XAML-Map-Control/MapProjections/Shared/WorldMercatorProjection.cs

// XAML Map Control - https://github.com/ClemensFischer/XAML-Map-Control
// © 2019 Clemens Fischer
// Licensed under the Microsoft Public License (Ms-PL)

using System;
#if !WINDOWS_UWP
using System.Windows;
#endif

namespace MapControl.Projections
{
    /// <summary>
    /// Elliptical Mercator Projection implemented by setting the WKT property of a GeoApiProjection.
    /// See "Map Projections - A Working Manual" (https://pubs.usgs.gov/pp/1395/report.pdf), p.44-45.
    /// </summary>
    public class WorldMercatorProjection : GeoApiProjection
    {
        public WorldMercatorProjection()
        {
            IsNormalCylindrical = true;
            WKT = "PROJCS[\"WGS 84 / World Mercator\","
                + "GEOGCS[\"WGS 84\","
                + "DATUM[\"WGS_1984\", SPHEROID[\"WGS 84\", 6378137, 298.257223563, AUTHORITY[\"EPSG\", \"7030\"]], AUTHORITY[\"EPSG\", \"6326\"]],"
                + "PRIMEM[\"Greenwich\", 0, AUTHORITY[\"EPSG\", \"8901\"]],"
                + "UNIT[\"degree\", 0.0174532925199433, AUTHORITY[\"EPSG\", \"9122\"]],"
                + "AUTHORITY[\"EPSG\", \"4326\"]],"
                + "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\"]]";
        }

        public override Vector GetMapScale(Location location)
        {
            var lat = location.Latitude * Math.PI / 180d;
            var eSinLat = Wgs84Eccentricity * Math.Sin(lat);
            var k = Math.Sqrt(1d - eSinLat * eSinLat) / Math.Cos(lat); // p.44 (7-8)

            return new Vector(ViewportScale * k, ViewportScale * k);
        }
    }
}