/// <summary>
/// Evaluate the gravity at an arbitrary point above (or below) the ellipsoid.
/// </summary>
/// <param name="lat">the geographic latitude (degrees).</param>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <param name="h">the height above the ellipsoid (meters).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>W</i>, the sum of the gravitational and centrifugal potentials (m^2 s^−2).</item>
/// <item><i>gx</i>, the easterly component of the acceleration (m s^−2).</item>
/// <item><i>gy</i>, the northerly component of the acceleration (m s^−2).</item>
/// <item><i>gz</i>, the upward component of the acceleration (m s^−2); this is usually negative.</item>
/// </list>
/// </returns>
/// <remarks>
/// The function includes the effects of the earth's rotation.
/// </remarks>
public (double W, double gx, double gy, double gz) Gravity(double lat, double lon, double h)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
var(X, Y, Z) = _earth.Earth.IntForward(lat, lon, h, M);
var(Wres, gx, gy, gz) = W(X, Y, Z);
Geocentric.Unrotate(M, gx, gy, gz, out gx, out gy, out gz);
return(Wres, gx, gy, gz);
}
/// <summary>
/// Evaluate the gravity disturbance vector at an arbitrary point above (or below) the ellipsoid.
/// </summary>
/// <param name="lat">the geographic latitude (degrees).</param>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <param name="h">the height above the ellipsoid (meters).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>T</i>, the corresponding disturbing potential (m2 s−2).</item>
/// <item><i>deltax</i>, the easterly component of the disturbance vector (m s^−2).</item>
/// <item><i>deltay</i>, the northerly component of the disturbance vector (m s^−2).</item>
/// <item><i>deltaz</i>, the upward component of the disturbance vector (m s^−2).</item>
/// </list>
/// </returns>
public (double T, double deltax, double deltay, double deltaz) Disturbance(double lat, double lon, double h)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
var(X, Y, Z) = _earth.Earth.IntForward(lat, lon, h, M);
var Tres = InternalT(X, Y, Z, out var deltax, out var deltay, out var deltaz, true, true);
Geocentric.Unrotate(M, deltax, deltay, deltaz, out deltax, out deltay, out deltaz);
return(Tres, deltax, deltay, deltaz);
}
/// <summary>
/// Evaluate the gravity.
/// </summary>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>W</i>, the sum of the gravitational and centrifugal potentials (m^2 s^−2).</item>
/// <item><i>gx</i>, the easterly component of the acceleration (m s^−2).</item>
/// <item><i>gy</i>, the northerly component of the acceleration (m s^−2).</item>
/// <item><i>gz</i>, the upward component of the acceleration (m s^−2); this is usually negative.</item>
/// </list>
/// </returns>
/// <remarks>The function includes the effects of the earth's rotation.</remarks>
public (double W, double gx, double gy, double gz) Gravity(double lon)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
SinCosd(lon, out var slam, out var clam);
var(Wres, gx, gy, gz) = W(slam, clam);
Geocentric.Rotation(_sphi, _cphi, slam, clam, M);
Geocentric.Unrotate(M, gx, gy, gz, out gx, out gy, out gz);
return(Wres, gx, gy, gz);
}
/// <summary>
/// Evaluate the gravity disturbance vector.
/// </summary>
/// <param name="lon">the geographic longitude (degrees).</param>
/// <returns>
/// <list type="bullet">
/// <item><i>T</i>, the corresponding disturbing potential (m2 s−2).</item>
/// <item><i>deltax</i>, the easterly component of the disturbance vector (m s^−2).</item>
/// <item><i>deltay</i>, the northerly component of the disturbance vector (m s^−2).</item>
/// <item><i>deltaz</i>, the upward component of the disturbance vector (m s^−2).</item>
/// </list>
/// </returns>
public (double T, double deltax, double deltay, double deltaz) Disturbance(double lon)
{
Span <double> M = stackalloc double[Geocentric.dim2_];
SinCosd(lon, out var slam, out var clam);
var Tres = InternalT(slam, clam, out var deltax, out var deltay, out var deltaz, true, true);
Geocentric.Rotation(_sphi, _cphi, slam, clam, M);
Geocentric.Unrotate(M, deltax, deltay, deltaz, out deltax, out deltay, out deltaz);
return(Tres, deltax, deltay, deltaz);
}
/// <summary>
/// Reset the origin.
/// </summary>
/// <param name="lat0">latitude at origin (degrees).</param>
/// <param name="lon0">longitude at origin (degrees).</param>
/// <param name="h0">height above ellipsoid at origin (meters); default 0.</param>
/// <remarks>
/// <paramref name="lat0"/> should be in the range [−90°, 90°].
/// </remarks>
public void Reset(double lat0, double lon0, double h0 = 0)
{
_lat0 = LatFix(lat0);
_lon0 = AngNormalize(lon0);
_h0 = h0;
(_x0, _y0, _z0) = _earth.Forward(_lat0, _lon0, _h0);
SinCosd(_lat0, out var sphi, out var cphi);
SinCosd(_lon0, out var slam, out var clam);
Geocentric.Rotation(sphi, cphi, slam, clam, _r.Span);
}
/// <summary>
/// Constructor for the normal gravity.
/// </summary>
/// <param name="a">equatorial radius (meters).</param>
/// <param name="GM">mass constant of the ellipsoid (meters^3/seconds^2);
/// this is the product of <i>G</i> the gravitational constant and <i>M</i> the mass of the earth
/// (usually including the mass of the earth's atmosphere).</param>
/// <param name="omega">the angular velocity (rad s^−1).</param>
/// <param name="f_J2">either the flattening of the ellipsoid <i>f</i> or the the dynamical form factor <i>J2</i>.</param>
/// <param name="geometricp">
/// if <see langword="true"/> (the default), then <paramref name="f_J2"/> denotes the flattening,
/// else it denotes the dynamical form factor <i>J2</i>.
/// </param>
/// <remarks>
/// The shape of the ellipsoid can be given in one of two ways:
/// <list type="bullet">
/// <item>geometrically (<paramref name="geometricp"/> = <see langword="true"/>), the ellipsoid is defined by
/// the flattening <i>f</i> = (<i>a</i> − <i>b</i>) / <i>a</i>,
/// where <i>a</i> and <i>b</i> are the equatorial radius and the polar semi-axis.
/// The parameters should obey <i>a</i> > 0, <i>f</i> < 1.
/// There are no restrictions on <paramref name="GM"/> or <paramref name="omega"/>, in particular, <paramref name="GM"/> need not be positive.</item>
/// <item>physically (<paramref name="geometricp"/> = <see langword="false"/>),
/// the ellipsoid is defined by the dynamical form factor <i>J2</i> = (<i>C</i> − <i>A</i>) / <i>Ma</i>^2,
/// where <i>A</i> and <i>C</i> are the equatorial and polar moments of inertia and <i>M</i> is the mass of the earth.
/// The parameters should obey <paramref name="a"/> > 0,
/// <paramref name="GM"/> > 0 and <i>J2</i> < 1/3 − (<paramref name="omega"/>^2 <paramref name="a"/>^3/<paramref name="GM"/>) 8/(45π).
/// There is no restriction on omega.</item>
/// </list>
/// </remarks>
public NormalGravity(double a, double GM, double omega, double f_J2,
bool geometricp = true)
{
_a = a;
if (!(IsFinite(_a) && _a > 0))
{
throw new GeographicException("Equatorial radius is not positive");
}
_GM = GM;
if (!IsFinite(_GM))
{
throw new GeographicException("Gravitational constant is not finite");
}
_omega = omega;
_omega2 = Sq(_omega);
_aomega2 = Sq(_omega * _a);
if (!(IsFinite(_omega2) && IsFinite(_aomega2)))
{
throw new GeographicException("Rotation velocity is not finite");
}
_f = geometricp ? f_J2 : J2ToFlattening(_a, _GM, _omega, f_J2);
_b = _a * (1 - _f);
if (!(IsFinite(_b) && _b > 0))
{
throw new GeographicException("Polar semi-axis is not positive");
}
_J2 = geometricp ? FlatteningToJ2(_a, _GM, _omega, f_J2) : f_J2;
_e2 = _f * (2 - _f);
_ep2 = _e2 / (1 - _e2);
var ex2 = _f < 0 ? -_e2 : _ep2;
_Q0 = Qf(ex2, _f < 0);
_earth = new Geocentric(_a, _f);
_E = _a * Sqrt(Abs(_e2)); // H+M, Eq 2-54
// H+M, Eq 2-61
_U0 = _GM * Atanzz(ex2, _f < 0) / _b + _aomega2 / 3;
var P = Hf(ex2, _f < 0) / (6 * _Q0);
// H+M, Eq 2-73
_gammae = _GM / (_a * _b) - (1 + P) * _a * _omega2;
// H+M, Eq 2-74
_gammap = _GM / (_a * _a) + 2 * P * _b * _omega2;
// k = gammae * (b * gammap / (a * gammae) - 1)
// = (b * gammap - a * gammae) / a
_k = -_e2 * _GM / (_a * _b) +
_omega2 * (P * (_a + 2 * _b * (1 - _f)) + _a);
// f* = (gammap - gammae) / gammae
_fstar = (-_f * _GM / (_a * _b) + _omega2 * (P * (_a + 2 * _b) + _a)) /
_gammae;
}
private (double Bx, double By, double Bz) Field(double t, double lat, double lon, double h, bool diffp,
out double Bxt, out double Byt, out double Bzt)
{
Bxt = Byt = Bzt = default;
Span <double> M = stackalloc double[Geocentric.dim2_];
var(X, Y, Z) = _earth.IntForward(lat, lon, h, M);
// Components in geocentric basis
// initial values to suppress warning
var(BX, BY, BZ) = FieldGeocentric(t, X, Y, Z, out var BXt, out var BYt, out var BZt);
if (diffp)
{
Geocentric.Unrotate(M, BXt, BYt, BZt, out Bxt, out Byt, out Bzt);
}
Geocentric.Unrotate(M, BX, BY, BZ, out var Bx, out var By, out var Bz);
return(Bx, By, Bz);
}
private (double Bx, double By, double Bz) Field(double lon, bool diffp,
out double Bxt, out double Byt, out double Bzt)
{
Bxt = Byt = Bzt = default;
SinCosd(lon, out var slam, out var clam);
Span <double> M = stackalloc double[Geocentric.dim2_];
Geocentric.Rotation(_sphi, _cphi, slam, clam, M);
var(BX, BY, BZ) = FieldGeocentric(slam, clam, out var BXt, out var BYt, out var BZt);
if (diffp)
{
Geocentric.Unrotate(M, BXt, BYt, BZt, out Bxt, out Byt, out Bzt);
}
Geocentric.Unrotate(M, BX, BY, BZ, out var Bx, out var By, out var Bz);
return(Bx, By, Bz);
}
/// <summary>
/// Evaluate the components of the gravity anomaly vector using the spherical approximation.
/// </summary>
/// <param name="lon">the geographic longitude (degrees).</param> w
/// <returns>
/// <list type="bullet">
/// <item><i>Dg01</i>, the gravity anomaly (m s^−2).</item>
/// <item><i>xi</i>, the northerly component of the deflection of the vertical (degrees).</item>
/// <item><i>eta</i>, the easterly component of the deflection of the vertical (degrees).</item>
/// </list>
/// </returns>
/// <remarks>
/// The spherical approximation (see Heiskanen and Moritz, Sec 2-14) is used so that the results of the NGA codes are
/// reproduced accurately. approximations used here.
/// Details are given in
/// <a href="https://geographiclib.sourceforge.io/html/gravity.html#gravitygeoid">Details of the geoid height and anomaly calculations</a>.
/// </remarks>
public (double Dg01, double xi, double eta) SphericalAnomaly(double lon)
{
if (_caps.HasFlag(GravityFlags.SphericalAnomaly))
{
return(double.NaN, double.NaN, double.NaN);
}
SinCosd(lon, out var slam, out var clam);
double
deltax, deltay, deltaz,
T = InternalT(slam, clam, out deltax, out deltay, out deltaz, true, false);
// Rotate cartesian into spherical coordinates
Span <double> MC = stackalloc double[Geocentric.dim2_];
Geocentric.Rotation(_spsi, _cpsi, slam, clam, MC);
Geocentric.Unrotate(MC, deltax, deltay, deltaz, out deltax, out deltay, out deltaz);
// H+M, Eq 2-151c
var Dg01 = -deltaz - 2 * T * _invR;
var xi = -(deltay / _gamma) / Degree;
var eta = -(deltax / _gamma) / Degree;
return(Dg01, xi, eta);
}
/// <summary>
/// Construct a magnetic model.
/// </summary>
/// <param name="name">the name of the model</param>
/// <param name="path">(optional) directory for data file.</param>
/// <param name="earth">(optional) <see cref="Geocentric"/> object for converting coordinates; default <see cref="Geocentric.WGS84"/>.</param>
/// <param name="Nmax">(optional) if non-negative, truncate the degree of the model this value.</param>
/// <param name="Mmax">(optional) if non-negative, truncate the order of the model this value.</param>
/// <remarks>
/// A filename is formed by appending ".wmm" (World Magnetic Model) to the name.
/// If path is specified (and is non-empty), then the file is loaded from directory, <paramref name="path"/>.
/// Otherwise the path is given by the <see cref="DefaultMagneticPath"/>.
/// <para>
/// This file contains the metadata which specifies the properties of the model.
/// The coefficients for the spherical harmonic sums are obtained from a file obtained by appending ".cof" to metadata file (so the filename ends in ".wwm.cof").
/// </para>
/// <para>
/// The model is not tied to a particular ellipsoidal model of the earth.
/// The final earth argument to the constructor specifies an ellipsoid to allow geodetic coordinates to the
/// transformed into the spherical coordinates used in the spherical harmonic sum.
/// </para>
/// <para>
/// If <paramref name="Nmax"/> ≥ 0 and <paramref name="Mmax"/> < 0, then <paramref name="Mmax"/> is set to <paramref name="Nmax"/>.
/// After the model is loaded, the maximum degree and order of the model can be found by the <see cref="Degree"/> and <see cref="Order"/> methods.
/// </para>
/// </remarks>
public MagneticModel(string name, string path = "", Geocentric earth = null, int Nmax = -1, int Mmax = -1)
{
earth = earth ?? Geocentric.WGS84;
_name = name;
_dir = path;
_description = "NONE";
_t0 = double.NaN;
_dt0 = 1;
_tmin = double.NaN;
_tmax = double.NaN;
_a = double.NaN;
_hmin = double.NaN;
_hmax = double.NaN;
_Nmodels = 1;
_Nconstants = 0;
_nmx = -1;
_mmx = -1;
_norm = Normalization.Schmidt;
_earth = earth;
if (string.IsNullOrEmpty(path))
{
_dir = DefaultMagneticPath;
}
bool truncate = Nmax >= 0 || Mmax >= 0;
if (truncate)
{
if (Nmax >= 0 && Mmax < 0)
{
Mmax = Nmax;
}
if (Nmax < 0)
{
Nmax = int.MaxValue;
}
if (Mmax < 0)
{
Mmax = int.MaxValue;
}
}
ReadMetadata(_name,
ref _filename, ref _id, ref _name, ref _description, ref _date,
ref _a, ref _t0, ref _dt0, ref _tmin, ref _tmax, ref _hmin, ref _hmax,
ref _Nmodels, ref _Nconstants, ref _norm);
string coeff = _filename + ".cof";
using (var stream = File.OpenRead(coeff))
{
Span <byte> id = stackalloc byte[idlength_];
if (stream.Read(id) != idlength_)
{
throw new GeographicException("No header in " + coeff);
}
if (MemoryMarshal.Cast <char, byte>(_id.AsSpan()).SequenceEqual(id))
{
throw new GeographicException($"ID mismatch: {_id} vs {Encoding.ASCII.GetString(id.ToArray())}");
}
for (int i = 0; i < _Nmodels + 1 + _Nconstants; ++i)
{
int N = 0, M = 0;
if (truncate)
{
N = Nmax; M = Mmax;
}
var c = SphericalEngine.Coeff.FromStream(stream, ref N, ref M, truncate);
if (!(M < 0 || c.Cv(0) == 0))
{
throw new GeographicException("A degree 0 term is not permitted");
}
var sh = new SphericalHarmonic(c, _a, _norm);
_harm.Add(sh);
_nmx = Max(_nmx, sh.Coefficients.Nmx);
_mmx = Max(_mmx, sh.Coefficients.Mmx);
}
if (stream.Position != stream.Length)
{
throw new GeographicException("Extra data in " + coeff);
}
}
}
/// <summary>
/// Initialize a new <see cref="LocalCartesian"/> instance.
/// </summary>
/// <param name="earth"><see cref="Geocentric"/> object for the transformation; default <see cref="Geocentric.WGS84"/>.</param>
public LocalCartesian(Geocentric earth = null) : this(0, 0, earth : earth)
{
}
/// <summary>
/// Initialize a new <see cref="LocalCartesian"/> instance with specified origin.
/// </summary>
/// <param name="lat0">latitude at origin (degrees).</param>
/// <param name="lon0">longitude at origin (degrees).</param>
/// <param name="h0">height above ellipsoid at origin (meters); default 0.</param>
/// <param name="earth"><see cref="Geocentric"/> object for the transformation; default <see cref="Geocentric.WGS84"/>.</param>
/// <remarks>
/// <paramref name="lat0"/> should be in the range [−90°, 90°].
/// </remarks>
public LocalCartesian(double lat0, double lon0, double h0 = 0, Geocentric earth = null)
{
_earth = earth ?? Geocentric.WGS84;
Reset(lat0, lon0, h0);
}
