int EXP_LVL9 CSvdgrnF (Const struct cs_Vdgrn_ *vdgrn,double xy [2],Const double ll [2])
{
extern double cs_Degree; /* 1.0 / RADIAN */
extern double cs_Pi; /* 3.14159..... */
extern double cs_Two_pi; /* 2 pi */
extern double cs_Mpi; /* -3.14159..... */
extern double cs_Pi_o_2; /* Pi over 2 */
extern double cs_Zero; /* 0.0 */
extern double cs_Half; /* 0.5 */
extern double cs_One; /* 1.0 */
extern double cs_Two; /* 2.0 */
extern double cs_NPTest; /* 0.001 seconds of arc
short of the north pole,
in radians. */
extern double cs_AnglTest; /* 0.001 seconds of arc,
in radians. */
int rtn_val;
double lng; /* The given longitude, after conversion
to radians. */
double lat; /* The given latitude after conversion
to radians. */
double del_lng;
double abs_lat;
double xx;
double yy;
double theta;
double sin_theta, cos_theta;
double A, A_sq;
double P, P_sq;
double G;
double Q;
double tmp1, tmp2, tmp3;
rtn_val = cs_CNVRT_NRML;
/* For this projection, we only support the spherical form,
therefore there is only one set of equations. */
lng = ll [LNG] * cs_Degree;
del_lng = lng - vdgrn->org_lng;
if (del_lng > cs_Pi && vdgrn->org_lng < 0.0) del_lng -= cs_Two_pi;
else if (del_lng < cs_Mpi && vdgrn->org_lng > 0.0) del_lng += cs_Two_pi;
if (fabs (del_lng) > cs_Pi)
{
rtn_val = cs_CNVRT_RNG;
del_lng = CS_adj2piI (del_lng);
}
lat = ll [LAT] * cs_Degree;
abs_lat = fabs (lat);
if (abs_lat > cs_NPTest)
{
rtn_val = cs_CNVRT_INDF;
if (abs_lat > cs_Pi_o_2)
{
rtn_val = cs_CNVRT_RNG;
lat = CS_adj1pi (lat);
abs_lat = fabs (lat);
}
}
if (abs_lat > cs_NPTest)
{
/* The sign of yy gets reversed below, we can simply
use cs_Pi here. */
xx = cs_Zero;
yy = cs_Pi * vdgrn->ka;
}
else if (abs_lat <= cs_AnglTest)
{
/* This is the calculation for the equator.
The sign of X gets reversed below, we need to use
the absolute value here. */
xx = vdgrn->ka * fabs (del_lng);
yy = cs_Zero;
}
else if (fabs (del_lng) < cs_AnglTest)
{
/* We're on the central meridian, BUT NOT on the
equator, and not at either pole. Npte, sign of
result is dealt with below. */
xx = cs_Zero;
theta = asin (abs_lat / cs_Pi_o_2);
yy = cs_Pi * vdgrn->ka * tan (theta * cs_Half);
}
else
{
/* OK, we're not at either pole, or the equator. The
rest of this should be pretty safe. */
sin_theta = fabs (lat) * vdgrn->two_ovr_pi;
cos_theta = sqrt (cs_One - sin_theta * sin_theta);
tmp1 = (cs_Pi / del_lng) - (del_lng / cs_Pi);
A = cs_Half * fabs (tmp1);
A_sq = A * A;
G = cos_theta / (sin_theta + cos_theta - cs_One);
P = G * ((cs_Two / sin_theta) - cs_One);
P_sq = P * P;
Q = A_sq + G;
tmp1 = P_sq + A_sq;
tmp2 = G - P_sq;
tmp3 = tmp1 * ((G * G) - P_sq);
tmp3 = (A_sq * tmp2 * tmp2) - tmp3;
if (tmp3 < 0.0) tmp3 = cs_Zero;
tmp3 = (A * tmp2) + sqrt (tmp3);
xx = vdgrn->piR * tmp3 / tmp1;
tmp3 = ((A_sq + cs_One) * tmp1) - (Q * Q);
if (tmp3 < 0.0) tmp3 = cs_Zero;
tmp3 = (P * Q) - (A * sqrt (tmp3));
yy = vdgrn->piR * tmp3 / tmp1;
}
/* Apply the appropriate sign and false origin. */
xy [XX] = (del_lng >= 0.0) ? xx : -xx;
xy [YY] = (lat >= 0.0) ? yy : -yy;
if (vdgrn->quad == 0)
{
xy [XX] += vdgrn->x_off;
xy [YY] += vdgrn->y_off;
}
else
{
CS_quadF (xy,xy [XX],xy [YY],vdgrn->x_off,vdgrn->y_off,vdgrn->quad);
}
return (rtn_val);
}
int EXP_LVL9 CSlmtanF (Const struct cs_Lmtan_ *lmtan,double xy [2],Const double ll [2])
{
extern double cs_Degree; /* 1.0 / RADIAN */
extern double cs_Pi; /* 3.14159... */
extern double cs_Mpi; /* -3.14159... */
extern double cs_Two_pi; /* 2 PI */
extern double cs_Pi_o_2; /* PI / 2.0 */
extern double cs_Pi_o_4; /* PI / 4.0 */
extern double cs_Zero; /* 0.0 */
extern double cs_One; /* 1.0 */
extern double cs_Half; /* 0.5 */
extern double cs_NPTest; /* 0.001 arc seconds short
of the north pole, in
in radians. */
extern double cs_SPTest; /* 0.001 arc seconds short
of the south pole, in
in radians. */
int rtn_val;
double lng; /* The given longitude, after conversion
to radians. */
double lat; /* The given latitude after conversion
to radians. */
double del_lng;
double L0;
double Gamma;
double R;
double tmp1;
double tmp2;
rtn_val = cs_CNVRT_NRML;
lng = cs_Degree * ll [LNG];
lat = cs_Degree * ll [LAT];
/* Compute the polar angle, Gamma, also known as the
convergence angle. */
del_lng = lng - lmtan->org_lng;
if (del_lng > cs_Pi && lmtan->org_lng < 0.0) del_lng -= cs_Two_pi;
else if (del_lng < cs_Mpi && lmtan->org_lng > 0.0) del_lng += cs_Two_pi;
if (fabs (del_lng) > cs_Pi)
{
rtn_val = cs_CNVRT_RNG;
del_lng = CS_adj2piI (del_lng);
}
Gamma = lmtan->sin_org_lat * del_lng;
/* Now, we compute the radius of the polar arc. R will be
negative (lmtan->c is negative) if the south pole is
the focus pole of the coordinate system. */
if (fabs (lat) > cs_NPTest)
{
if ((lat > 0.0) == (lmtan->sin_org_lat > 0.0)) /*lint !e731 !e777 */
{
rtn_val = cs_CNVRT_INDF;
}
if (fabs (lat) > cs_Pi_o_2)
{
rtn_val = cs_CNVRT_RNG;
lat = CS_adj1pi (lat);
}
}
if (lat > cs_NPTest)
{
R = (lmtan->sin_org_lat > 0.0) ? cs_Zero : lmtan->max_R;
}
else if (lat < cs_SPTest)
{
R = (lmtan->sin_org_lat < 0.0) ? cs_Zero : lmtan->max_R;
}
else
{
tmp1 = lmtan->ecent * sin (lat);
tmp1 = (cs_One + tmp1) / (cs_One - tmp1);
tmp1 = lmtan->e_ovr_2 * log (tmp1);
tmp2 = cs_Pi_o_4 + (lat * cs_Half);
/* Tmp2 can be zero (and thus tan(tmp2) can be zero)
at the south pole, but we've already dealt with
that. */
tmp2 = log (tan (tmp2));
L0 = tmp2 - tmp1;
R = lmtan->c * exp (-lmtan->sin_org_lat * L0);
}
/* Convert to cartesian coordinates. Note, ys has the false
northing and the radius of the origin latitude built into
it by the setup function. */
xy [XX] = R * sin (Gamma);
xy [YY] = lmtan->R0 - (R * cos (Gamma));
if (lmtan->quad == 0)
{
xy [XX] += lmtan->x_off;
xy [YY] += lmtan->y_off;
}
else
{
CS_quadF (xy,xy [XX],xy [YY],lmtan->x_off,lmtan->y_off,
lmtan->quad);
}
return (rtn_val);
}