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Abstract MapProjection.RelativeScale

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ClemensFischer 2026-01-25 18:04:59 +01:00
parent ceb19a9ae4
commit e8e7cacac0
4 changed files with 54 additions and 44 deletions
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72
MapControl/Shared/TransverseMercatorProjection.cs
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@ -1,6 +1,7 @@
using System;
#if WPF
using System.Windows;
using System.Windows.Media;
#elif AVALONIA
using Avalonia;
#endif
@ -59,6 +60,42 @@ namespace MapControl
Flattening = Wgs84Flattening;
}
public override Matrix RelativeScale(double latitude, double longitude)
{
// h = k/k0 for relative scale
var h = 1d;
#if TM_RELATIVE_SCALE // relative scale is usually < 1.001 and hence neglectable
// φ
var phi = latitude * Math.PI / 180d;
var sinPhi = Math.Sin(phi);
// t
var t = Math.Sinh(Atanh(sinPhi) - f2 * Atanh(f2 * sinPhi));
// λ - λ0
var dLambda = (longitude - CentralMeridian) * Math.PI / 180d;
var cosLambda = Math.Cos(dLambda);
// ξ'
var xi_ = Math.Atan2(t, cosLambda);
// η'
var eta_ = Atanh(Math.Sin(dLambda) / Math.Sqrt(1d + t * t));
// σ
var sigma = 1 +
2d * a1 * Math.Cos(2d * xi_) * Math.Cosh(2d * eta_) +
4d * a2 * Math.Cos(4d * xi_) * Math.Cosh(4d * eta_) +
6d * a3 * Math.Cos(6d * xi_) * Math.Cosh(6d * eta_);
// τ
var tau =
2d * a1 * Math.Sin(2d * xi_) * Math.Sinh(2d * eta_) +
4d * a2 * Math.Sin(4d * xi_) * Math.Sinh(4d * eta_) +
6d * a3 * Math.Sin(6d * xi_) * Math.Sinh(6d * eta_);
var n = Flattening / (2d - Flattening);
var u = (1d - n) / (1d + n) * Math.Tan(phi);
h = f1 * Math.Sqrt((1d + u * u) * (sigma * sigma + tau * tau) / (t * t + cosLambda * cosLambda));
#endif
return new Matrix(h, 0d, 0d, h, 0d, 0d);
}
public override Point? LocationToMap(double latitude, double longitude)
{
// φ
@ -126,40 +163,5 @@ namespace MapControl
#else
private static double Atanh(double x) => Math.Atanh(x);
#endif
/*
* Relative scale is usually < 1.001 and hence neglectable.
*
public override Matrix RelativeScale(double latitude, double longitude)
{
// φ
var phi = latitude * Math.PI / 180d;
var sinPhi = Math.Sin(phi);
// t
var t = Math.Sinh(Atanh(sinPhi) - f2 * Atanh(f2 * sinPhi));
// λ - λ0
var dLambda = (longitude - CentralMeridian) * Math.PI / 180d;
var cosLambda = Math.Cos(dLambda);
// ξ'
var xi_ = Math.Atan2(t, cosLambda);
// η'
var eta_ = Atanh(Math.Sin(dLambda) / Math.Sqrt(1d + t * t));
// σ
var sigma = 1 +
2d * a1 * Math.Cos(2d * xi_) * Math.Cosh(2d * eta_) +
4d * a2 * Math.Cos(4d * xi_) * Math.Cosh(4d * eta_) +
6d * a3 * Math.Cos(6d * xi_) * Math.Cosh(6d * eta_);
// τ
var tau =
2d * a1 * Math.Sin(2d * xi_) * Math.Sinh(2d * eta_) +
4d * a2 * Math.Sin(4d * xi_) * Math.Sinh(4d * eta_) +
6d * a3 * Math.Sin(6d * xi_) * Math.Sinh(6d * eta_);
// h = k/k0 for relative scale
var n = Flattening / (2d - Flattening);
var u = (1d - n) / (1d + n) * Math.Tan(phi);
var h = f1 * Math.Sqrt((1d + u * u) * (sigma * sigma + tau * tau) / (t * t + cosLambda * cosLambda));
return new Matrix(h, 0d, 0d, h, 0d, 0d);
}*/
}
}