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Fixed RelativeTransform of azimuthal projections

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ClemensFischer 2026-01-28 09:52:11 +01:00
parent 8d25310b8e
commit 3922297e7b
12 changed files with 72 additions and 39 deletions
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21
MapControl/Shared/AzimuthalEquidistantProjection.cs
View file

@ -29,21 +29,22 @@ namespace MapControl
public override Matrix RelativeTransform(double latitude, double longitude)
{
var p = GetProjectedPoint(latitude, longitude);
if (p.CosC == 1d)
{
return new Matrix(1d, 0d, 0d, 1d, 0d, 0d);
}
var scaleX = 1d;
var scaleY = 1d;
if (p.CosC == -1d)
{
return new Matrix(1d, 0d, 0d, double.PositiveInfinity, 0d, 0d);
scaleY = double.PositiveInfinity;
}
else if (p.CosC != 1d)
{
var c = Math.Acos(p.CosC);
var k = c / Math.Sin(c); // p.195 (25-2)
(scaleX, scaleY) = p.RelativeScale(1d, k);
}
var c = Math.Acos(p.CosC);
var k = c / Math.Sin(c); // p.195 (25-2)
return p.RelativeScale(1d, k);
return RelativeTransform(latitude, longitude, scaleX, scaleY);
}
public override Point? LocationToMap(double latitude, double longitude)

23
MapControl/Shared/AzimuthalProjection.cs
View file

@ -1,7 +1,4 @@
using System;
#if WPF
using System.Windows.Media;
#endif
namespace MapControl
{
@ -36,16 +33,26 @@ namespace MapControl
CosC = Math.Min(Math.Max(cosC, -1d), 1d); // protect against rounding errors
}
public Matrix RelativeScale(double radialScale, double perpendicularScale)
public (double, double) RelativeScale(double radialScale, double perpendicularScale)
{
var scale = new Matrix(radialScale, 0d, 0d, perpendicularScale, 0d, 0d);
var scaleX = radialScale;
var scaleY = perpendicularScale;
if (radialScale != perpendicularScale)
if (scaleX != scaleY)
{
scale.Rotate(-Math.Atan2(Y, X) * 180d / Math.PI);
var s = Math.Sqrt(X * X + Y * Y);
// sin and cos of azimuth from projection center, i.e. Atan2(Y/X)
var cos = X / s;
var sin = Y / s;
var x1 = scaleX * cos;
var y1 = scaleY * sin;
var x2 = scaleX * sin;
var y2 = scaleY * cos;
scaleX = Math.Sqrt(x1 * x1 + y1 * y1);
scaleY = Math.Sqrt(x2 * x2 + y2 * y2);
}
return scale;
return (scaleX, scaleY);
}
}

3
MapControl/Shared/GnomonicProjection.cs
View file

@ -31,8 +31,9 @@ namespace MapControl
var p = GetProjectedPoint(latitude, longitude);
var k = 1d / p.CosC; // p.165 (22-3)
var h = k * k; // p.165 (22-2)
(var scaleX, var scaleY) = p.RelativeScale(h, k);
return p.RelativeScale(h, k);
return RelativeTransform(latitude, longitude, scaleX, scaleY);
}
public override Point? LocationToMap(double latitude, double longitude)

25
MapControl/Shared/MapProjection.cs
View file

@ -207,5 +207,30 @@ namespace MapControl
{
return CrsId;
}
/// <summary>
/// Used by azimuthal projections, where local skewing can not be directly calculated.
/// </summary>
protected Matrix RelativeTransform(double latitude, double longitude, double scaleX, double scaleY)
{
var north = LocationToMap(latitude - 1e-3, longitude);
var south = LocationToMap(latitude + 1e-3, longitude);
var west = LocationToMap(latitude, longitude - 1e-3);
var east = LocationToMap(latitude, longitude + 1e-3);
var tanSkewX = 0d;
var tanSkewY = 0d;
if (north.HasValue && south.HasValue && west.HasValue && east.HasValue)
{
var dx1 = east.Value.X - west.Value.X;
var dy1 = east.Value.Y - west.Value.Y;
var dx2 = north.Value.X - south.Value.X;
var dy2 = north.Value.Y - south.Value.Y;
tanSkewX = -dx2 / dy2;
tanSkewY = -dy1 / dx1;
}
return new Matrix(scaleX, scaleX * tanSkewY, scaleY * tanSkewX, scaleY, 0d, 0d);
}
}
}

3
MapControl/Shared/OrthographicProjection.cs
View file

@ -29,8 +29,9 @@ namespace MapControl
public override Matrix RelativeTransform(double latitude, double longitude)
{
var p = GetProjectedPoint(latitude, longitude);
(var scaleX, var scaleY) = p.RelativeScale(p.CosC, 1d); // p.149 (20-5), k == 1
return p.RelativeScale(p.CosC, 1d); // p.149 (20-5), k == 1
return RelativeTransform(latitude, longitude, scaleX, scaleY);
}
public override Point? LocationToMap(double latitude, double longitude)

8
MapControl/Shared/PolarStereographicProjection.cs
View file

@ -21,7 +21,7 @@ namespace MapControl
public double FalseNorthing { get; set; } = 2e6;
public Hemisphere Hemisphere { get; set; }
public static double RelativeScale(Hemisphere hemisphere, double flattening, double latitude)
public static double RelativeScale(Hemisphere hemisphere, double flattening, double scaleFactor, double latitude)
{
var sign = hemisphere == Hemisphere.North ? 1d : -1d;
var phi = sign * latitude * Math.PI / 180d;
@ -32,8 +32,8 @@ namespace MapControl
var t = Math.Tan(Math.PI / 4d - phi / 2d)
/ Math.Pow((1d - eSinPhi) / (1d + eSinPhi), e / 2d); // p.161 (15-9)
// r == ρ/(a*k0), omit k0 for relative scale
var r = 2d * t / Math.Sqrt(Math.Pow(1d + e, 1d + e) * Math.Pow(1d - e, 1d - e)); // p.161 (21-33)
// r == ρ/a
var r = scaleFactor * 2d * t / Math.Sqrt(Math.Pow(1d + e, 1d + e) * Math.Pow(1d - e, 1d - e)); // p.161 (21-33)
var m = Math.Cos(phi) / Math.Sqrt(1d - eSinPhi * eSinPhi); // p.160 (14-15)
return r / m; // p.161 (21-32)
@ -41,7 +41,7 @@ namespace MapControl
public override Matrix RelativeTransform(double latitude, double longitude)
{
var k = RelativeScale(Hemisphere, Flattening, latitude);
var k = RelativeScale(Hemisphere, Flattening, ScaleFactor, latitude);
return new Matrix(k, 0d, 0d, k, 0d, 0d);
}

2
MapControl/Shared/StereographicProjection.cs
View file

@ -31,7 +31,7 @@ namespace MapControl
var p = GetProjectedPoint(latitude, longitude);
var k = 2d / (1d + p.CosC); // p.157 (21-4), k0 == 1
return p.RelativeScale(k, k);
return RelativeTransform(latitude, longitude, k, k);
}
public override Point? LocationToMap(double latitude, double longitude)

7
MapControl/Shared/TransverseMercatorProjection.cs
View file

@ -68,6 +68,7 @@ namespace MapControl
// λ - λ0
var dLambda = (longitude - CentralMeridian) * Math.PI / 180d;
var cosLambda = Math.Cos(dLambda);
var tanLambda = Math.Tan(dLambda);
// t
var t = Math.Sinh(Atanh(sinPhi) - f2 * Atanh(f2 * sinPhi));
var u = Math.Sqrt(1d + t * t);
@ -88,14 +89,12 @@ namespace MapControl
var n = Flattening / (2d - Flattening);
var m = (1d - n) / (1d + n) * Math.Tan(phi);
// h = k/k0 for relative scale
var h = f1 * Math.Sqrt((1d + m * m) * (sigma * sigma + tau * tau) / (t * t + cosLambda * cosLambda));
var k = ScaleFactor * f1 * Math.Sqrt((1d + m * m) * (sigma * sigma + tau * tau) / (t * t + cosLambda * cosLambda));
var tanLambda = Math.Tan(dLambda);
// γ, meridian convergence angle
var gamma = Math.Atan2(tau * u + sigma * t * tanLambda, sigma * u - tau * t * tanLambda);
var transform = new Matrix(h, 0d, 0d, h, 0d, 0d);
var transform = new Matrix(k, 0d, 0d, k, 0d, 0d);
transform.Rotate(-gamma * 180d / Math.PI);
return transform;

10
MapControl/Shared/TransverseMercatorProjectionSnyder.cs
View file

@ -47,10 +47,8 @@ namespace MapControl
public override Matrix RelativeTransform(double latitude, double longitude)
{
// h = k/k0 for relative scale
var h = 1d;
// γ, meridian convergence angle
var gamma = 0d;
var k = ScaleFactor;
var gamma = 0d; // γ, meridian convergence angle
if (latitude > -90d && latitude < 90d)
{
@ -69,14 +67,14 @@ namespace MapControl
var A4 = A2 * A2;
var A6 = A2 * A4;
h = 1d + (1d + C) * A2 / 2d +
k *= 1d + (1d + C) * A2 / 2d +
(5d - 4d * T + 42d * C + 13d * C * C - 28d * e_2) * A4 / 24d +
(61d - 148d * T + 16 * T * T) * A6 / 720d; // (8-11)
gamma = Math.Atan(Math.Tan(dLambda) * sinPhi);
}
var transform = new Matrix(h, 0d, 0d, h, 0d, 0d);
var transform = new Matrix(k, 0d, 0d, k, 0d, 0d);
transform.Rotate(-gamma * 180d / Math.PI);
return transform;

3
MapProjections/Shared/Wgs84OrthographicProjection.cs
View file

@ -37,8 +37,9 @@ namespace MapControl.Projections
public override Matrix RelativeTransform(double latitude, double longitude)
{
var p = new AzimuthalProjection.ProjectedPoint(Center.Latitude, Center.Longitude, latitude, longitude);
(var scaleX, var scaleY) = p.RelativeScale(p.CosC, 1d); // p.149 (20-5), k == 1
return p.RelativeScale(p.CosC, 1d); // p.149 (20-5), k == 1
return RelativeTransform(latitude, longitude, scaleX, scaleY);
}
}
}

2
MapProjections/Shared/Wgs84StereographicProjection.cs
View file

@ -39,7 +39,7 @@ namespace MapControl.Projections
var p = new AzimuthalProjection.ProjectedPoint(Center.Latitude, Center.Longitude, latitude, longitude);
var k = 2d / (1d + p.CosC); // p.157 (21-4), k0 == 1
return p.RelativeScale(k, k);
return RelativeTransform(latitude, longitude, k, k);
}
}
}

4
MapProjections/Shared/Wgs84UpsProjections.cs
View file

@ -23,7 +23,7 @@ namespace MapControl.Projections
public override Matrix RelativeTransform(double latitude, double longitude)
{
var k = PolarStereographicProjection.RelativeScale(Hemisphere.North, Wgs84Flattening, latitude);
var k = PolarStereographicProjection.RelativeScale(Hemisphere.North, Wgs84Flattening, 0.994, latitude);
return new Matrix(k, 0d, 0d, k, 0d, 0d);
}
@ -48,7 +48,7 @@ namespace MapControl.Projections
public override Matrix RelativeTransform(double latitude, double longitude)
{
var k = PolarStereographicProjection.RelativeScale(Hemisphere.South, Wgs84Flattening, latitude);
var k = PolarStereographicProjection.RelativeScale(Hemisphere.South, Wgs84Flattening, 0.994, latitude);
return new Matrix(k, 0d, 0d, k, 0d, 0d);
}