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Position.cs
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Position.cs
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using System;
using System.Threading;
using System.Globalization;
using System.Xml;
using System.Xml.Schema;
using System.Xml.Serialization;
#if !PocketPC || DesignTime
using System.ComponentModel;
#endif
namespace GeoFramework
{
/// <summary>Represents a specific location on Earth's surface.</summary>
/// <remarks>
/// <para>Instances of this class are guaranteed to be thread-safe because the class is
/// immutable (its properties can only be changed via constructors).</para>
/// </remarks>
#if !PocketPC || DesignTime
[TypeConverter("GeoFramework.Design.PositionConverter, GeoFramework.Design, Culture=neutral, Version=2.0.0.0, PublicKeyToken=d77afaeb30e3236a")]
#endif
public struct Position : IFormattable, IEquatable<Position>, ICloneable<Position>, IXmlSerializable
{
private Latitude _Latitude;
private Longitude _Longitude;
#region Constants
// Accuracy is set to 1.0E-12, the smallest value allowed by a Latitude or Longitude
private const double TargetAccuracy = 1.0E-12;
#endregion
#region Fields
/// <summary>Represents the location at 0°, 0°.</summary>
public static readonly Position Empty = new Position(Latitude.Empty, Longitude.Empty);
/// <summary>Represents the smallest possible location of 90°S, 180°W.</summary>
public static readonly Position Minimum = new Position(Latitude.Minimum, Longitude.Minimum);
/// <summary>Represents the largest possible location of 90°N, 180°E.</summary>
public static readonly Position Maximum = new Position(Latitude.Maximum, Longitude.Maximum);
/// <summary>Represents the single point at the top of Earth: 90°N, 0°E.</summary>
public static readonly Position NorthPole = new Position(Latitude.Maximum, Longitude.Empty);
/// <summary>Represents the single point at the bottom of Earth: 90°S, 0°E.</summary>
public static readonly Position SouthPole = new Position(Latitude.Minimum, Longitude.Empty);
/// <summary>Represents an invalid or unspecified value.</summary>
public static readonly Position Invalid = new Position(Latitude.Invalid, Longitude.Invalid);
#endregion
#region Constructors
/// <summary>
/// Creates a new instance from the specified longitude and latitude.
/// </summary>
/// <param name="longitude"></param>
/// <param name="latitude"></param>
public Position(Longitude longitude, Latitude latitude)
{
_Latitude = latitude;
_Longitude = longitude;
}
/// <summary>
/// Creates a new instance from the specified latitude and longitude.
/// </summary>
/// <param name="longitude"></param>
/// <param name="latitude"></param>
public Position(Latitude latitude, Longitude longitude)
{
_Latitude = latitude;
_Longitude = longitude;
}
/// <summary>
/// Creates a new instance by parsing latitude and longitude from a single string.
/// </summary>
/// <param name="value">A <strong>String</strong> containing both a latitude and longitude to parse.</param>
public Position(string value)
: this(value, CultureInfo.CurrentCulture)
{}
/// <summary>
/// Creates a new instance by interpreting the specified latitude and longitude.
/// </summary>
/// <param name="latitude">A <strong>String</strong> describing a latitude in the current culture.</param>
/// <param name="longitude">A <strong>String</strong> describing a longitude in the current culture.</param>
/// <remarks>Latitude and longitude values are parsed using the current local culture. For better support
/// of international cultures, add a CultureInfo parameter.</remarks>
public Position(string latitude, string longitude)
: this(latitude, longitude, CultureInfo.CurrentCulture)
{}
/// <summary>
/// Creates a new instance by interpreting the specified latitude and longitude.
/// </summary>
/// <param name="latitude">A <strong>String</strong> describing a latitude in the current culture.</param>
/// <param name="longitude">A <strong>String</strong> describing a longitude in the current culture.</param>
/// <remarks>Latitude and longitude values are parsed using the current local culture. For better support
/// of international cultures, a CultureInfo parameter should be specified to indicate how numbers should
/// be parsed.</remarks>
public Position(string latitude, string longitude, CultureInfo culture)
: this(Latitude.Parse(latitude, culture),
Longitude.Parse(longitude, culture))
{ }
/// <summary>
/// Creates a new instance by converting the specified string using the specific culture.
/// </summary>
/// <param name="value"></param>
/// <param name="culture"></param>
public Position(string value, CultureInfo culture)
{
// Empty values mean "Empty"
if (value.Length == 0)
{
_Latitude = Latitude.Empty;
_Longitude = Longitude.Empty;
return;
}
else if (value == "Empty")
{
_Latitude = Latitude.Empty;
_Longitude = Longitude.Empty;
return;
}
// Try to parse the value as latitude/longitude
Position Result = ParseAsLatLong(value, culture);
if (!Result.IsInvalid)
{
_Latitude = Result.Latitude.Normalize();
_Longitude = Result.Longitude.Normalize();
return;
}
// Raise an exception
#if PocketPC
throw new ArgumentException(Properties.Resources.Position_InvalidFormat);
#else
throw new ArgumentException(Properties.Resources.Position_InvalidFormat, "value");
#endif
}
/// <summary>
/// Creates a copy of the specified object.
/// </summary>
/// <param name="position"></param>
public Position(Position position)
: this(position.Latitude, position.Longitude)
{}
/// <summary>
/// Creates a new position by deserializing the specified XML content.
/// </summary>
/// <param name="reader"></param>
public Position(XmlReader reader)
{
// Initialize all fields
_Latitude = Latitude.Invalid;
_Longitude = Longitude.Invalid;
// Deserialize the object from XML
ReadXml(reader);
}
#endregion
#region Public Properties
/// <summary>Represents the vertical North/South portion of the location.</summary>
public Latitude Latitude
{
get { return _Latitude; }
}
/// <summary>Represents the horizontal East/West portion of the location.</summary>
public Longitude Longitude
{
get { return _Longitude; }
}
/// <summary>Indicates if the position has no value.</summary>
public bool IsEmpty
{
get
{
return _Latitude.IsEmpty && _Longitude.IsEmpty;
}
}
/// <summary>Indicates if the position has an invalid or unspecified value.</summary>
public bool IsInvalid
{
get
{
return _Latitude.IsInvalid || _Longitude.IsInvalid;
}
}
/// <summary>Indicates whether the position has been normalized and is within the
/// allowed bounds of -90° and 90° latitude and -180° and 180° longitude.</summary>
public bool IsNormalized
{
get
{
return _Latitude.IsNormalized && _Longitude.IsNormalized;
}
}
#endregion
#region Public Methods
/// <overloads>Outputs the current instance as a formatted string.</overloads>
/// <summary>
/// Outputs the current instance as a string using the specified format.
/// </summary>
/// <returns></returns>
public string ToString(string format)
{
return ToString(format, CultureInfo.CurrentCulture);
}
/// <summary>
/// Converts the current instance into an Earth-centered, Earth-fixed (ECEF) Cartesian point.
/// </summary>
/// <returns></returns>
public CartesianPoint ToCartesianPoint()
{
return ToCartesianPoint(Ellipsoid.Wgs1984, Distance.Empty);
}
public CartesianPoint ToCartesianPoint(Ellipsoid ellipsoid, Distance altitude)
{
// % LLA2ECEF - convert latitude, longitude, and altitude to
// % earth-centered, earth-fixed (ECEF) cartesian
// %
// % USAGE:
// % [x,y,z] = lla2ecef(lat,lon,alt)
// %
// % x = ECEF X-coordinate (m)
// % y = ECEF Y-coordinate (m)
// % z = ECEF Z-coordinate (m)
// % lat = geodetic latitude (radians)
// % lon = longitude (radians)
// % alt = height above WGS84 ellipsoid (m)
// %
// % Notes: This function assumes the WGS84 model.
// % Latitude is customary geodetic (not geocentric).
// %
// % Source: "Department of Defense World Geodetic System 1984"
// % Page 4-4
// % National Imagery and Mapping Agency
// % Last updated June, 2004
// % NIMA TR8350.2
// %
// % Michael Kleder, July 2005
//
// function [x,y,z]=lla2ecef(lat,lon,alt)
double lat = Latitude.ToRadians().Value;
double lon = Longitude.ToRadians().Value;
// Altitude is assumed at 100 meters
double alt = altitude.ToMeters().Value;
//
// % WGS84 ellipsoid constants:
// a = 6378137;
double a = ellipsoid.EquatorialRadius.ToMeters().Value;
// e = 8.1819190842622e-2;
double e = ellipsoid.Eccentricity;
//
// % intermediate calculation
// % (prime vertical radius of curvature)
// N = a ./ sqrt(1 - e^2 .* sin(lat).^2);
double N = a / Math.Sqrt(1.0 - Math.Pow(e, 2) * Math.Pow(Math.Sin(lat), 2));
//
// % results:
// x = (N+alt) .* cos(lat) .* cos(lon);
double x = (N + alt) * Math.Cos(lat) * Math.Cos(lon);
// y = (N+alt) .* cos(lat) .* sin(lon);
double y = (N + alt) * Math.Cos(lat) * Math.Sin(lon);
// z = ((1-e^2) .* N + alt) .* sin(lat);
double z = ((1.0 - Math.Pow(e, 2)) * N + alt) * Math.Sin(lat);
//
// return
return new CartesianPoint(
new Distance(x, DistanceUnit.Meters),
new Distance(y, DistanceUnit.Meters),
new Distance(z, DistanceUnit.Meters));
}
public Position Normalize()
{
return new Position(_Latitude.Normalize(), _Longitude.Normalize());
}
/// <summary>
/// Calculates the direction of travel to the specified destination.
/// </summary>
/// <param name="destination">A <strong>Position</strong> object to which the bearing is calculated.</param>
/// <returns>An <strong>Azimuth</strong> object representing the calculated distance.</returns>
public Azimuth BearingTo(Position destination)
{
return BearingTo(destination, Ellipsoid.Wgs1984);
}
/// <summary>
/// Calculates the direction of travel to the specified destination using the specified interpretation of Earth's shape.
/// </summary>
/// <param name="destination">A <strong>Position</strong> object to which the bearing is calculated.</param>
/// <param name="ellipsoid">An <strong>Ellipsoid</strong> object used to fine-tune bearing calculations.</param>
/// <returns>An <strong>Azimuth</strong> object representing the calculated distance.</returns>
public Azimuth BearingTo(Position destination, Ellipsoid ellipsoid)
{
// From: http://www.mathworks.com/matlabcentral/files/8607/vdist.m
/*
function varargout = vdist(lat1,lon1,lat2,lon2)
% VDIST - Using the WGS-84 Earth ellipsoid, compute the distance between
% two points within a few millimeters of accuracy, compute forward
% azimuth, and compute backward azimuth, all using a vectorized
% version of Vincenty's algorithm.
%
% s = vdist(lat1,lon1,lat2,lon2)
% [s,a12] = vdist(lat1,lon1,lat2,lon2)
% [s,a12,a21] = vdist(lat1,lon1,lat2,lon2)
%
% s = distance in meters (inputs may be scalars, vectors, or matrices)
% a12 = azimuth in degrees from first point to second point (forward)
% a21 = azimuth in degrees from second point to first point (backward)
% (Azimuths are in degrees clockwise from north.)
% lat1 = GEODETIC latitude of first point (degrees)
% lon1 = longitude of first point (degrees)
% lat2, lon2 = second point (degrees)
%
% Original algorithm source:
% T. Vincenty, "Direct and Inverse Solutions of Geodesics on the Ellipsoid
% with Application of Nested Equations", Survey Review, vol. 23, no. 176,
% April 1975, pp 88-93.
% Available at: http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
%
% Notes: (1) lat1,lon1,lat2,lon2 can be any (identical) size/shape. Outputs
% will have the same size and shape.
% (2) Error correcting code, convergence failure traps, antipodal
% corrections, polar error corrections, WGS84 ellipsoid
% parameters, testing, and comments: Michael Kleder, 2004.
% (3) Azimuth implementation (including quadrant abiguity
% resolution) and code vectorization, Michael Kleder, Sep 2005.
% (4) Vectorization is convergence sensitive; that is, quantities
% which have already converged to within tolerance are not
% recomputed during subsequent iterations (while other
% quantities are still converging).
% (5) Vincenty describes his distance algorithm as precise to within
% 0.01 millimeters, subject to the ellipsoidal model.
% (6) For distance calculations, essentially antipodal points are
% treated as exactly antipodal, potentially reducing accuracy
% slightly.
% (7) Distance failures for points exactly at the poles are
% eliminated by moving the points by 0.6 millimeters.
% (8) The Vincenty distance algorithm was transcribed verbatim by
% Peter Cederholm, August 12, 2003. It was modified and
% translated to English by Michael Kleder.
% Mr. Cederholm's website is http://www.plan.aau.dk/~pce/
% (9) Distances agree with the Mapping Toolbox, version 2.2 (R14SP3)
% with a max relative difference of about 5e-9, except when the
% two points are nearly antipodal, and except when one point is
% near the equator and the two longitudes are nearly 180 degrees
% apart. This function (vdist) is more accurate in such cases.
% For example, note this difference (as of this writing):
% >>vdist(0.2,305,15,125)
% 18322827.0131551
% >>distance(0.2,305,15,125,[6378137 0.08181919])
% 0
% (10) Azimuths FROM the north pole (either forward starting at the
% north pole or backward when ending at the north pole) are set
% to 180 degrees by convention. Azimuths FROM the south pole are
% set to 0 degrees by convention.
% (11) Azimuths agree with the Mapping Toolbox, version 2.2 (R14SP3)
% to within about a hundred-thousandth of a degree, except when
% traversing to or from a pole, where the convention for this
% function is described in (10), and except in the cases noted
% above in (9).
% (12) No warranties; use at your own risk.
% reshape inputs
keepsize = size(lat1);
lat1=lat1(:);
lon1=lon1(:);
lat2=lat2(:);
lon2=lon2(:);
% Input check:
if any(abs(lat1)>90 | abs(lat2)>90)
error('Input latitudes must be between -90 and 90 degrees, inclusive.')
end
% Supply WGS84 earth ellipsoid axis lengths in meters:
a = 6378137; % definitionally
b = 6356752.31424518; % computed from WGS84 earth flattening coefficient
% preserve true input latitudes:
lat1tr = lat1;
lat2tr = lat2;
% convert inputs in degrees to radians:
lat1 = lat1 * 0.0174532925199433;
lon1 = lon1 * 0.0174532925199433;
lat2 = lat2 * 0.0174532925199433;
lon2 = lon2 * 0.0174532925199433;
% correct for errors at exact poles by adjusting 0.6 millimeters:
kidx = abs(pi/2-abs(lat1)) < 1e-10;
if any(kidx);
lat1(kidx) = sign(lat1(kidx))*(pi/2-(1e-10));
end
kidx = abs(pi/2-abs(lat2)) < 1e-10;
if any(kidx)
lat2(kidx) = sign(lat2(kidx))*(pi/2-(1e-10));
end
f = (a-b)/a;
U1 = atan((1-f)*tan(lat1));
U2 = atan((1-f)*tan(lat2));
lon1 = mod(lon1,2*pi);
lon2 = mod(lon2,2*pi);
L = abs(lon2-lon1);
kidx = L > pi;
if any(kidx)
L(kidx) = 2*pi - L(kidx);
end
lambda = L;
lambdaold = 0*lat1;
itercount = 0;
notdone = logical(1+0*lat1);
alpha = 0*lat1;
sigma = 0*lat1;
cos2sigmam = 0*lat1;
C = 0*lat1;
warninggiven = logical(0);
while any(notdone) % force at least one execution
%disp(['lambda(21752) = ' num2str(lambda(21752),20)]);
itercount = itercount+1;
if itercount > 50
if ~warninggiven
warning(['Essentially antipodal points encountered. ' ...
'Precision may be reduced slightly.']);
end
lambda(notdone) = pi;
break
end
lambdaold(notdone) = lambda(notdone);
sinsigma(notdone) = sqrt((cos(U2(notdone)).*sin(lambda(notdone)))...
.^2+(cos(U1(notdone)).*sin(U2(notdone))-sin(U1(notdone)).*...
cos(U2(notdone)).*cos(lambda(notdone))).^2);
cossigma(notdone) = sin(U1(notdone)).*sin(U2(notdone))+...
cos(U1(notdone)).*cos(U2(notdone)).*cos(lambda(notdone));
% eliminate rare imaginary portions at limit of numerical precision:
sinsigma(notdone)=real(sinsigma(notdone));
cossigma(notdone)=real(cossigma(notdone));
sigma(notdone) = atan2(sinsigma(notdone),cossigma(notdone));
alpha(notdone) = asin(cos(U1(notdone)).*cos(U2(notdone)).*...
sin(lambda(notdone))./sin(sigma(notdone)));
cos2sigmam(notdone) = cos(sigma(notdone))-2*sin(U1(notdone)).*...
sin(U2(notdone))./cos(alpha(notdone)).^2;
C(notdone) = f/16*cos(alpha(notdone)).^2.*(4+f*(4-3*...
cos(alpha(notdone)).^2));
lambda(notdone) = L(notdone)+(1-C(notdone)).*f.*sin(alpha(notdone))...
.*(sigma(notdone)+C(notdone).*sin(sigma(notdone)).*...
(cos2sigmam(notdone)+C(notdone).*cos(sigma(notdone)).*...
(-1+2.*cos2sigmam(notdone).^2)));
%disp(['then, lambda(21752) = ' num2str(lambda(21752),20)]);
% correct for convergence failure in the case of essentially antipodal
% points
if any(lambda(notdone) > pi)
warning(['Essentially antipodal points encountered. ' ...
'Precision may be reduced slightly.']);
warninggiven = logical(1);
lambdaold(lambda>pi) = pi;
lambda(lambda>pi) = pi;
end
notdone = abs(lambda-lambdaold) > 1e-12;
end
u2 = cos(alpha).^2.*(a^2-b^2)/b^2;
A = 1+u2./16384.*(4096+u2.*(-768+u2.*(320-175.*u2)));
B = u2./1024.*(256+u2.*(-128+u2.*(74-47.*u2)));
deltasigma = B.*sin(sigma).*(cos2sigmam+B./4.*(cos(sigma).*(-1+2.*...
cos2sigmam.^2)-B./6.*cos2sigmam.*(-3+4.*sin(sigma).^2).*(-3+4*...
cos2sigmam.^2)));
varargout{1} = reshape(b.*A.*(sigma-deltasigma),keepsize);
if nargout > 1
% From point #1 to point #2
% correct sign of lambda for azimuth calcs:
lambda = abs(lambda);
kidx=sign(sin(lon2-lon1)) .* sign(sin(lambda)) < 0;
lambda(kidx) = -lambda(kidx);
numer = cos(U2).*sin(lambda);
denom = cos(U1).*sin(U2)-sin(U1).*cos(U2).*cos(lambda);
a12 = atan2(numer,denom);
kidx = a12<0;
a12(kidx)=a12(kidx)+2*pi;
% from poles:
a12(lat1tr <= -90) = 0;
a12(lat1tr >= 90 ) = pi;
varargout{2} = reshape(a12 * 57.2957795130823,keepsize); % to degrees
end
if nargout > 2
a21=NaN*lat1;
% From point #2 to point #1
% correct sign of lambda for azimuth calcs:
lambda = abs(lambda);
kidx=sign(sin(lon1-lon2)) .* sign(sin(lambda)) < 0;
lambda(kidx)=-lambda(kidx);
numer = cos(U1).*sin(lambda);
denom = sin(U1).*cos(U2)-cos(U1).*sin(U2).*cos(lambda);
a21 = atan2(numer,denom);
kidx=a21<0;
a21(kidx)= a21(kidx)+2*pi;
% backwards from poles:
a21(lat2tr >= 90) = pi;
a21(lat2tr <= -90) = 0;
varargout{3} = reshape(a21 * 57.2957795130823,keepsize); % to degrees
end
return
*
*
*/
// If positions are equivalent, return zero
if (Equals(destination))
return Azimuth.Empty;
#region Newer code
double goodlambda = 0;
double goodalpha = 0;
double goodsigma = 0;
double goodcos2sigmam = 0;
// % reshape inputs
//keepsize = size(lat1);
//lat1=lat1(:);
//lon1=lon1(:);
//lat2=lat2(:);
//lon2=lon2(:);
// ?
//% Input check:
//if any(abs(lat1)>90 | abs(lat2)>90)
// error('Input latitudes must be between -90 and 90 degrees, inclusive.')
//end
// The -90 to 90 check is handled by Normalize
//% Supply WGS84 earth ellipsoid axis lengths in meters:
//a = 6378137; % definitionally
//b = 6356752.31424518; % computed from WGS84 earth flattening coefficient
double a = ellipsoid.EquatorialRadiusMeters;
double b = ellipsoid.PolarRadiusMeters;
//% preserve true input latitudes:
//lat1tr = lat1;
//lat2tr = lat2;
double lat1tr = _Latitude.DecimalDegrees;
/* FxCop says that "lat2tr" is only assigned to, but never used.
*
double lat2tr = destination.Latitude.DecimalDegrees;
*/
//% convert inputs in degrees to radians:
//lat1 = lat1 * 0.0174532925199433;
//lon1 = lon1 * 0.0174532925199433;
//lat2 = lat2 * 0.0174532925199433;
//lon2 = lon2 * 0.0174532925199433;
// Convert inputs into radians
double lat1 = this.Latitude.Normalize().ToRadians().Value;
double lon1 = this.Longitude.Normalize().ToRadians().Value;
double lat2 = destination.Latitude.Normalize().ToRadians().Value;
double lon2 = destination.Longitude.Normalize().ToRadians().Value;
//% correct for errors at exact poles by adjusting 0.6 millimeters:
//kidx = abs(pi/2-abs(lat1)) < 1e-10;
//if any(kidx);
// lat1(kidx) = sign(lat1(kidx))*(pi/2-(1e-10));
//end
// Correct for errors at exact poles by adjusting 0.6mm
if (Math.Abs(Math.PI * 0.5 - Math.Abs(lat1)) < 1E-10)
{
lat1 = Math.Sign(lat1) * (Math.PI * 0.5 - 1E-10);
}
//kidx = abs(pi/2-abs(lat2)) < 1e-10;
//if any(kidx)
// lat2(kidx) = sign(lat2(kidx))*(pi/2-(1e-10));
//end
if (Math.Abs(Math.PI * 0.5 - Math.Abs(lat2)) < 1E-10)
{
lat2 = Math.Sign(lat2) * (Math.PI * 0.5 - 1E-10);
}
//f = (a-b)/a;
double f = ellipsoid.Flattening;
//U1 = atan((1-f)*tan(lat1));
double U1 = Math.Atan((1 - f) * Math.Tan(lat1));
//U2 = atan((1-f)*tan(lat2));
double U2 = Math.Atan((1 - f) * Math.Tan(lat2));
//lon1 = mod(lon1,2*pi);
lon1 = lon1 % (2 * Math.PI);
//lon2 = mod(lon2,2*pi);
lon2 = lon2 % (2 * Math.PI);
//L = abs(lon2-lon1);
double L = Math.Abs(lon2 - lon1);
//kidx = L > pi;
//if any(kidx)
// L(kidx) = 2*pi - L(kidx);
//end
if (L > Math.PI)
{
L = 2.0 * Math.PI - L;
}
//lambda = L;
double lambda = L;
//lambdaold = 0*lat1;
double lambdaold = 0;
//itercount = 0;
int itercount = 0;
//notdone = logical(1+0*lat1);
bool notdone = true;
//alpha = 0*lat1;
double alpha = 0;
//sigma = 0*lat1;
double sigma = 0;
//cos2sigmam = 0*lat1;
double cos2sigmam = 0;
//C = 0*lat1;
double C = 0;
//warninggiven = logical(0);
//bool warninggiven = false;
//while any(notdone) % force at least one execution
while (notdone)
{
// %disp(['lambda(21752) = ' num2str(lambda(21752),20)]);
// itercount = itercount+1;
itercount++;
// if itercount > 50
if (itercount > 50)
{
// if ~warninggiven
//if (!warninggiven)
//{
// // warning(['Essentially antipodal points encountered. ' ...
// // 'Precision may be reduced slightly.']);
// warninggiven = true;
// throw new WarningException("Distance calculation accuracy may be reduced because the two endpoints are antipodal.");
//}
// end
// lambda(notdone) = pi;
lambda = Math.PI;
// break
break;
// end
}
// lambdaold(notdone) = lambda(notdone);
lambdaold = lambda;
// sinsigma(notdone) = sqrt((cos(U2(notdone)).*sin(lambda(notdone)))...
// .^2+(cos(U1(notdone)).*sin(U2(notdone))-sin(U1(notdone)).*...
// cos(U2(notdone)).*cos(lambda(notdone))).^2);
double sinsigma = Math.Sqrt(Math.Pow((Math.Cos(U2) * Math.Sin(lambda))
, 2) + Math.Pow((Math.Cos(U1) * Math.Sin(U2) - Math.Sin(U1) *
Math.Cos(U2) * Math.Cos(lambda)), 2));
// cossigma(notdone) = sin(U1(notdone)).*sin(U2(notdone))+...
// cos(U1(notdone)).*cos(U2(notdone)).*cos(lambda(notdone));
double cossigma = Math.Sin(U1) * Math.Sin(U2) +
Math.Cos(U1) * Math.Cos(U2) * Math.Cos(lambda);
// % eliminate rare imaginary portions at limit of numerical precision:
// sinsigma(notdone)=real(sinsigma(notdone));
// cossigma(notdone)=real(cossigma(notdone));
// Eliminate rare imaginary portions at limit of numerical precision:
// ?
// sigma(notdone) = atan2(sinsigma(notdone),cossigma(notdone));
sigma = Math.Atan2(sinsigma, cossigma);
// alpha(notdone) = asin(cos(U1(notdone)).*cos(U2(notdone)).*...
// sin(lambda(notdone))./sin(sigma(notdone)));
alpha = Math.Asin(Math.Cos(U1) * Math.Cos(U2) *
Math.Sin(lambda) / Math.Sin(sigma));
// cos2sigmam(notdone) = cos(sigma(notdone))-2*sin(U1(notdone)).*...
// sin(U2(notdone))./cos(alpha(notdone)).^2;
cos2sigmam = Math.Cos(sigma) - 2.0 * Math.Sin(U1) *
Math.Sin(U2) / Math.Pow(Math.Cos(alpha), 2);
// C(notdone) = f/16*cos(alpha(notdone)).^2.*(4+f*(4-3*...
// cos(alpha(notdone)).^2));
C = f / 16 * Math.Pow(Math.Cos(alpha), 2) * (4 + f * (4 - 3 *
Math.Pow(Math.Cos(alpha), 2)));
// lambda(notdone) = L(notdone)+(1-C(notdone)).*f.*sin(alpha(notdone))...
// .*(sigma(notdone)+C(notdone).*sin(sigma(notdone)).*...
// (cos2sigmam(notdone)+C(notdone).*cos(sigma(notdone)).*...
// (-1+2.*cos2sigmam(notdone).^2)));
lambda = L + (1 - C) * f * Math.Sin(alpha)
* (sigma + C * Math.Sin(sigma) *
(cos2sigmam + C * Math.Cos(sigma) *
(-1 + 2 * Math.Pow(cos2sigmam, 2))));
// %disp(['then, lambda(21752) = ' num2str(lambda(21752),20)]);
// % correct for convergence failure in the case of essentially antipodal
// % points
// Correct for convergence failure in the case of essentially antipodal points
// if any(lambda(notdone) > pi)
if (lambda > Math.PI)
{
// if ~warninggiven
//if (!warninggiven)
//{
// // warning(['Essentially antipodal points encountered. ' ...
// // 'Precision may be reduced slightly.']);
// warninggiven = true;
// throw new WarningException("Distance calculation accuracy may be reduced because the two endpoints are antipodal.");
//}
// end
// lambdaold(lambda>pi) = pi;
lambdaold = Math.PI;
// lambda(lambda>pi) = pi;
lambda = Math.PI;
// end
}
// notdone = abs(lambda-lambdaold) > 1e-12;
notdone = Math.Abs(lambda - lambdaold) > TargetAccuracy;
//end
// NOTE: In some cases "alpha" would return a "NaN". If values are healthy,
// remember them so we get a good distance calc.
if (!double.IsNaN(alpha))
{
goodlambda = lambda;
goodalpha = alpha;
goodsigma = sigma;
goodcos2sigmam = cos2sigmam;
}
}
//u2 = cos(alpha).^2.*(a^2-b^2)/b^2;
double u2 = Math.Pow(Math.Cos(goodalpha), 2) * (Math.Pow(a, 2) - Math.Pow(b, 2)) / Math.Pow(b, 2);
//A = 1+u2./16384.*(4096+u2.*(-768+u2.*(320-175.*u2)));
double A = 1 + u2 / 16384 * (4096 + u2 * (-768 + u2 * (320 - 175 * u2)));
//B = u2./1024.*(256+u2.*(-128+u2.*(74-47.*u2)));
double B = u2 / 1024 * (256 + u2 * (-128 + u2 * (74 - 47 * u2)));
//deltasigma = B.*sin(sigma).*(cos2sigmam+B./4.*(cos(sigma).*(-1+2.*...
// cos2sigmam.^2)-B./6.*cos2sigmam.*(-3+4.*sin(sigma).^2).*(-3+4*...
// cos2sigmam.^2)));
double deltasigma = B * Math.Sin(goodsigma) * (goodcos2sigmam + B / 4 * (Math.Cos(goodsigma) * (-1 + 2 *
Math.Pow(goodcos2sigmam, 2)) - B / 6 * goodcos2sigmam * (-3 + 4 * Math.Pow(Math.Sin(goodsigma), 2)) * (-3 + 4 *
Math.Pow(goodcos2sigmam, 2))));
//varargout{1} = reshape(b.*A.*(sigma-deltasigma),keepsize);
/* FxCop says that this variable "double s" is only assigned to, but never used.
*
double s = b * A * (goodsigma - deltasigma);
*/
// Return the Distance in meters
//return new Distance(s, DistanceUnit.Meters).ToLocalUnitType();
//if nargout > 1
// % From point #1 to point #2
// % correct sign of lambda for azimuth calcs:
// lambda = abs(lambda);
goodlambda = Math.Abs(goodlambda);
// kidx=sign(sin(lon2-lon1)) .* sign(sin(lambda)) < 0;
bool kidx = Math.Sign(Math.Sin(lon2 - lon1)) * Math.Sign(Math.Sin(goodlambda)) < 0;
// lambda(kidx) = -lambda(kidx);
if (kidx)
goodlambda = -goodlambda;
// numer = cos(U2).*sin(lambda);
double numer = Math.Cos(U2) * Math.Sin(goodlambda);
// denom = cos(U1).*sin(U2)-sin(U1).*cos(U2).*cos(lambda);
double denom = Math.Cos(U1) * Math.Sin(U2) - Math.Sin(U1) * Math.Cos(U2) * Math.Cos(goodlambda);
// a12 = atan2(numer,denom);
double a12 = Math.Atan2(numer, denom);
// kidx = a12<0;
kidx = a12 < 0;
// a12(kidx)=a12(kidx)+2*pi;
if (kidx)
a12 = a12 + 2 * Math.PI;
// % from poles:
// a12(lat1tr <= -90) = 0;
if (lat1tr <= -90.0)
a12 = 0;
// a12(lat1tr >= 90 ) = pi;
if (lat1tr >= 90)
a12 = Math.PI;
// varargout{2} = reshape(a12 * 57.2957795130823,keepsize); % to degrees
// Convert to degrees
return Azimuth.FromRadians(a12);
//end
//if nargout > 2
// a21=NaN*lat1;
// % From point #2 to point #1
// % correct sign of lambda for azimuth calcs:
// lambda = abs(lambda);
// kidx=sign(sin(lon1-lon2)) .* sign(sin(lambda)) < 0;
// lambda(kidx)=-lambda(kidx);
// numer = cos(U1).*sin(lambda);
// denom = sin(U1).*cos(U2)-cos(U1).*sin(U2).*cos(lambda);
// a21 = atan2(numer,denom);
// kidx=a21<0;
// a21(kidx)= a21(kidx)+2*pi;
// % backwards from poles:
// a21(lat2tr >= 90) = pi;
// a21(lat2tr <= -90) = 0;
// varargout{3} = reshape(a21 * 57.2957795130823,keepsize); % to degrees
//end
//return
#endregion
#region Unused Code (Commented Out)
/*
double lonrad = pLongitude.ToRadians().Value;
double latrad = pLatitude.ToRadians().Value;
double destlonrad = destination.Longitude.ToRadians().Value;
double destlatrad = destination.Latitude.ToRadians().Value;
double y = Math.Sin(lonrad - destlonrad) * Math.Cos(destlatrad);
double x = Math.Cos(latrad) * Math.Sin(destlatrad)
- Math.Sin(latrad) * Math.Cos(destlatrad) * Math.Cos(lonrad - destlonrad);
double rad = Math.Atan2(-y, x);
return Azimuth.FromRadians(rad).Normalize();
*/
// try
//// {
// //Dim AdjustedDestination As Position = destination.ToEllipsoid(Ellipsoid.Type)
//
// double y = -Math.Sin(Longitude.ToRadians().Value - destination.Longitude.ToRadians().Value)
// * Math.Cos(destination.Latitude.ToRadians().Value);
// double x = Math.Cos(Latitude.ToRadians().Value) * Math.Sin(destination.Latitude.ToRadians().Value)
// - Math.Sin(Latitude.ToRadians().Value) * Math.Cos(destination.Latitude.ToRadians().Value)
// * Math.Cos(Longitude.ToRadians().Value - destination.Longitude.ToRadians().Value);
//
// //Console.WriteLine(String.Format("X: {0}, Y: {1}
//
//// atan2( -sin(long1-long2).cos(lat2),
////cos(lat1).sin(lat2) - sin(lat1).cos(lat2).cos(long1-long2) )
//
//
// return new Azimuth(((Math.Atan2(y, x) * 180.0 / Math.PI) + 360) % 360); //+ 1 / 7200.0)
// }
// catch
// {
// throw new GpsException("Error while calculating initial bearing.");
// }
// Test Data
//
// Name: Denver Oklahoma City
// Latitude: 39 ° 45 ' 0.00000 '' 35 ° 26 ' 0.00000 ''
// Longitude: 105 ° 0 ' 0.00000 '' 97 ° 28 ' 0.00000 ''
// Forward Azimuth: 236 ° 35 ' 21.15 ''
// Reverse Azimuth: 51 ° 59 ' 10.32 ''
// Datumal Distance: 819373.914 meters
// '' Converted from JavaScript: http://www.movable-type.co.uk/scripts/LatLong.html
// ''
// '' LatLong.bearing = function(p1, p2) {
// '' var y = Math.sin(p1.long-p2.long) * Math.cos(p2.lat);
// '' var x = Math.cos(p1.lat)*Math.sin(p2.lat) -
// '' Math.sin(p1.lat)*Math.cos(p2.lat)*Math.cos(p1.long-p2.long);
// '' return(Math.atan2(-y, x)); // -y 'cos Williams treats W as +ve!
// 'Try
// ' Dim AdjustedDestination As Position = destination ' destination.ToDatum(Datum.Type)
// ' Dim StartLatRad As Double = Latitude.ToRadians().Value
// ' Dim StartLonRad As Double = Longitude.ToRadians().Value
// ' Dim DestLatRad As Double = AdjustedDestination.Latitude.ToRadians().Value
// ' Dim DestLonRad As Double = AdjustedDestination.Longitude.ToRadians().Value
// ' Dim y As Double = -Math.Sin(StartLonRad - DestLonRad) * Math.Cos(DestLatRad)