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MapProjection.GridConvergence, rotation instead of Matrix

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ClemensFischer 2026-01-29 21:36:11 +01:00
parent 45b47bbae4
commit 4ad9f2ea2a
15 changed files with 272 additions and 239 deletions
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117
MapControl/Shared/TransverseMercatorProjectionSnyder.cs
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@ -45,41 +45,6 @@ namespace MapControl
e6 * 35d / 3072d * Math.Sin(6d * phi)); // (3-21)
}
public override Matrix RelativeTransform(double latitude, double longitude)
{
var k = ScaleFactor;
var gamma = 0d; // γ, meridian convergence angle
if (latitude > -90d && latitude < 90d)
{
var phi = latitude * Math.PI / 180d;
var sinPhi = Math.Sin(phi);
var cosPhi = Math.Cos(phi);
var tanPhi = sinPhi / cosPhi;
var dLambda = (longitude - CentralMeridian) * Math.PI / 180d;
var e2 = (2d - Flattening) * Flattening;
var e_2 = e2 / (1d - e2); // (8-12)
var T = tanPhi * tanPhi; // (8-13)
var C = e_2 * cosPhi * cosPhi; // (8-14)
var A = dLambda * cosPhi; // (8-15)
var A2 = A * A;
var A4 = A2 * A2;
var A6 = A2 * A4;
k *= 1d + (1d + C) * A2 / 2d +
(5d - 4d * T + 42d * C + 13d * C * C - 28d * e_2) * A4 / 24d +
(61d - 148d * T + 16 * T * T) * A6 / 720d; // (8-11)
gamma = Math.Atan(Math.Tan(dLambda) * sinPhi);
}
var transform = new Matrix(k, 0d, 0d, k, 0d, 0d);
transform.Rotate(-gamma * 180d / Math.PI);
return transform;
}
public override Point LocationToMap(double latitude, double longitude)
{
var phi = latitude * Math.PI / 180d;
@ -118,6 +83,41 @@ namespace MapControl
return new Point(x + FalseEasting, y + FalseNorthing);
}
public override Matrix RelativeTransform(double latitude, double longitude)
{
var k = ScaleFactor;
var gamma = 0d; // γ, https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Convergence
if (latitude > -90d && latitude < 90d)
{
var phi = latitude * Math.PI / 180d;
var sinPhi = Math.Sin(phi);
var cosPhi = Math.Cos(phi);
var tanPhi = sinPhi / cosPhi;
var dLambda = (longitude - CentralMeridian) * Math.PI / 180d;
var e2 = (2d - Flattening) * Flattening;
var e_2 = e2 / (1d - e2); // (8-12)
var T = tanPhi * tanPhi; // (8-13)
var C = e_2 * cosPhi * cosPhi; // (8-14)
var A = dLambda * cosPhi; // (8-15)
var A2 = A * A;
var A4 = A2 * A2;
var A6 = A2 * A4;
k *= 1d + (1d + C) * A2 / 2d +
(5d - 4d * T + 42d * C + 13d * C * C - 28d * e_2) * A4 / 24d +
(61d - 148d * T + 16 * T * T) * A6 / 720d; // (8-11)
gamma = Math.Atan(Math.Tan(dLambda) * sinPhi) * 180d / Math.PI;
}
var transform = new Matrix(k, 0d, 0d, k, 0d, 0d);
transform.Rotate(-gamma);
return transform;
}
public override Location MapToLocation(double x, double y)
{
var e2 = (2d - Flattening) * Flattening;
@ -164,5 +164,52 @@ namespace MapControl
phi * 180d / Math.PI,
dLambda * 180d / Math.PI + CentralMeridian);
}
public override double GridConvergence(double x, double y)
{
var e2 = (2d - Flattening) * Flattening;
var e4 = e2 * e2;
var e6 = e2 * e4;
var s = Math.Sqrt(1d - e2);
var e1 = (1d - s) / (1d + s); // (3-24)
var e12 = e1 * e1;
var e13 = e1 * e12;
var e14 = e1 * e13;
var M = M0 + (y - FalseNorthing) / ScaleFactor; // (8-20)
var mu = M / (EquatorialRadius * (1d - e2 / 4d - e4 * 3d / 64d - e6 * 5d / 256d)); // (7-19)
var phi1 = mu +
(e1 * 3d / 2d - e13 * 27d / 32d) * Math.Sin(2d * mu) +
(e12 * 21d / 16d - e14 * 55d / 32d) * Math.Sin(4d * mu) +
e13 * 151d / 96d * Math.Sin(6d * mu) +
e14 * 1097d / 512d * Math.Sin(8d * mu); // (3-26)
var sinPhi1 = Math.Sin(phi1);
var cosPhi1 = Math.Cos(phi1);
var tanPhi1 = sinPhi1 / cosPhi1;
var e_2 = e2 / (1d - e2); // (8-12)
var C1 = e_2 * cosPhi1 * cosPhi1; // (8-21)
var T1 = sinPhi1 * sinPhi1 / (cosPhi1 * cosPhi1); // (8-22)
s = Math.Sqrt(1d - e2 * sinPhi1 * sinPhi1);
var N1 = EquatorialRadius / s; // (8-23)
var R1 = EquatorialRadius * (1d - e2) / (s * s * s); // (8-24)
var D = (x - FalseEasting) / (N1 * ScaleFactor); // (8-25)
var D2 = D * D;
var D3 = D * D2;
var D4 = D * D3;
var D5 = D * D4;
var D6 = D * D5;
var phi = phi1 - N1 * tanPhi1 / R1 * (D2 / 2d - (5d + 3d * T1 + 10d * C1 - 4d * C1 * C1 - 9d * e_2) * D4 / 24d +
(61d + 90d * T1 + 45d * T1 * T1 + 298 * C1 - 3d * C1 * C1 - 252d * e_2) * D6 / 720d); // (8-17)
var dLambda = (D - (1d + 2d * T1 + C1) * D3 / 6d +
(5d - 2d * C1 - 3d * C1 * C1 + 28d * T1 + 24d * T1 * T1 + 8d * e_2) * D5 / 120d) / cosPhi1; // (8-18)
// γ, https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Convergence
//
return Math.Atan(Math.Tan(dLambda) * Math.Sin(phi)) * 180d / Math.PI;
}
}
}