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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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10
MapControl/Shared/MapProjection.cs
View file

@ -108,7 +108,7 @@ namespace MapControl
/// Gets the relative scale at the specified geographic coordinates.
/// The returned Matrix represents the local distortion of the map projection.
/// </summary>
public virtual Matrix RelativeScale(double latitude, double longitude) => new Matrix(1d, 0d, 0d, 1d, 0d, 0d);
public abstract Matrix RelativeScale(double latitude, double longitude);
/// <summary>
/// Transforms geographic coordinates to a Point in projected map coordinates.
@ -143,7 +143,7 @@ namespace MapControl
/// Transforms a BoundingBox in geographic coordinates to a Rect in projected map coordinates.
/// Returns null when the BoundingBox can not be transformed.
/// </summary>
public virtual Rect? BoundingBoxToMap(BoundingBox boundingBox)
public Rect? BoundingBoxToMap(BoundingBox boundingBox)
{
var southWest = LocationToMap(boundingBox.South, boundingBox.West);
var northEast = LocationToMap(boundingBox.North, boundingBox.East);
@ -153,9 +153,9 @@ namespace MapControl
/// <summary>
/// Transforms a Rect in projected map coordinates to a BoundingBox in geographic coordinates.
/// Returns null when the MapRect can not be transformed.
/// Returns null when the Rect can not be transformed.
/// </summary>
public virtual BoundingBox MapToBoundingBox(Rect rect)
public BoundingBox MapToBoundingBox(Rect rect)
{
var southWest = MapToLocation(rect.X, rect.Y);
var northEast = MapToLocation(rect.X + rect.Width, rect.Y + rect.Height);
@ -167,7 +167,7 @@ namespace MapControl
/// Transforms a LatLonBox in geographic coordinates to a rotated Rect in projected map coordinates.
/// Returns null when the LatLonBox can not be transformed.
/// </summary>
public virtual (Rect?, double) LatLonBoxToMap(LatLonBox latLonBox)
public (Rect?, double) LatLonBoxToMap(LatLonBox latLonBox)
{
Rect? rect = null;
var rotation = 0d;

72
MapControl/Shared/TransverseMercatorProjection.cs
View file

@ -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);
}*/
}
}

10
MapControl/Shared/TransverseMercatorProjectionSnyder.cs
View file

@ -47,8 +47,10 @@ namespace MapControl
public override Matrix RelativeScale(double latitude, double longitude)
{
var k = 1d; // omit k0 for relative scale
// h = k/k0 for relative scale
var h = 1d;
#if TM_RELATIVE_SCALE // relative scale is usually < 1.001 and hence neglectable
if (latitude > -90d && latitude < 90d)
{
var phi = latitude * Math.PI / 180d;
@ -64,12 +66,12 @@ namespace MapControl
var A4 = A2 * A2;
var A6 = A2 * A4;
k *= 1d + (1d + C) * A2 / 2d +
h = 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)
}
return new Matrix(k, 0d, 0d, k, 0d, 0d);
#endif
return new Matrix(h, 0d, 0d, h, 0d, 0d);
}
public override Point? LocationToMap(double latitude, double longitude)

6
MapProjections/Shared/ProjNetMapProjection.cs
View file

@ -3,6 +3,7 @@ using ProjNet.CoordinateSystems.Transformations;
using System;
#if WPF
using System.Windows;
using System.Windows.Media;
#elif AVALONIA
using Avalonia;
#endif
@ -70,6 +71,11 @@ namespace MapControl.Projections
public MathTransform MapToLocationTransform { get; private set; }
public override Matrix RelativeScale(double latitude, double longitude)
{
return new Matrix(1d, 0d, 0d, 1d, 0d, 0d);
}
public override Point? LocationToMap(double latitude, double longitude)
{
if (LocationToMapTransform == null)