public void GeographicCoordinate_CanUpdateValidLongitude(double longitude)
{
ISphericalCoordinate expected = new Longitude(longitude);
IGeographicCoordinate sut = InstantiateNewGeographicCoordinate();
sut.Longitude = new Longitude(longitude);
var result = sut.Longitude;
Assert.Equal(expected, result);
}
public void Vincenty_CorrectlyCalculatesDestinationCoordinates(double latA, double lonA, double bearingInRadians, double distanceInMeters,
double expectedLat, double expectedLon, int maxIterations, double tolerance)
{
IGeographicCoordinate pointA = new GeographicCoordinate(latA, lonA);
IGeographicCoordinate expected = new GeographicCoordinate(expectedLat, expectedLon);
IGeographicCoordinate result = pointA.DestinationCoordinates(new Angle(bearingInRadians, AngleMeasurement.Radians), new Distance(distanceInMeters, DistanceMeasurement.Meters),
maxIterations, tolerance);
Assert.Equal(expected, result);
}
private static VincentyFormulaVariables VincentysDirectFormula(IGeographicCoordinate pointA, IAngle initialBearing, IDistance distance,
int maxInterations = 200, double tolerance = 1.0E-12)
{
// Source: https://www.movable-type.co.uk/scripts/latlong-vincenty.html
VincentyFormulaVariables v = PrepareσConvergenceLoop(pointA, initialBearing, distance);
v = RecalculateσUntilConvergence(distance, maxInterations, tolerance, v);
v.DestinationCoordinates = CalculateDestinationCoordinates(pointA, v);
v.FinalBearing = Math.Atan2(v.sinα, -1.0 * (v.SinU1 * v.Sinσ - v.CosU1 * v.Cosσ * v.Cosα1));
return(v);
}
private static IGeographicCoordinate CalculateDestinationCoordinates(IGeographicCoordinate pointA, VincentyFormulaVariables v)
{
var tmp = v.SinU1 * v.Sinσ - v.CosU1 * v.Cosσ * v.Cosα1;
v.φ2 = Math.Atan2(v.SinU1 * v.Cosσ + v.CosU1 * v.Sinσ * v.Cosα1, (1 - f) * Math.Sqrt(Math.Pow(v.sinα, 2.0) + Math.Pow(tmp, 2.0)));
v.λ = Math.Atan2(v.Sinσ * v.Sinα1, v.CosU1 * v.Cosσ - v.SinU1 * v.Sinσ * v.Cosα1);
v.C = f / 16.0 * v.CosSqα * (4.0 + f * (4.0 - 3.0 * v.CosSqα));
v.L = v.λ - (1.0 - v.C) * f * v.sinα *
(v.σ + v.C * v.Sinσ * (v.Cos2σM + v.C * v.Cosσ * (-1.0 + 2.0 * Math.Pow(v.Cos2σM, 2.0))));
v.λ2 = (pointA.Longitude.Angle.ToRadians() + v.L + 3.0 * Math.PI) % (2.0 * Math.PI) - Math.PI; // normalise to -180...+180
var latitude = Angle.ToDegrees(v.φ2);
var longitude = Angle.ToDegrees(v.λ2);
return(new GeographicCoordinate(latitude, longitude));
}
private static VincentyFormulaVariables PrepareλConvergenceLoop(IGeographicCoordinate pointA, IGeographicCoordinate pointB)
{
var v = new VincentyFormulaVariables
{
U1 = Math.Atan((1.0 - f) * Math.Tan(pointA.Latitude.Angle.ToRadians())),
U2 = Math.Atan((1.0 - f) * Math.Tan(pointB.Latitude.Angle.ToRadians())),
L = Angle.ToRadians(pointB.Longitude.Angle.ToDegrees() - pointA.Longitude.Angle.ToDegrees())
};
v.λ = v.L;
v.SinU1 = Math.Sin(v.U1);
v.CosU1 = Math.Cos(v.U1);
v.SinU2 = Math.Sin(v.U2);
v.CosU2 = Math.Cos(v.U2);
return(v);
}
private static IBearingDistance VincentysInverseFormula(IGeographicCoordinate pointA, IGeographicCoordinate pointB, int maxInterations = 200, double tolerance = 1.0E-12)
{
// Source: https://nathanrooy.github.io/posts/2016-12-18/vincenty-formula-with-python/
VincentyFormulaVariables v = PrepareλConvergenceLoop(pointA, pointB);
v = RecalculateλUntilConvergence(v, maxInterations, tolerance);
v = CalculateGeodesicDistanceAzimuth(v);
IBearingDistance bearingDistance = new BearingDistance()
{
Distance = new Distance(v.GeodesicLength, DistanceMeasurement.Meters),
InitialBearing = new Angle(v.ForwardAzimuth, AngleMeasurement.Radians),
FinalBearing = new Angle(v.BackwardAzimuth, AngleMeasurement.Radians)
};
return(bearingDistance);
}
private static VincentyFormulaVariables PrepareσConvergenceLoop(IGeographicCoordinate pointA, IAngle initialBearing, IDistance distance)
{
VincentyFormulaVariables v = new VincentyFormulaVariables();
v.Sinα1 = Math.Sin(initialBearing.ToRadians());
v.Cosα1 = Math.Cos(initialBearing.ToRadians());
v.TanU1 = (1.0 - f) * Math.Tan(pointA.Latitude.Angle.ToRadians());
v.CosU1 = 1.0 / Math.Sqrt((1 + Math.Pow(v.TanU1, 2.0)));
v.SinU1 = v.TanU1 * v.CosU1;
v.σ1 = Math.Atan2(v.TanU1, v.Cosα1);
v.sinα = v.CosU1 * v.Sinα1;
v.CosSqα = 1.0 - Math.Pow(v.sinα, 2.0);
v.USquared = v.CosSqα * (Math.Pow(a, 2.0) - Math.Pow(b, 2.0)) / Math.Pow(b, 2.0);
v.A = 1 + v.USquared / 16384.0 * (4096.0 + v.USquared * (-768.0 + v.USquared * (320.0 - 175.0 * v.USquared)));
v.B = v.USquared / 1024.0 * (256.0 + v.USquared * (-128.0 + v.USquared * (74.0 - 47.0 * v.USquared)));
v.σ = distance.ToMeters() / (b * v.A);
return(v);
}
public static IAngle BearingFrom(this IGeographicCoordinate pointA, IGeographicCoordinate pointB, int maxInterations = 200, double tolerance = 1.0E-12)
{
return(VincentysInverseFormula(pointA, pointB, maxInterations, tolerance).FinalBearing);
}
public static IAngle BearingFrom(this IGeographicCoordinate pointA, IAngle initialBearing, IDistance distance, int maxInterations = 200, double tolerance = 1.0E-12)
{
var backwardAzimuth = VincentysDirectFormula(pointA, initialBearing, distance, maxInterations, tolerance).BackwardAzimuth;
return(new Angle(backwardAzimuth, AngleMeasurement.Radians));
}
public static IAngle FinalBearing(this IGeographicCoordinate pointA, IAngle initialBearing, IDistance distance, int maxInterations = 200, double tolerance = 1.0E-12)
{
var finalBearing = VincentysDirectFormula(pointA, initialBearing, distance, maxInterations, tolerance).FinalBearing;
return(new Angle(finalBearing, AngleMeasurement.Radians));
}
public static IGeographicCoordinate DestinationCoordinates(this IGeographicCoordinate pointA, IAngle initialBearing, IDistance distance,
int maxInterations = 200, double tolerance = 1.0E-12)
{
return(VincentysDirectFormula(pointA, initialBearing, distance, maxInterations, tolerance).DestinationCoordinates);
}
public static IDistance GreatCircleDistanceTo(this IGeographicCoordinate pointA, IGeographicCoordinate pointB, int maxInterations = 200, double tolerance = 1.0E-12)
{
return(VincentysInverseFormula(pointA, pointB, maxInterations, tolerance).Distance);
}
public void GeographicCoordinate_CannotUpdateInvalidLatitude(double angle)
{
IGeographicCoordinate sut = InstantiateNewGeographicCoordinate();
Assert.Throws <ArgumentOutOfRangeException>(() => sut.Latitude = new Latitude(angle));
}
public void GeographicCoordinate_CanInstantiate()
{
IGeographicCoordinate result = InstantiateNewGeographicCoordinate();
Assert.NotNull(result);
}
