46 # pragma warning (disable: 4127)
55 : tol_(numeric_limits<real>::epsilon())
56 , tol1_(real(0.1) * sqrt(tol_))
57 , tol2_(real(0.1) * tol_)
58 , taytol_(pow(tol_, real(0.6)))
60 , _f(f <= 1 ? f : 1/f)
99 stol = tol_ * max(
real(1), abs(taup));
106 dtau = (taup - taupa) * (1 + _mv *
Math::sq(tau)) /
109 if (!(abs(dtau) >= stol))
125 t1 = (d1 ? snu * dnv / d1 : (snu < 0 ? -overflow() : overflow())),
126 t2 = (d2 ? sinh( _e * Math::asinh(_e * snu / d2) ) :
127 (snu < 0 ? -overflow() : overflow()));
131 lam = (d1 != 0 && d2 != 0) ?
132 atan2(dnu * snv, cnu * cnv) - _e * atan2(_e * cnu * snv, dnu * cnv) :
136 void TransverseMercatorExact::dwdzeta(
real ,
149 bool TransverseMercatorExact::zetainv0(
real psi,
real lam,
real& u,
real& v)
153 lam > (1 - 2 * _e) *
Math::pi()/2 &&
154 psi < lam - (1 - _e) *
Math::pi()/2) {
169 v = atan2(cos(lamx), sinh(psix)) * (1 + _mu/2);
172 }
else if (psi < _e *
Math::pi()/2 &&
173 lam > (1 - 2 * _e) *
Math::pi()/2) {
186 dlam = lam - (1 - _e) *
Math::pi()/2,
193 ang = atan2(dlam-psi, psi+dlam) -
real(0.75) *
Math::pi();
195 retval = rad < _e * taytol_;
199 v = rad * sin(ang) + _Ev.
K();
205 u = atan2(sinh(psi), cos(lam));
214 void TransverseMercatorExact::zetainv(
real taup,
real lam,
real& u,
real& v)
219 if (zetainv0(psi, lam, u, v))
224 real snu, cnu, dnu, snv, cnv, dnv;
225 _Eu.
sncndn(u, snu, cnu, dnu);
226 _Ev.
sncndn(v, snv, cnv, dnv);
227 real tau1, lam1, du1, dv1;
228 zeta(u, snu, cnu, dnu, v, snv, cnv, dnv, tau1, lam1);
229 dwdzeta(u, snu, cnu, dnu, v, snv, cnv, dnv, du1, dv1);
234 delu = tau1 * du1 - lam1 * dv1,
235 delv = tau1 * dv1 + lam1 * du1;
241 if (!(delw2 >= stol2))
252 xi = _Eu.
E(snu, cnu, dnu) - _mu * snu * cnu * dnu / d;
253 eta = v - _Ev.
E(snv, cnv, dnv) + _mv * snv * cnv * dnv / d;
256 void TransverseMercatorExact::dwdsigma(
real ,
265 dnr = dnu * cnv * dnv,
266 dni = - _mu * snu * cnu * snv;
268 dv = 2 * dnr * dni / d;
272 bool TransverseMercatorExact::sigmainv0(
real xi,
real eta,
real& u,
real& v)
275 if (eta >
real(1.25) * _Ev.
KE() ||
276 (xi < -
real(0.25) * _Eu.
E() && xi < eta - _Ev.
KE())) {
287 }
else if ((eta >
real(0.75) * _Ev.
KE() && xi <
real(0.25) * _Eu.
E())
302 deta = eta - _Ev.
KE(),
306 ang = atan2(deta-xi, xi+deta) -
real(0.75) *
Math::pi();
308 retval = rad < 2 * taytol_;
312 v = rad * sin(ang) + _Ev.
K();
315 u = xi * _Eu.
K()/_Eu.
E();
316 v = eta * _Eu.
K()/_Eu.
E();
324 if (sigmainv0(xi, eta, u, v))
328 real snu, cnu, dnu, snv, cnv, dnv;
329 _Eu.
sncndn(u, snu, cnu, dnu);
330 _Ev.
sncndn(v, snv, cnv, dnv);
331 real xi1, eta1, du1, dv1;
332 sigma(u, snu, cnu, dnu, v, snv, cnv, dnv, xi1, eta1);
333 dwdsigma(u, snu, cnu, dnu, v, snv, cnv, dnv, du1, dv1);
337 delu = xi1 * du1 - eta1 * dv1,
338 delv = xi1 * dv1 + eta1 * du1;
344 if (!(delw2 >= tol2_))
349 void TransverseMercatorExact::Scale(
real tau,
real ,
356 gamma = atan2(_mv * snu * snv * cnv, cnu * dnu * dnv);
370 k = sqrt(_mv + _mu / sec2) * sqrt(sec2) *
376 real& x, real& y, real& gamma, real& k)
381 latsign = (!_extendp && lat < 0) ? -1 : 1,
382 lonsign = (!_extendp && lon < 0) ? -1 : 1;
385 bool backside = !_extendp && lon > 90;
401 }
else if (lat == 0 && lon == 90 * (1 - _e)) {
405 zetainv(taup(tau), lam, u, v);
407 real snu, cnu, dnu, snv, cnv, dnv;
408 _Eu.
sncndn(u, snu, cnu, dnu);
409 _Ev.
sncndn(v, snv, cnv, dnv);
412 sigma(u, snu, cnu, dnu, v, snv, cnv, dnv, xi, eta);
414 xi = 2 * _Eu.
E() - xi;
415 y = xi * _a * _k0 * latsign;
416 x = eta * _a * _k0 * lonsign;
423 zeta(u, snu, cnu, dnu, v, snv, cnv, dnv, tau, lam);
425 Scale(tau, lam, snu, cnu, dnu, snv, cnv, dnv, gamma, k);
430 gamma *= latsign * lonsign;
435 real& lat, real& lon,
436 real& gamma, real& k)
441 eta = x / (_a * _k0);
444 latsign = !_extendp && y < 0 ? -1 : 1,
445 lonsign = !_extendp && x < 0 ? -1 : 1;
448 bool backside = !_extendp && xi > _Eu.
E();
450 xi = 2 * _Eu.
E()- xi;
454 if (xi == 0 && eta == _Ev.
KE()) {
458 sigmainv(xi, eta, u, v);
460 real snu, cnu, dnu, snv, cnv, dnv;
461 _Eu.
sncndn(u, snu, cnu, dnu);
462 _Ev.
sncndn(v, snv, cnv, dnv);
464 if (v != 0 || u != _Eu.
K()) {
465 zeta(u, snu, cnu, dnu, v, snv, cnv, dnv, tau, lam);
470 Scale(tau, lam, snu, cnu, dnu, snv, cnv, dnv, gamma, k);
474 lon = lam = gamma = 0;
485 gamma *= latsign * lonsign;
static T AngNormalize(T x)
static const TransverseMercatorExact & UTM()
An exact implementation of the transverse Mercator projection.
GeographicLib::Math::real real
static bool isfinite(T x)
Header for GeographicLib::TransverseMercatorExact class.
TransverseMercatorExact(real a, real f, real k0, bool extendp=false)
Namespace for GeographicLib.
void sncndn(real x, real &sn, real &cn, real &dn) const
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
static T AngDiff(T x, T y)
Exception handling for GeographicLib.
#define GEOGRAPHICLIB_PANIC