/// <summary>
/// Returns the XYZ-coordinates from longitude, latitude and height on a given reference ellipsoid.
/// </summary>
public static V3d XyzFromLonLatHeight(V3d lonLatHeight, GeoEllipsoid ellipsoid)
{
double lam = Conversion.RadiansFromDegrees(lonLatHeight.X);
double phi = Conversion.RadiansFromDegrees(lonLatHeight.Y);
double h = lonLatHeight.Z;
double cos_lam = System.Math.Cos(lam);
double cos_phi = System.Math.Cos(phi);
double sin_lam = System.Math.Sin(lam);
double sin_phi = System.Math.Sin(phi);
// eccentricity square
double eq = ellipsoid.EQ;
// radius of the curvature in prime vertical
double Rv = ellipsoid.A / (1.0 - eq * sin_phi * sin_phi).Sqrt();
V3d result = new V3d();
result.X = (Rv + h) * cos_phi * cos_lam;
result.Y = (Rv + h) * cos_phi * sin_lam;
result.Z = ((1.0 - eq) * Rv + h) * sin_phi;
return(result);
}
/// <summary>
/// Enumerates all vertex indexes at which
/// both outgoing edges meet at an angle that
/// is less than the given threshold.
/// </summary>
public static IEnumerable <int> GetSpikes(
this Polygon3d self, double toleranceInDegrees = 0.1)
{
if (toleranceInDegrees < 0.0)
{
throw new ArgumentOutOfRangeException();
}
var threshold = Conversion.RadiansFromDegrees(toleranceInDegrees).Cos();
var edges = self.GetEdgeArray();
edges.Apply(e => e.Normalized);
var ec = edges.Length;
if (V3d.Dot(-edges[ec - 1], edges[0]) > threshold)
{
yield return(0);
}
for (int i = 1; i < ec; i++)
{
if (V3d.Dot(-edges[i - 1], edges[i]) > threshold)
{
yield return(i);
}
}
}
public void SetClippingParams(double horizontalFovInDegrees, double near, double far, double aspectRatio = 1.0)
{
var d = System.Math.Tan(Conversion.RadiansFromDegrees(horizontalFovInDegrees) * 0.5) * near;
m_box.Min.X = -d;
m_box.Max.X = +d;
m_box.Min.Y = -d / aspectRatio;
m_box.Max.Y = +d / aspectRatio;
m_box.Min.Z = near;
m_box.Max.Z = far;
UpdateProjectionTrafo();
}
/// <summary>
/// Gauss-Krueger projection from a reference ellipsoid datum (Lon/Lat/Height) to local GK-coordinates (in meters).
/// </summary>
/// <param name="lonLatHeight">V3d with Lon/Lat/Height.</param>
/// <param name="ellipsoid"></param>
/// <param name="zeroMeridian"></param>
public static V3d GaussKruegerEllipsoidToPlane(
V3d lonLatHeight, GeoEllipsoid ellipsoid, double zeroMeridian
)
{
double phi = Conversion.RadiansFromDegrees(lonLatHeight.Y);
double lam = Conversion.RadiansFromDegrees(lonLatHeight.X - zeroMeridian);
double cosphi = phi.Cos();
double a = ellipsoid.A;
double b = ellipsoid.B;
double n = (a - b) / (a + b);
//n = (a-b)/(a+b);
double nTo2 = n * n;
double nTo3 = nTo2 * n;
double nTo4 = nTo3 * n;
double nTo5 = nTo4 * n;
// arc length approx. polynom coefficients
double c1 = (a + b) / 2.0 * (1.0 + nTo2 / 4.0 + nTo4 / 64.0);
double c2 = -(3.0 / 2.0) * n + (9.0 / 16.0) * nTo3 - (3.0 / 32.0) * nTo5;
double c3 = (15.0 / 16.0) * nTo2 - (15.0 / 32.0) * nTo4;
double c4 = -(35.0 / 48.0) * nTo3 + (105.0 / 256.0) * nTo5;
double c5 = (315.0 / 512.0) * nTo4;
// sine of multiple of phi
double sin2phi = (2.0 * phi).Sin();
double sin4phi = (4.0 * phi).Sin();
double sin6phi = (6.0 * phi).Sin();
double sin8phi = (8.0 * phi).Sin();
// arc lenght of the meridan
double B = c1 * (phi + c2 * sin2phi + c3 * sin4phi + c4 * sin6phi + c5 * sin8phi);
//% second nummerical eccentrencity
double e2q = ellipsoid.E2Q;
// cos(phi) to powers
double cosphiTo2 = cosphi * cosphi;
double cosphiTo3 = cosphiTo2 * cosphi;
double cosphiTo4 = cosphiTo3 * cosphi;
double cosphiTo5 = cosphiTo4 * cosphi;
double cosphiTo6 = cosphiTo5 * cosphi;
double cosphiTo7 = cosphiTo6 * cosphi;
double cosphiTo8 = cosphiTo7 * cosphi;
//% auxilary quantity 1
double nuTo2 = e2q * cosphiTo2;
//%radius of the curvature in prime vertical
double N = (a * a) / (b * (1.0 + nuTo2).Sqrt());
// lambda to powers
double lamTo2 = lam * lam;
double lamTo3 = lamTo2 * lam;
double lamTo4 = lamTo3 * lam;
double lamTo5 = lamTo4 * lam;
double lamTo6 = lamTo5 * lam;
double lamTo7 = lamTo6 * lam;
double lamTo8 = lamTo7 * lam;
//% auxilary quantity 2
double t = phi.Tan();
// t to powers
double tTo2 = t * t;
double tTo4 = tTo2 * tTo2;
double tTo6 = tTo2 * tTo4;
// nu^2 to powers
double nuTo4 = nuTo2 * nuTo2;
//double nuqTo22 = nuq.Pow(22);
//% x-coord: breite
double x1 = t / 2.0 * N * cosphiTo2 * lamTo2;
double x2 = t / 24.0 * N * cosphiTo4 * (5.0 - tTo2 + 9.0 * nuTo2 + 4.0 * nuTo4) * lamTo4;
double x3 = t / 720.0 * N * cosphiTo6 * (61.0 - 58.0 * tTo2 + tTo4 + 270.0 * nuTo2 - 330.0 * tTo2 * nuTo4) * lamTo6;
double x4 = t / 403204.0 * N * cosphiTo8 * (1385.0 - 3111.0 * tTo2 + 543.0 * tTo4 - tTo6) * lamTo8;
double nX = B + x1 + x2 + x3 + x4;
nX = nX - 5000000; // <-- im model
// y-coord: laenge
double y1 = N * cosphi * lam;
double y2 = N / 6.0 * cosphiTo3 * (1.0 - tTo2 + nuTo2) * lamTo3;
double y3 = N / 120.0 * cosphiTo5 * (5.0 - 18.0 * tTo2 + tTo4 + 14 * nuTo2 - 58.0 * tTo2 * nuTo2) * lamTo5;
double y4 = N / 5040.0 * cosphiTo7 * (61.0 - 479.0 * tTo2 + 179.0 * tTo4 - tTo6) * lamTo7;
double nY = y1 + y2 + y3 + y4;
//%nY = nY + 500000+L0/3*1000000; %<-- potsdam datum
return(new V3d(nY, nX, lonLatHeight.Z)); //<-- Laenge, Breite, Hoehe
}
public static Trafo3d RotationZInDegrees(double angleInDegrees)
{
return(RotationZ(Conversion.RadiansFromDegrees(angleInDegrees)));
}
public static Trafo3d RotationInDegrees(V3d axis, double angleInDegrees)
{
return(Rotation(axis, Conversion.RadiansFromDegrees(angleInDegrees)));
}
public static Trafo3d RotationYInDegrees(double angleInDegrees) => RotationY(Conversion.RadiansFromDegrees(angleInDegrees));
