Unified map projections

MapControl/Shared/Etrs89UtmProjection.cs

@@ -14,7 +14,7 @@ namespace MapControl
 
         public int Zone { get; }
 
-        public Etrs89UtmProjection(int zone)
+        public Etrs89UtmProjection(int zone) : base(zone)
         {
             if (zone < FirstZone || zone > LastZone)
             {
@@ -27,7 +27,6 @@ namespace MapControl
             // GRS 1980
             EquatorialRadius = 6378137d;
             Flattening = 1d / 298.257222101;
-            CentralMeridian = zone * 6d - 183d;
         }
     }
 }

MapControl/Shared/MapProjection.cs

@@ -43,16 +43,15 @@ namespace MapControl
         /// </summary>
         public string CrsId { get; protected set; }
 
-        /// <summary>
+        public double EquatorialRadius { get; protected set; } = Wgs84EquatorialRadius;
-        /// Indicates whether the projection is normal cylindrical, see
+        public double Flattening { get; protected set; } = Wgs84Flattening;
-        /// https://en.wikipedia.org/wiki/Map_projection#Normal_cylindrical.
+        public double ScaleFactor { get; protected set; } = 1d;
-        /// </summary>
+        public double CentralMeridian { get; protected set; }
+        public double LatitudeOfOrigin { get; protected set; }
+        public double FalseEasting { get; protected set; }
+        public double FalseNorthing { get; protected set; }
         public bool IsNormalCylindrical { get; protected set; }
 
-        public double EquatorialRadius { get; set; } = Wgs84EquatorialRadius;
-        public double CentralMeridian { get; set; }
-        public double LatitudeOfOrigin { get; set; }
-
         /// <summary>
         /// Gets the grid convergence angle in degrees at the specified geographic coordinates.
         /// Used for rotating the Rect resulting from BoundingBoxToMap in non-normal-cylindrical
@@ -64,7 +63,12 @@ namespace MapControl
         /// Gets the relative transform at the specified geographic coordinates.
         /// The returned Matrix represents the local relative scale and rotation.
         /// </summary>
-        public abstract Matrix RelativeTransform(double latitude, double longitude);
+        public virtual Matrix RelativeTransform(double latitude, double longitude)
+        {
+            var transform = new Matrix(ScaleFactor, 0d, 0d, ScaleFactor, 0d, 0d);
+            transform.Rotate(-GridConvergence(latitude, longitude));
+            return transform;
+        }
 
         /// <summary>
         /// Transforms geographic coordinates to a Point in projected map coordinates.

MapControl/Shared/MapProjectionFactory.cs

@@ -59,9 +59,9 @@ namespace MapControl
                 var c when c is >= Nad83UtmProjection.FirstZoneEpsgCode
                             and <= Nad83UtmProjection.LastZoneEpsgCode => new Nad83UtmProjection(c % 100),
                 var c when c is >= Wgs84UtmProjection.FirstZoneNorthEpsgCode
-                            and <= Wgs84UtmProjection.LastZoneNorthEpsgCode => new Wgs84UtmProjection(c % 100, Hemisphere.North),
+                            and <= Wgs84UtmProjection.LastZoneNorthEpsgCode => new Wgs84UtmProjection(c % 100, true),
                 var c when c is >= Wgs84UtmProjection.FirstZoneSouthEpsgCode
-                            and <= Wgs84UtmProjection.LastZoneSouthEpsgCode => new Wgs84UtmProjection(c % 100, Hemisphere.South),
+                            and <= Wgs84UtmProjection.LastZoneSouthEpsgCode => new Wgs84UtmProjection(c % 100, false),
                 _ => null
             };
         }

MapControl/Shared/Nad27UtmProjection.cs

@@ -14,7 +14,7 @@ namespace MapControl
 
         public int Zone { get; }
 
-        public Nad27UtmProjection(int zone)
+        public Nad27UtmProjection(int zone) : base(zone)
         {
             if (zone < FirstZone || zone > LastZone)
             {
@@ -27,7 +27,6 @@ namespace MapControl
             // Clarke 1866
             EquatorialRadius = 6378206.4;
             Flattening = 1d / 294.978698213898;
-            CentralMeridian = zone * 6d - 183d;
         }
     }
 }

MapControl/Shared/Nad83UtmProjection.cs

@@ -14,7 +14,7 @@ namespace MapControl
 
         public int Zone { get; }
 
-        public Nad83UtmProjection(int zone)
+        public Nad83UtmProjection(int zone) : base(zone)
         {
             if (zone < FirstZone || zone > LastZone)
             {
@@ -27,7 +27,6 @@ namespace MapControl
             // GRS 1980
             EquatorialRadius = 6378137d;
             Flattening = 1d / 298.257222101;
-            CentralMeridian = zone * 6d - 183d;
         }
     }
 }

MapControl/Shared/PolarStereographicProjection.cs

@@ -15,10 +15,13 @@ namespace MapControl
     /// </summary>
     public class PolarStereographicProjection : MapProjection
     {
-        public double Flattening { get; set; } = Wgs84Flattening;
+        public PolarStereographicProjection(bool north)
-        public double ScaleFactor { get; set; } = 0.994;
+        {
-        public double FalseEasting { get; set; } = 2e6;
+            LatitudeOfOrigin = north ? 90d : -90d;
-        public double FalseNorthing { get; set; } = 2e6;
+            ScaleFactor = 0.994;
+            FalseEasting = 2e6;
+            FalseNorthing = 2e6;
+        }
 
         public override double GridConvergence(double latitude, double longitude)
         {
@@ -29,20 +32,17 @@ namespace MapControl
         {
             var sign = Math.Sign(LatitudeOfOrigin);
             var phi = sign * latitude * Math.PI / 180d;
-
             var e = Math.Sqrt((2d - Flattening) * Flattening);
             var eSinPhi = e * Math.Sin(phi);
-
             var t = Math.Tan(Math.PI / 4d - phi / 2d)
                   / Math.Pow((1d - eSinPhi) / (1d + eSinPhi), e / 2d); // p.161 (15-9)
-
             // r == ρ/a
             var r = 2d * ScaleFactor * 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)
             var k = r / m; // p.161 (21-32)
 
             var transform = new Matrix(k, 0d, 0d, k, 0d, 0d);
-            transform.Rotate(-sign * longitude);
+            transform.Rotate(-sign * (longitude - CentralMeridian));
 
             return transform;
         }
@@ -99,10 +99,9 @@ namespace MapControl
         {
         }
 
-        public Wgs84UpsNorthProjection(string crsId)
+        public Wgs84UpsNorthProjection(string crsId) : base(true)
         {
             CrsId = crsId;
-            LatitudeOfOrigin = 90d;
         }
     }
 
@@ -118,10 +117,9 @@ namespace MapControl
         {
         }
 
-        public Wgs84UpsSouthProjection(string crsId)
+        public Wgs84UpsSouthProjection(string crsId) : base(false)
         {
             CrsId = crsId;
-            LatitudeOfOrigin = -90d;
         }
     }
 }

MapControl/Shared/StereographicProjection.cs

@@ -25,7 +25,7 @@ namespace MapControl
                 "{0},1,{1:0.########},{2:0.########}", crsId, centerLongitude, centerLatitude);
         }
 
-        public override double GridConvergence(double latitude, double longitude)
+        private void GetScaleAndGridConvergence(double latitude, double longitude, out double scale, out double gamma)
         {
             var phi0 = LatitudeOfOrigin * Math.PI / 180d; // φ1
             var phi1 = latitude * Math.PI / 180d;
@@ -44,13 +44,26 @@ namespace MapControl
             var dCosPhi = k2 * cosPhi2 - k1 * cosPhi1;
             var dSinPhi = k2 * sinPhi2 - k1 * sinPhi1;
 
-            return Math.Atan2(-sinLambda * dCosPhi,
+            scale = k1;
+            gamma = Math.Atan2(-sinLambda * dCosPhi,
                 cosPhi0 * dSinPhi - sinPhi0 * cosLambda * dCosPhi) * 180d / Math.PI;
         }
 
+        public override double GridConvergence(double latitude, double longitude)
+        {
+            GetScaleAndGridConvergence(latitude, longitude, out double _, out double gamma);
+
+            return gamma;
+        }
+
         public override Matrix RelativeTransform(double latitude, double longitude)
         {
-            return new Matrix(1d, 0d, 0d, 1d, 0d, 0d);
+            GetScaleAndGridConvergence(latitude, longitude, out double scale, out double gamma);
+
+            var transform = new Matrix(scale, 0d, 0d, scale, 0d, 0d);
+            transform.Rotate(-gamma);
+
+            return transform;
         }
 
         public override Point LocationToMap(double latitude, double longitude)

MapControl/Shared/TransverseMercatorProjection.cs

@@ -16,6 +16,8 @@ namespace MapControl
     /// </summary>
     public class TransverseMercatorProjection : MapProjection
     {
+        private double f;
+        private double n;
         private double a1; // α1
         private double a2; // α2
         private double a3; // α3
@@ -28,38 +30,36 @@ namespace MapControl
         private double f1; // A/a
         private double f2; // 2*sqrt(n)/(1+n)
 
+        private void InitializeParameters()
+        {
+            f = Flattening;
+            n = f / (2d - f);
+            var n2 = n * n;
+            var n3 = n * n2;
+            a1 = n / 2d - n2 * 2d / 3d + n3 * 5d / 16d;
+            a2 = n2 * 13d / 48d - n3 * 3d / 5d;
+            a3 = n3 * 61d / 240d;
+            b1 = n / 2d - n2 * 2d / 3d + n3 * 37d / 96d;
+            b2 = n2 / 48d + n3 / 15d;
+            b3 = n3 * 17d / 480d;
+            d1 = n * 2d - n2 * 2d / 3d - n3 * 2d;
+            d2 = n2 * 7d / 3d - n3 * 8d / 5d;
+            d3 = n3 * 56d / 15d;
+            f1 = (1d + n2 / 4d + n2 * n2 / 64d) / (1d + n);
+            f2 = 2d * Math.Sqrt(n) / (1d + n);
+        }
+
         public TransverseMercatorProjection()
         {
-            Flattening = Wgs84Flattening;
         }
 
-        public double Flattening
+        public TransverseMercatorProjection(int utmZone) : this()
         {
-            get;
+            CentralMeridian = utmZone * 6d - 183d;
-            set
+            ScaleFactor = 0.9996;
-            {
+            FalseEasting = 5e5;
-                field = value;
-                var n = field / (2d - field);
-                var n2 = n * n;
-                var n3 = n * n2;
-                a1 = n / 2d - n2 * 2d / 3d + n3 * 5d / 16d;
-                a2 = n2 * 13d / 48d - n3 * 3d / 5d;
-                a3 = n3 * 61d / 240d;
-                b1 = n / 2d - n2 * 2d / 3d + n3 * 37d / 96d;
-                b2 = n2 / 48d + n3 / 15d;
-                b3 = n3 * 17d / 480d;
-                d1 = n * 2d - n2 * 2d / 3d - n3 * 2d;
-                d2 = n2 * 7d / 3d - n3 * 8d / 5d;
-                d3 = n3 * 56d / 15d;
-                f1 = (1d + n2 / 4d + n2 * n2 / 64d) / (1d + n);
-                f2 = 2d * Math.Sqrt(n) / (1d + n);
-            }
         }
 
-        public double ScaleFactor { get; set; } = 0.9996;
-        public double FalseEasting { get; set; } = 5e5;
-        public double FalseNorthing { get; set; }
-
         public override double GridConvergence(double latitude, double longitude)
         {
             // φ
@@ -74,6 +74,11 @@ namespace MapControl
 
         public override Matrix RelativeTransform(double latitude, double longitude)
         {
+            if (f != Flattening)
+            {
+                InitializeParameters();
+            }
+
             // φ
             var phi = latitude * Math.PI / 180d;
             var sinPhi = Math.Sin(phi);
@@ -99,7 +104,6 @@ namespace MapControl
                 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 m = (1d - n) / (1d + n) * Math.Tan(phi);
             var k = ScaleFactor * f1 * Math.Sqrt((1d + m * m) * (sigma * sigma + tau * tau) / (t * t + cosLambda * cosLambda));
 
@@ -114,6 +118,11 @@ namespace MapControl
 
         public override Point LocationToMap(double latitude, double longitude)
         {
+            if (f != Flattening)
+            {
+                InitializeParameters();
+            }
+
             // φ
             var phi = latitude * Math.PI / 180d;
             var sinPhi = Math.Sin(phi);
@@ -143,6 +152,11 @@ namespace MapControl
 
         public override Location MapToLocation(double x, double y)
         {
+            if (f != Flattening)
+            {
+                InitializeParameters();
+            }
+
             // k0 * A
             var k0A = ScaleFactor * EquatorialRadius * f1;
             // ξ

MapControl/Shared/TransverseMercatorProjectionSnyder.cs

@@ -15,10 +15,16 @@ namespace MapControl
     /// </summary>
     public class TransverseMercatorProjectionSnyder : MapProjection
     {
-        public double Flattening { get; set; } = Wgs84Flattening;
+        public TransverseMercatorProjectionSnyder()
-        public double ScaleFactor { get; set; } = 0.9996;
+        {
-        public double FalseEasting { get; set; } = 5e5;
+        }
-        public double FalseNorthing { get; set; }
+
+        public TransverseMercatorProjectionSnyder(int utmZone) : this()
+        {
+            CentralMeridian = utmZone * 6d - 183d;
+            ScaleFactor = 0.9996;
+            FalseEasting = 5e5;
+        }
 
         public override double GridConvergence(double latitude, double longitude)
         {

MapControl/Shared/Wgs84UtmProjection.cs

@@ -2,12 +2,6 @@
 
 namespace MapControl
 {
-    public enum Hemisphere
-    {
-        North,
-        South
-    }
-
     /// <summary>
     /// WGS84 Universal Transverse Mercator Projection -
     /// EPSG:32601 to EPSG:32660 and EPSG:32701 to EPSG:32760.
@@ -22,9 +16,8 @@ namespace MapControl
         public const int LastZoneSouthEpsgCode = 32700 + LastZone;
 
         public int Zone { get; }
-        public Hemisphere Hemisphere { get; }
 
-        public Wgs84UtmProjection(int zone, Hemisphere hemisphere)
+        public Wgs84UtmProjection(int zone, bool north) : base(zone)
         {
             if (zone < FirstZone || zone > LastZone)
             {
@@ -32,10 +25,8 @@ namespace MapControl
             }
 
             Zone = zone;
-            Hemisphere = hemisphere;
+            CrsId = $"EPSG:{(north ? 32600 : 32700) + zone}";
-            CrsId = $"EPSG:{(hemisphere == Hemisphere.North ? 32600 : 32700) + zone}";
+            FalseNorthing = north ? 0d : 1e7;
-            CentralMeridian = zone * 6d - 183d;
-            FalseNorthing = hemisphere == Hemisphere.North ? 0d : 1e7;
         }
     }
 }

MapControl/Shared/WorldMercatorProjection.cs

@@ -16,8 +16,6 @@ namespace MapControl
     {
         public const string DefaultCrsId = "EPSG:3395";
 
-        public double Flattening { get; set; } = Wgs84Flattening;
-
         public WorldMercatorProjection() // parameterless constructor for XAML
             : this(DefaultCrsId)
         {
@@ -31,8 +29,8 @@ namespace MapControl
 
         public override Matrix RelativeTransform(double latitude, double longitude)
         {
-            var phi = latitude * Math.PI / 180d;
             var e2 = (2d - Flattening) * Flattening;
+            var phi = latitude * Math.PI / 180d;
             var sinPhi = Math.Sin(phi);
             var k = Math.Sqrt(1d - e2 * sinPhi * sinPhi) / Math.Cos(phi); // p.44 (7-8)
 

MapProjections/Shared/Ed50UtmProjection.cs

@@ -1,46 +0,0 @@
-using System;
-
-namespace MapControl.Projections
-{
-    /// <summary>
-    /// ED50 Universal Transverse Mercator Projection.
-    /// </summary>
-    public class Ed50UtmProjection : ProjNetMapProjection
-    {
-        public const int FirstZone = 28;
-        public const int LastZone = 38;
-        public const int FirstZoneEpsgCode = 23000 + FirstZone;
-        public const int LastZoneEpsgCode = 23000 + LastZone;
-
-        public int Zone { get; }
-
-        public Ed50UtmProjection(int zone)
-            : base(new TransverseMercatorProjection
-            {
-                EquatorialRadius = 6378388d,
-                Flattening = 297,
-                CentralMeridian = 6 * zone - 183,
-            })
-        {
-            if (zone < FirstZone || zone > LastZone)
-            {
-                throw new ArgumentException($"Invalid ED50 UTM zone {zone}.", nameof(zone));
-            }
-
-            Zone = zone;
-            CoordinateSystemWkt =
-                $"PROJCS[\"ED50 / UTM zone {zone}N\"," +
-                WktConstants.GeogCsEd50 + "," +
-                "PROJECTION[\"Transverse_Mercator\"]," +
-                "PARAMETER[\"latitude_of_origin\",0]," +
-                $"PARAMETER[\"central_meridian\",{6 * zone - 183}]," +
-                "PARAMETER[\"scale_factor\",0.9996]," +
-                "PARAMETER[\"false_easting\",500000]," +
-                "PARAMETER[\"false_northing\",0]," +
-                "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
-                "AXIS[\"Easting\",EAST]," +
-                "AXIS[\"Northing\",NORTH]," +
-                $"AUTHORITY[\"EPSG\",\"230{zone:00}\"]]";
-        }
-    }
-}

MapProjections/Shared/Etrs89UtmProjection.cs

@@ -1,29 +0,0 @@
-namespace MapControl.Projections
-{
-    /// <summary>
-    /// ETRS89 Universal Transverse Mercator Projection - EPSG:25828 to EPSG:25838.
-    /// </summary>
-    public class Etrs89UtmProjection : ProjNetMapProjection
-    {
-        public int Zone { get; }
-
-        public Etrs89UtmProjection(int zone)
-            : base(new MapControl.Etrs89UtmProjection(zone))
-        {
-            Zone = zone;
-            CoordinateSystemWkt =
-                $"PROJCS[\"ETRS89 / UTM zone {zone}N\"," +
-                WktConstants.GeogCsEtrs89 + "," +
-                "PROJECTION[\"Transverse_Mercator\"]," +
-                "PARAMETER[\"latitude_of_origin\",0]," +
-                $"PARAMETER[\"central_meridian\",{6 * zone - 183}]," +
-                "PARAMETER[\"scale_factor\",0.9996]," +
-                "PARAMETER[\"false_easting\",500000]," +
-                "PARAMETER[\"false_northing\",0]," +
-                "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
-                "AXIS[\"Easting\",EAST]," +
-                "AXIS[\"Northing\",NORTH]," +
-                $"AUTHORITY[\"EPSG\",\"258{zone:00}\"]]";
-        }
-    }
-}

MapProjections/Shared/Nad27UtmProjection.cs

@@ -1,29 +0,0 @@
-namespace MapControl.Projections
-{
-    /// <summary>
-    /// NAD27 Universal Transverse Mercator Projection - EPSG:26701 to EPSG:26722.
-    /// </summary>
-    public class Nad27UtmProjection : ProjNetMapProjection
-    {
-        public int Zone { get; }
-
-        public Nad27UtmProjection(int zone)
-            : base(new MapControl.Nad27UtmProjection(zone))
-        {
-            Zone = zone;
-            CoordinateSystemWkt =
-                $"PROJCS[\"NAD27 / UTM zone {zone}N\"," +
-                WktConstants.GeogCsNad27 + "," +
-                "PROJECTION[\"Transverse_Mercator\"]," +
-                "PARAMETER[\"latitude_of_origin\",0]," +
-                $"PARAMETER[\"central_meridian\",{6 * zone - 183}]," +
-                "PARAMETER[\"scale_factor\",0.9996]," +
-                "PARAMETER[\"false_easting\",500000]," +
-                "PARAMETER[\"false_northing\",0]," +
-                "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
-                "AXIS[\"Easting\",EAST]," +
-                "AXIS[\"Northing\",NORTH]," +
-                $"AUTHORITY[\"EPSG\",\"267{zone:00}\"]]";
-        }
-    }
-}

MapProjections/Shared/Nad83UtmProjection.cs

@@ -1,29 +0,0 @@
-namespace MapControl.Projections
-{
-    /// <summary>
-    /// NAD83 Universal Transverse Mercator Projection - EPSG:26901 to EPSG:26923.
-    /// </summary>
-    public class Nad83UtmProjection : ProjNetMapProjection
-    {
-        public int Zone { get; }
-
-        public Nad83UtmProjection(int zone)
-            : base(new MapControl.Nad83UtmProjection(zone))
-        {
-            Zone = zone;
-            CoordinateSystemWkt =
-                $"PROJCS[\"NAD83 / UTM zone {zone}N\"," +
-                WktConstants.GeogCsNad83 + "," +
-                "PROJECTION[\"Transverse_Mercator\"]," +
-                "PARAMETER[\"latitude_of_origin\",0]," +
-                $"PARAMETER[\"central_meridian\",{6 * zone - 183}]," +
-                "PARAMETER[\"scale_factor\",0.9996]," +
-                "PARAMETER[\"false_easting\",500000]," +
-                "PARAMETER[\"false_northing\",0]," +
-                "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
-                "AXIS[\"Easting\",EAST]," +
-                "AXIS[\"Northing\",NORTH]," +
-                $"AUTHORITY[\"EPSG\",\"269{zone:00}\"]]";
-        }
-    }
-}

MapProjections/Shared/ProjNetMapProjection.cs

@@ -15,11 +15,9 @@ namespace MapControl.Projections
     /// </summary>
     public class ProjNetMapProjection : MapProjection
     {
-        protected MapProjection FallbackProjection { get; private set; }
+        public ProjNetMapProjection(ProjectedCoordinateSystem coordinateSystem)
-
-        protected ProjNetMapProjection(MapProjection fallbackProjection)
         {
-            FallbackProjection = fallbackProjection;
+            CoordinateSystem = coordinateSystem;
         }
 
         public ProjNetMapProjection(string coordinateSystemWkt)
@@ -52,7 +50,9 @@ namespace MapControl.Projections
                 var projection = field.Projection ??
                     throw new ArgumentException("CoordinateSystem.Projection must not be null.", nameof(value));
 
-                var ellipsoid = field.GeographicCoordinateSystem.HorizontalDatum.Ellipsoid;
+                IsNormalCylindrical = projection.Name.Contains("Pseudo-Mercator") ||
+                                      projection.Name.StartsWith("Mercator");
+
                 var transformFactory = new CoordinateTransformationFactory();
 
                 CrsId = !string.IsNullOrEmpty(field.Authority) && field.AuthorityCode > 0
@@ -67,47 +67,24 @@ namespace MapControl.Projections
                     .CreateFromCoordinateSystems(field, GeographicCoordinateSystem.WGS84)
                     .MathTransform;
 
-                if (projection.Name.Contains("Pseudo-Mercator"))
+                var ellipsoid = field.HorizontalDatum.Ellipsoid;
-                {
+                EquatorialRadius = ellipsoid.SemiMajorAxis;
-                    IsNormalCylindrical = true;
+                Flattening = 1d / ellipsoid.InverseFlattening;
-                    FallbackProjection = new MapControl.WebMercatorProjection
+
-                    {
+                var parameter = projection.GetParameter("scale_factor");
-                        EquatorialRadius = ellipsoid.SemiMajorAxis
+                ScaleFactor = parameter != null ? parameter.Value : 1d;
-                    };
+
-                }
+                parameter = projection.GetParameter("central_meridian");
-                else if (projection.Name.StartsWith("Mercator"))
+                CentralMeridian = parameter != null ? parameter.Value : 0d;
-                {
+
-                    IsNormalCylindrical = true;
+                parameter = projection.GetParameter("latitude_of_origin");
-                    FallbackProjection = new MapControl.WorldMercatorProjection
+                LatitudeOfOrigin = parameter != null ? parameter.Value : 0d;
-                    {
+
-                        EquatorialRadius = ellipsoid.SemiMajorAxis,
+                parameter = projection.GetParameter("false_easting");
-                        Flattening = 1d / ellipsoid.InverseFlattening
+                FalseEasting = parameter != null ? parameter.Value : 0d;
-                    };
+
-                }
+                parameter = projection.GetParameter("false_northing");
-                else if (projection.Name.StartsWith("Transverse_Mercator"))
+                FalseNorthing = parameter != null ? parameter.Value : 0d;
-                {
-                    FallbackProjection = new TransverseMercatorProjection
-                    {
-                        EquatorialRadius = ellipsoid.SemiMajorAxis,
-                        Flattening = 1d / ellipsoid.InverseFlattening,
-                        CentralMeridian = projection.GetParameter("central_meridian").Value,
-                        ScaleFactor = projection.GetParameter("scale_factor").Value,
-                        FalseEasting = projection.GetParameter("false_easting").Value,
-                        FalseNorthing = projection.GetParameter("false_northing").Value
-                    };
-                }
-                else if (projection.Name.StartsWith("Polar_Stereographic"))
-                {
-                    FallbackProjection = new PolarStereographicProjection
-                    {
-                        EquatorialRadius = ellipsoid.SemiMajorAxis,
-                        Flattening = 1d / ellipsoid.InverseFlattening,
-                        ScaleFactor = projection.GetParameter("scale_factor").Value,
-                        FalseEasting = projection.GetParameter("false_easting").Value,
-                        FalseNorthing = projection.GetParameter("false_northing").Value,
-                        LatitudeOfOrigin = projection.GetParameter("latitude_of_origin").Value
-                    };
-                }
             }
         }
 
@@ -139,18 +116,91 @@ namespace MapControl.Projections
             return new Location(coordinate[1], coordinate[0]);
         }
 
-        public override Matrix RelativeTransform(double latitude, double longitude)
+        public override double GridConvergence(double latitude, double longitude)
         {
-            return FallbackProjection != null
+            var projection = CoordinateSystem.Projection.Name;
-                ? FallbackProjection.RelativeTransform(latitude, longitude)
+
-                : new Matrix(1d, 0d, 0d, 1d, 0d, 0d);
+            if (projection.StartsWith("Transverse_Mercator"))
+            {
+                return TransverseMercatorGridConvergence(latitude, longitude);
+            }
+
+            if (projection.StartsWith("Polar_Stereographic"))
+            {
+                return PolarStereographicGridConvergence(longitude);
+            }
+
+            return base.GridConvergence(latitude, longitude);
         }
 
-        public override double GridConvergence(double x, double y)
+        public override Matrix RelativeTransform(double latitude, double longitude)
         {
-            return FallbackProjection != null
+            var projection = CoordinateSystem.Projection.Name;
-                ? FallbackProjection.GridConvergence(x, y)
+
-                : 0d;
+            if (projection.Contains("Pseudo-Mercator"))
+            {
+                return WebMercatorRelativeTransform(latitude);
+            }
+
+            if (projection.StartsWith("Mercator"))
+            {
+                return WorldMercatorRelativeTransform(latitude);
+            }
+
+            if (projection.StartsWith("Polar_Stereographic"))
+            {
+                return PolarStereographicRelativeTransform(latitude, longitude);
+            }
+
+            return base.RelativeTransform(latitude, longitude);
+        }
+
+        protected static Matrix WebMercatorRelativeTransform(double latitude)
+        {
+            var k = 1d / Math.Cos(latitude * Math.PI / 180d); // p.44 (7-3)
+
+            return new Matrix(k, 0d, 0d, k, 0d, 0d);
+        }
+
+        protected Matrix WorldMercatorRelativeTransform(double latitude)
+        {
+            var e2 = (2d - Flattening) * Flattening;
+            var phi = latitude * Math.PI / 180d;
+            var sinPhi = Math.Sin(phi);
+            var k = Math.Sqrt(1d - e2 * sinPhi * sinPhi) / Math.Cos(phi); // p.44 (7-8)
+
+            return new Matrix(k, 0d, 0d, k, 0d, 0d);
+        }
+
+        protected double TransverseMercatorGridConvergence(double latitude, double longitude)
+        {
+            return 180d / Math.PI * Math.Atan(
+                Math.Tan((longitude - CentralMeridian) * Math.PI / 180d) *
+                Math.Sin(latitude * Math.PI / 180d));
+        }
+
+        protected double PolarStereographicGridConvergence(double longitude)
+        {
+            return Math.Sign(LatitudeOfOrigin) * (longitude - CentralMeridian);
+        }
+
+        protected Matrix PolarStereographicRelativeTransform(double latitude, double longitude)
+        {
+            var sign = Math.Sign(LatitudeOfOrigin);
+            var phi = sign * latitude * Math.PI / 180d;
+            var e = Math.Sqrt((2d - Flattening) * Flattening);
+            var eSinPhi = e * Math.Sin(phi);
+            var t = Math.Tan(Math.PI / 4d - phi / 2d)
+                  / Math.Pow((1d - eSinPhi) / (1d + eSinPhi), e / 2d); // p.161 (15-9)
+            // r == ρ/a
+            var r = 2d * ScaleFactor * 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)
+            var k = r / m; // p.161 (21-32)
+
+            var transform = new Matrix(k, 0d, 0d, k, 0d, 0d);
+            transform.Rotate(-sign * (longitude - CentralMeridian));
+
+            return transform;
         }
     }
 }

MapProjections/Shared/ProjNetMapProjectionFactory.cs

@@ -1,4 +1,5 @@
-using System.Collections.Generic;
+using ProjNet.CoordinateSystems;
+using System.Collections.Generic;
 
 namespace MapControl.Projections
 {
@@ -54,11 +55,175 @@ namespace MapControl.Projections
                 var c when c is >= MapControl.Nad83UtmProjection.FirstZoneEpsgCode
                             and <= MapControl.Nad83UtmProjection.LastZoneEpsgCode => new Nad83UtmProjection(c % 100),
                 var c when c is >= MapControl.Wgs84UtmProjection.FirstZoneNorthEpsgCode
-                            and <= MapControl.Wgs84UtmProjection.LastZoneNorthEpsgCode => new Wgs84UtmProjection(c % 100, Hemisphere.North),
+                            and <= MapControl.Wgs84UtmProjection.LastZoneNorthEpsgCode => new Wgs84UtmProjection(c % 100, true),
                 var c when c is >= MapControl.Wgs84UtmProjection.FirstZoneSouthEpsgCode
-                            and <= MapControl.Wgs84UtmProjection.LastZoneSouthEpsgCode => new Wgs84UtmProjection(c % 100, Hemisphere.South),
+                            and <= MapControl.Wgs84UtmProjection.LastZoneSouthEpsgCode => new Wgs84UtmProjection(c % 100, false),
                 _ => base.CreateProjection(epsgCode)
             };
         }
     }
+    /// <summary>
+    /// Spherical Mercator Projection - EPSG:3857,
+    /// implemented by setting the CoordinateSystem property of a ProjNetMapProjection.
+    /// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/pp/1395/report.pdf), p.41-44.
+    /// </summary>
+    public class WebMercatorProjection : ProjNetMapProjection
+    {
+        public WebMercatorProjection()
+            : base(ProjectedCoordinateSystem.WebMercator)
+        {
+        }
+    }
+
+    /// <summary>
+    /// Elliptical Mercator Projection - EPSG:3395,
+    /// implemented by setting the CoordinateSystemWkt property of a ProjNetMapProjection.
+    /// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/pp/1395/report.pdf), p.44-45.
+    /// </summary>
+    public class WorldMercatorProjection : ProjNetMapProjection
+    {
+        public WorldMercatorProjection() : base(
+            "PROJCS[\"WGS 84 / World Mercator\"," +
+            WktConstants.GeogCsWgs84 + "," +
+            "PROJECTION[\"Mercator_1SP\"]," +
+            "PARAMETER[\"latitude_of_origin\",0]," +
+            "PARAMETER[\"central_meridian\",0]," +
+            "PARAMETER[\"scale_factor\",1]," +
+            "PARAMETER[\"false_easting\",0]," +
+            "PARAMETER[\"false_northing\",0]," +
+            "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
+            "AXIS[\"Easting\",EAST]," +
+            "AXIS[\"Northing\",NORTH]," +
+            "AUTHORITY[\"EPSG\",\"3395\"]]")
+        {
+        }
+    }
+
+    /// <summary>
+    /// WGS84 Universal Transverse Mercator Projection -
+    /// EPSG:32601 to EPSG:32660 and EPSG:32701 to EPSG:32760.
+    /// </summary>
+    public class Wgs84UtmProjection(int zone, bool north) : ProjNetMapProjection(
+        ProjectedCoordinateSystem.WGS84_UTM(zone, north))
+    {
+        public int Zone => zone;
+    }
+
+    /// <summary>
+    /// ETRS89 Universal Transverse Mercator Projection - EPSG:25828 to EPSG:25838.
+    /// </summary>
+    public class Etrs89UtmProjection(int zone) : ProjNetMapProjection(
+        $"PROJCS[\"ETRS89 / UTM zone {zone}N\"," +
+        WktConstants.GeogCsEtrs89 + "," +
+        "PROJECTION[\"Transverse_Mercator\"]," +
+        "PARAMETER[\"latitude_of_origin\",0]," +
+        $"PARAMETER[\"central_meridian\",{6 * zone - 183}]," +
+        "PARAMETER[\"scale_factor\",0.9996]," +
+        "PARAMETER[\"false_easting\",500000]," +
+        "PARAMETER[\"false_northing\",0]," +
+        "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
+        "AXIS[\"Easting\",EAST]," +
+        "AXIS[\"Northing\",NORTH]," +
+        $"AUTHORITY[\"EPSG\",\"258{zone:00}\"]]")
+    {
+        public int Zone => zone;
+    }
+
+    /// <summary>
+    /// NAD27 Universal Transverse Mercator Projection - EPSG:26701 to EPSG:26722.
+    /// </summary>
+    public class Nad27UtmProjection(int zone) : ProjNetMapProjection(
+        $"PROJCS[\"NAD27 / UTM zone {zone}N\"," +
+        WktConstants.GeogCsNad27 + "," +
+        "PROJECTION[\"Transverse_Mercator\"]," +
+        "PARAMETER[\"latitude_of_origin\",0]," +
+        $"PARAMETER[\"central_meridian\",{6 * zone - 183}]," +
+        "PARAMETER[\"scale_factor\",0.9996]," +
+        "PARAMETER[\"false_easting\",500000]," +
+        "PARAMETER[\"false_northing\",0]," +
+        "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
+        "AXIS[\"Easting\",EAST]," +
+        "AXIS[\"Northing\",NORTH]," +
+        $"AUTHORITY[\"EPSG\",\"267{zone:00}\"]]")
+    {
+        public int Zone => zone;
+    }
+    /// <summary>
+    /// NAD83 Universal Transverse Mercator Projection - EPSG:26901 to EPSG:26923.
+    /// </summary>
+    public class Nad83UtmProjection(int zone) : ProjNetMapProjection(
+        $"PROJCS[\"NAD83 / UTM zone {zone}N\"," +
+        WktConstants.GeogCsNad83 + "," +
+        "PROJECTION[\"Transverse_Mercator\"]," +
+        "PARAMETER[\"latitude_of_origin\",0]," +
+        $"PARAMETER[\"central_meridian\",{6 * zone - 183}]," +
+        "PARAMETER[\"scale_factor\",0.9996]," +
+        "PARAMETER[\"false_easting\",500000]," +
+        "PARAMETER[\"false_northing\",0]," +
+        "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
+        "AXIS[\"Easting\",EAST]," +
+        "AXIS[\"Northing\",NORTH]," +
+        $"AUTHORITY[\"EPSG\",\"269{zone:00}\"]]")
+    {
+        public int Zone => zone;
+    }
+
+    /// <summary>
+    /// ED50 Universal Transverse Mercator Projection.
+    /// </summary>
+    public class Ed50UtmProjection(int zone) : ProjNetMapProjection(
+        $"PROJCS[\"ED50 / UTM zone {zone}N\"," +
+        WktConstants.GeogCsEd50 + "," +
+        "PROJECTION[\"Transverse_Mercator\"]," +
+        "PARAMETER[\"latitude_of_origin\",0]," +
+        $"PARAMETER[\"central_meridian\",{6 * zone - 183}]," +
+        "PARAMETER[\"scale_factor\",0.9996]," +
+        "PARAMETER[\"false_easting\",500000]," +
+        "PARAMETER[\"false_northing\",0]," +
+        "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
+        "AXIS[\"Easting\",EAST]," +
+        "AXIS[\"Northing\",NORTH]," +
+        $"AUTHORITY[\"EPSG\",\"230{zone:00}\"]]")
+    {
+        public const int FirstZone = 28;
+        public const int LastZone = 38;
+        public const int FirstZoneEpsgCode = 23000 + FirstZone;
+        public const int LastZoneEpsgCode = 23000 + LastZone;
+
+        public int Zone { get; } = zone;
+    }
+
+    public class Wgs84UpsNorthProjection : ProjNetMapProjection
+    {
+        public Wgs84UpsNorthProjection() : base(
+            "PROJCS[\"WGS 84 / UPS North (N,E)\"," +
+            WktConstants.GeogCsWgs84 + "," +
+            "PROJECTION[\"Polar_Stereographic\"]," +
+            "PARAMETER[\"latitude_of_origin\",90]," +
+            "PARAMETER[\"central_meridian\",0]," +
+            "PARAMETER[\"scale_factor\",0.994]," +
+            "PARAMETER[\"false_easting\",2000000]," +
+            "PARAMETER[\"false_northing\",2000000]," +
+            "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
+            "AUTHORITY[\"EPSG\",\"32661\"]]")
+        {
+        }
+    }
+
+    public class Wgs84UpsSouthProjection : ProjNetMapProjection
+    {
+        public Wgs84UpsSouthProjection() : base(
+            "PROJCS[\"WGS 84 / UPS South (N,E)\"," +
+            WktConstants.GeogCsWgs84 + "," +
+            "PROJECTION[\"Polar_Stereographic\"]," +
+            "PARAMETER[\"latitude_of_origin\",-90]," +
+            "PARAMETER[\"central_meridian\",0]," +
+            "PARAMETER[\"scale_factor\",0.994]," +
+            "PARAMETER[\"false_easting\",2000000]," +
+            "PARAMETER[\"false_northing\",2000000]," +
+            "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
+            "AUTHORITY[\"EPSG\",\"32761\"]]")
+        {
+        }
+    }
 }

MapProjections/Shared/WebMercatorProjection.cs

@@ -1,17 +0,0 @@
-using ProjNet.CoordinateSystems;
-
-namespace MapControl.Projections
-{
-    /// <summary>
-    /// Spherical Mercator Projection implemented by setting the CoordinateSystem property of a ProjNetMapProjection.
-    /// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/pp/1395/report.pdf), p.41-44.
-    /// </summary>
-    public class WebMercatorProjection : ProjNetMapProjection
-    {
-        public WebMercatorProjection()
-            : base(new MapControl.WebMercatorProjection())
-        {
-            CoordinateSystem = ProjectedCoordinateSystem.WebMercator;
-        }
-    }
-}

MapProjections/Shared/Wgs84UpsProjections.cs

@@ -1,44 +0,0 @@
-#if WPF
-using System.Windows.Media;
-#endif
-
-namespace MapControl.Projections
-{
-    public class Wgs84UpsNorthProjection : ProjNetMapProjection
-    {
-        public Wgs84UpsNorthProjection()
-            : base(new MapControl.Wgs84UpsNorthProjection())
-        {
-            CoordinateSystemWkt =
-                "PROJCS[\"WGS 84 / UPS North (N,E)\"," +
-                WktConstants.GeogCsWgs84 + "," +
-                "PROJECTION[\"Polar_Stereographic\"]," +
-                "PARAMETER[\"latitude_of_origin\",90]," +
-                "PARAMETER[\"central_meridian\",0]," +
-                "PARAMETER[\"scale_factor\",0.994]," +
-                "PARAMETER[\"false_easting\",2000000]," +
-                "PARAMETER[\"false_northing\",2000000]," +
-                "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
-                "AUTHORITY[\"EPSG\",\"32661\"]]";
-        }
-    }
-
-    public class Wgs84UpsSouthProjection : ProjNetMapProjection
-    {
-        public Wgs84UpsSouthProjection()
-            : base(new MapControl.Wgs84UpsSouthProjection())
-        {
-            CoordinateSystemWkt =
-                "PROJCS[\"WGS 84 / UPS South (N,E)\"," +
-                WktConstants.GeogCsWgs84 + "," +
-                "PROJECTION[\"Polar_Stereographic\"]," +
-                "PARAMETER[\"latitude_of_origin\",-90]," +
-                "PARAMETER[\"central_meridian\",0]," +
-                "PARAMETER[\"scale_factor\",0.994]," +
-                "PARAMETER[\"false_easting\",2000000]," +
-                "PARAMETER[\"false_northing\",2000000]," +
-                "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
-                "AUTHORITY[\"EPSG\",\"32761\"]]";
-        }
-    }
-}

MapProjections/Shared/Wgs84UtmProjection.cs

@@ -1,22 +0,0 @@
-using ProjNet.CoordinateSystems;
-
-namespace MapControl.Projections
-{
-    /// <summary>
-    /// WGS84 Universal Transverse Mercator Projection -
-    /// EPSG:32601 to EPSG:32660 and EPSG:32701 to EPSG:32760.
-    /// </summary>
-    public class Wgs84UtmProjection : ProjNetMapProjection
-    {
-        public int Zone { get; }
-        public Hemisphere Hemisphere { get; }
-
-        public Wgs84UtmProjection(int zone, Hemisphere hemisphere)
-            : base(new MapControl.Wgs84UtmProjection(zone, hemisphere))
-        {
-            Zone = zone;
-            Hemisphere = hemisphere;
-            CoordinateSystem = ProjectedCoordinateSystem.WGS84_UTM(zone, hemisphere == Hemisphere.North);
-        }
-    }
-}

MapProjections/Shared/WorldMercatorProjection.cs

@@ -1,27 +0,0 @@
-namespace MapControl.Projections
-{
-    /// <summary>
-    /// Elliptical Mercator Projection implemented by setting the WKT property of a ProjNetMapProjection.
-    /// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/pp/1395/report.pdf), p.44-45.
-    /// </summary>
-    public class WorldMercatorProjection : ProjNetMapProjection
-    {
-        public WorldMercatorProjection()
-            : base(new MapControl.WorldMercatorProjection())
-        {
-            CoordinateSystemWkt =
-                "PROJCS[\"WGS 84 / World Mercator\"," +
-                WktConstants.GeogCsWgs84 + "," +
-                "PROJECTION[\"Mercator_1SP\"]," +
-                "PARAMETER[\"latitude_of_origin\",0]," +
-                "PARAMETER[\"central_meridian\",0]," +
-                "PARAMETER[\"scale_factor\",1]," +
-                "PARAMETER[\"false_easting\",0]," +
-                "PARAMETER[\"false_northing\",0]," +
-                "UNIT[\"metre\",1,AUTHORITY[\"EPSG\",\"9001\"]]," +
-                "AXIS[\"Easting\",EAST]," +
-                "AXIS[\"Northing\",NORTH]," +
-                "AUTHORITY[\"EPSG\",\"3395\"]]";
-        }
-    }
-}