int G_begin_geodesic_equation(double lon1, double lat1, double lon2,
double lat2)
{
double sin21, tan1, tan2;
adjust_lon(&lon1);
adjust_lon(&lon2);
adjust_lat(&lat1);
adjust_lat(&lat2);
if (lon1 > lon2) {
double temp;
temp = lon1; lon1 = lon2; lon2 = temp;
temp = lat1; lat1 = lat2; lat2 = temp;
}
if (lon1 == lon2) {
st->A = st->B = 0.0;
return 0;
}
lon1 = Radians(lon1);
lon2 = Radians(lon2);
lat1 = Radians(lat1);
lat2 = Radians(lat2);
sin21 = sin(lon2 - lon1);
tan1 = tan(lat1);
tan2 = tan(lat2);
st->A = (tan2 * cos(lon1) - tan1 * cos(lon2)) / sin21;
st->B = (tan2 * sin(lon1) - tan1 * sin(lon2)) / sin21;
return 1;
}
int G_begin_geodesic_equation(double lon1, double lat1, double lon2,
double lat2)
{
double sin21, tan1, tan2;
adjust_lon(&lon1);
adjust_lon(&lon2);
adjust_lat(&lat1);
adjust_lat(&lat2);
if (lon1 > lon2) {
register double temp;
SWAP(lon1, lon2);
SWAP(lat1, lat2);
}
if (lon1 == lon2) {
A = B = 0.0;
return 0;
}
lon1 = Radians(lon1);
lon2 = Radians(lon2);
lat1 = Radians(lat1);
lat2 = Radians(lat2);
sin21 = sin(lon2 - lon1);
tan1 = tan(lat1);
tan2 = tan(lat2);
A = (tan2 * cos(lon1) - tan1 * cos(lon2)) / sin21;
B = (tan2 * sin(lon1) - tan1 * sin(lon2)) / sin21;
return 1;
}
/* Sinusoidal inverse equations--mapping x,y to lat,long
-----------------------------------------------------*/
int sininv(
double x, /* (I) X projection coordinate */
double y, /* (I) Y projection coordinate */
double *lon, /* (O) Longitude */
double *lat) /* (O) Latitude */
{
double temp; /* Re-used temporary variable */
double mu, ml;
double sin_phi, cos_phi;
/* Inverse equations
-----------------*/
x -= false_easting;
y -= false_northing;
if (ind != 0) /* Spherical */
{
*lat = y / R;
if (fabs(*lat) > HALF_PI)
{
p_error("Input data error","sinusoidal-inverse");
return(164);
}
temp = fabs(*lat) - HALF_PI;
if (fabs(temp) > EPSLN)
{
temp = lon_center + x / (R * cos(*lat));
*lon = adjust_lon(temp);
}
else *lon = lon_center;
return(OK);
}
else /* Ellipsoidal */
{
ml = y;
mu = ml / (r_major * imu);
*lat = mu +
(e2 * sin(2.0 * mu)) +
(e3 * sin(4.0 * mu)) +
(e4 * sin(6.0 * mu)) +
(e5 * sin(8.0 * mu));
if (fabs(*lat) > HALF_PI)
{
p_error("Input data error","sinusoidal-inverse");
return(164);
}
temp = fabs(*lat) - HALF_PI;
if (fabs(temp) > EPSLN)
{
sin_phi = sin(*lat);
cos_phi = cos(*lat);
temp = lon_center +
x * sqrt(1.0 - es * SQUARE(sin_phi)) / (r_major * cos_phi);
*lon = adjust_lon(temp);
}
else *lon = lon_center;
return(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);
}
/* Polar Stereographic inverse equations--mapping x,y to lat/long
--------------------------------------------------------------*/
long psinv
(
double x, /* (O) X projection coordinate */
double y, /* (O) Y projection coordinate */
double *lon, /* (I) Longitude */
double *lat /* (I) Latitude */
)
{
double rh; /* height above ellipsiod */
double ts; /* small value t */
double temp; /* temporary variable */
long flag; /* error flag */
flag = 0;
x = (x - false_easting) * fac;
y = (y - false_northing) *fac;
rh = sqrt(x * x + y * y);
if (ind != 0)
ts = rh * tcs/(r_major * mcs);
else
ts = rh * e4 / (r_major * 2.0);
*lat = fac * phi2z(e,ts,&flag);
if (flag != 0)
return(flag);
if (rh == 0)
*lon = fac * center_lon;
else
{
temp = atan2(x, -y);
*lon = adjust_lon(fac *temp + center_lon);
}
return(GCTP_OK);
}
/* Lambert Azimuthal Equal Area forward equations--mapping lat,long to x,y
-----------------------------------------------------------------------*/
long 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 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];
/* Forward equations
-----------------*/
delta_lon = adjust_lon(lon - lon_center);
gctp_sincos(lat, &sin_lat, &cos_lat);
gctp_sincos(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 = %f\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;
return(GCTP_OK);
}
/* Mollweide inverse equations--mapping x,y to lat,long
----------------------------------------------------*/
long molwinv
(
double x, /* (I) X projection coordinate */
double y, /* (I) Y projection coordinate */
double *lon, /* (O) Longitude */
double *lat /* (O) Latitude */
)
{
double theta;
double arg;
/* Inverse equations
-----------------*/
x -= false_easting;
y -= false_northing;
arg = y / (1.4142135623731 * R);
/* Because of division by zero problems, 'arg' can not be 1.0. Therefore
a number very close to one is used instead.
-------------------------------------------------------------------*/
if(fabs(arg) > 0.999999999999) arg=0.999999999999;
theta = asin(arg);
*lon = adjust_lon(lon_center + (x / (0.900316316158 * R * cos(theta))));
if(*lon < (-PI)) *lon= -PI;
if(*lon > PI) *lon= PI;
arg = (2.0 * theta + sin(2.0 * theta)) / PI;
if(fabs(arg) > 1.0)arg=1.0;
*lat = asin(arg);
return(OK);
}
/* Orthographic forward equations--mapping lat,long to x,y
---------------------------------------------------*/
long orthfor
(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y /* (O) Y projection coordinate */
)
{
double sinphi, cosphi; /* sin and cos value */
double dlon; /* delta longitude value */
double coslon; /* cos of longitude */
double ksp; /* scale factor */
double g;
/* Forward equations
-----------------*/
dlon = adjust_lon(lon - lon_center);
sincos(lat,&sinphi,&cosphi);
coslon = cos(dlon);
g = sin_p14 * sinphi + cos_p14 * cosphi * coslon;
ksp = 1.0;
if ((g > 0) || (fabs(g) <= EPSLN))
{
*x = false_easting + r_major * ksp * cosphi * sin(dlon);
*y = false_northing + r_major * ksp * (cos_p14 * sinphi -
sin_p14 * cosphi * coslon);
}
else
{
GCTP_PRINT_ERROR("Point can not be projected");
return(143);
}
return(OK);
}
// Polar Stereographic inverse equations--mapping x,y to lat/long
long Projectoid::psinv(
double x, // (O) X projection coordinate
double y, // (O) Y projection coordinate
double *lon, // (I) Longitude
double *lat) // (I) Latitude
{
double rh; // height above ellipsiod
double ts; // small value t
double temp; // temporary variable
long flag; // error flag
flag = 0;
x = (x - false_easting) * fac;
y = (y - false_northing) * fac;
rh = sqrt(x * x + y * y);
if (ind != 0)
ts = rh * tcs / (r_major * mcs);
else
ts = rh * e4 / (r_major * 2.0);
*lat = fac * phi2z(e, ts, &flag);
if (flag != 0)
return(flag);
if (rh == 0)
*lon = fac * center_lon;
else
{
temp = atan2(x, -y);
*lon = adjust_lon(fac * temp + center_lon);
}
return(OK);
}
/* Cylinderical Equal Area forward equations--mapping lat,long to x,y
--------------------------------------------------*/
int ceafor(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y) /* (O) Y projection coordinate */
{
double dlon; /* delta longitude value */
double sinphi; /* sin value */
double q;
/* Forward equations
-----------------*/
dlon = adjust_lon(lon - lon_center);
sinphi = sin(lat);
if( ind != 0) /* sphere */
{
*x = false_easting + r_major * dlon * cosphi1;
*y = false_northing + r_major * sinphi / cosphi1;
}
else /* ellipsoid */
{
q = (1.0 - es) * ((sinphi / (1.0 - es * sinphi * sinphi))
- (1.0 / (2.0 * e)) *
log((1.0 - e * sinphi)/(1.0 + e * sinphi)));
*x = false_easting + (r_major * kz * dlon);
*y = false_northing + (r_major * q) / (2.0 * kz);
}
return(OK);
}
/* Polyconic forward equations--mapping lat,long to x,y
---------------------------------------------------*/
long polyfor
(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y /* (O) Y projection coordinate */
)
{
double sinphi, cosphi; /* sin and cos value */
double con, ml; /* cone constant, small m */
double ms; /* small m */
/* Forward equations
-----------------*/
con = adjust_lon(lon - lon_center);
if (fabs(lat) <= .0000001)
{
*x = false_easting + r_major * con;
*y = false_northing - r_major * ml0;
}
else
{
gctp_sincos(lat,&sinphi,&cosphi);
ml = mlfn(e0, e1, e2, e3, lat);
ms = msfnz(e,sinphi,cosphi);
con *= sinphi;
*x = false_easting + r_major * ms * sin(con)/sinphi;
*y = false_northing + r_major * (ml - ml0 + ms * (1.0 - cos(con))/sinphi);
}
return(GCTP_OK);
}
// Sinusoidal inverse equations--mapping x,y to lat,long
long Projectoid::sininv(
double x, // (I) X projection coordinate
double y, // (I) Y projection coordinate
double *lon, // (O) Longitude
double *lat) // (O) Latitude
{
double temp; // Re-used temporary variable
// Inverse equations
x -= false_easting;
y -= false_northing;
*lat = y / R;
if (fabs(*lat) > HALF_PI)
{
p_error("Input data error", "sinusoidal-inverse");
return(164);
}
temp = fabs(*lat) - HALF_PI;
if (fabs(temp) > EPSLN)
{
temp = lon_center + x / (R * cos(*lat));
*lon = adjust_lon(temp);
}
else
*lon = lon_center;
return(OK);
}
/* Wagner IV forward equations--mapping lat,long to x,y
----------------------------------------------------*/
long wivfor
(
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 theta;
double delta_theta;
double con;
long i;
/* Forward equations
-----------------*/
delta_lon = adjust_lon(lon - lon_center);
theta = lat;
con = 2.9604205062 * sin(lat);
/* Iterate using the Newton-Raphson method to find theta
-----------------------------------------------------*/
for (i=0;;i++)
{
delta_theta = -(theta + sin(theta) - con) / (1.0 + cos(theta));
theta += delta_theta;
if (fabs(delta_theta) < EPSLN) break;
if (i >= 30) p_error("Iteration failed to converge","wagneriv-forward");
}
theta /= 2.0;
*x = 0.86310 * R * delta_lon * cos(theta) + false_easting;
*y = 1.56548 * R * sin(theta) + false_northing;
return(GCTP_OK);
}
/* General Vertical Near-Side Perspective forward equations--mapping
lat,long to x,y
----------------------------------------------------------------*/
long gvnspfor
(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y /* (O) Y projection coordinate */
)
{
double dlon;
double sinphi,cosphi;
double coslon;
double g;
double ksp;
/* Forward equations
-----------------*/
dlon = adjust_lon(lon - lon_center);
gctp_sincos(lat,&sinphi,&cosphi);
coslon = cos(dlon);
g = sin_p15 * sinphi + cos_p15 * cosphi * coslon;
if (g < (1.0/ p))
{
p_error("Point cannot be projected","gvnsp-for");
return(153);
}
ksp = (p - 1.0)/(p - g);
*x = false_easting + R * ksp * cosphi * sin(dlon);
*y = false_northing + R * ksp * (cos_p15 * sinphi - sin_p15 * cosphi * coslon);
return(GCTP_OK);
}
/* Polar Stereographic forward equations--mapping lat,long to x,y
--------------------------------------------------------------*/
int psfor(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y) /* (O) Y projection coordinate */
{
double con1; /* adjusted longitude */
double con2; /* adjusted latitude */
double rh; /* height above ellipsoid */
double sinphi; /* sin value */
double ts; /* value of small t */
con1 = fac * adjust_lon(lon - center_lon);
con2 = fac * lat;
sinphi = sin(con2);
ts = tsfnz(e,con2,sinphi);
if (ind != 0)
rh = r_major * mcs * ts / tcs;
else
rh = 2.0 * r_major * ts / e4;
*x = fac * rh * sin(con1) + false_easting;
*y = -fac * rh * cos(con1) + false_northing;;
return(OK);
}
/* Sinusoidal inverse equations--mapping x,y to lat,long
-----------------------------------------------------*/
long sininv
(
double x, /* (I) X projection coordinate */
double y, /* (I) Y projection coordinate */
double *lon, /* (O) Longitude */
double *lat /* (O) Latitude */
)
{
double temp; /* Re-used temporary variable */
/* Inverse equations
-----------------*/
x -= false_easting;
y -= false_northing;
*lat = y / R;
if (fabs(*lat) > HALF_PI)
{
GCTP_PRINT_ERROR("Input data error");
return(164);
}
temp = fabs(*lat) - HALF_PI;
if (fabs(temp) > EPSLN)
{
temp = lon_center + x / (R * cos(*lat));
*lon = adjust_lon(temp);
}
else *lon = lon_center;
return(OK);
}
// 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);
}
double G_geodesic_lat_from_lon(double lon)
{
adjust_lon(&lon);
lon = Radians(lon);
return Degrees(atan(st->A * sin(lon) - st->B * cos(lon)));
}
/* Mercator inverse equations--mapping x,y to lat/long
--------------------------------------------------*/
long merinv
(
double x, /* (O) X projection coordinate */
double y, /* (O) Y projection coordinate */
double *lon, /* (I) Longitude */
double *lat /* (I) Latitude */
)
{
double ts; /* small t value */
long flag; /* error flag */
/* Inverse equations
-----------------*/
flag = 0;
x -= false_easting;
y -= false_northing;
ts = exp(-y/(r_major * m1));
flag = gctp_calc_phi2(e,ts,lat);
if (flag != GCTP_SUCCESS)
return GCTP_ERROR;
*lon = adjust_lon(lon_center + x/(r_major * m1));
return(OK);
}
/* Albers Conical Equal Area inverse equations--mapping x,y to lat/long
-------------------------------------------------------------------*/
int alberinv(
double x, /* (O) X projection coordinate */
double y, /* (O) Y projection coordinate */
double *lon, /* (I) Longitude */
double *lat) /* (I) Latitude */
{
double rh1; /* height above ellipsoid */
double qs; /* function q */
double con; /* temporary sign value */
double theta; /* angle */
long flag; /* error flag; */
flag = 0;
x -= false_easting;
y = rh - y + false_northing;;
if (ns0 >= 0)
{
rh1 = sqrt(x * x + y * y);
con = 1.0;
}
else
{
rh1 = -sqrt(x * x + y * y);
con = -1.0;
}
theta = 0.0;
if (rh1 != 0.0)
theta = atan2(con * x, con * y);
con = rh1 * ns0 / r_major;
qs = (c - con * con) / ns0;
if (e3 >= 1e-10)
{
con = 1 - .5 * (1.0 - es) * log((1.0 - e3) / (1.0 + e3))/e3;
if (fabs(fabs(con) - fabs(qs)) > .0000000001 )
{
*lat = phi1z(e3,qs,&flag);
if (flag != 0)
return(flag);
}
else
{
if (qs >= 0)
*lat = .5 * PI;
else
*lat = -.5 * PI;
}
}
else
{
*lat = phi1z(e3,qs,&flag);
if (flag != 0)
return(flag);
}
*lon = adjust_lon(theta/ns0 + lon_center);
return(OK);
}
/* Universal Transverse Mercator forward equations--mapping lat,long to x,y
Note: The algorithm for UTM is exactly the same as TM and therefore
if a change is implemented, also make the change to TMFOR.c
-----------------------------------------------------------------------*/
long utmfor
(
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_phi, cos_phi;/* sin and cos value */
double al, als; /* temporary values */
double b; /* temporary values */
double c, t, tq; /* temporary values */
double con, n, ml; /* cone constant, small m */
/* Forward equations
-----------------*/
delta_lon = adjust_lon(lon - lon_center);
gctp_sincos(lat, &sin_phi, &cos_phi);
/* This part was in the fortran code and is for the spherical form
----------------------------------------------------------------*/
if (ind != 0)
{
b = cos_phi * sin(delta_lon);
if ((fabs(fabs(b) - 1.0)) < .0000000001)
{
p_error("Point projects into infinity","utm-for");
return(93);
}
else
{
*x = .5 * r_major * scale_factor * log((1.0 + b)/(1.0 - b));
con = acos(cos_phi * cos(delta_lon)/sqrt(1.0 - b*b));
if (lat < 0)
con = - con;
*y = r_major * scale_factor * (con - lat_origin);
return(GCTP_OK);
}
}
al = cos_phi * delta_lon;
als = SQUARE(al);
c = esp * SQUARE(cos_phi);
tq = tan(lat);
t = SQUARE(tq);
con = 1.0 - es * SQUARE(sin_phi);
n = r_major / sqrt(con);
ml = r_major * mlfn(e0, e1, e2, e3, lat);
*x = scale_factor * n * al * (1.0 + als / 6.0 * (1.0 - t + c + als / 20.0 *
(5.0 - 18.0 * t + SQUARE(t) + 72.0 * c - 58.0 * esp))) + false_easting;
*y = scale_factor * (ml - ml0 + n * tq * (als * (0.5 + als / 24.0 *
(5.0 - t + 9.0 * c + 4.0 * SQUARE(c) + als / 30.0 * (61.0 - 58.0 * t
+ SQUARE(t) + 600.0 * c - 330.0 * esp))))) + false_northing;
return(GCTP_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);
}
/* Van Der Grinten inverse equations--mapping x,y to lat/long
---------------------------------------------------------*/
long vandginv
(
double x, /* (O) X projection coordinate */
double y, /* (O) Y projection coordinate */
double *lon, /* (I) Longitude */
double *lat /* (I) Latitude */
)
{
double xx,yy,xys,c1,c2,c3;
double a1;
double m1;
double con;
double th1;
double d;
/* inverse equations
-----------------*/
x -= false_easting;
y -= false_northing;
con = PI * R;
xx = x / con;
yy = y / con;
xys = xx * xx + yy * yy;
c1 = -fabs(yy) * (1.0 + xys);
c2 = c1 - 2.0 * yy * yy + xx * xx;
c3 = -2.0 * c1 + 1.0 + 2.0 * yy * yy + xys * xys;
d = yy * yy / c3 + (2.0 * c2 * c2 * c2 / c3 / c3 / c3 - 9.0 * c1 * c2 / c3 /c3)
/ 27.0;
a1 = (c1 - c2 * c2 / 3.0 / c3) / c3;
m1 = 2.0 * sqrt( -a1 / 3.0);
con = ((3.0 * d) / a1) / m1;
if (fabs(con) > 1.0)
{
if (con >= 0.0)
con = 1.0;
else
con = -1.0;
}
th1 = acos(con) / 3.0;
if (y >= 0)
*lat = (-m1 * cos(th1 + PI / 3.0) - c2 / 3.0 / c3) * PI;
else
*lat = -(-m1 * cos(th1 + PI / 3.0) - c2 / 3.0 / c3) * PI;
if (fabs(xx) < EPSLN)
{
*lon = lon_center;
return(GCTP_OK);
}
*lon = adjust_lon(lon_center + PI * (xys - 1.0 + sqrt(1.0 + 2.0 *
(xx * xx - yy * yy) + xys * xys)) / 2.0 / xx);
return(GCTP_OK);
}
long imolwinv
(
double x, /* (I) X projection coordinate */
double y, /* (I) Y projection coordinate */
double *lon, /* (O) Longitude */
double *lat /* (O) Latitude */
)
{
double theta;
long region;
/* Inverse equations
-----------------*/
if (y >= 0.0)
{
if (x <= R * -1.41421356248) region = 0;
else if (x <= R * 0.942809042) region = 1;
else region = 2;
}
else
{
if (x <= R * -0.942809042) region = 3;
else if (x <= R * 1.41421356248) region = 4;
else region = 5;
}
x = x - feast[region];
theta = asin(y / (1.4142135623731 * R));
*lon = adjust_lon(lon_center[region] + (x / (0.900316316158*R * cos(theta))));
*lat = asin((2.0 * theta + sin(2.0 * theta)) / PI);
/* Are we in a interrupted area? If so, return status code of GCTP_IN_BREAK.
---------------------------------------------------------------------*/
if (region == 0 && (*lon < 0.34906585 || *lon > 1.91986217719))
return(GCTP_IN_BREAK);
if (region == 1 && ((*lon < 1.91986217719 && *lon > 0.34906585) ||
(*lon > -1.74532925199 && *lon < 0.34906585)))
return(GCTP_IN_BREAK);
if (region == 2 && (*lon < -1.745329252 || *lon > 0.34906585))
return(GCTP_IN_BREAK);
if (region == 3 && (*lon < 0.34906585 || *lon > 2.44346095279))
return(GCTP_IN_BREAK);
if (region == 4 && ((*lon < 2.44346095279 && *lon > 0.34906585) ||
(*lon > -1.2217304764 && *lon < 0.34906585)))
return(GCTP_IN_BREAK);
if (region == 5 && (*lon < -1.2217304764 || *lon> 0.34906585))
return(GCTP_IN_BREAK);
return(GCTP_OK);
}
/* Equirectangular forward equations--mapping lat,long to x,y
---------------------------------------------------------*/
int equifor(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y) /* (O) Y projection coordinate */
{
double dlon; /* delta longitude value */
/* Forward equations
-----------------*/
dlon = adjust_lon(lon - lon_center);
*x = false_easting + r_major * dlon * cos(lat_origin);
*y = false_northing + r_major * lat;
return(OK);
}
/* Miller Cylindrical forward equations--mapping lat,long to x,y
------------------------------------------------------------*/
int millfor(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y) /* (O) Y projection coordinate */
{
double dlon;
/* Forward equations
-----------------*/
dlon = adjust_lon(lon - lon_center);
*x = false_easting + R * dlon;
*y = false_northing + R * log(tan((PI / 4.0) + (lat / 2.5))) * 1.25;
return(OK);
}
// Lambert Conformal Conic inverse equations--mapping x,y to lat/long
long Projectoid::lamccinv(
double x, // (O) X projection coordinate
double y, // (O) Y projection coordinate
double *lon, // (I) Longitude
double *lat) // (I) Latitude
{
double rh1; // height above ellipsoid
double con; // sign variable
double ts; // small t
double theta; // angle
long flag; // error flag
flag = 0;
x -= false_easting;
y = rh - y + false_northing;
if (ns > 0)
{
rh1 = sqrt(x * x + y * y);
con = 1.0;
}
else
{
rh1 = -sqrt(x * x + y * y);
con = -1.0;
}
theta = 0.0;
if (rh1 != 0)
theta = atan2((con * x), (con * y));
if ((rh1 != 0) || (ns > 0.0))
{
con = 1.0 / ns;
ts = pow((rh1 / (r_major * f0)), con);
*lat = phi2z(e, ts, &flag);
if (flag != 0)
return(flag);
}
else
*lat = -HALF_PI;
*lon = adjust_lon(theta / ns + center_lon);
return(OK);
}
/* Mollweide forward equations--mapping lat,long to x,y
----------------------------------------------------*/
long molwfor
(
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 theta;
double delta_theta;
double con;
long i;
/* Forward equations
-----------------*/
delta_lon = adjust_lon(lon - lon_center);
theta = lat;
con = PI * sin(lat);
/* Iterate using the Newton-Raphson method to find theta
-----------------------------------------------------*/
for (i=0;;i++)
{
delta_theta = -(theta + sin(theta) - con)/ (1.0 + cos(theta));
theta += delta_theta;
if (fabs(delta_theta) < EPSLN) break;
if (i >= 50)
{
GCTP_PRINT_ERROR("Iteration failed to converge");
return(241);
}
}
theta /= 2.0;
/* If the latitude is 90 deg, force the x coordinate to be "0 + false easting"
this is done here because of precision problems with "cos(theta)"
--------------------------------------------------------------------------*/
if (PI/2 - fabs(lat) < EPSLN)
delta_lon =0;
*x = 0.900316316158 * R * delta_lon * cos(theta) + false_easting;
*y = 1.4142135623731 * R * sin(theta) + false_northing;
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);
}
/* Azimuthal forward equations--mapping lat,long to x,y
---------------------------------------------------*/
long azimfor
(
double lon, /* (I) Longitude */
double lat, /* (I) Latitude */
double *x, /* (O) X projection coordinate */
double *y /* (O) Y projection coordinate */
)
{
double sinphi, cosphi; /* sin and cos value */
double dlon; /* delta longitude value */
double coslon; /* cos of longitude */
double ksp; /* scale factor */
double g;
double con; /* radius of circle */
double z; /* angle */
/* Forward equations
-----------------*/
dlon = adjust_lon(lon - lon_center);
sincos(lat,&sinphi,&cosphi);
coslon = cos(dlon);
g = sin_p12 * sinphi + cos_p12 * cosphi * coslon;
if (fabs(fabs(g) - 1.0) < EPSLN)
{
ksp = 1.0;
if (g < 0.0)
{
con = 2.0 * HALF_PI * r_major;
GCTP_PRINT_ERROR("Point projects into a circle of radius = %12.2f",con);
return(123);
}
}
else
{
z = acos(g);
ksp = z/ sin(z);
}
*x = false_easting + r_major * ksp * cosphi * sin(dlon);
*y = false_northing + r_major * ksp * (cos_p12 * sinphi - sin_p12 *
cosphi * coslon);
return(OK);
}
