// Polyconic inverse equations--mapping x,y to lat/long
long Projectoid::polyinv(
double x, // (O) X projection coordinate
double y, // (O) Y projection coordinate
double *lon, // (I) Longitude
double *lat) // (I) Latitude
{
double al; // temporary values
double b; // temporary values
double c; // temporary values
double t; // <<<F2 OPT>>>
long iflg; // error flag
// Inverse equations
x -= false_easting;
y -= false_northing;
al = ml0 + y / r_major;
iflg = 0;
t = x / r_major;
if (fabs(al) <= .0000001)
{
*lon = t + lon_center;
*lat = 0.0;
}
else
{
b = al * al + t * t;
iflg = phi4z(es, e0, e1, e2, e3, al, b, &c, lat);
if (iflg != OK)
return(iflg);
*lon = adjust_lon((asinz(t * c) / sin(*lat)) + lon_center);
}
return(OK);
}
/* Van Der Grinten forward equations--mapping lat,long to x,y
---------------------------------------------------------*/
long vandgfor
(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y /* (O) Y projection coordinate */
)
{
double dlon;
double theta;
double al,asq;
double g,gsq;
double m,msq;
double con;
double costh,sinth;
/* Forward equations
-----------------*/
dlon = adjust_lon(lon - lon_center);
if (fabs(lat) <= EPSLN)
{
*x = false_easting + R * dlon;
*y = false_northing;
return (GCTP_OK);
}
theta = asinz(2.0 * fabs(lat / PI));
if ((fabs(dlon) <= EPSLN) || (fabs(fabs(lat) - HALF_PI) <= EPSLN))
{
*x = false_easting;
if (lat >= 0)
*y = false_northing + PI * R * tan(.5 * theta);
else
*y = false_northing + PI * R * -tan(.5 * theta);
return(GCTP_OK);
}
al = .5 * fabs((PI / dlon) - (dlon / PI));
asq = al * al;
gctp_sincos(theta,&sinth,&costh);
g = costh / (sinth + costh - 1.0);
gsq = g * g;
m = g * (2.0 / sinth - 1.0);
msq = m * m;
con = PI * R * (al * (g - msq) + sqrt(asq * (g - msq) * (g - msq) - (msq + asq)
* (gsq - msq))) / (msq + asq);
if (dlon < 0)
con = -con;
*x = false_easting + con;
con = fabs(con / (PI * R));
if (lat >= 0)
*y = false_northing + PI * R * sqrt(1.0 - con * con - 2.0 * al * con);
else
*y = false_northing - PI * R * sqrt(1.0 - con * con - 2.0 * al * con);
return(GCTP_OK);
}
/* Azimuthal inverse equations--mapping x,y to lat/long
---------------------------------------------------*/
long aziminv
(
double x, /* (O) X projection coordinate */
double y, /* (O) Y projection coordinate */
double *lon, /* (I) Longitude */
double *lat /* (I) Latitude */
)
{
double rh; /* height above ellipsoid */
double z; /* angle */
double sinz,cosz; /* sin of z and cos of z */
double con;
/* Inverse equations
-----------------*/
x -= false_easting;
y -= false_northing;
rh = sqrt(x * x + y * y);
if (rh > (2.0 * HALF_PI * r_major))
{
GCTP_PRINT_ERROR("Input data error");
return(125);
}
z = rh / r_major;
sincos(z,&sinz,&cosz);
*lon = lon_center;
if (fabs(rh) <= EPSLN)
{
*lat = lat_origin;
return(OK);
}
*lat = asinz(cosz * sin_p12 + (y * sinz * cos_p12) / rh);
con = fabs(lat_origin) - HALF_PI;
if (fabs(con) <= EPSLN)
{
if (lat_origin >= 0.0)
{
*lon = adjust_lon(lon_center + atan2(x , -y));
return(OK);
}
else
{
*lon = adjust_lon(lon_center - atan2(-x , y));
return(OK);
}
}
con = cosz - sin_p12 * sin(*lat);
if ((fabs(con) < EPSLN) && (fabs(x) < EPSLN))
return(OK);
*lon = adjust_lon(lon_center + atan2((x * sinz * cos_p12), (con * rh)));
return(OK);
}
// Wagner VII inverse equations--mapping x,y to lat,long
long Projectoid::wviiinv(
double x, // (I) X projection coordinate
double y, // (I) Y projection coordinate
double *lon, // (O) Longitude
double *lat) // (O) Latitude
{
double t1, t2, p, c;
// Inverse equations
x -= false_easting;
y -= false_northing;
t1 = x * (1.0 / 2.66723); // <<<F2 OPT>>>
t2 = y * (1.0 / 1.24104); // <<<F2 OPT>>>
t1 *= t1;
t2 *= t2;
p = sqrt(t1 + t2);
c = 2.0 * asinz(p / (2.0 * R));
*lat = asinz(y * sin(c) / (1.24104 * 0.90631 * p));
*lon = adjust_lon(lon_center + 3.0 * atan2(x * tan(c), 2.66723 * p));
return(OK);
}
/* Wagner VII inverse equations--mapping x,y to lat,long
-----------------------------------------------------*/
long wviiinv
(
double x, /* (I) X projection coordinate */
double y, /* (I) Y projection coordinate */
double *lon, /* (O) Longitude */
double *lat /* (O) Latitude */
)
{
double t1, t2, p, c;
/* Inverse equations
-----------------*/
x -= false_easting;
y -= false_northing;
t1 = x / 2.66723;
t2 = y / 1.24104;
t1 *= t1;
t2 *= t2;
p = sqrt(t1 + t2);
c = 2.0 * asinz(p / (2.0 * R));
*lat = asinz(y * sin(c) / (1.24104 * 0.90631 * p));
*lon = adjust_lon(lon_center + 3.0 * atan2(x * tan(c), 2.66723 * p));
return(OK);
}
/* HAMMER inverse equations--mapping x,y to lat/long
------------------------------------------------*/
int haminv(
double x, /* (O) X projection coordinate */
double y, /* (O) Y projection coordinate */
double *lon, /* (I) Longitude */
double *lat) /* (I) Latitude */
{
double fac;
/* Inverse equations
-----------------*/
x -= false_easting;
y -= false_northing;
fac = sqrt(4.0 * R * R - (x * x)/ 4.0 - y * y) / 2.0;
*lon = adjust_lon(lon_center + 2.0 *
atan2((x * fac), (2.0 * R * R - x * x/4 - y * y)));
*lat = asinz(y * fac / R / R);
return(OK);
}
double Util::phi1z ( double eccent, /* Eccentricity angle in radians */
double qs, /* Angle in radians */
long *flag ) /* Error flag number */
{
double eccnts;
double dphi;
double con;
double com;
double sinpi;
double cospi;
double phi;
long i;
phi = asinz(.5 * qs);
if (eccent < EPSLN)
return(phi);
eccnts = eccent * eccent;
for (i = 1; i <= 25; i++)
{
Util::gctp_sincos(phi,&sinpi,&cospi);
con = eccent * sinpi;
com = 1.0 - con * con;
dphi = .5 * com * com / cospi * (qs / (1.0 - eccnts) - sinpi / com +
.5 / eccent * log ((1.0 - con) / (1.0 + con)));
phi = phi + dphi;
if (fabs(dphi) <= 1e-7)
return(phi);
}
// p_error ("Convergence error","phi1z-conv");
*flag = 001;
return(ERROR);
}
/* ALASKA CONFORMAL inverse equations--mapping x,y to lat/long
----------------------------------------------------------*/
long alconinv
(
double x, /* (O) X projection coordinate */
double y, /* (O) Y projection coordinate */
double *lon, /* (I) Longitude */
double *lat /* (I) Latitude */
)
{
double esphi;
double r;
double s;
double br;
double bi;
double ai;
double ar;
double ci;
double cr;
double di;
double dr;
double arn = 0.0;
double ain = 0.0;
double crn;
double cin;
double fxyr;
double fxyi;
double fpxyr;
double fpxyi;
double xp,yp;
double den;
double dxp;
double dyp;
double ds;
double z;
double cosz;
double sinz;
double rh;
double chi;
double dphi;
double phi;
long j;
long nn;
/* Inverse equations
-----------------*/
x = (x - false_easting) / r_major;
y = (y - false_northing) / r_major;
xp = x;
yp = y;
nn = 0;
/* Use Knuth algorithm for summing complex terms, to convert Modified-
Stereographic conformal to Oblique Stereographic coordinates.
--------------------------------------------------------------------*/
do
{
r = xp + xp;
s = xp * xp + yp * yp;
ar = acoef[n];
ai = bcoef[n];
br = acoef[n -1];
bi = bcoef[n - 1];
cr = (double) (n) * ar;
ci = (double) (n) * ai;
dr = (double) (n -1) * br;
di = (double) (n -1) * bi;
for (j = 2; j <= n; j++)
{
arn = br + r * ar;
ain = bi + r * ai;
if (j < n)
{
br = acoef[n -j] - s * ar;
bi = bcoef[n - j] - s * ai;
ar = arn;
ai = ain;
crn = dr + r * cr;
cin = di + r * ci;
dr = (double) (n - j) * acoef[n -j] - s * cr;
di = (double) (n - j) * bcoef[n -j] - s * ci;
cr = crn;
ci = cin;
}
}
br = -s * ar;
bi = -s * ai;
ar = arn;
ai = ain;
fxyr = xp * ar - yp * ai + br - x;
fxyi = yp * ar + xp * ai + bi - y;
fpxyr = xp * cr - yp * ci + dr;
fpxyi = yp * cr + xp * ci + ci;
den = fpxyr * fpxyr + fpxyi * fpxyi;
dxp = -(fxyr * fpxyr + fxyi * fpxyi) / den;
dyp = -(fxyi * fpxyr - fxyr * fpxyi) / den;
xp = xp + dxp;
yp = yp + dyp;
ds = fabs(dxp) + fabs(dyp);
nn++;
if (nn > 20)
{
p_error("Too many iterations in inverse","alcon-inv");
return(235);
}
}
while (ds > EPSLN);
/* convert Oblique Stereographic coordinates to LAT/LONG
------------------------------------------------------*/
rh = sqrt(xp * xp + yp * yp);
z = 2.0 * atan(rh / 2.0);
gctp_sincos(z,&sinz,&cosz);
*lon = lon_center;
if (fabs(rh) <= EPSLN)
{
*lat = lat_center;
return(GCTP_OK);
}
chi = asinz(cosz * sin_p26 + (yp * sinz * cos_p26) / rh);
nn = 0;
phi = chi;
do
{
esphi = e * sin(phi);
dphi = 2.0 * atan(tan((HALF_PI + chi) / 2.0) *
pow(((1.0 + esphi) / (1.0 - esphi)),(e / 2.0))) - HALF_PI - phi;
phi += dphi;
nn++;
if (nn > 20)
{
p_error("Too many iterations in inverse","alcon-inv");
return(236);
}
}
while(fabs(dphi) > EPSLN);
*lat = phi;
*lon = adjust_lon (lon_center + atan2((xp * sinz), (rh * cos_p26 * cosz - yp *
sin_p26 * sinz)));
return(GCTP_OK);
}
/*****************************************************************************
Name: inverse_transform
Purpose: Transforms UTM/TM X,Y to lat,long
Returns:
GCTP_SUCCESS or GCTP_ERROR
*****************************************************************************/
static int inverse_transform
(
const TRANSFORMATION *trans, /* I: transformation information */
double x, /* I: X projection coordinate */
double y, /* I: Y projection coordinate */
double *lon, /* O: Longitude */
double *lat /* O: Latitude */
)
{
struct tm_proj *cache_ptr = (struct tm_proj *)trans->cache;
double con,phi; /* temporary angles */
double delta_phi; /* difference between longitudes */
long i; /* counter variable */
double sin_phi, cos_phi, tan_phi; /* sin cos and tangent values */
double c, cs, t, ts, n, r, d, ds; /* temporary variables */
double f, h, g, temp; /* temporary variables */
long max_iter = 6; /* maximun number of iterations */
/* Use the spherical form if possible */
if (cache_ptr->is_sphere)
{
f = exp(x / (cache_ptr->r_major * cache_ptr->scale_factor));
g = 0.5 * (f - 1.0/f);
temp = cache_ptr->lat_origin + y
/(cache_ptr->r_major * cache_ptr->scale_factor);
h = cos(temp);
con = sqrt((1.0 - h * h)/(1.0 + g * g));
*lat = asinz(con);
if (temp < 0)
*lat = -*lat;
if ((g == 0) && (h == 0))
{
*lon = cache_ptr->lon_center;
return GCTP_SUCCESS;
}
else
{
*lon = adjust_lon(atan2(g,h) + cache_ptr->lon_center);
return GCTP_SUCCESS;
}
}
/* Inverse equations */
x = x - cache_ptr->false_easting;
y = y - cache_ptr->false_northing;
con = (cache_ptr->ml0 + y / cache_ptr->scale_factor) / cache_ptr->r_major;
phi = con;
for (i = 0; ; i++)
{
delta_phi = ((con + cache_ptr->e1 * sin(2.0*phi) - cache_ptr->e2
* sin(4.0*phi) + cache_ptr->e3 * sin(6.0*phi))
/ cache_ptr->e0) - phi;
phi += delta_phi;
if (fabs(delta_phi) <= EPSLN)
break;
if (i >= max_iter)
{
GCTP_PRINT_ERROR("Latitude failed to converge in inverse "
"transform");
return GCTP_ERROR;
}
}
if (fabs(phi) < HALF_PI)
{
sincos(phi, &sin_phi, &cos_phi);
tan_phi = tan(phi);
c = cache_ptr->esp * SQUARE(cos_phi);
cs = SQUARE(c);
t = SQUARE(tan_phi);
ts = SQUARE(t);
con = 1.0 - cache_ptr->es * SQUARE(sin_phi);
n = cache_ptr->r_major / sqrt(con);
r = n * (1.0 - cache_ptr->es) / con;
d = x / (n * cache_ptr->scale_factor);
ds = SQUARE(d);
*lat = phi - (n * tan_phi * ds / r) * (0.5 - ds / 24.0 * (5.0 + 3.0
* t + 10.0 * c - 4.0 * cs - 9.0 * cache_ptr->esp - ds / 30.0
* (61.0 + 90.0 * t + 298.0 * c + 45.0 * ts - 252.0
* cache_ptr->esp - 3.0 * cs)));
*lon = adjust_lon(cache_ptr->lon_center + (d * (1.0 - ds / 6.0
* (1.0 + 2.0 * t + c - ds / 20.0 * (5.0 - 2.0 * c + 28.0
* t - 3.0 * cs + 8.0 * cache_ptr->esp + 24.0 * ts)))
/ cos_phi));
}
else
{
*lat = HALF_PI * gctp_get_sign(y);
*lon = cache_ptr->lon_center;
}
return GCTP_SUCCESS;
}
int inverse_albers_conic_equal_area_ellipsoid(mapx_class *current,
double x, double y,
double *lat, double *lon)
{
double phi, lam, rho, rmy, theta, q;
double q_test;
double cos_phi;
double sin_phi;
double esin_phi;
double one_m_e2sin2_phi;
double delta_phi;
double one_m_e2;
double one_over_2e;
double epsilon = 1e-6;
int it_max = 35;
int i;
x -= current->false_easting;
y -= current->false_northing;
rmy = current->rho0 - y;
rho = sqrt( x*x + rmy*rmy );
theta = current->n >= 0 ?
atan2( x, rmy) :
atan2(-x, -rmy);
lam = theta / current->n;
q = (current->C - ( (rho*rho*current->n*current->n) /
(current->Rg*current->Rg) ) ) / current->n;
/*** Calculate phi using equation 3-16, Snyder 1987, p102 ***/
q_test = 1.0 - (1.0 - current->e2)/(2.0 * current->eccentricity) *
log((1.0 - current->eccentricity) / (1.0 + current->eccentricity));
if (fabs(fabs(q) - fabs(q_test)) < epsilon) {
phi = sign(q) * PI / 2;
} else {
phi = asinz(q / 2.0);
one_m_e2 = 1.0 - current->e2;
one_over_2e = 1.0 / (2.0 * current->eccentricity);
for (i = 0; i < it_max; i++) {
cos_phi = cos(phi);
if (cos_phi < epsilon) {
phi = sign(q) * PI / 2;
break;
}
sin_phi = sin(phi);
esin_phi = current->eccentricity * sin_phi;
one_m_e2sin2_phi = 1.0 - esin_phi * esin_phi;
delta_phi = one_m_e2sin2_phi * one_m_e2sin2_phi / (2.0 * cos_phi) *
(q / one_m_e2 - sin_phi / one_m_e2sin2_phi + one_over_2e *
log((1.0 - esin_phi) / (1.0 + esin_phi)));
phi += delta_phi;
if (fabs(delta_phi) < epsilon)
break;
}
}
*lat = DEGREES(phi);
*lon = DEGREES(lam) + current->lon0;
NORMALIZE(*lon);
return 0;
}
/* Initialize the General Lambert Azimuthal Equal Area projection
--------------------------------------------------------------*/
int lamazforint(
double r_maj, /* major axis */
double r_min, /* minor axis */
double center_long, /* (I) Center longitude */
double center_lat, /* (I) Center latitude */
double false_east, /* x offset in meters */
double false_north) /* y offset in meters */
{
/* Place parameters in static storage for common use
-------------------------------------------------*/
R = r_maj;
if(fabs(r_min) < EPSLN ) /* sphere */
{
r_major = r_maj;
r_minor = r_maj;
}
else /* sphere or ellipsoide */
{
r_major = r_maj;
r_minor = r_min;
}
lon_center = center_long;
lat_center = center_lat;
false_easting = false_east;
false_northing = false_north;
tsincos(center_lat, &sin_lat_o, &cos_lat_o);
sinphi1 = sin_lat_o;
cosphi1 = cos_lat_o;
es = 1.0 - SQUARE(r_minor / r_major);
e = sqrt(es);
if(es < 0.00001)
{
ind = 1; /* sphere */
qp = 2.0;
q1 = 2.0;
}
else
{
ind = 0; /* ellipsoid */
qp = (1.0 - es)* (((1.0/(1.0 - es))-(1.0/(2.0*e))*log((1.0 - e)/(1.0 + e))));
if((fabs (lat_center - HALF_PI) <= EPSLN ) || (fabs (lat_center + HALF_PI) <= EPSLN ))
{
/* no other constants needed for LA with North and South polar Aspects lat_center = 90 or -90*/
}
else
{
tsincos(lat_center, &sinphi1, &cosphi1);
q1 = (1.0 - es) * ((sinphi1 / (1.0 - es * sinphi1 * sinphi1))
- (1.0 / (2.0 * e)) *
log((1.0 - e * sinphi1)/(1.0 + e * sinphi1)));
Rq = r_major * sqrt(qp/2.0);
if(fabs(q1) >= fabs(qp))
{
beta1 = HALF_PI * (fabs(q1/qp)/(q1/qp));
}
else
{
beta1 = asinz(q1/qp);
}
tsincos(beta1, &sin_beta1, &cos_beta1);
m1 = cosphi1 / sqrt(1.0 - es * sinphi1 * sinphi1);
D = (r_major * m1)/ (Rq * cos_beta1);
}
}
/* Report parameters to the user
-----------------------------*/
ptitle("LAMBERT AZIMUTHAL EQUAL-AREA");
radius2(r_major, r_minor);
cenlon(center_long);
cenlat(center_lat);
offsetp(false_easting,false_northing);
return(OK);
}
/* Lambert Azimuthal Equal Area forward equations--mapping lat,long to x,y
-----------------------------------------------------------------------*/
int lamazfor(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y) /* (O) Y projection coordinate */
{
double delta_lon; /* Delta longitude (Given longitude - center */
double sin_delta_lon; /* Sine of the delta longitude */
double cos_delta_lon; /* Cosine of the delta longitude */
double sinphi; /* Sine of the center latitude */
double cosphi; /* Cosine of the center latitude */
double sin_lat; /* Sine of the given latitude */
double cos_lat; /* Cosine of the given latitude */
double g; /* temporary varialbe */
double ksp; /* heigth above elipsiod */
char mess[60];
double qpmq, qppq, rho;
double beta, sin_beta, cos_beta;
double q, B;
/* Forward equations
-----------------*/
if( ind != 0) /* sphere */
{
delta_lon = adjust_lon(lon - lon_center);
tsincos(lat, &sin_lat, &cos_lat);
tsincos(delta_lon, &sin_delta_lon, &cos_delta_lon);
g = sin_lat_o * sin_lat + cos_lat_o * cos_lat * cos_delta_lon;
if (g == -1.0)
{
sprintf(mess, "Point projects to a circle of radius = %lf\n", 2.0 * R);
p_error(mess, "lamaz-forward");
return(113);
}
ksp = R * sqrt(2.0 / (1.0 + g));
*x = ksp * cos_lat * sin_delta_lon + false_easting;
*y = ksp * (cos_lat_o * sin_lat - sin_lat_o * cos_lat * cos_delta_lon) +
false_northing;
}
else /* ellipsoid */
{
delta_lon = adjust_lon(lon - lon_center);
tsincos(lat, &sinphi, &cosphi);
q = (1.0 - es) * ((sinphi / (1.0 - es * sinphi * sinphi))
- (1.0 / (2.0 * e)) *
log((1.0 - e * sinphi)/(1.0 + e * sinphi)));
if (fabs(lat_center - HALF_PI) <= EPSLN) /* if Northern Polar Aspect */
{
qpmq = qp - q;
if (fabs(qpmq) <= EPSLN)
{
rho = 0.0;
}
else
{
rho = r_major * sqrt(qpmq);
}
*x = false_easting + rho * sin(delta_lon);
*y = false_northing - rho * cos(delta_lon);
}
else if (fabs(lat_center + HALF_PI) <= EPSLN) /* if Southern Polar Aspect */
{
qppq = qp + q;
if (fabs(qppq) <= EPSLN)
{
rho = 0.0;
}
else
{
rho = r_major * sqrt(qppq);
}
*x = false_easting + rho * sin(delta_lon);
*y = false_northing + rho * cos(delta_lon);
}
else /* with any other latitude of origin */
{
beta = asinz(q/qp);
tsincos(beta, &sin_beta, &cos_beta);
B = Rq * sqrt((2.0/(1.0 + sin_beta1 * sin_beta + cos_beta1 * cos_beta * cos(delta_lon))));
*x = false_easting + (B*D) * (cos_beta * sin(delta_lon));
*y = false_northing + (B/D) * (cos_beta1 * sin_beta - sin_beta1 * cos_beta * cos(delta_lon));
}
}
return(OK);
}
