/// New functions
void DistanceBearingMercator(double lat0, double lon0, double lat1, double lon1, double *dist, double *brg)
{
// Calculate bearing by conversion to SM (Mercator) coordinates, then simple trigonometry
double lon0x = lon0;
double lon1x = lon1;
// Make lon points the same phase
if ((lon0x * lon1x) < 0.)
{
lon0x < 0.0 ? lon0x += 360.0 : lon1x += 360.0;
// Choose the shortest distance
if (fabs(lon0x - lon1x) > 180.)
{
lon0x > lon1x ? lon0x -= 360.0 : lon1x -= 360.0;
}
// Make always positive
lon1x += 360.;
lon0x += 360.;
}
// Classic formula, which fails for due east/west courses....
if (dist)
{
// In the case of exactly east or west courses
// we must make an adjustment if we want true Mercator distances
// This idea comes from Thomas(Cagney)
// We simply require the dlat to be (slightly) non-zero, and carry on.
// MAS022210 for HamishB from 1e-4 && .001 to 1e-9 for better precision
// on small latitude diffs
const double mlat0 = fabs(lat1 - lat0) < 1e-9 ? lat0 + 1e-9 : lat0;
double east, north;
toSM_ECC(lat1, lon1x, mlat0, lon0x, &east, &north);
const double C = atan2(east, north);
if (cos(C))
{
const double dlat = (lat1 - mlat0) * 60.; // in minutes
*dist = (dlat / cos(C));
}
else
{
*dist = DistGreatCircle(lat0, lon0, lat1, lon1);
}
}
// Calculate the bearing using the un-adjusted original latitudes and Mercator Sailing
if (brg)
{
double east, north;
toSM_ECC(lat1, lon1x, lat0, lon0x, &east, &north);
const double C = atan2(east, north);
const double brgt = 180. + (C * 180. / PI);
if (brgt < 0)
*brg = brgt + 360.;
else if (brgt >= 360.)
*brg = brgt - 360.;
else
*brg = brgt;
}
}
void DistanceBearingMercator(double lat0, double lon0, double lat1, double lon1, double *brg, double *dist)
{
double east, north, brgt, C;
double lon0x, lon1x, dlat;
double mlat0;
// Calculate bearing by conversion to SM (Mercator) coordinates, then simple trigonometry
lon0x = lon0;
lon1x = lon1;
// Make lon points the same phase
if((lon0x * lon1x) < 0.)
{
if(lon0x < 0.)
lon0x += 360.;
else
lon1x += 360.;
// Choose the shortest distance
if(fabs(lon0x - lon1x) > 180.)
{
if(lon0x > lon1x)
lon0x -= 360.;
else
lon1x -= 360.;
}
// Make always positive
lon1x += 360.;
lon0x += 360.;
}
// In the case of exactly east or west courses
// we must make an adjustment if we want true Mercator distances
// This idea comes from Thomas(Cagney)
// We simply require the dlat to be (slightly) non-zero, and carry on.
// MAS022210 for HamishB from 1e-4 && .001 to 1e-9 for better precision
// on small latitude diffs
mlat0 = lat0;
if(fabs(lat1 - lat0) < 1e-9)
mlat0 += 1e-9;
toSM_ECC(lat1, lon1x, mlat0, lon0x, &east, &north);
C = atan2(east, north);
dlat = (lat1 - mlat0) * 60.; // in minutes
// Classic formula, which fails for due east/west courses....
if(dist)
{
if(cos(C))
*dist = (dlat /cos(C));
else
*dist = DistGreatCircle(lat0, lon0, lat1, lon1);
}
// Calculate the bearing using the un-adjusted original latitudes and Mercator Sailing
if(brg)
{
toSM_ECC(lat1, lon1x, lat0, lon0x, &east, &north);
C = atan2(east, north);
brgt = 180. + (C * 180. / PI);
if (brgt < 0)
brgt += 360.;
if (brgt > 360.)
brgt -= 360;
*brg = brgt;
}
// Alternative formulary
// From Roy Williams, "Geometry of Navigation", we have p = Dlo (Dlat/DMP) where p is the departure.
// Then distance is then:D = sqrt(Dlat^2 + p^2)
/*
double dlo = (lon1x - lon0x) * 60.;
double departure = dlo * dlat / ((north/1852.));
if(dist)
*dist = sqrt((dlat*dlat) + (departure * departure));
*/
}
