XAML-Map-Control/MapControl/Shared/AzimuthalProjection.cs

using System;

namespace MapControl
{
    public abstract class AzimuthalProjection : MapProjection
    {
        protected AzimuthalProjection()
        {
            EnableCenterUpdates();
        }

        public readonly struct ProjectedPoint
        {
            public double X { get; }
            public double Y { get; }
            public double CosC { get; }

            public ProjectedPoint(double centerLatitude, double centerLongitude, double latitude, double longitude)
            {
                var phi = latitude * Math.PI / 180d;
                var phi1 = centerLatitude * Math.PI / 180d;
                var dLambda = (longitude - centerLongitude) * Math.PI / 180d; // λ - λ0
                var cosPhi = Math.Cos(phi);
                var sinPhi = Math.Sin(phi);
                var cosPhi1 = Math.Cos(phi1);
                var sinPhi1 = Math.Sin(phi1);
                var cosLambda = Math.Cos(dLambda);
                var sinLambda = Math.Sin(dLambda);
                var cosC = sinPhi1 * sinPhi + cosPhi1 * cosPhi * cosLambda; // (5-3)

                X = cosPhi * sinLambda;
                Y = cosPhi1 * sinPhi - sinPhi1 * cosPhi * cosLambda;
                CosC = Math.Min(Math.Max(cosC, -1d), 1d); // protect against rounding errors
            }

            public (double, double) RelativeScale(double radialScale, double perpendicularScale)
            {
                var scaleX = radialScale;
                var scaleY = perpendicularScale;

                if (scaleX != scaleY)
                {
                    var s = Math.Sqrt(X * X + Y * Y);
                    // sin and cos of azimuth from projection center, i.e. Atan2(Y/X)
                    var cos = X / s;
                    var sin = Y / s;
                    var x1 = scaleX * cos;
                    var y1 = scaleY * sin;
                    var x2 = scaleX * sin;
                    var y2 = scaleY * cos;
                    scaleX = Math.Sqrt(x1 * x1 + y1 * y1);
                    scaleY = Math.Sqrt(x2 * x2 + y2 * y2);
                }

                return (scaleX, scaleY);
            }
        }

        protected ProjectedPoint GetProjectedPoint(double latitude, double longitude)
        {
            return new ProjectedPoint(Center.Latitude, Center.Longitude, latitude, longitude);
        }

        protected Location GetLocation(double x, double y, double rho, double sinC)
        {
            var cos2C = 1d - sinC * sinC;

            if (cos2C < 0d)
            {
                return null;
            }

            var cosC = Math.Sqrt(cos2C);
            var phi1 = Center.Latitude * Math.PI / 180d;
            var cosPhi1 = Math.Cos(phi1);
            var sinPhi1 = Math.Sin(phi1);
            var phi = Math.Asin(cosC * sinPhi1 + y * sinC * cosPhi1 / rho); // (20-14)
            double u, v;

            if (Center.Latitude == 90d) // (20-16)
            {
                u = x;
                v = -y;
            }
            else if (Center.Latitude == -90d) // (20-17)
            {
                u = x;
                v = y;
            }
            else // (20-15)
            {
                u = x * sinC;
                v = rho * cosPhi1 * cosC - y * sinPhi1 * sinC;
            }

            return new Location(
                phi * 180d / Math.PI,
                Math.Atan2(u, v) * 180d / Math.PI + Center.Longitude);
        }
    }
}