public void CreateRotationZ()
{
double angle = (double)MathHelper.ToRadians(30);
Matrix33D m = Matrix33D.CreateRotationZ(angle);
Assert.IsTrue(Vector3D.AreNumericallyEqual(new Vector3D((double)Math.Cos(angle), (double)Math.Sin(angle), 0), m * Vector3D.UnitX));
QuaternionD q = QuaternionD.CreateRotation(Vector3D.UnitZ, angle);
Assert.IsTrue(Vector3D.AreNumericallyEqual(q.Rotate(Vector3D.One), m * Vector3D.One));
Assert.IsTrue(Matrix33D.AreNumericallyEqual(Matrix33D.CreateRotation(Vector3D.UnitZ, angle), m));
}
public void Orthogonalize()
{
var m = Matrix33D.CreateRotationX(0.1) * Matrix33D.CreateRotationX(20) * Matrix33D.CreateRotationZ(1000);
// Introduce error.
m.M01 += 0.1f;
m.M22 += 0.1f;
Assert.IsFalse(m.IsOrthogonal);
Assert.IsFalse(m.IsRotation);
m.Orthogonalize();
Assert.IsTrue(m.IsOrthogonal);
Assert.IsTrue(m.IsRotation);
// Orthogonalizing and orthogonal matrix does not change the matrix.
var n = m;
n.Orthogonalize();
Assert.IsTrue(Matrix33D.AreNumericallyEqual(m, n));
}
/// <summary>
/// Computes the derived values, like sun/moon positions, transformation matrices and light
/// intensities. This method must be called when the location or time has changed.
/// </summary>
/// <remarks>
/// This method must be called when the input properties <see cref="Latitude"/>,
/// <see cref="Longitude"/>, <see cref="Altitude"/>, or <see cref="Time"/>) have changed.
/// </remarks>
public void Update()
{
_epoch2000Centuries = ToEpoch2000Centuries(Time, true);
_epoch1990Days = ToEpoch1990Days(Time, false);
// To transform from ecliptic to equatorial, we rotate by the obliquity of the ecliptic.
_e = 0.409093 - 0.000227 * _epoch2000Centuries;
EclipticToEquatorial = Matrix33D.CreateRotationX(_e);
// GMST = Greenwich mean sidereal time (mittlere Greenwich-Sternzeit) in radians.
double gmst = 4.894961 + 230121.675315 * ToEpoch2000Centuries(Time, false);
EquatorialToGeographic = Matrix33D.CreateRotationZ(-gmst);
// The earth axis slowly changes over time (precession). The precession movement repeats
// itself approx. all 26000 years. When we move from to horizontal or geographics,
// we need to apply the precession.
// In Game Engine Gems:
//var Rx = Matrix33D.CreateRotationX(0.1118 * _epoch2000Centuries);
//var Ry = Matrix33D.CreateRotationY(-0.00972 * _epoch2000Centuries);
//var Rz = Matrix33D.CreateRotationZ(0.01118 * _epoch2000Centuries);
//var precession = Rz * (Ry * Rx);
// In original article:
var Ry = Matrix33D.CreateRotationY(-0.00972 * _epoch2000Centuries);
var Rz = Matrix33D.CreateRotationZ(0.01118 * _epoch2000Centuries);
var precession = Rz * Ry * Rz;
// In game engine gems precession is applied in EclipticToWorld and in
// EquatorialToWorld. This makes no sense since precession cannot be valid for both
// coordinate systems. --> We assume the precession is given in equatorial space.
//EclipticToWorld = rLat * rLong * EclipticToEquatorial * precession;
// Latitude rotation
var rLat = Matrix33D.CreateRotationY(MathHelper.ToRadians(Latitude) - ConstantsD.PiOver2);
// Longitude rotation
// LMST = Local mean sidereal time (mittlere Ortssternzeit) in radians.
double lmst = gmst + MathHelper.ToRadians(Longitude);
var rLong = Matrix33D.CreateRotationZ(-lmst);
// Earth radius at the equator. (We assume a perfect sphere. We do not support geodetic
// systems with imperfect earth spheres.)
const double earthRadius = 6378.137 * 1000;
var equatorialToHorizontalTranslation = new Vector3D(0, -earthRadius - Altitude, 0);
// Switching of the coordinate axes between Equatorial (z up) and Horizontal (y up).
var axisSwitch = new Matrix33D(0, 1, 0,
0, 0, 1,
1, 0, 0);
EquatorialToWorld = new Matrix44D(axisSwitch * rLat * rLong * precession,
equatorialToHorizontalTranslation);
_equatorialToWorldNoPrecession = new Matrix44D(axisSwitch * rLat * rLong,
equatorialToHorizontalTranslation);
//WorldToGeographic = EquatorialToGeographic * EquatorialToWorld.Minor.Transposed;
ComputeSunPosition();
ComputeMoonPosition();
ComputeEarthPosition();
//for (int i = 0; i < NumberOfPlanets; i++)
//{
// var planet = (VisiblePlanets)i;
// if (planet != VisiblePlanets.Earth)
// ComputePlanetData(planet);
//}
}