1 > 0))
58 throw GeographicErr("Scale is not positive");
59 if (!(fabs(stdlat1) <= Math::qd))
60 throw GeographicErr("Standard latitude 1 not in [-"
61 + to_string(Math::qd) + "d, "
62 + to_string(Math::qd) + "d]");
63 if (!(fabs(stdlat2) <= Math::qd))
64 throw GeographicErr("Standard latitude 2 not in [-"
65 + to_string(Math::qd) + "d, "
66 + to_string(Math::qd) + "d]");
67 real sphi1, cphi1, sphi2, cphi2;
68 Math::sincosd(stdlat1, sphi1, cphi1);
69 Math::sincosd(stdlat2, sphi2, cphi2);
70 Init(sphi1, cphi1, sphi2, cphi2, k1);
71 }
72
73 LambertConformalConic::LambertConformalConic(real a, real f,
74 real sinlat1, real coslat1,
75 real sinlat2, real coslat2,
76 real k1)
77 : eps_(numeric_limits<real>::epsilon())
78 , epsx_(Math::sq(eps_))
79 , ahypover_(Math::digits() * log(real(numeric_limits<real>::radix)) + 2)
80 , _a(a)
81 , _f(f)
82 , _fm(1 - _f)
83 , _e2(_f * (2 - _f))
84 , _es((_f < 0 ? -1 : 1) * sqrt(fabs(_e2)))
85 {
86 if (!(isfinite(_a) && _a > 0))
87 throw GeographicErr("Equatorial radius is not positive");
88 if (!(isfinite(_f) && _f < 1))
89 throw GeographicErr("Polar semiaxis is not positive");
90 if (!(isfinite(k1) && k1 > 0))
91 throw GeographicErr("Scale is not positive");
92 if (signbit(coslat1))
93 throw GeographicErr("Standard latitude 1 not in [-"
94 + to_string(Math::qd) + "d, "
95 + to_string(Math::qd) + "d]");
96 if (signbit(coslat2))
97 throw GeographicErr("Standard latitude 2 not in [-"
98 + to_string(Math::qd) + "d, "
99 + to_string(Math::qd) + "d]");
100 if (!(fabs(sinlat1) <= 1 && coslat1 <= 1) || (coslat1 == 0 && sinlat1 == 0))
101 throw GeographicErr("Bad sine/cosine of standard latitude 1");
102 if (!(fabs(sinlat2) <= 1 && coslat2 <= 1) || (coslat2 == 0 && sinlat2 == 0))
103 throw GeographicErr("Bad sine/cosine of standard latitude 2");
104 if (coslat1 == 0 || coslat2 == 0)
105 if (!(coslat1 == coslat2 && sinlat1 == sinlat2))
106 throw GeographicErr
107 ("Standard latitudes must be equal is either is a pole");
108 Init(sinlat1, coslat1, sinlat2, coslat2, k1);
109 }
110
111 void LambertConformalConic::Init(real sphi1, real cphi1,
112 real sphi2, real cphi2, real k1) {
113 {
114 real r;
115 r = hypot(sphi1, cphi1);
116 sphi1 /= r; cphi1 /= r;
117 r = hypot(sphi2, cphi2);
118 sphi2 /= r; cphi2 /= r;
119 }
120 bool polar = (cphi1 == 0);
121 cphi1 = fmax(epsx_, cphi1); // Avoid singularities at poles
122 cphi2 = fmax(epsx_, cphi2);
123 // Determine hemisphere of tangent latitude
124 _sign = sphi1 + sphi2 >= 0 ? 1 : -1;
125 // Internally work with tangent latitude positive
126 sphi1 *= _sign; sphi2 *= _sign;
127 if (sphi1 > sphi2) {
128 swap(sphi1, sphi2); swap(cphi1, cphi2); // Make phi1 < phi2
129 }
130 real
131 tphi1 = sphi1/cphi1, tphi2 = sphi2/cphi2, tphi0;
132 //
133 // Snyder: 15-8: n = (log(m1) - log(m2))/(log(t1)-log(t2))
134 //
135 // m = cos(bet) = 1/sec(bet) = 1/sqrt(1+tan(bet)^2)
136 // bet = parametric lat, tan(bet) = (1-f)*tan(phi)
137 //
138 // t = tan(pi/4-chi/2) = 1/(sec(chi) + tan(chi)) = sec(chi) - tan(chi)
139 // log(t) = -asinh(tan(chi)) = -psi
140 // chi = conformal lat
141 // tan(chi) = tan(phi)*cosh(xi) - sinh(xi)*sec(phi)
142 // xi = eatanhe(sin(phi)), eatanhe(x) = e * atanh(e*x)
143 //
144 // n = (log(sec(bet2))-log(sec(bet1)))/(asinh(tan(chi2))-asinh(tan(chi1)))
145 //
146 // Let log(sec(bet)) = b(tphi), asinh(tan(chi)) = c(tphi)
147 // Then n = Db(tphi2, tphi1)/Dc(tphi2, tphi1)
148 // In limit tphi2 -> tphi1, n -> sphi1
149 //
150 real
151 tbet1 = _fm * tphi1, scbet1 = hyp(tbet1),
152 tbet2 = _fm * tphi2, scbet2 = hyp(tbet2);
153 real
154 scphi1 = 1/cphi1,
155 xi1 = Math::eatanhe(sphi1, _es), shxi1 = sinh(xi1), chxi1 = hyp(shxi1),
156 tchi1 = chxi1 * tphi1 - shxi1 * scphi1, scchi1 = hyp(tchi1),
157 scphi2 = 1/cphi2,
158 xi2 = Math::eatanhe(sphi2, _es), shxi2 = sinh(xi2), chxi2 = hyp(shxi2),
159 tchi2 = chxi2 * tphi2 - shxi2 * scphi2, scchi2 = hyp(tchi2),
160 psi1 = asinh(tchi1);
161 if (tphi2 - tphi1 != 0) {
162 // Db(tphi2, tphi1)
163 real num = Dlog1p(Math::sq(tbet2)/(1 + scbet2),
164 Math::sq(tbet1)/(1 + scbet1))
165 * Dhyp(tbet2, tbet1, scbet2, scbet1) * _fm;
166 // Dc(tphi2, tphi1)
167 real den = Dasinh(tphi2, tphi1, scphi2, scphi1)
168 - Deatanhe(sphi2, sphi1) * Dsn(tphi2, tphi1, sphi2, sphi1);
169 _n = num/den;
170
171 if (_n < 1/real(4))
172 _nc = sqrt((1 - _n) * (1 + _n));
173 else {
174 // Compute nc = cos(phi0) = sqrt((1 - n) * (1 + n)), evaluating 1 - n
175 // carefully. First write
176 //
177 // Dc(tphi2, tphi1) * (tphi2 - tphi1)
178 // = log(tchi2 + scchi2) - log(tchi1 + scchi1)
179 //
180 // then den * (1 - n) =
181 // (log((tchi2 + scchi2)/(2*scbet2)) -
182 // log((tchi1 + scchi1)/(2*scbet1))) / (tphi2 - tphi1)
183 // = Dlog1p(a2, a1) * (tchi2+scchi2 + tchi1+scchi1)/(4*scbet1*scbet2)
184 // * fm * Q
185 //
186 // where
187 // a1 = ( (tchi1 - scbet1) + (scchi1 - scbet1) ) / (2 * scbet1)
188 // Q = ((scbet2 + scbet1)/fm)/((scchi2 + scchi1)/D(tchi2, tchi1))
189 // - (tbet2 + tbet1)/(scbet2 + scbet1)
190 real t;
191 {
192 real
193 // s1 = (scbet1 - scchi1) * (scbet1 + scchi1)
194 s1 = (tphi1 * (2 * shxi1 * chxi1 * scphi1 - _e2 * tphi1) -
195 Math::sq(shxi1) * (1 + 2 * Math::sq(tphi1))),
196 s2 = (tphi2 * (2 * shxi2 * chxi2 * scphi2 - _e2 * tphi2) -
197 Math::sq(shxi2) * (1 + 2 * Math::sq(tphi2))),
198 // t1 = scbet1 - tchi1
199 t1 = tchi1 < 0 ? scbet1 - tchi1 : (s1 + 1)/(scbet1 + tchi1),
200 t2 = tchi2 < 0 ? scbet2 - tchi2 : (s2 + 1)/(scbet2 + tchi2),
201 a2 = -(s2 / (scbet2 + scchi2) + t2) / (2 * scbet2),
202 a1 = -(s1 / (scbet1 + scchi1) + t1) / (2 * scbet1);
203 t = Dlog1p(a2, a1) / den;
204 }
205 // multiply by (tchi2 + scchi2 + tchi1 + scchi1)/(4*scbet1*scbet2) * fm
206 t *= ( ( (tchi2 >= 0 ? scchi2 + tchi2 : 1/(scchi2 - tchi2)) +
207 (tchi1 >= 0 ? scchi1 + tchi1 : 1/(scchi1 - tchi1)) ) /
208 (4 * scbet1 * scbet2) ) * _fm;
209
210 // Rewrite
211 // Q = (1 - (tbet2 + tbet1)/(scbet2 + scbet1)) -
212 // (1 - ((scbet2 + scbet1)/fm)/((scchi2 + scchi1)/D(tchi2, tchi1)))
213 // = tbm - tam
214 // where
215 real tbm = ( ((tbet1 > 0 ? 1/(scbet1+tbet1) : scbet1 - tbet1) +
216 (tbet2 > 0 ? 1/(scbet2+tbet2) : scbet2 - tbet2)) /
217 (scbet1+scbet2) );
218
219 // tam = (1 - ((scbet2+scbet1)/fm)/((scchi2+scchi1)/D(tchi2, tchi1)))
220 //
221 // Let
222 // (scbet2 + scbet1)/fm = scphi2 + scphi1 + dbet
223 // (scchi2 + scchi1)/D(tchi2, tchi1) = scphi2 + scphi1 + dchi
224 // then
225 // tam = D(tchi2, tchi1) * (dchi - dbet) / (scchi1 + scchi2)
226 real
227 // D(tchi2, tchi1)
228 dtchi = den / Dasinh(tchi2, tchi1, scchi2, scchi1),
229 // (scbet2 + scbet1)/fm - (scphi2 + scphi1)
230 dbet = (_e2/_fm) * ( 1 / (scbet2 + _fm * scphi2) +
231 1 / (scbet1 + _fm * scphi1) );
232
233 // dchi = (scchi2 + scchi1)/D(tchi2, tchi1) - (scphi2 + scphi1)
234 // Let
235 // tzet = chxiZ * tphi - shxiZ * scphi
236 // tchi = tzet + nu
237 // scchi = sczet + mu
238 // where
239 // xiZ = eatanhe(1), shxiZ = sinh(xiZ), chxiZ = cosh(xiZ)
240 // nu = scphi * (shxiZ - shxi) - tphi * (chxiZ - chxi)
241 // mu = - scphi * (chxiZ - chxi) + tphi * (shxiZ - shxi)
242 // then
243 // dchi = ((mu2 + mu1) - D(nu2, nu1) * (scphi2 + scphi1)) /
244 // D(tchi2, tchi1)
245 real
246 xiZ = Math::eatanhe(real(1), _es),
247 shxiZ = sinh(xiZ), chxiZ = hyp(shxiZ),
248 // These are differences not divided differences
249 // dxiZ1 = xiZ - xi1; dshxiZ1 = shxiZ - shxi; dchxiZ1 = chxiZ - chxi
250 dxiZ1 = Deatanhe(real(1), sphi1)/(scphi1*(tphi1+scphi1)),
251 dxiZ2 = Deatanhe(real(1), sphi2)/(scphi2*(tphi2+scphi2)),
252 dshxiZ1 = Dsinh(xiZ, xi1, shxiZ, shxi1, chxiZ, chxi1) * dxiZ1,
253 dshxiZ2 = Dsinh(xiZ, xi2, shxiZ, shxi2, chxiZ, chxi2) * dxiZ2,
254 dchxiZ1 = Dhyp(shxiZ, shxi1, chxiZ, chxi1) * dshxiZ1,
255 dchxiZ2 = Dhyp(shxiZ, shxi2, chxiZ, chxi2) * dshxiZ2,
256 // mu1 + mu2
257 amu12 = (- scphi1 * dchxiZ1 + tphi1 * dshxiZ1
258 - scphi2 * dchxiZ2 + tphi2 * dshxiZ2),
259 // D(xi2, xi1)
260 dxi = Deatanhe(sphi1, sphi2) * Dsn(tphi2, tphi1, sphi2, sphi1),
261 // D(nu2, nu1)
262 dnu12 =
263 ( (_f * 4 * scphi2 * dshxiZ2 > _f * scphi1 * dshxiZ1 ?
264 // Use divided differences
265 (dshxiZ1 + dshxiZ2)/2 * Dhyp(tphi1, tphi2, scphi1, scphi2)
266 - ( (scphi1 + scphi2)/2
267 * Dsinh(xi1, xi2, shxi1, shxi2, chxi1, chxi2) * dxi ) :
268 // Use ratio of differences
269 (scphi2 * dshxiZ2 - scphi1 * dshxiZ1)/(tphi2 - tphi1))
270 + ( (tphi1 + tphi2)/2 * Dhyp(shxi1, shxi2, chxi1, chxi2)
271 * Dsinh(xi1, xi2, shxi1, shxi2, chxi1, chxi2) * dxi )
272 - (dchxiZ1 + dchxiZ2)/2 ),
273 // dtchi * dchi
274 dchia = (amu12 - dnu12 * (scphi2 + scphi1)),
275 tam = (dchia - dtchi * dbet) / (scchi1 + scchi2);
276 t *= tbm - tam;
277 _nc = sqrt(fmax(real(0), t) * (1 + _n));
278 }
279 {
280 real r = hypot(_n, _nc);
281 _n /= r;
282 _nc /= r;
283 }
284 tphi0 = _n / _nc;
285 } else {
286 tphi0 = tphi1;
287 _nc = 1/hyp(tphi0);
288 _n = tphi0 * _nc;
289 if (polar)
290 _nc = 0;
291 }
292
293 _scbet0 = hyp(_fm * tphi0);
294 real shxi0 = sinh(Math::eatanhe(_n, _es));
295 _tchi0 = tphi0 * hyp(shxi0) - shxi0 * hyp(tphi0); _scchi0 = hyp(_tchi0);
296 _psi0 = asinh(_tchi0);
297
298 _lat0 = atan(_sign * tphi0) / Math::degree();
299 _t0nm1 = expm1(- _n * _psi0); // Snyder's t0^n - 1
300 // a * k1 * m1/t1^n = a * k1 * m2/t2^n = a * k1 * n * (Snyder's F)
301 // = a * k1 / (scbet1 * exp(-n * psi1))
302 _scale = _a * k1 / scbet1 *
303 // exp(n * psi1) = exp(- (1 - n) * psi1) * exp(psi1)
304 // with (1-n) = nc^2/(1+n) and exp(-psi1) = scchi1 + tchi1
305 exp( - (Math::sq(_nc)/(1 + _n)) * psi1 )
306 * (tchi1 >= 0 ? scchi1 + tchi1 : 1 / (scchi1 - tchi1));
307 // Scale at phi0 = k0 = k1 * (scbet0*exp(-n*psi0))/(scbet1*exp(-n*psi1))
308 // = k1 * scbet0/scbet1 * exp(n * (psi1 - psi0))
309 // psi1 - psi0 = Dasinh(tchi1, tchi0) * (tchi1 - tchi0)
310 _k0 = k1 * (_scbet0/scbet1) *
311 exp( - (Math::sq(_nc)/(1 + _n)) *
312 Dasinh(tchi1, _tchi0, scchi1, _scchi0) * (tchi1 - _tchi0))
313 * (tchi1 >= 0 ? scchi1 + tchi1 : 1 / (scchi1 - tchi1)) /
314 (_scchi0 + _tchi0);
315 _nrho0 = polar ? 0 : _a * _k0 / _scbet0;
316 {
317 // Figure _drhomax using code at beginning of Forward with lat = -90
318 real
319 sphi = -1, cphi = epsx_,
320 tphi = sphi/cphi,
321 scphi = 1/cphi, shxi = sinh(Math::eatanhe(sphi, _es)),
322 tchi = hyp(shxi) * tphi - shxi * scphi, scchi = hyp(tchi),
323 psi = asinh(tchi),
324 dpsi = Dasinh(tchi, _tchi0, scchi, _scchi0) * (tchi - _tchi0);
325 _drhomax = - _scale * (2 * _nc < 1 && dpsi != 0 ?
326 (exp(Math::sq(_nc)/(1 + _n) * psi ) *
327 (tchi > 0 ? 1/(scchi + tchi) : (scchi - tchi))
328 - (_t0nm1 + 1))/(-_n) :
329 Dexp(-_n * psi, -_n * _psi0) * dpsi);
330 }
331 }
332
333 const LambertConformalConic& LambertConformalConic::Mercator() {
334 static const LambertConformalConic mercator(Constants::WGS84_a(),
335 Constants::WGS84_f(),
336 real(0), real(1));
337 return mercator;
338 }
339
340 void LambertConformalConic::Forward(real lon0, real lat, real lon,
341 real& x, real& y,
342 real& gamma, real& k) const {
343 lon = Math::AngDiff(lon0, lon);
344 // From Snyder, we have
345 //
346 // theta = n * lambda
347 // x = rho * sin(theta)
348 // = (nrho0 + n * drho) * sin(theta)/n
349 // y = rho0 - rho * cos(theta)
350 // = nrho0 * (1-cos(theta))/n - drho * cos(theta)
351 //
352 // where nrho0 = n * rho0, drho = rho - rho0
353 // and drho is evaluated with divided differences
354 real sphi, cphi;
355 Math::sincosd(Math::LatFix(lat) * _sign, sphi, cphi);
356 cphi = fmax(epsx_, cphi);
357 real
358 lam = lon * Math::degree(),
359 tphi = sphi/cphi, scbet = hyp(_fm * tphi),
360 scphi = 1/cphi, shxi = sinh(Math::eatanhe(sphi, _es)),
361 tchi = hyp(shxi) * tphi - shxi * scphi, scchi = hyp(tchi),
362 psi = asinh(tchi),
363 theta = _n * lam, stheta = sin(theta), ctheta = cos(theta),
364 dpsi = Dasinh(tchi, _tchi0, scchi, _scchi0) * (tchi - _tchi0),
365 drho = - _scale * (2 * _nc < 1 && dpsi != 0 ?
366 (exp(Math::sq(_nc)/(1 + _n) * psi ) *
367 (tchi > 0 ? 1/(scchi + tchi) : (scchi - tchi))
368 - (_t0nm1 + 1))/(-_n) :
369 Dexp(-_n * psi, -_n * _psi0) * dpsi);
370 x = (_nrho0 + _n * drho) * (_n != 0 ? stheta / _n : lam);
371 y = _nrho0 *
372 (_n != 0 ?
373 (ctheta < 0 ? 1 - ctheta : Math::sq(stheta)/(1 + ctheta)) / _n : 0)
374 - drho * ctheta;
375 k = _k0 * (scbet/_scbet0) /
376 (exp( - (Math::sq(_nc)/(1 + _n)) * dpsi )
377 * (tchi >= 0 ? scchi + tchi : 1 / (scchi - tchi)) / (_scchi0 + _tchi0));
378 y *= _sign;
379 gamma = _sign * theta / Math::degree();
380 }
381
382 void LambertConformalConic::Reverse(real lon0, real x, real y,
383 real& lat, real& lon,
384 real& gamma, real& k) const {
385 // From Snyder, we have
386 //
387 // x = rho * sin(theta)
388 // rho0 - y = rho * cos(theta)
389 //
390 // rho = hypot(x, rho0 - y)
391 // drho = (n*x^2 - 2*y*nrho0 + n*y^2)/(hypot(n*x, nrho0-n*y) + nrho0)
392 // theta = atan2(n*x, nrho0-n*y)
393 //
394 // From drho, obtain t^n-1
395 // psi = -log(t), so
396 // dpsi = - Dlog1p(t^n-1, t0^n-1) * drho / scale
397 y *= _sign;
398 real
399 // Guard against 0 * inf in computation of ny
400 nx = _n * x, ny = _n != 0 ? _n * y : 0, y1 = _nrho0 - ny,
401 den = hypot(nx, y1) + _nrho0, // 0 implies origin with polar aspect
402 // isfinite test is to avoid inf/inf
403 drho = ((den != 0 && isfinite(den))
404 ? (x*nx + y * (ny - 2*_nrho0)) / den
405 : den);
406 drho = fmin(drho, _drhomax);
407 if (_n == 0)
408 drho = fmax(drho, -_drhomax);
409 real
410 tnm1 = _t0nm1 + _n * drho/_scale,
411 dpsi = (den == 0 ? 0 :
412 (tnm1 + 1 != 0 ? - Dlog1p(tnm1, _t0nm1) * drho / _scale :
413 ahypover_));
414 real tchi;
415 if (2 * _n <= 1) {
416 // tchi = sinh(psi)
417 real
418 psi = _psi0 + dpsi, tchia = sinh(psi), scchi = hyp(tchia),
419 dtchi = Dsinh(psi, _psi0, tchia, _tchi0, scchi, _scchi0) * dpsi;
420 tchi = _tchi0 + dtchi; // Update tchi using divided difference
421 } else {
422 // tchi = sinh(-1/n * log(tn))
423 // = sinh((1-1/n) * log(tn) - log(tn))
424 // = + sinh((1-1/n) * log(tn)) * cosh(log(tn))
425 // - cosh((1-1/n) * log(tn)) * sinh(log(tn))
426 // (1-1/n) = - nc^2/(n*(1+n))
427 // cosh(log(tn)) = (tn + 1/tn)/2; sinh(log(tn)) = (tn - 1/tn)/2
428 real
429 tn = tnm1 + 1 == 0 ? epsx_ : tnm1 + 1,
430 sh = sinh( -Math::sq(_nc)/(_n * (1 + _n)) *
431 (2 * tn > 1 ? log1p(tnm1) : log(tn)) );
432 tchi = sh * (tn + 1/tn)/2 - hyp(sh) * (tnm1 * (tn + 1)/tn)/2;
433 }
434
435 // log(t) = -asinh(tan(chi)) = -psi
436 gamma = atan2(nx, y1);
437 real
438 tphi = Math::tauf(tchi, _es),
439 scbet = hyp(_fm * tphi), scchi = hyp(tchi),
440 lam = _n != 0 ? gamma / _n : x / y1;
441 lat = Math::atand(_sign * tphi);
442 lon = lam / Math::degree();
443 lon = Math::AngNormalize(lon + Math::AngNormalize(lon0));
444 k = _k0 * (scbet/_scbet0) /
445 (exp(_nc != 0 ? - (Math::sq(_nc)/(1 + _n)) * dpsi : 0)
446 * (tchi >= 0 ? scchi + tchi : 1 / (scchi - tchi)) / (_scchi0 + _tchi0));
447 gamma /= _sign * Math::degree();
448 }
449
450 void LambertConformalConic::SetScale(real lat, real k) {
451 if (!(isfinite(k) && k > 0))
452 throw GeographicErr("Scale is not positive");
453 if (!(fabs(lat) <= Math::qd))
454 throw GeographicErr("Latitude for SetScale not in [-"
455 + to_string(Math::qd) + "d, "
456 + to_string(Math::qd) + "d]");
457 if (fabs(lat) == Math::qd && !(_nc == 0 && lat * _n > 0))
458 throw GeographicErr("Incompatible polar latitude in SetScale");
459 real x, y, gamma, kold;
460 Forward(0, lat, 0, x, y, gamma, kold);
461 k /= kold;
462 _scale *= k;
463 _k0 *= k;
464 }
465
466} // namespace GeographicLib
real
GeographicLib::Math::real real
Definition Geod3Solve.cpp:25
LambertConformalConic.hpp
Header for GeographicLib::LambertConformalConic class.
GeographicLib::Constants::WGS84_f
static T WGS84_f()
Definition Constants.hpp:118
GeographicLib::Constants::WGS84_a
static T WGS84_a()
Definition Constants.hpp:112
GeographicLib::GeographicErr
Exception handling for GeographicLib.
Definition Constants.hpp:344
GeographicLib::LambertConformalConic::LambertConformalConic
LambertConformalConic(real a, real f, real stdlat, real k0)
Definition LambertConformalConic.cpp:16
GeographicLib::LambertConformalConic::Reverse
void Reverse(real lon0, real x, real y, real &lat, real &lon, real &gamma, real &k) const
Definition LambertConformalConic.cpp:382
GeographicLib::LambertConformalConic::Forward
void Forward(real lon0, real lat, real lon, real &x, real &y, real &gamma, real &k) const
Definition LambertConformalConic.cpp:340
GeographicLib::LambertConformalConic::SetScale
void SetScale(real lat, real k=real(1))
Definition LambertConformalConic.cpp:450
GeographicLib::LambertConformalConic::Mercator
static const LambertConformalConic & Mercator()
Definition LambertConformalConic.cpp:333
GeographicLib::Math
Mathematical functions needed by GeographicLib.
Definition Math.hpp:82
GeographicLib::Math::degree
static T degree()
Definition Math.hpp:197
GeographicLib::Math::LatFix
static T LatFix(T x)
Definition Math.hpp:303
GeographicLib::Math::sincosd
static void sincosd(T x, T &sinx, T &cosx)
Definition Math.cpp:104
GeographicLib::Math::sq
static T sq(T x)
Definition Math.hpp:209
GeographicLib::Math::qd
static constexpr int qd
degrees per quarter turn
Definition Math.hpp:142
GeographicLib::Math::tauf
static T tauf(T taup, T es)
Definition Math.cpp:251
GeographicLib::Math::AngNormalize
static T AngNormalize(T x)
Definition Math.cpp:69
GeographicLib::Math::atand
static T atand(T x)
Definition Math.cpp:234
GeographicLib::Math::AngDiff
static T AngDiff(T x, T y, T &e)
Definition Math.cpp:80
GeographicLib::Math::eatanhe
static T eatanhe(T x, T es)
Definition Math.cpp:237
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std::swap
void swap(GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &a, GeographicLib::NearestNeighbor< dist_t, pos_t, distfun_t > &b)
Definition NearestNeighbor.hpp:819