Revised Location calculations

MapControl/Shared/AzimuthalEquidistantProjection.cs

@@ -31,7 +31,7 @@ namespace MapControl
                 return new Point();
             }
 
-            GetAzimuthDistance(Center, location, out double azimuth, out double distance);
+            Center.GetAzimuthDistance(location, out double azimuth, out double distance);
 
             var mapDistance = distance * Wgs84EquatorialRadius;
 
@@ -50,7 +50,7 @@ namespace MapControl
 
             var distance = mapDistance / Wgs84EquatorialRadius;
 
-            return GetLocation(Center, azimuth, distance);
+            return Center.GetLocation(azimuth, distance);
         }
     }
 }

MapControl/Shared/AzimuthalProjection.cs

@@ -1,5 +1,4 @@
-using System;
+#if WPF
-#if WPF
 using System.Windows;
 #endif
 
@@ -46,55 +45,5 @@ namespace MapControl
 
             return boundingBox;
         }
-
-        /// <summary>
-        /// Calculates azimuth and spherical distance in radians from location1 to location2.
-        /// The returned distance has to be multiplied with an appropriate earth radius.
-        /// </summary>
-        public static void GetAzimuthDistance(Location location1, Location location2, out double azimuth, out double distance)
-        {
-            var lat1 = location1.Latitude * Math.PI / 180d;
-            var lon1 = location1.Longitude * Math.PI / 180d;
-            var lat2 = location2.Latitude * Math.PI / 180d;
-            var lon2 = location2.Longitude * Math.PI / 180d;
-            var cosLat1 = Math.Cos(lat1);
-            var sinLat1 = Math.Sin(lat1);
-            var cosLat2 = Math.Cos(lat2);
-            var sinLat2 = Math.Sin(lat2);
-            var cosLon12 = Math.Cos(lon2 - lon1);
-            var sinLon12 = Math.Sin(lon2 - lon1);
-            var cosDistance = sinLat1 * sinLat2 + cosLat1 * cosLat2 * cosLon12;
-
-            azimuth = Math.Atan2(sinLon12, cosLat1 * sinLat2 / cosLat2 - sinLat1 * cosLon12);
-            distance = Math.Acos(Math.Min(Math.Max(cosDistance, -1d), 1d));
-        }
-
-        /// <summary>
-        /// Calculates the Location of the point given by azimuth and spherical distance in radians from location.
-        /// </summary>
-        public static Location GetLocation(Location location, double azimuth, double distance)
-        {
-            var lat = location.Latitude;
-            var lon = location.Longitude;
-
-            if (distance > 0d)
-            {
-                var lat1 = lat * Math.PI / 180d;
-                var sinDistance = Math.Sin(distance);
-                var cosDistance = Math.Cos(distance);
-                var cosAzimuth = Math.Cos(azimuth);
-                var sinAzimuth = Math.Sin(azimuth);
-                var cosLat1 = Math.Cos(lat1);
-                var sinLat1 = Math.Sin(lat1);
-                var sinLat2 = sinLat1 * cosDistance + cosLat1 * sinDistance * cosAzimuth;
-                var lat2 = Math.Asin(Math.Min(Math.Max(sinLat2, -1d), 1d));
-                var dLon = Math.Atan2(sinDistance * sinAzimuth, cosLat1 * cosDistance - sinLat1 * sinDistance * cosAzimuth);
-
-                lat = lat2 * 180d / Math.PI;
-                lon += dLon * 180d / Math.PI;
-            }
-
-            return new Location(lat, lon);
-        }
     }
 }

MapControl/Shared/GnomonicProjection.cs

@@ -31,7 +31,7 @@ namespace MapControl
                 return new Point();
             }
 
-            GetAzimuthDistance(Center, location, out double azimuth, out double distance);
+            Center.GetAzimuthDistance(location, out double azimuth, out double distance);
 
             var mapDistance = distance < Math.PI / 2d
                 ? Math.Tan(distance) * Wgs84EquatorialRadius
@@ -52,7 +52,7 @@ namespace MapControl
 
             var distance = Math.Atan(mapDistance / Wgs84EquatorialRadius);
 
-            return GetLocation(Center, azimuth, distance);
+            return Center.GetLocation(azimuth, distance);
         }
     }
 }

MapControl/Shared/Location.cs

@@ -5,6 +5,10 @@ namespace MapControl
 {
     /// <summary>
     /// A geographic location with latitude and longitude values in degrees.
+    /// For calculations with azimuth and distance on great circles, see
+    /// https://en.wikipedia.org/wiki/Great_circle
+    /// https://en.wikipedia.org/wiki/Great-circle_distance
+    /// https://en.wikipedia.org/wiki/Great-circle_navigation
     /// </summary>
 #if UWP || WINUI
     [Windows.Foundation.Metadata.CreateFromString(MethodName = "Parse")]
@@ -81,54 +85,63 @@ namespace MapControl
         }
 
         /// <summary>
-        /// Calculates the great circle distance between this and the specified Location.
+        /// Calculates great circle azimuth and distance in radians between this and the specified Location.
-        /// https://en.wikipedia.org/wiki/Great_circle
-        /// https://en.wikipedia.org/wiki/Great-circle_distance
-        /// https://en.wikipedia.org/wiki/Great-circle_navigation
         /// </summary>
-        public double GetDistance(
+        public void GetAzimuthDistance(Location location, out double azimuth, out double distance)
-            Location location, double earthRadius = MapProjection.Wgs84EquatorialRadius)
         {
             var lat1 = Latitude * Math.PI / 180d;
             var lon1 = Longitude * Math.PI / 180d;
             var lat2 = location.Latitude * Math.PI / 180d;
             var lon2 = location.Longitude * Math.PI / 180d;
-            var sinLat1 = Math.Sin(lat1);
             var cosLat1 = Math.Cos(lat1);
-            var sinLat2 = Math.Sin(lat2);
+            var sinLat1 = Math.Sin(lat1);
             var cosLat2 = Math.Cos(lat2);
-            var sinLon12 = Math.Sin(lon2 - lon1);
+            var sinLat2 = Math.Sin(lat2);
             var cosLon12 = Math.Cos(lon2 - lon1);
-            var a = cosLat1 * sinLat2 - sinLat1 * cosLat2 * cosLon12;
+            var sinLon12 = Math.Sin(lon2 - lon1);
-            var b = cosLat2 * sinLon12;
+            var a = cosLat2 * sinLon12;
-            var c = sinLat1 * sinLat2 + cosLat1 * cosLat2 * cosLon12;
+            var b = cosLat1 * sinLat2 - sinLat1 * cosLat2 * cosLon12;
-            var s12 = Math.Atan2(Math.Sqrt(a * a + b * b), c);
+            // α1
-
+            azimuth = Math.Atan2(a, b);
-            return earthRadius * s12;
+            // σ12
+            distance = Math.Atan2(Math.Sqrt(a * a + b * b), sinLat1 * sinLat2 + cosLat1 * cosLat2 * cosLon12);
         }
 
         /// <summary>
-        /// Calculates the Location on a great circle at the specified azimuth angle and distance from this Location.
+        /// Calculates the great circle distance in meters between this and the specified Location.
-        /// https://en.wikipedia.org/wiki/Great_circle
-        /// https://en.wikipedia.org/wiki/Great-circle_navigation
         /// </summary>
-        public Location GetLocation(
+        public double GetDistance(Location location, double earthRadius = MapProjection.Wgs84EquatorialRadius)
-            double azimuth, double distance, double earthRadius = MapProjection.Wgs84EquatorialRadius)
+        {
+            GetAzimuthDistance(location, out double _, out double distance);
+
+            return earthRadius * distance;
+        }
+
+        /// <summary>
+        /// Calculates the Location on a great circle at the specified azimuth and distance in radians from this Location.
+        /// </summary>
+        public Location GetLocation(double azimuth, double distance)
         {
-            var s12 = distance / earthRadius;
-            var az1 = azimuth * Math.PI / 180d;
             var lat1 = Latitude * Math.PI / 180d;
             var lon1 = Longitude * Math.PI / 180d;
-            var sinS12 = Math.Sin(s12);
+            var cosD = Math.Cos(distance);
-            var cosS12 = Math.Cos(s12);
+            var sinD = Math.Sin(distance);
-            var sinAz1 = Math.Sin(az1);
+            var cosA = Math.Cos(azimuth);
-            var cosAz1 = Math.Cos(az1);
+            var sinA = Math.Sin(azimuth);
-            var sinLat1 = Math.Sin(lat1);
             var cosLat1 = Math.Cos(lat1);
-            var lat2 = Math.Asin(sinLat1 * cosS12 + cosLat1 * sinS12 * cosAz1);
+            var sinLat1 = Math.Sin(lat1);
-            var lon2 = lon1 + Math.Atan2(sinS12 * sinAz1, cosLat1 * cosS12 - sinLat1 * sinS12 * cosAz1);
+            var lat2 = Math.Asin(sinLat1 * cosD + cosLat1 * sinD * cosA);
+            var lon2 = lon1 + Math.Atan2(sinD * sinA, cosLat1 * cosD - sinLat1 * sinD * cosA);
 
             return new Location(lat2 * 180d / Math.PI, lon2 * 180d / Math.PI);
         }
+
+        /// <summary>
+        /// Calculates the Location on a great circle at the specified azimuth in degrees and distance in meters from this Location.
+        /// </summary>
+        public Location GetLocation(double azimuth, double distance, double earthRadius = MapProjection.Wgs84EquatorialRadius)
+        {
+            return GetLocation(azimuth * Math.PI / 180d, distance / earthRadius);
+        }
     }
 }

MapControl/Shared/LocationCollection.cs

@@ -67,31 +67,29 @@ namespace MapControl
         /// <summary>
         /// Calculates a series of Locations on a great circle, or orthodrome, that connects the two specified Locations,
         /// with an optional angular resolution specified in degrees.
-        ///
+        /// https://en.wikipedia.org/wiki/Great-circle_navigation
-        /// See https://en.wikipedia.org/wiki/Great-circle_navigation
         /// </summary>
         public static LocationCollection OrthodromeLocations(Location location1, Location location2, double resolution = 1d)
         {
             if (resolution <= 0d)
             {
                 throw new ArgumentOutOfRangeException(
-                    nameof(resolution), "The resolution argument must be greater than zero.");
+                    nameof(resolution), $"The {nameof(resolution)} argument must be greater than zero.");
             }
 
             var lat1 = location1.Latitude * Math.PI / 180d;
             var lon1 = location1.Longitude * Math.PI / 180d;
             var lat2 = location2.Latitude * Math.PI / 180d;
             var lon2 = location2.Longitude * Math.PI / 180d;
-
             var cosLat1 = Math.Cos(lat1);
             var sinLat1 = Math.Sin(lat1);
             var cosLat2 = Math.Cos(lat2);
             var sinLat2 = Math.Sin(lat2);
             var cosLon12 = Math.Cos(lon2 - lon1);
             var sinLon12 = Math.Sin(lon2 - lon1);
-
+            var a = cosLat2 * sinLon12;
-            var a = cosLat1 * sinLat2 - sinLat1 * cosLat2 * cosLon12;
+            var b = cosLat1 * sinLat2 - sinLat1 * cosLat2 * cosLon12;
-            var b = cosLat2 * sinLon12;
+            // σ12
             var s12 = Math.Atan2(Math.Sqrt(a * a + b * b), sinLat1 * sinLat2 + cosLat1 * cosLat2 * cosLon12);
 
             var n = (int)Math.Ceiling(s12 / resolution * 180d / Math.PI); // s12 in radians
@@ -100,15 +98,18 @@ namespace MapControl
 
             if (n > 1)
             {
-                var az1 = Math.Atan2(sinLon12, cosLat1 * sinLat2 / cosLat2 - sinLat1 * cosLon12);
+                // https://en.wikipedia.org/wiki/Great-circle_navigation#Finding_way-points
+                // α1
+                var az1 = Math.Atan2(a, b);
                 var cosAz1 = Math.Cos(az1);
                 var sinAz1 = Math.Sin(az1);
-
+                // α0
                 var az0 = Math.Atan2(sinAz1 * cosLat1, Math.Sqrt(cosAz1 * cosAz1 + sinAz1 * sinAz1 * sinLat1 * sinLat1));
-                var sinAz0 = Math.Sin(az0);
                 var cosAz0 = Math.Cos(az0);
-
+                var sinAz0 = Math.Sin(az0);
+                // σ01
                 var s01 = Math.Atan2(sinLat1, cosLat1 * cosAz1);
+                // λ0
                 var lon0 = lon1 - Math.Atan2(sinAz0 * Math.Sin(s01), Math.Cos(s01));
 
                 for (var i = 1; i < n; i++)
@@ -139,7 +140,7 @@ namespace MapControl
             if (resolution <= 0d)
             {
                 throw new ArgumentOutOfRangeException(
-                    nameof(resolution), "The resolution argument must be greater than zero.");
+                    nameof(resolution), $"The {nameof(resolution)} argument must be greater than zero.");
             }
 
             var lat1 = location1.Latitude;
@@ -153,13 +154,13 @@ namespace MapControl
             if (double.IsInfinity(y1))
             {
                 throw new ArgumentOutOfRangeException(
-                    nameof(location1), "The location1 argument must have an absolute latitude value of less than 90.");
+                    nameof(location1), $"The {nameof(location1)} argument must have an absolute latitude value of less than 90.");
             }
 
             if (double.IsInfinity(y2))
             {
                 throw new ArgumentOutOfRangeException(
-                    nameof(location2), "The location2 argument must have an absolute latitude value of less than 90.");
+                    nameof(location2), $"The {nameof(location2)} argument must have an absolute latitude value of less than 90.");
             }
 
             var dlat = lat2 - lat1;

MapControl/Shared/StereographicProjection.cs

@@ -31,7 +31,7 @@ namespace MapControl
                 return new Point();
             }
 
-            GetAzimuthDistance(Center, location, out double azimuth, out double distance);
+            Center.GetAzimuthDistance(location, out double azimuth, out double distance);
 
             var mapDistance = Math.Tan(distance / 2d) * 2d * Wgs84EquatorialRadius;
 
@@ -50,7 +50,7 @@ namespace MapControl
 
             var distance = 2d * Math.Atan(mapDistance / (2d * Wgs84EquatorialRadius));
 
-            return GetLocation(Center, azimuth, distance);
+            return Center.GetLocation(azimuth, distance);
         }
     }
 }