/// <summary>
/// see https://en.wikipedia.org/wiki/Rhumb_line
/// </summary>
public static LocationCollection CalculateRhumbLineLocations(this Location location1, Location location2, double resolution = 1d)
{
if (resolution <= 0d)
{
throw new ArgumentOutOfRangeException("The parameter resolution must be greater than zero.");
}
var y1 = WebMercatorProjection.LatitudeToY(location1.Latitude);
if (double.IsInfinity(y1))
{
throw new ArgumentOutOfRangeException("The parameter location1 must have an absolute latitude value of less than 90 degrees.");
}
var y2 = WebMercatorProjection.LatitudeToY(location2.Latitude);
if (double.IsInfinity(y2))
{
throw new ArgumentOutOfRangeException("The parameter location2 must have an absolute latitude value of less than 90 degrees.");
}
var x1 = location1.Longitude;
var x2 = location2.Longitude;
var dx = x2 - x1;
var dy = y2 - y1;
var s = Math.Sqrt(dx * dx + dy * dy);
var n = (int)Math.Ceiling(s / resolution);
var locations = new LocationCollection(new Location(location1.Latitude, location1.Longitude));
for (int i = 1; i < n; i++)
{
double x = x1 + i * dx / n;
double y = y1 + i * dy / n;
locations.Add(WebMercatorProjection.YToLatitude(y), x);
}
locations.Add(location2.Latitude, location2.Longitude);
return(locations);
}
public static LocationCollection CalculateMeridianLocations(this Location location, double latitude2, double resolution = 1d)
{
if (resolution <= 0d)
{
throw new ArgumentOutOfRangeException("The parameter resolution must be greater than zero.");
}
var locations = new LocationCollection();
var s = latitude2 - location.Latitude;
var n = (int)Math.Ceiling(Math.Abs(s) / resolution);
for (int i = 0; i <= n; i++)
{
locations.Add(new Location(location.Latitude + i * s / n, location.Longitude));
}
return(locations);
}
public static void Add(this LocationCollection locations, double latitude, double longitude)
{
if (locations.Count > 0)
{
var deltaLon = longitude - locations.Last().Longitude;
if (deltaLon < -180d)
{
longitude += 360d;
}
else if (deltaLon > 180)
{
longitude -= 360;
}
}
locations.Add(new Location(latitude, longitude));
}
/// <summary>
/// Calculates a series of Locations on a rhumb line, or loxodrome, that connects the two specified Locations,
/// with an optional angular resolution specified in degrees.
///
/// See https://en.wikipedia.org/wiki/Rhumb_line
/// </summary>
public static LocationCollection LoxodromeLocations(Location location1, Location location2, double resolution = 1d)
{
if (resolution <= 0d)
{
throw new ArgumentOutOfRangeException(
nameof(resolution), "The resolution argument must be greater than zero.");
}
var lat1 = location1.Latitude;
var lon1 = location1.Longitude;
var lat2 = location2.Latitude;
var lon2 = location2.Longitude;
var y1 = WebMercatorProjection.LatitudeToY(lat1);
var y2 = WebMercatorProjection.LatitudeToY(lat2);
if (double.IsInfinity(y1))
{
throw new ArgumentOutOfRangeException(
nameof(location1), "The 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.");
}
var dlat = lat2 - lat1;
var dlon = lon2 - lon1;
var dy = y2 - y1;
// beta = atan(dlon,dy)
// sec(beta) = 1 / cos(atan(dlon,dy)) = sqrt(1 + (dlon/dy)^2)
var sec = Math.Sqrt(1d + dlon * dlon / (dy * dy));
const double secLimit = 1000d; // beta approximately +/-90°
double s12;
if (sec > secLimit)
{
var lat = (lat1 + lat2) * Math.PI / 360d; // mean latitude
s12 = Math.Abs(dlon * Math.Cos(lat)); // distance in degrees along parallel of latitude
}
else
{
s12 = Math.Abs(dlat * sec); // distance in degrees along loxodrome
}
var n = (int)Math.Ceiling(s12 / resolution);
var locations = new LocationCollection(new Location(lat1, lon1));
if (sec > secLimit)
{
for (var i = 1; i < n; i++)
{
var lon = lon1 + i * dlon / n;
var lat = WebMercatorProjection.YToLatitude(y1 + i * dy / n);
locations.Add(lat, lon);
}
}
else
{
for (var i = 1; i < n; i++)
{
var lat = lat1 + i * dlat / n;
var lon = lon1 + dlon * (WebMercatorProjection.LatitudeToY(lat) - y1) / dy;
locations.Add(lat, lon);
}
}
locations.Add(lat2, lon2);
return(locations);
}
