double EXP_LVL9 CSnzlndK (Const struct cs_Nzlnd_ *nzlnd,Const double ll [2])
{
extern double cs_Mone; /* -1.0, the value we return
when presented with bogus
lat/long coordinates. */
int status;
double kk;
double ll_dd;
double xy_dd;
double del_xx, del_yy;
double xy1 [2];
double xy2 [2];
double ll1 [2];
double ll2 [2];
/* Establish two points along the parallel which are
about .5 seconds (about 15 meters) apart from each
other, with the point in question in the middle.
Then convert each point to the equivalent grid
coordinates. */
ll1 [LNG] = ll [LNG];
ll1 [LAT] = ll [LAT] - (0.5 / 3600.0);
status = CSnzlndF (nzlnd,xy1,ll1);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
ll2 [LNG] = ll [LNG];
ll2 [LAT] = ll [LAT] + (0.5 / 3600.0);
status = CSnzlndF (nzlnd,xy2,ll2);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
/* Calculate the geodetic distance between the two lat/long
points. Note, we provide the geodetic calculator with
the scaled radius of the earth so that the distance
it computes will be in the same units as the X and
Y coordinates. */
(void)CS_llazdd (nzlnd->ka,nzlnd->e_sq,ll1,ll2,&ll_dd);
/* Calculate the grid distance between the two points. */
del_xx = xy1 [XX] - xy2 [XX];
del_yy = xy1 [YY] - xy2 [YY];
xy_dd = sqrt (del_xx * del_xx + del_yy * del_yy);
/* Return the ratio of the two distances as the parallel
scale factor at the indicated point. */
kk = xy_dd / ll_dd;
return (kk);
}
double EXP_LVL9 CSazmedK (Const struct cs_Azmed_ *azmed,Const double ll [2])
{
extern double cs_Degree; /* 1.0 / 57.29577... */
extern double cs_Radian; /* 57.29577... */
extern double cs_Pi_o_2; /* PI / 2.0 */
extern double cs_One; /* 1.0 */
extern double cs_Mone; /* -1.0 */
extern double cs_NPTest; /* 0.001 arc seconds short
of the north pole, in
radians. */
extern double cs_SPTest; /* 0.001 arc seconds short
of the south pole, in
radians. */
extern double cs_AnglTest1; /* 1 - sin of 0.001 seconds
of arc. */
extern double cs_SclInf; /* 9.9E+04, the value we
return for an infinite
scale factor. */
int status;
double kk;
double lng;
double lat;
double del_lng;
double sin_lat;
double cos_lat;
double cos_cc;
double cc;
double xy_dd;
double ll_dd;
double del_xx;
double del_yy;
double rho;
double tmp;
double M;
double oll [2];
double ll1 [2];
double ll2 [2];
double xy1 [2];
double xy2 [2];
if (azmed->ecent == 0.0)
{
/* Here for the spherical case. */
lat = ll [LAT] * cs_Degree;
lng = ll [LNG] * cs_Degree;
del_lng = CS_adj2pi (lng - azmed->org_lng);
/* What aspect? */
switch (azmed->aspect) {
case cs_AZMED_NORTH:
if (lat >= cs_NPTest)
{
kk = cs_One;
}
else if (lat <= cs_SPTest)
{
kk = cs_SclInf;
}
else
{
kk = (cs_Pi_o_2 - lat) / cos (lat);
}
break;
case cs_AZMED_SOUTH:
if (lat <= cs_SPTest)
{
kk = cs_One;
}
else if (lat >= cs_NPTest)
{
kk = cs_SclInf;
}
else
{
kk = (cs_Pi_o_2 + lat) / cos (lat);
}
break;
default:
case cs_AZMED_GUAM:
case cs_AZMED_EQUATOR:
case cs_AZMED_OBLIQUE:
lng = ll [LNG] * cs_Degree;
del_lng = CS_adj2pi (lng - azmed->org_lng);
/* Read cc as the angular distance to the
point in question, from the origin. */
cos_cc = azmed->sin_org_lat * sin (lat) +
azmed->cos_org_lat * cos (lat) *
cos (del_lng);
if (cos_cc > cs_AnglTest1)
{
/* The origin. */
kk = cs_One;
}
else if (cos_cc < -cs_AnglTest1)
{
/* AntiPodal */
kk = cs_SclInf;
}
else
{
/* We can divide by sin (cc). */
cc = acos (cos_cc);
kk = cc / sin (cc);
}
break;
}
}
else
{
/* Here for the ellipsoidal case. */
switch (azmed->aspect) {
case cs_AZMED_NORTH:
lat = ll [LAT] * cs_Degree;
if (lat >= cs_NPTest)
{
kk = cs_One;
}
else if (lat < cs_SPTest)
{
kk = cs_SclInf;
}
else
{
/* Here when we can divide by cos (lat) */
sin_lat = sin (lat);
cos_lat = cos (lat);
M = CSmmFcal (&azmed->mmcofF,lat,sin_lat,cos_lat);
rho = azmed->Mp - M;
tmp = cs_One - azmed->e_sq * sin_lat * sin_lat;
kk = rho * sqrt (tmp) / (cos_lat * azmed->ka);
}
break;
case cs_AZMED_SOUTH:
lat = ll [LAT] * cs_Degree;
if (lat <= cs_SPTest)
{
kk = cs_One;
}
else if (lat >= cs_NPTest)
{
kk = cs_SclInf;
}
else
{
/* Here when we can divide by cos (lat) */
sin_lat = sin (lat);
cos_lat = cos (lat);
M = CSmmFcal (&azmed->mmcofF,lat,sin_lat,cos_lat);
rho = M + azmed->Mp;
tmp = cs_One - azmed->e_sq * sin_lat * sin_lat;
kk = rho * sqrt (tmp) / (cos_lat * azmed->ka);
}
break;
default:
case cs_AZMED_GUAM:
case cs_AZMED_EQUATOR:
case cs_AZMED_OBLIQUE:
/* We do not have analytical formulas for these aspects,
so until we do:
CSllnrml computes the lat/long of two points
which form a geodesic of one arc second which
is normal to the geodesic from the origin
(oll) to the point in question (ll). */
oll [0] = azmed->org_lng * cs_Radian;
oll [1] = azmed->org_lat * cs_Radian;
CSllnrml (oll,ll,ll1,ll2);
/* Convert the resulting lat/longs to cartesian
coordinates. */
status = CSazmedF (azmed,xy1,ll1);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
status = CSazmedF (azmed,xy2,ll2);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
/* Calculate the geodetic distance between the two
lat/long points. Note, we provide the geodetic
calculator with the scaled radius of the earth
so that the distance it computes will be in the
same units as the X and Y coordinates. */
CS_llazdd (azmed->ka,azmed->e_sq,ll1,ll2,&ll_dd);
/* Calculate the grid distance between the two
points. */
del_xx = xy1 [XX] - xy2 [XX];
del_yy = xy1 [YY] - xy2 [YY];
xy_dd = sqrt (del_xx * del_xx + del_yy * del_yy);
/* Return the ratio of the two distances as the
parallel scale factor at the indicated point. */
kk = xy_dd / ll_dd;
break;
}
}
return (kk);
}
double EXP_LVL9 CSsinusH (Const struct cs_Sinus_ *sinus,Const double ll [2])
{
extern double cs_Degree; /* 1.0 / RADIAN */
extern double cs_Pi_o_2; /* Pi over 2 */
extern double cs_One; /* 1.0 */
extern double cs_Mone; /* -1.0 */
extern double cs_SclInf; /* 9.9E+04, the value we
return for an infinite
scale factor. */
extern double cs_NPTest; /* 0.001 arc seconds short
of the north pole, in
radians. */
int status;
Const struct cs_Zone_ *zp;
double hh;
double lng;
double lat;
double del_lng;
double sin_lat;
double cent_lng;
double ll_dd;
double xy_dd;
double del_xx, del_yy;
double xy1 [2];
double xy2 [2];
double ll1 [2];
double ll2 [2];
lng = ll [LNG] * cs_Degree;
lat = ll [LAT] * cs_Degree;
/* A latitude above either pole is an error. At either pole,
the scale is 1.0. We deal with these now to prevent
divides by zero below. */
if (fabs (lat) > cs_NPTest)
{
if (fabs (lat) > cs_Pi_o_2)
{
return (cs_Mone);
}
else
{
return (cs_One);
}
}
/* Determine which zone we're in, assuming there are some
zones active. */
if (sinus->zone_cnt > 0)
{
zp = CS_znlocF (sinus->zones,sinus->zone_cnt,lng,lat);
if (zp != NULL)
{
cent_lng = zp->cent_lng;
}
else
{
/* Opps!!! No zone, even though they are
active. The lat/long are bogus. */
return (cs_Mone);
}
}
else
{
zp = NULL;
cent_lng = sinus->cent_lng;
}
/* Different algorithms for sphere or ellipsoid. */
if (sinus->ecent == 0.0)
{
del_lng = CS_adj2pi (lng - cent_lng);
sin_lat = sin (lat);
hh = sqrt (cs_One + (del_lng * del_lng) * (sin_lat * sin_lat));
}
else
{
/* We haven'y located a formula for the ellipsoid yet.
Establish two points along the meridian which are
about 1 second (about 30 meters) apart from each
other, with the point in question in the middle.
Then convert each point to the equivalent grid
coordinates. */
ll1 [LNG] = ll [LNG];
ll1 [LAT] = ll [LAT] - (0.5 / 3600.0);
status = CSsinusF (sinus,xy1,ll1);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
ll2 [LNG] = ll [LNG];
ll2 [LAT] = ll [LAT] + (0.5 / 3600.0);
status = CSsinusF (sinus,xy2,ll2);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
/* Calculate the geodetic distance between the two
lat/long points. Note, we provide the geodetic
calculator with the scaled radius of the earth
so that the distance it computes will be in the
same units as the X and Y coordinates. */
CS_llazdd (sinus->ka,sinus->e_sq,ll1,ll2,&ll_dd);
/* Calculate the grid distance between the two points. */
del_xx = xy1 [XX] - xy2 [XX];
del_yy = xy1 [YY] - xy2 [YY];
xy_dd = sqrt (del_xx * del_xx + del_yy * del_yy);
/* Return the ratio of the two distances as the
meridian scale factor at the indicated point.
ll_dd should never be zero here, but just in
case: */
if (ll_dd > sinus->one_mm)
{
hh = xy_dd / ll_dd;
}
else
{
hh = cs_SclInf;
}
}
return (hh);
}
double EXP_LVL9 CStacylH (Const struct cs_Tacyl_ *tacyl,Const double ll [2])
{
extern double cs_HlfSecDeg; /* One half second of arc in
degrees. */
extern double cs_Sin1Sec; /* Sine of one second of arc, used
here as one second of arc in
radians. */
extern double cs_Mone; /* -1, the value we return when
provided with a bogus point. */
extern double cs_SclInf; /* 9.9E+04, the value returned
to indicate an infinite
scale factor */
int status;
double hh;
double ll_dd;
double xy_dd;
double del_xx, del_yy;
double xy1 [2];
double xy2 [2];
double ll1 [2];
double ll2 [2];
/* Establish two points along the meridian which are
about 1 second (about 30 meters) apart from each
other, with the point in question in the middle.
Then convert each point to the equivalent grid
coordinates. */
ll1 [LNG] = ll [LNG];
ll1 [LAT] = ll [LAT] - cs_HlfSecDeg;
status = CStacylF (tacyl,xy1,ll1);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
ll2 [LNG] = ll [LNG];
ll2 [LAT] = ll [LAT] + cs_HlfSecDeg;
status = CStacylF (tacyl,xy2,ll2);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
/* Calculate the geodetic distance between the two lat/long
points. Note, we provide the geodetic calculator with
the scaled radius of the earth so that the distance
it computes will be in the same units as the X and
Y coordinates. */
if (tacyl->ecent == 0.0)
{
ll_dd = cs_Sin1Sec * tacyl->ka;
}
else
{
CS_llazdd (tacyl->ka,tacyl->e_sq,ll1,ll2,&ll_dd);
}
/* Calculate the grid distance between the two points. */
del_xx = xy1 [XX] - xy2 [XX];
del_yy = xy1 [YY] - xy2 [YY];
xy_dd = sqrt (del_xx * del_xx + del_yy * del_yy);
/* Return the ratio of the two distances as the meridian
scale factor at the indicated point. ll_dd should never
be zero, but just in case. */
if (ll_dd > 0.0)
{
hh = xy_dd / ll_dd;
}
else
{
hh = cs_SclInf;
}
return (hh);
}
double EXP_LVL9 CStacylK (Const struct cs_Tacyl_ *tacyl,Const double ll [2])
{
extern double cs_Degree; /* pi / 180.0 */
extern double cs_Sin1Sec; /* Sine of one arc second. */
extern double cs_SclInf; /* 9.9E+04, the value which we
return for an infinite
scale factor. */
extern double cs_Mone; /* -1.0 */
extern double cs_AnglTest; /* 0.001 arc seconds, in radians. */
extern double cs_HlfSecDeg; /* 0.5 seconds of arc, in degrees. */
int status;
double kk;
double xy_dd, ll_dd;
double del_xx, del_yy;
double ll1 [2];
double ll2 [2];
double xy1 [2];
double xy2 [2];
/* Establish two points along the parallel which
are about 1 second (about 30 meters) apart from
each other, with the point in question in the
middle. Then convert each point to the equivalent
grid coordinates. */
ll1 [LNG] = ll [LNG] - cs_HlfSecDeg;;
ll1 [LAT] = ll [LAT];
status = CStacylF (tacyl,xy1,ll1);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
ll2 [LNG] = ll [LNG] + cs_HlfSecDeg;
ll2 [LAT] = ll [LAT];
status = CStacylF (tacyl,xy2,ll2);
if (status != cs_CNVRT_NRML)
{
return (cs_Mone);
}
/* Calculate the grid distance between the two points. */
del_xx = xy1 [XX] - xy2 [XX];
del_yy = xy1 [YY] - xy2 [YY];
xy_dd = sqrt (del_xx * del_xx + del_yy * del_yy);
if (xy_dd == 0.0)
{
/* This can happen when very close to the singularity
point for this projection. */
return (cs_Mone);
}
if (tacyl->ecent == 0.0)
{
/* Here for a sphere. cs_Sin1Sec is the sine of one
arc second; which is essentially the same as
one arc second in radians. */
ll_dd = cs_Sin1Sec * tacyl->ka * cos (ll [LAT] * cs_Degree);
}
else
{
/* Calculate the geodetic distance between the two
lat/long points. */
CS_llazdd (tacyl->ka,tacyl->e_sq,ll1,ll2,&ll_dd);
}
/* Return the ration of the two distances as the grid
scale factor at the point. */
if (ll_dd > cs_AnglTest)
{
kk = xy_dd / ll_dd;
}
else
{
kk = cs_SclInf;
}
return (kk);
}
double EXP_LVL9 CSlmtanK (Const struct cs_Lmtan_ *lmtan,Const double ll [2])
{
extern double cs_SclInf; /* 9.9E+04, the value we return
for an infinite scale
factor. */
extern double cs_HlfSecDeg; /* One half arc second in
degrees. */
double kk;
double ll_dd;
double xy_dd;
double del_xx, del_yy;
double xy1 [2];
double xy2 [2];
double ll1 [2];
double ll2 [2];
/* Establish two points along the parallel which are
about 1 second (about 30 meters) apart from each
other, with the point in question in the middle.
Then convert each point to the equivalent grid
coordinates. */
ll1 [LNG] = ll [LNG];
ll1 [LAT] = ll [LAT] - cs_HlfSecDeg;
CSlmtanF (lmtan,xy1,ll1); /*lint !e534 */
ll2 [LNG] = ll [LNG];
ll2 [LAT] = ll [LAT] + cs_HlfSecDeg;
CSlmtanF (lmtan,xy2,ll2); /*lint !e534 */
/* Calculate the geodetic distance between the two lat/long
points. Note, we provide the geodetic calculator with
the scaled radius of the earth so that the distance
it computes will be in the same units as the X and
Y coordinates. */
CS_llazdd (lmtan->kerad,lmtan->e_sq,ll1,ll2,&ll_dd);
/* Calculate the grid distance between the two points. */
del_xx = xy1 [XX] - xy2 [XX];
del_yy = xy1 [YY] - xy2 [YY];
xy_dd = sqrt (del_xx * del_xx + del_yy * del_yy);
/* Return the ratio of the two distances as the parallel
scale factor at the indicated point. I don't think
ll_dd can be zero since we know that ll1 id not the
same as ll0. However, just to be safe: */
if (fabs (ll_dd) > lmtan->one_mm)
{
kk = xy_dd / ll_dd;
}
else
{
kk = cs_SclInf;
}
return (kk);
}
