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.;
}
inline void fwd(geographic_type& lp_lon, geographic_type& lp_lat, cartesian_type& xy_x, cartesian_type& xy_y) const
{
double t, z1, z2, dl1, dl2, sp, cp;
sp = sin(lp_lat);
cp = cos(lp_lat);
z1 = aacos(this->m_proj_parm.sp1 * sp + this->m_proj_parm.cp1 * cp * cos(dl1 = lp_lon + this->m_proj_parm.dlam2));
z2 = aacos(this->m_proj_parm.sp2 * sp + this->m_proj_parm.cp2 * cp * cos(dl2 = lp_lon - this->m_proj_parm.dlam2));
z1 *= z1;
z2 *= z2;
xy_x = this->m_proj_parm.r2z0 * (t = z1 - z2);
t = this->m_proj_parm.z02 - t;
xy_y = this->m_proj_parm.r2z0 * asqrt(4. * this->m_proj_parm.z02 * z2 - t * t);
if ((this->m_proj_parm.ccs * sp - cp * (this->m_proj_parm.cs * sin(dl1) - this->m_proj_parm.sc * sin(dl2))) < 0.)
xy_y = -xy_y;
}
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 XY s_forward (LP lp, PJ *P) { /* Spheroidal, forward */
XY xy = {0.0, 0.0};
struct pj_opaque *Q = P->opaque;
double t, z1, z2, dl1, dl2, sp, cp;
sp = sin(lp.phi);
cp = cos(lp.phi);
z1 = aacos(P->ctx, Q->sp1 * sp + Q->cp1 * cp * cos (dl1 = lp.lam + Q->dlam2));
z2 = aacos(P->ctx, Q->sp2 * sp + Q->cp2 * cp * cos (dl2 = lp.lam - Q->dlam2));
z1 *= z1;
z2 *= z2;
xy.x = Q->r2z0 * (t = z1 - z2);
t = Q->z02 - t;
xy.y = Q->r2z0 * asqrt (4. * Q->z02 * z2 - t * t);
if ((Q->ccs * sp - cp * (Q->cs * sin(dl1) - Q->sc * sin(dl2))) < 0.)
xy.y = -xy.y;
return xy;
}
// 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);
}
HRESULT math_acos(ScriptVariant **varlist , ScriptVariant **pretvar, int paramCount)
{
DOUBLE dbltemp;
if(SUCCEEDED(ScriptVariant_DecimalValue(varlist[0], &dbltemp)))
{
double PI = 3.14159265;
ScriptVariant_ChangeType(*pretvar, VT_DECIMAL);
(*pretvar)->dblVal = (DOUBLE)(aacos((double)dbltemp) * 180.0 / PI);
return S_OK;
}
*pretvar = NULL;
return E_FAIL;
}
PJ *PROJECTION(tpeqd) {
double lam_1, lam_2, phi_1, phi_2, A12, pp;
struct pj_opaque *Q = pj_calloc (1, sizeof (struct pj_opaque));
if (0==Q)
return freeup_new (P);
P->opaque = Q;
/* get control point locations */
phi_1 = pj_param(P->ctx, P->params, "rlat_1").f;
lam_1 = pj_param(P->ctx, P->params, "rlon_1").f;
phi_2 = pj_param(P->ctx, P->params, "rlat_2").f;
lam_2 = pj_param(P->ctx, P->params, "rlon_2").f;
if (phi_1 == phi_2 && lam_1 == lam_2)
E_ERROR(-25);
P->lam0 = adjlon (0.5 * (lam_1 + lam_2));
Q->dlam2 = adjlon (lam_2 - lam_1);
Q->cp1 = cos (phi_1);
Q->cp2 = cos (phi_2);
Q->sp1 = sin (phi_1);
Q->sp2 = sin (phi_2);
Q->cs = Q->cp1 * Q->sp2;
Q->sc = Q->sp1 * Q->cp2;
Q->ccs = Q->cp1 * Q->cp2 * sin(Q->dlam2);
Q->z02 = aacos(P->ctx, Q->sp1 * Q->sp2 + Q->cp1 * Q->cp2 * cos (Q->dlam2));
Q->hz0 = .5 * Q->z02;
A12 = atan2(Q->cp2 * sin (Q->dlam2),
Q->cp1 * Q->sp2 - Q->sp1 * Q->cp2 * cos (Q->dlam2));
Q->ca = cos(pp = aasin(P->ctx, Q->cp1 * sin(A12)));
Q->sa = sin(pp);
Q->lp = adjlon ( atan2 (Q->cp1 * cos(A12), Q->sp1) - Q->hz0);
Q->dlam2 *= .5;
Q->lamc = M_HALFPI - atan2(sin(A12) * Q->sp1, cos(A12)) - Q->dlam2;
Q->thz0 = tan (Q->hz0);
Q->rhshz0 = .5 / sin (Q->hz0);
Q->r2z0 = 0.5 / Q->z02;
Q->z02 *= Q->z02;
P->inv = s_inverse;
P->fwd = s_forward;
P->es = 0.;
return P;
}
inline void inv(cartesian_type& xy_x, cartesian_type& xy_y, geographic_type& lp_lon, geographic_type& lp_lat) const
{
double cz1, cz2, s, d, cp, sp;
cz1 = cos(boost::math::hypot(xy_y, xy_x + this->m_proj_parm.hz0));
cz2 = cos(boost::math::hypot(xy_y, xy_x - this->m_proj_parm.hz0));
s = cz1 + cz2;
d = cz1 - cz2;
lp_lon = - atan2(d, (s * this->m_proj_parm.thz0));
lp_lat = aacos(boost::math::hypot(this->m_proj_parm.thz0 * s, d) * this->m_proj_parm.rhshz0);
if ( xy_y < 0. )
lp_lat = - lp_lat;
/* lam--phi now in system relative to P1--P2 base equator */
sp = sin(lp_lat);
cp = cos(lp_lat);
lp_lat = aasin(this->m_proj_parm.sa * sp + this->m_proj_parm.ca * cp * (s = cos(lp_lon -= this->m_proj_parm.lp)));
lp_lon = atan2(cp * sin(lp_lon), this->m_proj_parm.sa * cp * s - this->m_proj_parm.ca * sp) + this->m_proj_parm.lamc;
}
static VECT /* distance and azimuth from point 1 to point 2 */
vect(projCtx ctx, double dphi, double c1, double s1, double c2, double s2, double dlam) {
VECT v;
double cdl, dp, dl;
cdl = cos(dlam);
if (fabs(dphi) > 1. || fabs(dlam) > 1.)
v.r = aacos(ctx, s1 * s2 + c1 * c2 * cdl);
else { /* more accurate for smaller distances */
dp = sin(.5 * dphi);
dl = sin(.5 * dlam);
v.r = 2. * aasin(ctx,sqrt(dp * dp + c1 * c2 * dl * dl));
}
if (fabs(v.r) > TOL)
v.Az = atan2(c2 * sin(dlam), c1 * s2 - s1 * c2 * cdl);
else
v.r = v.Az = 0.;
return v;
}
static LP s_inverse (XY xy, PJ *P) { /* Spheroidal, inverse */
LP lp = {0.0,0.0};
struct pj_opaque *Q = P->opaque;
double cz1, cz2, s, d, cp, sp;
cz1 = cos (hypot(xy.y, xy.x + Q->hz0));
cz2 = cos (hypot(xy.y, xy.x - Q->hz0));
s = cz1 + cz2;
d = cz1 - cz2;
lp.lam = - atan2(d, (s * Q->thz0));
lp.phi = aacos(P->ctx, hypot (Q->thz0 * s, d) * Q->rhshz0);
if ( xy.y < 0. )
lp.phi = - lp.phi;
/* lam--phi now in system relative to P1--P2 base equator */
sp = sin (lp.phi);
cp = cos (lp.phi);
lp.phi = aasin (P->ctx, Q->sa * sp + Q->ca * cp * (s = cos(lp.lam -= Q->lp)));
lp.lam = atan2 (cp * sin(lp.lam), Q->sa * cp * s - Q->ca * sp) + Q->lamc;
return lp;
}
inline void setup_tpeqd(Params const& params, Parameters& par, par_tpeqd<T>& proj_parm)
{
T lam_1, lam_2, phi_1, phi_2, A12, pp;
/* get control point locations */
phi_1 = pj_get_param_r<T, srs::spar::lat_1>(params, "lat_1", srs::dpar::lat_1);
lam_1 = pj_get_param_r<T, srs::spar::lon_1>(params, "lon_1", srs::dpar::lon_1);
phi_2 = pj_get_param_r<T, srs::spar::lat_2>(params, "lat_2", srs::dpar::lat_2);
lam_2 = pj_get_param_r<T, srs::spar::lon_2>(params, "lon_2", srs::dpar::lon_2);
if (phi_1 == phi_2 && lam_1 == lam_2)
BOOST_THROW_EXCEPTION( projection_exception(error_control_point_no_dist) );
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 = geometry::math::half_pi<T>() - 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.es = 0.;
}
#define PROJ_PARMS__ \ double theta; \ double m, n; \ double two_r_m, two_r_n, rm, rn, hm, hn; \ double cp0, sp0; #define PJ_LIB__ #include "projects.h" PROJ_HEAD(oea, "Oblated Equal Area") "\n\tMisc Sph\n\tn= m= theta="; FORWARD(s_forward); /* sphere */ double Az, hz, M, N, cp, sp, cl, shz; cp = cos(lp.phi); sp = sin(lp.phi); cl = cos(lp.lam); Az = aatan2(cp * sin(lp.lam), P->cp0 * sp - P->sp0 * cp * cl) + P->theta; shz = sin(0.5 * aacos(P->sp0 * sp + P->cp0 * cp * cl)); M = aasin(shz * sin(Az)); N = aasin(shz * cos(Az) * cos(M) / cos(M * P->two_r_m)); xy.y = P->n * sin(N * P->two_r_n); xy.x = P->m * sin(M * P->two_r_m) * cos(N) / cos(N * P->two_r_n); return (xy); } INVERSE(s_inverse); /* sphere */ double N, M, xp, yp, z, Az, cz, sz, cAz; N = P->hn * aasin(xy.y * P->rn); M = P->hm * aasin(xy.x * P->rm * cos(N * P->two_r_n) / cos(N)); xp = 2. * sin(M); yp = 2. * sin(N) * cos(M * P->two_r_m) / cos(M); cAz = cos(Az = aatan2(xp, yp) - P->theta); z = 2. * aasin(0.5 * hypot(xp, yp));
#define PROJ_PARMS__ \ double cp1, sp1, cp2, sp2, ccs, cs, sc, r2z0, z02, dlam2; \ double hz0, thz0, rhshz0, ca, sa, lp, lamc; #define PJ_LIB__ #include <projects.h> PROJ_HEAD(tpeqd, "Two Point Equidistant") "\n\tMisc Sph\n\tlat_1= lon_1= lat_2= lon_2="; FORWARD(s_forward); /* sphere */ double t, z1, z2, dl1, dl2, sp, cp; sp = sin(lp.phi); cp = cos(lp.phi); z1 = aacos(P->ctx, P->sp1 *sp + P->cp1 * cp * cos(dl1 = lp.lam + P->dlam2)); z2 = aacos(P->ctx, P->sp2 *sp + P->cp2 * cp * cos(dl2 = lp.lam - P->dlam2)); z1 *= z1; z2 *= z2; xy.x = P->r2z0 * (t = z1 - z2); t = P->z02 - t; xy.y = P->r2z0 * asqrt(4. * P->z02 * z2 - t * t); if ((P->ccs * sp - cp * (P->cs * sin(dl1) - P->sc * sin(dl2))) < 0.) xy.y = -xy.y; return xy; } INVERSE(s_inverse); /* sphere */ double cz1, cz2, s, d, cp, sp; cz1 = cos(hypot(xy.y, xy.x + P->hz0)); cz2 = cos(hypot(xy.y, xy.x - P->hz0)); s = cz1 + cz2; d = cz1 - cz2; lp.lam = -atan2(d, (s * P->thz0));
static double /* law of cosines */
lc(projCtx ctx, double b,double c,double a) {
return aacos(ctx, .5 * (b * b + c * c - a * a) / (b * c));
}