diff --git a/MapControl/Shared/MapProjection.cs b/MapControl/Shared/MapProjection.cs
index d21a6abd..fc694c6d 100644
--- a/MapControl/Shared/MapProjection.cs
+++ b/MapControl/Shared/MapProjection.cs
@@ -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.
///
- public virtual Matrix RelativeScale(double latitude, double longitude) => new Matrix(1d, 0d, 0d, 1d, 0d, 0d);
+ public abstract Matrix RelativeScale(double latitude, double longitude);
///
/// 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.
///
- 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
///
/// 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.
///
- 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.
///
- public virtual (Rect?, double) LatLonBoxToMap(LatLonBox latLonBox)
+ public (Rect?, double) LatLonBoxToMap(LatLonBox latLonBox)
{
Rect? rect = null;
var rotation = 0d;
diff --git a/MapControl/Shared/TransverseMercatorProjection.cs b/MapControl/Shared/TransverseMercatorProjection.cs
index 7654ff45..5ab6a681 100644
--- a/MapControl/Shared/TransverseMercatorProjection.cs
+++ b/MapControl/Shared/TransverseMercatorProjection.cs
@@ -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);
- }*/
}
}
diff --git a/MapControl/Shared/TransverseMercatorProjectionSnyder.cs b/MapControl/Shared/TransverseMercatorProjectionSnyder.cs
index 2dc924b7..c015dac0 100644
--- a/MapControl/Shared/TransverseMercatorProjectionSnyder.cs
+++ b/MapControl/Shared/TransverseMercatorProjectionSnyder.cs
@@ -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)
diff --git a/MapProjections/Shared/ProjNetMapProjection.cs b/MapProjections/Shared/ProjNetMapProjection.cs
index f3d3884c..f18c520c 100644
--- a/MapProjections/Shared/ProjNetMapProjection.cs
+++ b/MapProjections/Shared/ProjNetMapProjection.cs
@@ -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)