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Updated TransverseMercatorProjection
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ClemensFischer
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28146cbb20
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c50551d4fe
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@ -14,9 +14,15 @@ namespace MapControl
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/// </summary>
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public class TransverseMercatorProjection : MapProjection
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{
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private readonly double[] alpha = new double[3]; // α_j
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private readonly double[] beta = new double[3]; // β_j
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private readonly double[] delta = new double[3]; // δ_j
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private double a1; // α1
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private double a2; // α2
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private double a3; // α3
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private double b1; // β1
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private double b2; // β2
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private double b3; // β3
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private double d1; // δ1
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private double d2; // δ2
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private double d3; // δ3
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private double f1; // A / a
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private double f2; // 2 * sqrt(n) / (1+n)
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@ -26,26 +32,20 @@ namespace MapControl
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set
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{
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field = value;
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// n, n^2, n^3
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var n = field / (2d - field);
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var n2 = n * n;
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var n3 = n * n2;
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// A / a
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f1 = (1d + n2 / 4d + n2 * n2 / 64d) / (1d + n);
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// 2 * sqrt(n) / (1+n)
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var nn = n * n;
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var nnn = n * nn;
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a1 = n / 2d - nn * 2d / 3d + nnn * 5d / 16d;
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a2 = nn * 13d / 48d - nnn * 3d / 5d;
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a3 = nnn * 61d / 240d;
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b1 = n / 2d - nn * 2d / 3d + nnn * 37d / 96d;
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b2 = nn / 48d + nnn / 15d;
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b3 = nnn * 17d / 480d;
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d1 = n * 2d - nn * 2d / 3d - nnn * 2d;
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d2 = nn * 7d / 3d - nnn * 8d / 5d;
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d3 = nnn * 56d / 15d;
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f1 = (1d + nn / 4d + nn * nn / 64d) / (1d + n);
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f2 = 2d * Math.Sqrt(n) / (1d + n);
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// α_j
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alpha[0] = n / 2d - n2 * 2d / 3d + n3 * 5d / 16d;
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alpha[1] = n2 * 13d / 48d - n3 * 3d / 5d;
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alpha[2] = n3 * 61d / 240d;
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// β_j
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beta[0] = n / 2d - n2 * 2d / 3d + n3 * 37d / 96d;
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beta[1] = n2 / 48d + n3 / 15d;
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beta[2] = n3 * 17d / 480d;
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// δ_j
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delta[0] = n * 2d - n2 * 2d / 3d - n3 * 2d;
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delta[1] = n2 * 7d / 3d - n3 * 8d / 5d;
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delta[2] = n3 * 56d / 15d;
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}
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}
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@ -63,7 +63,7 @@ namespace MapControl
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public override Point RelativeScale(double latitude, double longitude)
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{
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return new Point(ScaleFactor, ScaleFactor);
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return new Point(ScaleFactor, ScaleFactor); // sufficiently precise
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}
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public override Point? LocationToMap(double latitude, double longitude)
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@ -73,7 +73,7 @@ namespace MapControl
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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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// k_0 * A
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// k0 * A
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var k0A = ScaleFactor * EquatorialRadius * f1;
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// φ
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var phi = latitude * Math.PI / 180d;
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@ -88,14 +88,14 @@ namespace MapControl
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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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+ alpha[0] * Math.Sin(2d * xi_) * Math.Cosh(2d * eta_)
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+ alpha[1] * Math.Sin(4d * xi_) * Math.Cosh(4d * eta_)
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+ alpha[2] * Math.Sin(6d * xi_) * Math.Cosh(6d * eta_);
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+ a1 * Math.Sin(2d * xi_) * Math.Cosh(2d * eta_)
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+ a2 * Math.Sin(4d * xi_) * Math.Cosh(4d * eta_)
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+ a3 * Math.Sin(6d * xi_) * Math.Cosh(6d * eta_);
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// η
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var eta = eta_
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+ alpha[0] * Math.Cos(2d * xi_) * Math.Sinh(2d * eta_)
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+ alpha[1] * Math.Cos(4d * xi_) * Math.Sinh(4d * eta_)
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+ alpha[2] * Math.Cos(6d * xi_) * Math.Sinh(6d * eta_);
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+ a1 * Math.Cos(2d * xi_) * Math.Sinh(2d * eta_)
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+ a2 * Math.Cos(4d * xi_) * Math.Sinh(4d * eta_)
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+ a3 * 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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@ -104,7 +104,7 @@ namespace MapControl
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public override Location MapToLocation(double x, double y)
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{
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// k_0 * A
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// k0 * A
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var k0A = ScaleFactor * EquatorialRadius * f1;
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// ξ
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var xi = (y - FalseNorthing) / k0A;
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@ -112,21 +112,21 @@ namespace MapControl
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var eta = (x - FalseEasting) / k0A;
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// ξ'
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var xi_ = xi
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- beta[0] * Math.Sin(2d * xi) * Math.Cosh(2d * eta)
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- beta[1] * Math.Sin(4d * xi) * Math.Cosh(4d * eta)
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- beta[2] * Math.Sin(6d * xi) * Math.Cosh(6d * eta);
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- b1 * Math.Sin(2d * xi) * Math.Cosh(2d * eta)
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- b2 * Math.Sin(4d * xi) * Math.Cosh(4d * eta)
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- b3 * Math.Sin(6d * xi) * Math.Cosh(6d * eta);
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// η'
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var eta_ = eta
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- beta[0] * Math.Cos(2d * xi) * Math.Sinh(2d * eta)
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- beta[1] * Math.Cos(4d * xi) * Math.Sinh(4d * eta)
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- beta[2] * Math.Cos(6d * xi) * Math.Sinh(6d * eta);
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- b1 * Math.Cos(2d * xi) * Math.Sinh(2d * eta)
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- b2 * Math.Cos(4d * xi) * Math.Sinh(4d * eta)
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- b3 * 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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+ delta[0] * Math.Sin(2d * chi)
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+ delta[1] * Math.Sin(4d * chi)
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+ delta[2] * Math.Sin(6d * chi);
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+ d1 * Math.Sin(2d * chi)
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+ d2 * Math.Sin(4d * chi)
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+ d3 * Math.Sin(6d * chi);
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// λ - λ0
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var lambda = Math.Atan(Math.Sinh(eta_) / Math.Cos(xi_));
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