/// <summary>
/// Решение обратной геодезической задачи на сфероиде
/// </summary>
private InverseProblemAnswer OrthodromicSpheroidDistance(Point coord1, Point coord2)
{
var ω = coord2.LonR - coord1.LonR;
var cosSigma = Math.Sin(coord1.LatR) * Math.Sin(coord2.LatR) + Math.Cos(coord1.LatR) * Math.Cos(coord2.LatR) * Math.Cos(ω);
double s;
if (cosSigma < 0)
{
s = _ellipsoid.PolarRadius * (Math.PI - Math.Abs(Math.Acos(cosSigma)));
}
else if (Math.Abs(cosSigma - 1) < TOLERANCE)
{
s = 0;
}
else
{
s = _ellipsoid.PolarRadius * Math.Acos(cosSigma);
}
var a1 =
Math.Atan(Math.Cos(coord2.LatR) * Math.Sin(ω) /
(Math.Cos(coord1.LatR) * Math.Sin(coord2.LatR) - Math.Sin(coord1.LatR) * Math.Cos(coord2.LatR) * Math.Cos(ω))) * 180 /
Math.PI;
var a2 =
Math.Atan(Math.Cos(coord1.LatR) * Math.Sin(ω) /
(Math.Cos(coord1.LatR) * Math.Sin(coord2.LatR) * Math.Cos(ω) - Math.Sin(coord1.LatR) * Math.Cos(coord2.LatR))) * 180 /
Math.PI;
a1 = Azimuth.AzimuthRecovery(coord1, coord2, a1);
a2 = Azimuth.AzimuthRecovery(coord2, coord1, a2);
return(new InverseProblemAnswer(a1, a2, s));
}
/// <summary>
/// Решение прямой геодезической задачи на сфероиде
/// </summary>
private DirectProblemAnswer DirectProblemSpheroid(Point coord, double a1, double s)
{
var aDegree = a1;
a1 = a1 * Math.PI / 180;
var lat1 = coord.LatR;
var sigma = s / _ellipsoid.PolarRadius;
var lat2 = Math.Asin(Math.Sin(lat1) * Math.Cos(sigma) + Math.Cos(lat1) * Math.Sin(sigma) * Math.Cos(a1));
var lambda = Math.Atan(Math.Sin(sigma) * Math.Sin(a1) /
(Math.Cos(sigma) * Math.Cos(lat1) - Math.Sin(sigma) * Math.Sin(lat1) * Math.Cos(a1)));
var lon2 = -lambda + coord.LonR;
var a2 = -Math.Atan(Math.Cos(lat1) * Math.Sin(a1) /
(Math.Cos(lat1) * Math.Cos(sigma) * Math.Cos(a1) - Math.Sin(lat1) * Math.Sin(sigma))) *
180 / Math.PI;
lon2 = lon2 * 180 / Math.PI;
lat2 = lat2 * 180 / Math.PI;
var point1 = IsPolisIntersect(coord, aDegree, s)
? new Point(lon2 + (lon2 < 0 ? 180 : -180), lat2)
: new Point(lon2, lat2);
a2 = Azimuth.AzimuthRecovery(point1, new Point(coord.Longitude, lat1 * 180 / Math.PI), a2);
return(new DirectProblemAnswer(point1, a2));
}
/// <summary>
/// Решение обратной геодезической задачи на элипсоиде
/// </summary>
private InverseProblemAnswer OrthodromicEllipsoidDistance(Point coord1, Point coord2)
{
double l = coord2.LonR - coord1.LonR; // Разность геодезических долгот
double u1 = Math.Atan((1 - _ellipsoid.F) * Math.Tan(coord1.LatR)); // Приведённая широта
double u2 = Math.Atan((1 - _ellipsoid.F) * Math.Tan(coord2.LatR));
double sinU1 = Math.Sin(u1), cosU1 = Math.Cos(u1);
double sinU2 = Math.Sin(u2), cosU2 = Math.Cos(u2);
double lambda = l, lambdaP;
double cosSqAlpha, sinSigma, cosSigma, cos2SigmaM, sigma;
int iterLimit = 100;
do
{
var sinLambda = Math.Sin(lambda);
var cosLambda = Math.Cos(lambda);
sinSigma =
Math.Sqrt(Math.Pow(cosU2 * sinLambda, 2) + Math.Pow(cosU1 * sinU2 - sinU1 * cosU2 * cosLambda, 2));
if (Math.Abs(sinSigma) < TOLERANCE)
{
return(new InverseProblemAnswer(0, 0, 0));
}
cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda;
sigma = Math.Atan(sinSigma / cosSigma);
var sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma;
cosSqAlpha = 1 - sinAlpha * sinAlpha;
if (Math.Abs(cosSqAlpha) > TOLERANCE)
{
cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha;
}
else
{
cos2SigmaM = 0;
}
double c = _ellipsoid.F / 16 * cosSqAlpha * (4 + _ellipsoid.F * (4 - 3 * cosSqAlpha));
lambdaP = lambda;
lambda = l +
(1 - c) * _ellipsoid.F * sinAlpha *
(sigma + c * sinSigma * (cos2SigmaM + c * cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
} while (Math.Abs(lambda - lambdaP) > 1e-12 && --iterLimit > 0);
double uSq = cosSqAlpha * (Math.Pow(_ellipsoid.EquatorialRadius, 2) - Math.Pow(_ellipsoid.PolarRadius, 2)) /
Math.Pow(_ellipsoid.PolarRadius, 2);
double a = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));
double b = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
double deltaSigma = b * sinSigma *
(cos2SigmaM +
b / 4 *
(cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) -
b / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) *
(-3 + 4 * cos2SigmaM * cos2SigmaM)));
double s = _ellipsoid.PolarRadius * a * (sigma - deltaSigma);
var a1 = Math.Atan(cosU2 * Math.Sin(lambda) / (cosU1 * sinU2 - sinU1 * cosU2 * Math.Cos(lambda))) * 180 /
Math.PI;
var a2 = Math.Atan(cosU1 * Math.Sin(lambda) / (-sinU1 * cosU2 + cosU1 * sinU2 * Math.Cos(lambda))) * 180 /
Math.PI;
a1 = Azimuth.AzimuthRecovery(coord1, coord2, a1);
a2 = Azimuth.AzimuthRecovery(coord2, coord1, a2);
return(new InverseProblemAnswer(a1, a2, s));
}
/// <summary>
/// Решение прямой геодезической задачи на эллипсоиде
/// </summary>
private DirectProblemAnswer DirectProblemEllipsoid(Point coord, double a1, double s)
{
var aDegree = a1;
a1 = a1 * Math.PI / 180;
double u1 = Math.Atan((1 - _ellipsoid.F) * Math.Tan(coord.LatR));
double sigma1 = Math.Atan(Math.Tan(u1) / Math.Cos(a1));
var sinAlpha = Math.Cos(u1) * Math.Sin(a1);
var cosSqAlpha = 1 - sinAlpha * sinAlpha;
double uSq = cosSqAlpha * (Math.Pow(_ellipsoid.EquatorialRadius, 2) - Math.Pow(_ellipsoid.PolarRadius, 2)) /
Math.Pow(_ellipsoid.PolarRadius, 2);
double a = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)));
double b = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)));
var si = s / _ellipsoid.PolarRadius / a;
double sigma = si;
double sigmaP, cos2SigmaM;
do
{
var sinSigma = Math.Sin(sigma);
var cosSigma = Math.Cos(sigma);
cos2SigmaM = Math.Cos(2 * sigma1 + sigma);
double deltaSigma = b * sinSigma *
(cos2SigmaM +
b / 4 *
(cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) -
b / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) *
(-3 + 4 * cos2SigmaM * cos2SigmaM)));
sigmaP = sigma;
sigma = si + deltaSigma;
} while (Math.Abs(sigma - sigmaP) > 1e-12);
var sinU2 = Math.Sin(u1) * Math.Cos(sigma) + Math.Cos(u1) * Math.Sin(sigma) * Math.Cos(a1);
var lat2 = sinU2 /
((1 - _ellipsoid.F) *
Math.Sqrt(sinAlpha * sinAlpha +
Math.Pow(
Math.Sin(u1) * Math.Sin(sigma) - Math.Cos(u1) * Math.Cos(sigma) * Math.Cos(a1), 2)));
lat2 = Math.Atan(lat2);
// Разность долгот
var lamda = Math.Atan(Math.Sin(sigma) * Math.Sin(a1) /
(Math.Cos(u1) * Math.Cos(sigma) - Math.Sin(u1) * Math.Sin(sigma) * Math.Cos(a1)));
double c = _ellipsoid.F / 16 * cosSqAlpha * (4 + _ellipsoid.F * (4 - 3 * cosSqAlpha));
var l = lamda - (1 - c) * _ellipsoid.F * sinAlpha *
(sigma +
c * Math.Sin(sigma) * (cos2SigmaM + c * Math.Cos(sigma) * (-1 + 2 * cos2SigmaM * cos2SigmaM)));
var lon2 = -l + coord.LonR;
lon2 = lon2 * 180 / Math.PI;
lat2 = lat2 * 180 / Math.PI;
var point1 = IsPolisIntersect(coord, aDegree, s)
? new Point(lon2 + (lon2 < 0 ? 180 : -180), lat2)
: new Point(lon2, lat2);
var a2 = -Math.Atan(sinAlpha / (-Math.Sin(u1) * Math.Sin(sigma) + Math.Cos(u1) * Math.Cos(sigma) * Math.Cos(a1))) * 180 / Math.PI;
a2 = Azimuth.AzimuthRecovery(point1, coord, a2);
return(new DirectProblemAnswer(point1, a2));
}
