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Add map projections

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Add TransverseMercatorProjection, PolarStereographicProjection and derived UTM/UPS projections to the base library.
This commit is contained in:
ClemensFischer 2022-12-13 18:22:18 +01:00
parent 568f55feb0
commit e45180b26a
18 changed files with 647 additions and 332 deletions
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36
MapControl/Shared/WorldMercatorProjection.cs
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@ -15,10 +15,8 @@ namespace MapControl
/// </summary>
public class WorldMercatorProjection : MapProjection
{
private const double ConvergenceTolerance = 1e-6;
private const int MaxIterations = 10;
public const string DefaultCrsId = "EPSG:3395";
public const int DefaultEpsgCode = 3395;
public static readonly string DefaultCrsId = $"EPSG:{DefaultEpsgCode}";
public WorldMercatorProjection()
{
@ -62,31 +60,33 @@ namespace MapControl
}
var lat = latitude * Math.PI / 180d;
var eSinLat = Wgs84Eccentricity * Math.Sin(lat);
var f = Math.Pow((1d - eSinLat) / (1d + eSinLat), Wgs84Eccentricity / 2d);
return Math.Log(Math.Tan(lat / 2d + Math.PI / 4d) * ConformalFactor(lat)) * 180d / Math.PI; // p.44 (7-7)
return Math.Log(Math.Tan(lat / 2d + Math.PI / 4d) * f) * 180d / Math.PI; // p.44 (7-7)
}
public static double YToLatitude(double y)
{
var t = Math.Exp(-y * Math.PI / 180d); // p.44 (7-10)
var lat = Math.PI / 2d - 2d * Math.Atan(t); // p.44 (7-11)
var relChange = 1d;
for (var i = 0; i < MaxIterations && relChange > ConvergenceTolerance; i++)
{
var newLat = Math.PI / 2d - 2d * Math.Atan(t * ConformalFactor(lat)); // p.44 (7-9)
relChange = Math.Abs(1d - newLat / lat);
lat = newLat;
}
return lat * 180d / Math.PI;
return LatitudeFromSeriesApproximation(Wgs84Eccentricity, t) * 180d / Math.PI;
}
private static double ConformalFactor(double lat)
internal static double LatitudeFromSeriesApproximation(double e, double t)
{
var eSinLat = Wgs84Eccentricity * Math.Sin(lat);
var e_2 = e * e;
var e_4 = e_2 * e_2;
var e_6 = e_2 * e_4;
var e_8 = e_2 * e_6;
return Math.Pow((1d - eSinLat) / (1d + eSinLat), Wgs84Eccentricity / 2d);
var lat = Math.PI / 2d - 2d * Math.Atan(t); // p.45 (7-13)
return lat
+ (e_2 / 2d + 5d * e_4 / 24d + e_6 / 12d + 13d * e_8 / 360d) * Math.Sin(2d * lat)
+ (7d * e_4 / 48d + 29d * e_6 / 240d + 811d * e_8 / 11520d) * Math.Sin(4d * lat)
+ (7d * e_6 / 120d + 81d * e_8 / 1120d) * Math.Sin(6d * lat)
+ (4279d * e_8 / 161280d) * Math.Sin(8d * lat); // p.45 (3-5)
}
}
}