inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
xy_y /= this->m_proj_parm.C_y;
lp_lat = this->m_proj_parm.m ? aasin((this->m_proj_parm.m * xy_y + sin(xy_y)) / this->m_proj_parm.n) :
( this->m_proj_parm.n != 1. ? aasin(sin(xy_y) / this->m_proj_parm.n) : xy_y );
lp_lon = xy_x / (this->m_proj_parm.C_x * (this->m_proj_parm.m + cos(xy_y)));
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double phip, lamp, phipp, lampp, cp, esp, con, delp;
int i;
phipp = 2. * (atan(exp(xy_y / this->m_proj_parm.kR)) - FORTPI);
lampp = xy_x / this->m_proj_parm.kR;
cp = cos(phipp);
phip = aasin(this->m_proj_parm.cosp0 * sin(phipp) + this->m_proj_parm.sinp0 * cp * cos(lampp));
lamp = aasin(cp * sin(lampp) / cos(phip));
con = (this->m_proj_parm.K - log(tan(FORTPI + 0.5 * phip)))/this->m_proj_parm.c;
for (i = NITER; i ; --i) {
esp = this->m_par.e * sin(phip);
delp = (con + log(tan(FORTPI + 0.5 * phip)) - this->m_proj_parm.hlf_e *
log((1. + esp)/(1. - esp)) ) *
(1. - esp * esp) * cos(phip) * this->m_par.rone_es;
phip -= delp;
if (fabs(delp) < EPS)
break;
}
if (i) {
lp_lat = phip;
lp_lon = lamp / this->m_proj_parm.c;
} else
throw proj_exception();
}
// INVERSE(s_inverse) spheroid
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
lp_lat = aasin(xy_y / this->m_proj_parm.C_y);
lp_lon = xy_x / (this->m_proj_parm.C_x * cos(lp_lat));
lp_lat += lp_lat;
lp_lat = aasin((lp_lat + sin(lp_lat)) / this->m_proj_parm.C_p);
}
// INVERSE(s_inverse) sphere
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(T const& xy_x, T xy_y, T& lp_lon, T& lp_lat) const
{
xy_y /= this->m_proj_parm.C_y;
lp_lat = (this->m_proj_parm.m != 0.0) ? aasin((this->m_proj_parm.m * xy_y + sin(xy_y)) / this->m_proj_parm.n) :
( this->m_proj_parm.n != 1. ? aasin(sin(xy_y) / this->m_proj_parm.n) : xy_y );
lp_lon = xy_x / (this->m_proj_parm.C_x * (this->m_proj_parm.m + cos(xy_y)));
}
static LP e_inverse (XY xy, PJ *P) { /* Ellipsoidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double phip, lamp, phipp, lampp, cp, esp, con, delp;
int i;
phipp = 2. * (atan (exp (xy.y / Q->kR)) - M_FORTPI);
lampp = xy.x / Q->kR;
cp = cos (phipp);
phip = aasin (P->ctx, Q->cosp0 * sin (phipp) + Q->sinp0 * cp * cos (lampp));
lamp = aasin (P->ctx, cp * sin (lampp) / cos (phip));
con = (Q->K - log (tan (M_FORTPI + 0.5 * phip)))/Q->c;
for (i = NITER; i ; --i) {
esp = P->e * sin(phip);
delp = (con + log(tan(M_FORTPI + 0.5 * phip)) - Q->hlf_e *
log((1. + esp)/(1. - esp)) ) *
(1. - esp * esp) * cos(phip) * P->rone_es;
phip -= delp;
if (fabs(delp) < EPS)
break;
}
if (i) {
lp.phi = phip;
lp.lam = lamp / Q->c;
} else {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return lp;
}
return (lp);
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double t;
lp_lat = C2 * (t = aasin(xy_y / C_y));
lp_lon = xy_x / (C_x * (1. + 3. * cos(lp_lat)/cos(t)));
lp_lat = aasin((C1 * sin(t) + sin(lp_lat)) / C3);
}
// INVERSE(s_inverse) spheroid
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
{
lp_lat = aasin(xy_y / this->m_proj_parm.C_y);
lp_lon = xy_x * cos(lp_lat) / this->m_proj_parm.C_x;
lp_lat *= 3.;
lp_lon /= cos(lp_lat);
lp_lat = aasin(1.13137085 * sin(lp_lat));
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double c;
lp_lat = aasin(xy_y / C_y);
lp_lon = xy_x / (C_x * ((c = cos(lp_lat)) - 0.5));
lp_lat = aasin((lp_lat + sin(lp_lat) * (c - 1.)) / C_p);
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
lp_lat = aasin(xy_y / this->m_proj_parm.C_y);
lp_lon = xy_x * cos(lp_lat) / this->m_proj_parm.C_x;
lp_lat *= 3.;
lp_lon /= cos(lp_lat);
lp_lat = aasin(1.13137085 * sin(lp_lat));
}
static PJ_LP s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
lp.phi = aasin(P->ctx, xy.y / Q->C_y);
lp.lam = xy.x / (Q->C_x * cos(lp.phi));
if (fabs(lp.lam) < M_PI) {
lp.phi += lp.phi;
lp.phi = aasin(P->ctx, (lp.phi + sin(lp.phi)) / Q->C_p);
} else {
lp.lam = lp.phi = HUGE_VAL;
}
return lp;
}
// FORWARD(s_forward) sphere
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(T const& lp_lon, T const& lp_lat, T& xy_x, T& xy_y) const
{
T Az, M, N, cp, sp, cl, shz;
cp = cos(lp_lat);
sp = sin(lp_lat);
cl = cos(lp_lon);
Az = aatan2(cp * sin(lp_lon), this->m_proj_parm.cp0 * sp - this->m_proj_parm.sp0 * cp * cl) + this->m_proj_parm.theta;
shz = sin(0.5 * aacos(this->m_proj_parm.sp0 * sp + this->m_proj_parm.cp0 * cp * cl));
M = aasin(shz * sin(Az));
N = aasin(shz * cos(Az) * cos(M) / cos(M * this->m_proj_parm.two_r_m));
xy_y = this->m_proj_parm.n * sin(N * this->m_proj_parm.two_r_n);
xy_x = this->m_proj_parm.m * sin(M * this->m_proj_parm.two_r_m) * cos(N) / cos(N * this->m_proj_parm.two_r_n);
}
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
double Az, M, N, cp, sp, cl, shz;
cp = cos(lp_lat);
sp = sin(lp_lat);
cl = cos(lp_lon);
Az = aatan2(cp * sin(lp_lon), this->m_proj_parm.cp0 * sp - this->m_proj_parm.sp0 * cp * cl) + this->m_proj_parm.theta;
shz = sin(0.5 * aacos(this->m_proj_parm.sp0 * sp + this->m_proj_parm.cp0 * cp * cl));
M = aasin(shz * sin(Az));
N = aasin(shz * cos(Az) * cos(M) / cos(M * this->m_proj_parm.two_r_m));
xy_y = this->m_proj_parm.n * sin(N * this->m_proj_parm.two_r_n);
xy_x = this->m_proj_parm.m * sin(M * this->m_proj_parm.two_r_m) * cos(N) / cos(N * this->m_proj_parm.two_r_n);
}
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
double phip, lamp, phipp, lampp, sp, cp;
sp = this->m_par.e * sin(lp_lat);
phip = 2.* atan( exp( this->m_proj_parm.c * (
log(tan(FORTPI + 0.5 * lp_lat)) - this->m_proj_parm.hlf_e * log((1. + sp)/(1. - sp)))
+ this->m_proj_parm.K)) - HALFPI;
lamp = this->m_proj_parm.c * lp_lon;
cp = cos(phip);
phipp = aasin(this->m_proj_parm.cosp0 * sin(phip) - this->m_proj_parm.sinp0 * cp * cos(lamp));
lampp = aasin(cp * sin(lamp) / cos(phipp));
xy_x = this->m_proj_parm.kR * lampp;
xy_y = this->m_proj_parm.kR * log(tan(FORTPI + 0.5 * phipp));
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
lp.phi = xy.y / C_y;
lp.lam = xy.x / (C_x * cos(lp.phi));
lp.phi = aasin (P->ctx,sin(lp.phi) / C_p1) / C_p2;
return (lp);
}
char *proobraz(char* input)
{
input = registr(input);
input= ficha(input);
for (int i=0;i<strlen(input);i++)
{
ssin(i,input);
ccos(i,input);
aasin(i,input);
aacos(i,input);
aatan(i,input);
cceil(i,input);
cch(i,input);
eexp(i,input);
aabs(i,input);
ffloor(i,input);
lln(i,input);
llog(i,input);
ssh(i,input);
ssqrt(i,input);
ttan(i,input);
tth(i,input);
cctg(i,input);
aactg(i,input);
ccth(i,input);
}
return input;
}
static PJ_LP s_inverse (PJ_XY xy, PJ *P) { /* Spheroidal, inverse */
PJ_LP lp = {0.0, 0.0};
xy.y /= static_cast<struct pj_opaque*>(P->opaque)->C_y;
lp.phi = aasin(P->ctx, sin (xy.y) / static_cast<struct pj_opaque*>(P->opaque)->n);
lp.lam = xy.x / (C_x * cos (xy.y));
return lp;
}
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
lp.phi = aasin (P->ctx,C_p1 * sin (C_p2 * lp.phi));
xy.x = C_x * lp.lam * cos (lp.phi);
xy.y = C_y * lp.phi;
return (xy);
}
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
lp_lat = aasin(0.883883476 * sin(lp_lat));
xy_x = this->m_proj_parm.C_x * lp_lon * cos(lp_lat);
xy_x /= cos(lp_lat *= 0.333333333333333);
xy_y = this->m_proj_parm.C_y * sin(lp_lat);
}
// INVERSE(s_inverse) sphere
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(T const& xy_x, T const& xy_y, T& lp_lon, T& lp_lat) const
{
T N, M, xp, yp, z, Az, cz, sz, cAz;
N = this->m_proj_parm.hn * aasin(xy_y * this->m_proj_parm.rn);
M = this->m_proj_parm.hm * aasin(xy_x * this->m_proj_parm.rm * cos(N * this->m_proj_parm.two_r_n) / cos(N));
xp = 2. * sin(M);
yp = 2. * sin(N) * cos(M * this->m_proj_parm.two_r_m) / cos(M);
cAz = cos(Az = aatan2(xp, yp) - this->m_proj_parm.theta);
z = 2. * aasin(0.5 * boost::math::hypot(xp, yp));
sz = sin(z);
cz = cos(z);
lp_lat = aasin(this->m_proj_parm.sp0 * cz + this->m_proj_parm.cp0 * sz * cAz);
lp_lon = aatan2(sz * sin(Az),
this->m_proj_parm.cp0 * cz - this->m_proj_parm.sp0 * sz * cAz);
}
void setup_tpeqd(Parameters& par, par_tpeqd& proj_parm)
{
double lam_1, lam_2, phi_1, phi_2, A12, pp;
/* get control point locations */
phi_1 = pj_param(par.params, "rlat_1").f;
lam_1 = pj_param(par.params, "rlon_1").f;
phi_2 = pj_param(par.params, "rlat_2").f;
lam_2 = pj_param(par.params, "rlon_2").f;
if (phi_1 == phi_2 && lam_1 == lam_2) throw proj_exception(-25);
par.lam0 = adjlon(0.5 * (lam_1 + lam_2));
proj_parm.dlam2 = adjlon(lam_2 - lam_1);
proj_parm.cp1 = cos(phi_1);
proj_parm.cp2 = cos(phi_2);
proj_parm.sp1 = sin(phi_1);
proj_parm.sp2 = sin(phi_2);
proj_parm.cs = proj_parm.cp1 * proj_parm.sp2;
proj_parm.sc = proj_parm.sp1 * proj_parm.cp2;
proj_parm.ccs = proj_parm.cp1 * proj_parm.cp2 * sin(proj_parm.dlam2);
proj_parm.z02 = aacos(proj_parm.sp1 * proj_parm.sp2 + proj_parm.cp1 * proj_parm.cp2 * cos(proj_parm.dlam2));
proj_parm.hz0 = .5 * proj_parm.z02;
A12 = atan2(proj_parm.cp2 * sin(proj_parm.dlam2),
proj_parm.cp1 * proj_parm.sp2 - proj_parm.sp1 * proj_parm.cp2 * cos(proj_parm.dlam2));
proj_parm.ca = cos(pp = aasin(proj_parm.cp1 * sin(A12)));
proj_parm.sa = sin(pp);
proj_parm.lp = adjlon(atan2(proj_parm.cp1 * cos(A12), proj_parm.sp1) - proj_parm.hz0);
proj_parm.dlam2 *= .5;
proj_parm.lamc = HALFPI - atan2(sin(A12) * proj_parm.sp1, cos(A12)) - proj_parm.dlam2;
proj_parm.thz0 = tan(proj_parm.hz0);
proj_parm.rhshz0 = .5 / sin(proj_parm.hz0);
proj_parm.r2z0 = 0.5 / proj_parm.z02;
proj_parm.z02 *= proj_parm.z02;
// par.inv = s_inverse;
// par.fwd = s_forward;
par.es = 0.;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
lp.lam = 2. * xy.x / (1. + cos(xy.y));
lp.phi = aasin(P->ctx,0.5 * (xy.y + sin(xy.y)));
return lp;
}
static PJ_XY s_forward (PJ_LP lp, PJ *P) { /* Spheroidal, forward */
PJ_XY xy = {0.0, 0.0};
lp.phi = aasin (P->ctx,static_cast<struct pj_opaque*>(P->opaque)->n * sin (lp.phi));
xy.x = C_x * lp.lam * cos (lp.phi);
xy.y = static_cast<struct pj_opaque*>(P->opaque)->C_y * lp.phi;
return xy;
}
static PJ_XY e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */
PJ_XY xy = {0.0,0.0};
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
int l, nn;
double lamt = 0.0, xlam, sdsq, c, d, s, lamdp = 0.0, phidp, lampp, tanph;
double lamtp, cl, sd, sp, sav, tanphi;
if (lp.phi > M_HALFPI)
lp.phi = M_HALFPI;
else if (lp.phi < -M_HALFPI)
lp.phi = -M_HALFPI;
if (lp.phi >= 0. )
lampp = M_HALFPI;
else
lampp = M_PI_HALFPI;
tanphi = tan(lp.phi);
for (nn = 0;;) {
double fac;
sav = lampp;
lamtp = lp.lam + Q->p22 * lampp;
cl = cos(lamtp);
if( cl < 0 )
fac = lampp + sin(lampp) * M_HALFPI;
else
fac = lampp - sin(lampp) * M_HALFPI;
for (l = 50; l; --l) {
lamt = lp.lam + Q->p22 * sav;
if (fabs(c = cos(lamt)) < TOL)
lamt -= TOL;
xlam = (P->one_es * tanphi * Q->sa + sin(lamt) * Q->ca) / c;
lamdp = atan(xlam) + fac;
if (fabs(fabs(sav) - fabs(lamdp)) < TOL)
break;
sav = lamdp;
}
if (!l || ++nn >= 3 || (lamdp > Q->rlm && lamdp < Q->rlm2))
break;
if (lamdp <= Q->rlm)
lampp = M_TWOPI_HALFPI;
else if (lamdp >= Q->rlm2)
lampp = M_HALFPI;
}
if (l) {
sp = sin(lp.phi);
phidp = aasin(P->ctx,(P->one_es * Q->ca * sp - Q->sa * cos(lp.phi) *
sin(lamt)) / sqrt(1. - P->es * sp * sp));
tanph = log(tan(M_FORTPI + .5 * phidp));
sd = sin(lamdp);
sdsq = sd * sd;
s = Q->p22 * Q->sa * cos(lamdp) * sqrt((1. + Q->t * sdsq)
/ ((1. + Q->w * sdsq) * (1. + Q->q * sdsq)));
d = sqrt(Q->xj * Q->xj + s * s);
xy.x = Q->b * lamdp + Q->a2 * sin(2. * lamdp) + Q->a4 *
sin(lamdp * 4.) - tanph * s / d;
xy.y = Q->c1 * sd + Q->c3 * sin(lamdp * 3.) + tanph * Q->xj / d;
} else
xy.x = xy.y = HUGE_VAL;
return xy;
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0, 0.0};
double phip, lamp, phipp, lampp, sp, cp;
struct pj_opaque *Q = P->opaque;
sp = P->e * sin (lp.phi);
phip = 2.* atan ( exp ( Q->c * (
log (tan (M_FORTPI + 0.5 * lp.phi)) - Q->hlf_e * log ((1. + sp)/(1. - sp)))
+ Q->K)) - M_HALFPI;
lamp = Q->c * lp.lam;
cp = cos(phip);
phipp = aasin (P->ctx, Q->cosp0 * sin (phip) - Q->sinp0 * cp * cos (lamp));
lampp = aasin (P->ctx, cp * sin (lamp) / cos (phipp));
xy.x = Q->kR * lampp;
xy.y = Q->kR * log (tan (M_FORTPI + 0.5 * phipp));
return xy;
}
// FORWARD(s_forward) spheroid
// Project coordinates from geographic (lon, lat) to cartesian (x, y)
inline void fwd(T const& lp_lon, T lp_lat, T& xy_x, T& xy_y) const
{
static T const third = detail::third<T>();
lp_lat = aasin(0.883883476 * sin(lp_lat));
xy_x = this->m_proj_parm.C_x * lp_lon * cos(lp_lat);
xy_x /= cos(lp_lat *= third);
xy_y = this->m_proj_parm.C_y * sin(lp_lat);
}
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
double t;
t = lp_lat = aasin(this->m_proj_parm.n * sin(lp_lat));
xy_x = this->m_proj_parm.m * lp_lon * cos(lp_lat);
t *= t;
xy_y = lp_lat * (1. + t * this->m_proj_parm.q3) * this->m_proj_parm.rmn;
}
static PJ_XY t_forward(PJ_LP lp, PJ *P) { /* spheroid */
struct pj_opaque *Q = static_cast<struct pj_opaque*>(P->opaque);
double cosphi, coslam;
cosphi = cos(lp.phi);
coslam = cos(lp.lam);
lp.lam = adjlon(aatan2(cosphi * sin(lp.lam), sin(lp.phi)) + Q->lamp);
lp.phi = aasin(P->ctx, - cosphi * coslam);
return Q->link->fwd(lp, Q->link);
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double r;
lp.phi = xy.y / Q->C_y;
r = sqrt(1. + lp.phi * lp.phi);
lp.lam = xy.x / (Q->C_x * (Q->D - r));
lp.phi = aasin( P->ctx, ( (Q->A - r) * lp.phi - log(lp.phi + r) ) / Q->B);
return lp;
}
// INVERSE(s_inverse) spheroid
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(T const& xy_x, T xy_y, T& lp_lon, T& lp_lat) const
{
T c;
xy_y /= this->m_proj_parm.C_y;
c = cos(lp_lat = this->m_proj_parm.tan_mode ? atan(xy_y) : aasin(xy_y));
lp_lat /= this->m_proj_parm.C_p;
lp_lon = xy_x / (this->m_proj_parm.C_x * cos(lp_lat));
if (this->m_proj_parm.tan_mode)
lp_lon /= c * c;
else
lp_lon *= c;
}
// INVERSE(s_inverse) spheroid
// Project coordinates from cartesian (x, y) to geographic (lon, lat)
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double c;
xy_y /= this->m_proj_parm.C_y;
c = cos(lp_lat = this->m_proj_parm.tan_mode ? atan(xy_y) : aasin(xy_y));
lp_lat /= this->m_proj_parm.C_p;
lp_lon = xy_x / (this->m_proj_parm.C_x * cos(lp_lat));
if (this->m_proj_parm.tan_mode)
lp_lon /= c * c;
else
lp_lon *= c;
}
