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)
86 void TransverseMercatorExact::zeta(real , real snu, real cnu, real dnu,
87 real , real snv, real cnv, real dnv,
88 real& taup, real& lam)
const {
96 t1 = (d1 ? snu * dnv / d1 : (snu < 0 ? -overflow() : overflow())),
97 t2 = (d2 ? sinh( _e *
Math::asinh(_e * snu / d2) ) :
98 (snu < 0 ? -overflow() : overflow()));
102 lam = (d1 != 0 && d2 != 0) ?
103 atan2(dnu * snv, cnu * cnv) - _e * atan2(_e * cnu * snv, dnu * cnv) :
107 void TransverseMercatorExact::dwdzeta(real ,
108 real snu, real cnu, real dnu,
110 real snv, real cnv, real dnv,
111 real& du, real& dv)
const {
120 bool TransverseMercatorExact::zetainv0(real psi, real lam, real& u, real& v)
124 lam > (1 - 2 * _e) *
Math::pi()/2 &&
125 psi < lam - (1 - _e) *
Math::pi()/2) {
140 v = atan2(cos(lamx), sinh(psix)) * (1 + _mu/2);
143 }
else if (psi < _e *
Math::pi()/2 &&
144 lam > (1 - 2 * _e) *
Math::pi()/2) {
157 dlam = lam - (1 - _e) *
Math::pi()/2,
164 ang = atan2(dlam-psi, psi+dlam) - real(0.75) *
Math::pi();
166 retval = rad < _e * taytol_;
170 v = rad * sin(ang) + _Ev.
K();
176 u = atan2(sinh(psi), cos(lam));
185 void TransverseMercatorExact::zetainv(real taup, real lam, real& u, real& v)
190 if (zetainv0(psi, lam, u, v))
192 real stol2 = tol2_ /
Math::sq(max(psi, real(1)));
195 real snu, cnu, dnu, snv, cnv, dnv;
196 _Eu.
sncndn(u, snu, cnu, dnu);
197 _Ev.
sncndn(v, snv, cnv, dnv);
198 real tau1, lam1, du1, dv1;
199 zeta(u, snu, cnu, dnu, v, snv, cnv, dnv, tau1, lam1);
200 dwdzeta(u, snu, cnu, dnu, v, snv, cnv, dnv, du1, dv1);
205 delu = tau1 * du1 - lam1 * dv1,
206 delv = tau1 * dv1 + lam1 * du1;
212 if (!(delw2 >= stol2))
217 void TransverseMercatorExact::sigma(real , real snu, real cnu, real dnu,
218 real v, real snv, real cnv, real dnv,
219 real& xi, real& eta)
const {
223 xi = _Eu.
E(snu, cnu, dnu) - _mu * snu * cnu * dnu / d;
224 eta = v - _Ev.
E(snv, cnv, dnv) + _mv * snv * cnv * dnv / d;
227 void TransverseMercatorExact::dwdsigma(real ,
228 real snu, real cnu, real dnu,
230 real snv, real cnv, real dnv,
231 real& du, real& dv)
const {
236 dnr = dnu * cnv * dnv,
237 dni = - _mu * snu * cnu * snv;
239 dv = 2 * dnr * dni / d;
243 bool TransverseMercatorExact::sigmainv0(real xi, real eta, real& u, real& v)
246 if (eta > real(1.25) * _Ev.
KE() ||
247 (xi < -real(0.25) * _Eu.
E() && xi < eta - _Ev.
KE())) {
258 }
else if ((eta > real(0.75) * _Ev.
KE() && xi < real(0.25) * _Eu.
E())
273 deta = eta - _Ev.
KE(),
277 ang = atan2(deta-xi, xi+deta) - real(0.75) *
Math::pi();
279 retval = rad < 2 * taytol_;
283 v = rad * sin(ang) + _Ev.
K();
286 u = xi * _Eu.
K()/_Eu.
E();
287 v = eta * _Eu.
K()/_Eu.
E();
293 void TransverseMercatorExact::sigmainv(real xi, real eta, real& u, real& v)
295 if (sigmainv0(xi, eta, u, v))
299 real snu, cnu, dnu, snv, cnv, dnv;
300 _Eu.
sncndn(u, snu, cnu, dnu);
301 _Ev.
sncndn(v, snv, cnv, dnv);
302 real xi1, eta1, du1, dv1;
303 sigma(u, snu, cnu, dnu, v, snv, cnv, dnv, xi1, eta1);
304 dwdsigma(u, snu, cnu, dnu, v, snv, cnv, dnv, du1, dv1);
308 delu = xi1 * du1 - eta1 * dv1,
309 delv = xi1 * dv1 + eta1 * du1;
315 if (!(delw2 >= tol2_))
320 void TransverseMercatorExact::Scale(real tau, real ,
321 real snu, real cnu, real dnu,
322 real snv, real cnv, real dnv,
323 real& gamma, real& k)
const {
327 gamma = atan2(_mv * snu * snv * cnv, cnu * dnu * dnv);
341 k = sqrt(_mv + _mu / sec2) * sqrt(sec2) *
347 real& x, real& y, real& gamma, real& k)
352 latsign = (!_extendp && lat < 0) ? -1 : 1,
353 lonsign = (!_extendp && lon < 0) ? -1 : 1;
356 bool backside = !_extendp && lon > 90;
371 }
else if (lat == 0 && lon == 90 * (1 - _e)) {
378 real snu, cnu, dnu, snv, cnv, dnv;
379 _Eu.
sncndn(u, snu, cnu, dnu);
380 _Ev.
sncndn(v, snv, cnv, dnv);
383 sigma(u, snu, cnu, dnu, v, snv, cnv, dnv, xi, eta);
385 xi = 2 * _Eu.
E() - xi;
386 y = xi * _a * _k0 * latsign;
387 x = eta * _a * _k0 * lonsign;
394 zeta(u, snu, cnu, dnu, v, snv, cnv, dnv, tau, lam);
396 Scale(tau, lam, snu, cnu, dnu, snv, cnv, dnv, gamma, k);
401 gamma *= latsign * lonsign;
406 real& lat, real& lon,
407 real& gamma, real& k)
412 eta = x / (_a * _k0);
415 latsign = !_extendp && y < 0 ? -1 : 1,
416 lonsign = !_extendp && x < 0 ? -1 : 1;
419 bool backside = !_extendp && xi > _Eu.
E();
421 xi = 2 * _Eu.
E()- xi;
425 if (xi == 0 && eta == _Ev.
KE()) {
429 sigmainv(xi, eta, u, v);
431 real snu, cnu, dnu, snv, cnv, dnv;
432 _Eu.
sncndn(u, snu, cnu, dnu);
433 _Ev.
sncndn(v, snv, cnv, dnv);
435 if (v != 0 || u != _Eu.
K()) {
436 zeta(u, snu, cnu, dnu, v, snv, cnv, dnv, tau, lam);
441 Scale(tau, lam, snu, cnu, dnu, snv, cnv, dnv, gamma, k);
445 lon = lam = gamma = 0;
456 gamma *= latsign * lonsign;
static T AngNormalize(T x)
void sncndn(real x, real &sn, real &cn, real &dn) const
static const TransverseMercatorExact & UTM()
An exact implementation of the transverse Mercator projection.
static bool isfinite(T x)
Header for GeographicLib::TransverseMercatorExact class.
void Reverse(real lon0, real x, real y, real &lat, real &lon, real &gamma, real &k) const
TransverseMercatorExact(real a, real f, real k0, bool extendp=false)
Namespace for GeographicLib.
static T AngDiff(T x, T y)
static T tauf(T taup, T es)
void Forward(real lon0, real lat, real lon, real &x, real &y, real &gamma, real &k) const
Exception handling for GeographicLib.
static T taupf(T tau, T es)
#define GEOGRAPHICLIB_PANIC