static PJ_XY calcofi_e_forward (PJ_LP lp, PJ *P) { /* Ellipsoidal, forward */
PJ_XY xy = {0.0,0.0};
double oy; /* pt O y value in Mercator */
double l1; /* l1 and l2 are distances calculated using trig that sum
to the east/west distance between point O and point xy */
double l2;
double ry; /* r is the point on the same station as o (60) and the same
line as xy xy, r, o form a right triangle */
if (fabs(fabs(lp.phi) - M_HALFPI) <= EPS10) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
xy.x = lp.lam;
xy.y = -log(pj_tsfn(lp.phi, sin(lp.phi), P->e)); /* Mercator transform xy*/
oy = -log(pj_tsfn(PT_O_PHI, sin(PT_O_PHI), P->e));
l1 = (xy.y - oy) * tan(ROTATION_ANGLE);
l2 = -xy.x - l1 + PT_O_LAMBDA;
ry = l2 * cos(ROTATION_ANGLE) * sin(ROTATION_ANGLE) + xy.y;
ry = pj_phi2(P->ctx, exp(-ry), P->e); /*inverse Mercator*/
xy.x = PT_O_LINE - RAD_TO_DEG *
(ry - PT_O_PHI) * DEG_TO_LINE / cos(ROTATION_ANGLE);
xy.y = PT_O_STATION + RAD_TO_DEG *
(ry - lp.phi) * DEG_TO_STATION / sin(ROTATION_ANGLE);
/* set a = 1, x0 = 0, and y0 = 0 so that no further unit adjustments
are done */
return xy;
}
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
double L, Ls, sinLs1, Ls1;
L= this->m_proj_parm.n1*lp_lon;
Ls= this->m_proj_parm.c+this->m_proj_parm.n1*log(pj_tsfn(-1.0*lp_lat,-1.0*sin(lp_lat),this->m_par.e));
sinLs1= sin(L)/cosh(Ls);
Ls1= log(pj_tsfn(-1.0*asin(sinLs1),0.0,0.0));
xy_x= (this->m_proj_parm.XS + this->m_proj_parm.n2*Ls1)*this->m_par.ra;
xy_y= (this->m_proj_parm.YS + this->m_proj_parm.n2*atan(sinh(Ls)/cos(L)))*this->m_par.ra;
/*fprintf(stderr,"fwd:\nL =%16.13f\nLs =%16.13f\nLs1 =%16.13f\nLP(%16.13f,%16.13f)=XY(%16.4f,%16.4f)\n",L,Ls,Ls1,lp_lon+this->m_par.lam0,lp_lat,(xy_x*this->m_par.a + this->m_par.x0)*this->m_par.to_meter,(xy_y*this->m_par.a + this->m_par.y0)*this->m_par.to_meter);*/
}
PJ *PROJECTION(lcc) {
double cosphi, sinphi;
int secant;
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return pj_default_destructor (P, ENOMEM);
P->opaque = Q;
Q->phi1 = pj_param(P->ctx, P->params, "rlat_1").f;
if (pj_param(P->ctx, P->params, "tlat_2").i)
Q->phi2 = pj_param(P->ctx, P->params, "rlat_2").f;
else {
Q->phi2 = Q->phi1;
if (!pj_param(P->ctx, P->params, "tlat_0").i)
P->phi0 = Q->phi1;
}
if (fabs(Q->phi1 + Q->phi2) < EPS10)
return pj_default_destructor(P, PJD_ERR_CONIC_LAT_EQUAL);
Q->n = sinphi = sin(Q->phi1);
cosphi = cos(Q->phi1);
secant = fabs(Q->phi1 - Q->phi2) >= EPS10;
if( (Q->ellips = (P->es != 0.)) ) {
double ml1, m1;
P->e = sqrt(P->es);
m1 = pj_msfn(sinphi, cosphi, P->es);
ml1 = pj_tsfn(Q->phi1, sinphi, P->e);
if (secant) { /* secant cone */
sinphi = sin(Q->phi2);
Q->n = log(m1 / pj_msfn(sinphi, cos(Q->phi2), P->es));
Q->n /= log(ml1 / pj_tsfn(Q->phi2, sinphi, P->e));
}
Q->c = (Q->rho0 = m1 * pow(ml1, -Q->n) / Q->n);
Q->rho0 *= (fabs(fabs(P->phi0) - M_HALFPI) < EPS10) ? 0. :
pow(pj_tsfn(P->phi0, sin(P->phi0), P->e), Q->n);
} else {
if (secant)
Q->n = log(cosphi / cos(Q->phi2)) /
log(tan(M_FORTPI + .5 * Q->phi2) /
tan(M_FORTPI + .5 * Q->phi1));
Q->c = cosphi * pow(tan(M_FORTPI + .5 * Q->phi1), Q->n) / Q->n;
Q->rho0 = (fabs(fabs(P->phi0) - M_HALFPI) < EPS10) ? 0. :
Q->c * pow(tan(M_FORTPI + .5 * P->phi0), -Q->n);
}
P->inv = e_inverse;
P->fwd = e_forward;
return P;
}
static XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double L, Ls, sinLs1, Ls1;
L = Q->n1*lp.lam;
Ls = Q->c + Q->n1 * log(pj_tsfn(-1.0 * lp.phi, -1.0 * sin(lp.phi), P->e));
sinLs1 = sin(L) / cosh(Ls);
Ls1 = log(pj_tsfn(-1.0 * asin(sinLs1), 0.0, 0.0));
xy.x = (Q->XS + Q->n2*Ls1) * P->ra;
xy.y = (Q->YS + Q->n2*atan(sinh(Ls) / cos(L))) * P->ra;
return xy;
}
static PJ *setup(PJ *P) { /* general initialization */
double t;
struct pj_opaque *Q = P->opaque;
if (fabs ((t = fabs (P->phi0)) - HALFPI) < EPS10)
Q->mode = P->phi0 < 0. ? S_POLE : N_POLE;
else
Q->mode = t > EPS10 ? OBLIQ : EQUIT;
Q->phits = fabs (Q->phits);
if (P->es) {
double X;
switch (Q->mode) {
case N_POLE:
case S_POLE:
if (fabs (Q->phits - HALFPI) < EPS10)
Q->akm1 = 2. * P->k0 /
sqrt (pow (1+P->e,1+P->e) * pow (1-P->e,1-P->e));
else {
Q->akm1 = cos (Q->phits) /
pj_tsfn (Q->phits, t = sin (Q->phits), P->e);
t *= P->e;
Q->akm1 /= sqrt(1. - t * t);
}
break;
case EQUIT:
case OBLIQ:
t = sin (P->phi0);
X = 2. * atan (ssfn_(P->phi0, t, P->e)) - HALFPI;
t *= P->e;
Q->akm1 = 2. * P->k0 * cos (P->phi0) / sqrt(1. - t * t);
Q->sinX1 = sin (X);
Q->cosX1 = cos (X);
break;
}
P->inv = e_inverse;
P->fwd = e_forward;
} else {
switch (Q->mode) {
case OBLIQ:
sinph0 = sin (P->phi0);
cosph0 = cos (P->phi0);
case EQUIT:
Q->akm1 = 2. * P->k0;
break;
case S_POLE:
case N_POLE:
Q->akm1 = fabs (Q->phits - HALFPI) >= EPS10 ?
cos (Q->phits) / tan (FORTPI - .5 * Q->phits) :
2. * P->k0 ;
break;
}
P->inv = s_inverse;
P->fwd = s_forward;
}
return P;
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
if (fabs(fabs(lp.phi) - M_HALFPI) <= EPS10)
F_ERROR;
xy.x = P->k0 * lp.lam;
xy.y = - P->k0 * log(pj_tsfn(lp.phi, sin(lp.phi), P->e));
return xy;
}
void setup_gstmerc(Parameters& par, par_gstmerc& proj_parm)
{
proj_parm.lamc= par.lam0;
proj_parm.n1= sqrt(1.0+par.es*pow(cos(par.phi0),4.0)/(1.0-par.es));
proj_parm.phic= asin(sin(par.phi0)/proj_parm.n1);
proj_parm.c= log(pj_tsfn(-1.0*proj_parm.phic,0.0,0.0))
-proj_parm.n1*log(pj_tsfn(-1.0*par.phi0,-1.0*sin(par.phi0),par.e));
proj_parm.n2= par.k0*par.a*sqrt(1.0-par.es)/(1.0-par.es*sin(par.phi0)*sin(par.phi0));
proj_parm.XS= 0;
/* -par.x0 */
proj_parm.YS= -1.0*proj_parm.n2*proj_parm.phic;
/* -par.y0 */
// par.inv= s_inverse;
// par.fwd= s_forward;
/*fprintf(stderr,"a (m) =%16.4f\ne =%16.13f\nl0(rad)=%16.13f\np0(rad)=%16.13f\nk0 =%16.4f\nX0 (m)=%16.4f\nY0 (m)=%16.4f\n\nlC(rad)=%16.13f\npC(rad)=%16.13f\nc =%16.13f\nn1 =%16.13f\nn2 (m) =%16.4f\nXS (m) =%16.4f\nYS (m) =%16.4f\n", par.a, par.e, par.lam0, par.phi0, par.k0, par.x0, par.y0, proj_parm.lamc, proj_parm.phic, proj_parm.c, proj_parm.n1, proj_parm.n2, proj_parm.XS +par.x0, proj_parm.YS + par.y0);
*/
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double L, LC, sinC;
L= atan(sinh((xy_x*this->m_par.a - this->m_proj_parm.XS)/this->m_proj_parm.n2)/cos((xy_y*this->m_par.a - this->m_proj_parm.YS)/this->m_proj_parm.n2));
sinC= sin((xy_y*this->m_par.a - this->m_proj_parm.YS)/this->m_proj_parm.n2)/cosh((xy_x*this->m_par.a - this->m_proj_parm.XS)/this->m_proj_parm.n2);
LC= log(pj_tsfn(-1.0*asin(sinC),0.0,0.0));
lp_lon= L/this->m_proj_parm.n1;
lp_lat= -1.0*pj_phi2(exp((LC-this->m_proj_parm.c)/this->m_proj_parm.n1),this->m_par.e);
/*fprintf(stderr,"inv:\nL =%16.13f\nsinC =%16.13f\nLC =%16.13f\nXY(%16.4f,%16.4f)=LP(%16.13f,%16.13f)\n",L,sinC,LC,((xy_x/this->m_par.ra)+this->m_par.x0)/this->m_par.to_meter,((xy_y/this->m_par.ra)+this->m_par.y0)/this->m_par.to_meter,lp_lon+this->m_par.lam0,lp_lat);*/
}
PJ *PROJECTION(gstmerc) {
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
Q->lamc = P->lam0;
Q->n1 = sqrt(1.0 + P->es * pow(cos(P->phi0), 4.0) / (1.0 - P->es));
Q->phic = asin(sin(P->phi0) / Q->n1);
Q->c = log(pj_tsfn(-1.0 * Q->phic, 0.0, 0.0))
- Q->n1 * log(pj_tsfn(-1.0 * P->phi0, -1.0 * sin(P->phi0), P->e));
Q->n2 = P->k0 * P->a * sqrt(1.0 - P->es) / (1.0 - P->es * sin(P->phi0) * sin(P->phi0));
Q->XS = 0;
Q->YS = -1.0 * Q->n2 * Q->phic;
P->inv = s_inverse;
P->fwd = s_forward;
return P;
}
static PJ_LP calcofi_e_inverse (PJ_XY xy, PJ *P) { /* Ellipsoidal, inverse */
PJ_LP lp = {0.0,0.0};
double ry; /* y value of point r */
double oymctr; /* Mercator-transformed y value of point O */
double rymctr; /* Mercator-transformed ry */
double xymctr; /* Mercator-transformed xy.y */
double l1;
double l2;
ry = PT_O_PHI - LINE_TO_RAD * (xy.x - PT_O_LINE) *
cos(ROTATION_ANGLE);
lp.phi = ry - STATION_TO_RAD * (xy.y - PT_O_STATION) * sin(ROTATION_ANGLE);
oymctr = -log(pj_tsfn(PT_O_PHI, sin(PT_O_PHI), P->e));
rymctr = -log(pj_tsfn(ry, sin(ry), P->e));
xymctr = -log(pj_tsfn(lp.phi, sin(lp.phi), P->e));
l1 = (xymctr - oymctr) * tan(ROTATION_ANGLE);
l2 = (rymctr - xymctr) / (cos(ROTATION_ANGLE) * sin(ROTATION_ANGLE));
lp.lam = PT_O_LAMBDA - (l1 + l2);
return lp;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double L, LC, sinC;
L = atan(sinh((xy.x * P->a - Q->XS) / Q->n2) / cos((xy.y * P->a - Q->YS) / Q->n2));
sinC = sin((xy.y * P->a - Q->YS) / Q->n2) / cosh((xy.x * P->a - Q->XS) / Q->n2);
LC = log(pj_tsfn(-1.0 * asin(sinC), 0.0, 0.0));
lp.lam = L / Q->n1;
lp.phi = -1.0 * pj_phi2(P->ctx, exp((LC - Q->c) / Q->n1), P->e);
return lp;
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double rho;
if (fabs(fabs(lp.phi) - M_HALFPI) < EPS10) {
if ((lp.phi * Q->n) <= 0.) {
proj_errno_set(P, PJD_ERR_TOLERANCE_CONDITION);
return xy;
}
rho = 0.;
} else {
rho = Q->c * (Q->ellips ? pow(pj_tsfn(lp.phi, sin(lp.phi),
P->e), Q->n) : pow(tan(M_FORTPI + .5 * lp.phi), -Q->n));
}
lp.lam *= Q->n;
xy.x = P->k0 * (rho * sin( lp.lam) );
xy.y = P->k0 * (Q->rho0 - rho * cos(lp.lam) );
return xy;
}
static XY e_forward (LP lp, PJ *P) { /* Ellipsoidal, forward */
XY xy = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double coslam, sinlam, sinX = 0.0, cosX = 0.0, X, A, sinphi;
coslam = cos (lp.lam);
sinlam = sin (lp.lam);
sinphi = sin (lp.phi);
if (Q->mode == OBLIQ || Q->mode == EQUIT) {
sinX = sin (X = 2. * atan(ssfn_(lp.phi, sinphi, P->e)) - HALFPI);
cosX = cos (X);
}
switch (Q->mode) {
case OBLIQ:
A = Q->akm1 / (Q->cosX1 * (1. + Q->sinX1 * sinX +
Q->cosX1 * cosX * coslam));
xy.y = A * (Q->cosX1 * sinX - Q->sinX1 * cosX * coslam);
goto xmul; /* but why not just xy.x = A * cosX; break; ? */
case EQUIT:
A = 2. * Q->akm1 / (1. + cosX * coslam);
xy.y = A * sinX;
xmul:
xy.x = A * cosX;
break;
case S_POLE:
lp.phi = -lp.phi;
coslam = - coslam;
sinphi = -sinphi;
case N_POLE:
xy.x = Q->akm1 * pj_tsfn (lp.phi, sinphi, P->e);
xy.y = - xy.x * coslam;
break;
}
xy.x = xy.x * sinlam;
return xy;
}
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
if (fabs(fabs(lp_lat) - HALFPI) <= EPS10) throw proj_exception();;
xy_x = this->m_par.k0 * lp_lon;
xy_y = - this->m_par.k0 * log(pj_tsfn(lp_lat, sin(lp_lat), this->m_par.e));
}
double lamc;\
double phic;\
double c;\
double n1;\
double n2;\
double XS;\
double YS;
#define PJ_LIB__
# include <projects.h>
PROJ_HEAD(gstmerc, "Gauss-Schreiber Transverse Mercator (aka Gauss-Laborde Reunion)")
"\n\tCyl, Sph&Ell\n\tlat_0= lon_0= k_0=";
FORWARD(s_forward); /* spheroid */
double L, Ls, sinLs1, Ls1;
L= P->n1*lp.lam;
Ls= P->c+P->n1*log(pj_tsfn(-1.0*lp.phi,-1.0*sin(lp.phi),P->e));
sinLs1= sin(L)/cosh(Ls);
Ls1= log(pj_tsfn(-1.0*asin(sinLs1),0.0,0.0));
xy.x= (P->XS + P->n2*Ls1)*P->ra;
xy.y= (P->YS + P->n2*atan(sinh(Ls)/cos(L)))*P->ra;
return (xy);
}
INVERSE(s_inverse); /* spheroid */
double L, LC, sinC;
L= atan(sinh((xy.x - P->XS)*P->a/P->n2)/cos((xy.y - P->YS)*P->a/P->n2));
sinC= sin((xy.y - P->YS)*P->a/P->n2)/cosh((xy.x - P->XS)*P->a/P->n2);
LC= log(pj_tsfn(-1.0*asin(sinC),0.0,0.0));
lp.lam= L/P->n1;
lp.phi= -1.0*pj_phi2(exp((LC-P->c)/P->n1),P->e);
return (lp);
}
