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Updated StereographicProjection

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ClemensFischer 2026-02-01 10:53:12 +01:00
parent cfed3575ac
commit a4bd11e26d
2 changed files with 40 additions and 27 deletions
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49
MapControl/Shared/StereographicProjection.cs
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@ -27,10 +27,25 @@ namespace MapControl
public override double GridConvergence(double latitude, double longitude)
{
var p0 = LocationToMap(latitude, longitude);
var p1 = LocationToMap(latitude + 1e-3, longitude);
var phi0 = LatitudeOfOrigin * Math.PI / 180d; // φ1
var phi1 = latitude * Math.PI / 180d;
var phi2 = (latitude + 1e-3) * Math.PI / 180d;
var dLambda = (longitude - CentralMeridian) * Math.PI / 180d; // λ - λ0
var sinPhi0 = Math.Sin(phi0);
var cosPhi0 = Math.Cos(phi0);
var sinPhi1 = Math.Sin(phi1);
var cosPhi1 = Math.Cos(phi1);
var sinPhi2 = Math.Sin(phi2);
var cosPhi2 = Math.Cos(phi2);
var sinLambda = Math.Sin(dLambda);
var cosLambda = Math.Cos(dLambda);
var k1 = 2d / (1d + sinPhi0 * sinPhi1 + cosPhi0 * cosPhi1 * cosLambda);
var k2 = 2d / (1d + sinPhi0 * sinPhi2 + cosPhi0 * cosPhi2 * cosLambda);
var dCosPhi = k2 * cosPhi2 - k1 * cosPhi1;
var dSinPhi = k2 * sinPhi2 - k1 * sinPhi1;
return Math.Atan2(p0.X - p1.X, p1.Y - p0.Y) * 180d / Math.PI;
return Math.Atan2(-sinLambda * dCosPhi,
cosPhi0 * dSinPhi - sinPhi0 * cosLambda * dCosPhi) * 180d / Math.PI;
}
public override Matrix RelativeTransform(double latitude, double longitude)
@ -40,20 +55,18 @@ namespace MapControl
public override Point LocationToMap(double latitude, double longitude)
{
var phi = latitude * Math.PI / 180d;
var phi1 = LatitudeOfOrigin * Math.PI / 180d;
var phi0 = LatitudeOfOrigin * Math.PI / 180d; // φ1
var phi = latitude * Math.PI / 180d; // φ
var dLambda = (longitude - CentralMeridian) * Math.PI / 180d; // λ - λ0
var cosPhi = Math.Cos(phi);
var sinPhi0 = Math.Sin(phi0);
var cosPhi0 = Math.Cos(phi0);
var sinPhi = Math.Sin(phi);
var cosPhi1 = Math.Cos(phi1);
var sinPhi1 = Math.Sin(phi1);
var cosLambda = Math.Cos(dLambda);
var cosPhi = Math.Cos(phi);
var sinLambda = Math.Sin(dLambda);
var cosPhiCosLambda = cosPhi * Math.Cos(dLambda);
var x = cosPhi * sinLambda;
var y = cosPhi1 * sinPhi - sinPhi1 * cosPhi * cosLambda;
var cosC = sinPhi1 * sinPhi + cosPhi1 * cosPhi * cosLambda; // (5-3)
cosC = Math.Min(Math.Max(cosC, -1d), 1d); // protect against rounding errors
var k = 2d / (1d + cosC); // p.157 (21-4), k0 == 1
var y = cosPhi0 * sinPhi - sinPhi0 * cosPhiCosLambda;
var k = 2d / (1d + sinPhi0 * sinPhi + cosPhi0 * cosPhiCosLambda); // p.157 (21-4), k0 == 1
return new Point(
EquatorialRadius * k * x,
@ -67,10 +80,10 @@ namespace MapControl
var cosC = Math.Cos(c);
var sinC = Math.Sin(c);
var phi1 = LatitudeOfOrigin * 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)
var phi0 = LatitudeOfOrigin * Math.PI / 180d; // φ1
var cosPhi0 = Math.Cos(phi0);
var sinPhi0 = Math.Sin(phi0);
var phi = Math.Asin(cosC * sinPhi0 + y * sinC * cosPhi0 / rho); // (20-14)
double u, v;
if (LatitudeOfOrigin == 90d) // (20-16)
@ -86,7 +99,7 @@ namespace MapControl
else // (20-15)
{
u = x * sinC;
v = rho * cosPhi1 * cosC - y * sinPhi1 * sinC;
v = rho * cosPhi0 * cosC - y * sinPhi0 * sinC;
}
return new Location(

18
MapControl/Shared/TransverseMercatorProjectionSnyder.cs
View file

@ -120,20 +120,20 @@ namespace MapControl
var M0 = MeridianDistance(LatitudeOfOrigin * Math.PI / 180d);
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 +
var phi0 = 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 sinPhi0 = Math.Sin(phi0);
var cosPhi0 = Math.Cos(phi0);
var tanPhi0 = sinPhi0 / cosPhi0;
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 C1 = e_2 * cosPhi0 * cosPhi0; // (8-21)
var T1 = sinPhi0 * sinPhi0 / (cosPhi0 * cosPhi0); // (8-22)
s = Math.Sqrt(1d - e2 * sinPhi0 * sinPhi0);
var N1 = EquatorialRadius / s; // (8-23)
var R1 = EquatorialRadius * (1d - e2) / (s * s * s); // (8-24)
var D = (x - FalseEasting) / (N1 * ScaleFactor); // (8-25)
@ -143,11 +143,11 @@ namespace MapControl
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 +
var phi = phi0 - N1 * tanPhi0 / 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)
(5d - 2d * C1 - 3d * C1 * C1 + 28d * T1 + 24d * T1 * T1 + 8d * e_2) * D5 / 120d) / cosPhi0; // (8-18)
return new Location(
phi * 180d / Math.PI,