GeographicLib 1.52
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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 (2010-2020) <charles@karney.com> and licensed
6 * under the MIT/X11 License. For more information, see
7 * https://geographiclib.sourceforge.io/
8 **********************************************************************/
9
11
12namespace 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 (!(isfinite(_a) && _a > 0))
28 throw GeographicErr("Equatorial radius is not positive");
29 if (!(isfinite(_f) && _f < 1))
30 throw GeographicErr("Polar semi-axis is not positive");
31 if (!(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 (!(isfinite(_a) && _a > 0))
53 throw GeographicErr("Equatorial radius is not positive");
54 if (!(isfinite(_f) && _f < 1))
55 throw GeographicErr("Polar semi-axis is not positive");
56 if (!(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 (!(isfinite(_a) && _a > 0))
82 throw GeographicErr("Equatorial radius is not positive");
83 if (!(isfinite(_f) && _f < 1))
84 throw GeographicErr("Polar semi-axis is not positive");
85 if (!(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 = hypot(sphi1, cphi1);
107 sphi1 /= r; cphi1 /= r;
108 r = 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 = 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)) -
173 // log((tchi1 + scchi1)/(2*scbet1))) / (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 = 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 = asinh(_tchi0);
288
289 _lat0 = atan(_sign * tphi0) / Math::degree();
290 _t0nm1 = 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 = 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,
333 real& gamma, real& k) 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 = 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 != 0 ? stheta / _n : lam);
362 y = _nrho0 *
363 (_n != 0 ?
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) const {
376 // From Snyder, we have
377 //
378 // x = rho * sin(theta)
379 // rho0 - y = rho * cos(theta)
380 //
381 // rho = hypot(x, rho0 - y)
382 // drho = (n*x^2 - 2*y*nrho0 + n*y^2)/(hypot(n*x, nrho0-n*y) + nrho0)
383 // theta = atan2(n*x, nrho0-n*y)
384 //
385 // From drho, obtain t^n-1
386 // psi = -log(t), so
387 // dpsi = - Dlog1p(t^n-1, t0^n-1) * drho / scale
388 y *= _sign;
389 real
390 // Guard against 0 * inf in computation of ny
391 nx = _n * x, ny = _n != 0 ? _n * y : 0, y1 = _nrho0 - ny,
392 den = hypot(nx, y1) + _nrho0, // 0 implies origin with polar aspect
393 // isfinite test is to avoid inf/inf
394 drho = ((den != 0 && isfinite(den))
395 ? (x*nx + y * (ny - 2*_nrho0)) / den
396 : den);
397 drho = min(drho, _drhomax);
398 if (_n == 0)
399 drho = max(drho, -_drhomax);
400 real
401 tnm1 = _t0nm1 + _n * drho/_scale,
402 dpsi = (den == 0 ? 0 :
403 (tnm1 + 1 != 0 ? - Dlog1p(tnm1, _t0nm1) * drho / _scale :
404 ahypover_));
405 real tchi;
406 if (2 * _n <= 1) {
407 // tchi = sinh(psi)
408 real
409 psi = _psi0 + dpsi, tchia = sinh(psi), scchi = hyp(tchia),
410 dtchi = Dsinh(psi, _psi0, tchia, _tchi0, scchi, _scchi0) * dpsi;
411 tchi = _tchi0 + dtchi; // Update tchi using divided difference
412 } else {
413 // tchi = sinh(-1/n * log(tn))
414 // = sinh((1-1/n) * log(tn) - log(tn))
415 // = + sinh((1-1/n) * log(tn)) * cosh(log(tn))
416 // - cosh((1-1/n) * log(tn)) * sinh(log(tn))
417 // (1-1/n) = - nc^2/(n*(1+n))
418 // cosh(log(tn)) = (tn + 1/tn)/2; sinh(log(tn)) = (tn - 1/tn)/2
419 real
420 tn = tnm1 + 1 == 0 ? epsx_ : tnm1 + 1,
421 sh = sinh( -Math::sq(_nc)/(_n * (1 + _n)) *
422 (2 * tn > 1 ? log1p(tnm1) : log(tn)) );
423 tchi = sh * (tn + 1/tn)/2 - hyp(sh) * (tnm1 * (tn + 1)/tn)/2;
424 }
425
426 // log(t) = -asinh(tan(chi)) = -psi
427 gamma = atan2(nx, y1);
428 real
429 tphi = Math::tauf(tchi, _es),
430 scbet = hyp(_fm * tphi), scchi = hyp(tchi),
431 lam = _n != 0 ? gamma / _n : x / y1;
432 lat = Math::atand(_sign * tphi);
433 lon = lam / Math::degree();
434 lon = Math::AngNormalize(lon + Math::AngNormalize(lon0));
435 k = _k0 * (scbet/_scbet0) /
436 (exp(_nc != 0 ? - (Math::sq(_nc)/(1 + _n)) * dpsi : 0)
437 * (tchi >= 0 ? scchi + tchi : 1 / (scchi - tchi)) / (_scchi0 + _tchi0));
438 gamma /= _sign * Math::degree();
439 }
440
441 void LambertConformalConic::SetScale(real lat, real k) {
442 if (!(isfinite(k) && k > 0))
443 throw GeographicErr("Scale is not positive");
444 if (!(abs(lat) <= 90))
445 throw GeographicErr("Latitude for SetScale not in [-90d, 90d]");
446 if (abs(lat) == 90 && !(_nc == 0 && lat * _n > 0))
447 throw GeographicErr("Incompatible polar latitude in SetScale");
448 real x, y, gamma, kold;
449 Forward(0, lat, 0, x, y, gamma, kold);
450 k /= kold;
451 _scale *= k;
452 _k0 *= k;
453 }
454
455} // namespace GeographicLib
GeographicLib::Math::real real
Definition: GeodSolve.cpp:31
Header for GeographicLib::LambertConformalConic class.
Exception handling for GeographicLib.
Definition: Constants.hpp:315
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 AngNormalize(T x)
Definition: Math.hpp:420
static T degree()
Definition: Math.hpp:159
static T LatFix(T x)
Definition: Math.hpp:433
static void sincosd(T x, T &sinx, T &cosx)
Definition: Math.cpp:126
static T sq(T x)
Definition: Math.hpp:171
static T tauf(T taup, T es)
Definition: Math.cpp:224
static T atand(T x)
Definition: Math.cpp:205
static T eatanhe(T x, T es)
Definition: Math.cpp:208
static T AngDiff(T x, T y, T &e)
Definition: Math.hpp:452
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)