mirror of
https://github.com/ClemensFischer/XAML-Map-Control.git
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138 lines
4.6 KiB
C#
138 lines
4.6 KiB
C#
// XAML Map Control - https://github.com/ClemensFischer/XAML-Map-Control
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// Copyright © Clemens Fischer
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// Licensed under the Microsoft Public License (Ms-PL)
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using System;
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#if WPF
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using System.Windows;
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#endif
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namespace MapControl
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{
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/// <summary>
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/// Universal Transverse Mercator Projection.
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/// See https://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system.
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/// </summary>
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public class TransverseMercatorProjection : MapProjection
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{
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public double EquatorialRadius { get; set; } = Wgs84EquatorialRadius;
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public double Flattening { get; set; } = Wgs84Flattening;
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public double ScaleFactor { get; set; } = 0.9996;
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public double CentralMeridian { get; set; }
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public double FalseEasting { get; set; } = 5e5;
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public double FalseNorthing { get; set; }
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public TransverseMercatorProjection()
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{
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Type = MapProjectionType.TransverseCylindrical;
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}
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public override Point GetRelativeScale(Location location)
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{
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return new Point(ScaleFactor, ScaleFactor);
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}
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public override Point? LocationToMap(Location location)
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{
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#if NETFRAMEWORK || UWP
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double Atanh(double x) => Math.Log((1d + x) / (1d - x)) / 2d;
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#else
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static double Atanh(double x) => Math.Atanh(x);
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#endif
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var n = Flattening / (2d - Flattening);
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var n2 = n * n;
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var n3 = n * n2;
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var k0A = ScaleFactor * EquatorialRadius / (1d + n) * (1d + n2 / 4d + n2 * n2 / 64d);
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// α_j
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var alpha1 = n / 2d - n2 * 2d / 3d + n3 * 5d / 16d;
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var alpha2 = n2 * 13d / 48d - n3 * 3d / 5d;
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var alpha3 = n3 * 61d / 240d;
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// φ
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var phi = location.Latitude * Math.PI / 180d;
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// (λ - λ0)
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var lambda = (location.Longitude - CentralMeridian) * Math.PI / 180d;
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var s = 2d * Math.Sqrt(n) / (1d + n);
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var sinPhi = Math.Sin(phi);
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var t = Math.Sinh(Atanh(sinPhi) - s * Atanh(s * sinPhi));
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// ξ'
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var xi_ = Math.Atan(t / Math.Cos(lambda));
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// η'
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var eta_ = Atanh(Math.Sin(lambda) / Math.Sqrt(1d + t * t));
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// ξ
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var xi = xi_
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+ alpha1 * Math.Sin(2d * xi_) * Math.Cosh(2d * eta_)
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+ alpha2 * Math.Sin(4d * xi_) * Math.Cosh(4d * eta_)
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+ alpha3 * Math.Sin(6d * xi_) * Math.Cosh(6d * eta_);
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// η
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var eta = eta_
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+ alpha1 * Math.Cos(2d * xi_) * Math.Sinh(2d * eta_)
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+ alpha2 * Math.Cos(4d * xi_) * Math.Sinh(4d * eta_)
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+ alpha3 * Math.Cos(6d * xi_) * Math.Sinh(6d * eta_);
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return new Point(
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k0A * eta + FalseEasting,
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k0A * xi + FalseNorthing);
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}
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public override Location MapToLocation(Point point)
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{
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var n = Flattening / (2d - Flattening);
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var n2 = n * n;
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var n3 = n * n2;
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var k0A = ScaleFactor * EquatorialRadius / (1d + n) * (1d + n2 / 4d + n2 * n2 / 64d);
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// β_j
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var beta1 = n / 2d - n2 * 2d / 3d + n3 * 37d / 96d;
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var beta2 = n2 / 48d + n3 / 15d;
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var beta3 = n3 * 17d / 480d;
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// δ_j
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var delta1 = n * 2d - n2 * 2d / 3d - n3 * 2d;
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var delta2 = n2 * 7d / 3d - n3 * 8d / 5d;
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var delta3 = n3 * 56d / 15d;
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// ξ
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var xi = (point.Y - FalseNorthing) / k0A;
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// η
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var eta = (point.X - FalseEasting) / k0A;
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// ξ'
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var xi_ = xi
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- beta1 * Math.Sin(2d * xi) * Math.Cosh(2d * eta)
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- beta2 * Math.Sin(4d * xi) * Math.Cosh(4d * eta)
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- beta3 * Math.Sin(6d * xi) * Math.Cosh(6d * eta);
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// η'
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var eta_ = eta
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- beta1 * Math.Cos(2d * xi) * Math.Sinh(2d * eta)
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- beta2 * Math.Cos(4d * xi) * Math.Sinh(4d * eta)
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- beta3 * Math.Cos(6d * xi) * Math.Sinh(6d * eta);
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// χ
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var chi = Math.Asin(Math.Sin(xi_) / Math.Cosh(eta_));
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// φ
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var phi = chi
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+ delta1 * Math.Sin(2d * chi)
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+ delta2 * Math.Sin(4d * chi)
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+ delta3 * Math.Sin(6d * chi);
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// λ
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var lambda = Math.Atan(Math.Sinh(eta_) / Math.Cos(xi_));
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return new Location(
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phi * 180d / Math.PI,
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lambda * 180d / Math.PI + CentralMeridian);
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}
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}
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}
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