public static void spherical_harmonic_values_test()
//****************************************************************************80
//
// Purpose:
//
// SPHERICAL_HARMONIC_VALUES_TEST tests SPHERICAL_HARMONIC_VALUES.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 08 February 2007
//
// Author:
//
// John Burkardt
//
{
int l = 0;
int m = 0;
double phi = 0;
double theta = 0;
double yi = 0;
double yr = 0;
Console.WriteLine("");
Console.WriteLine("SPHERICAL_HARMONIC_VALUES_TEST:");
Console.WriteLine(" SPHERICAL_HARMONIC_VALUES stores values of");
Console.WriteLine(" the spherical harmonic function.");
Console.WriteLine("");
Console.WriteLine(" L M THETA PHI Yr Yi");
Console.WriteLine("");
int n_data = 0;
for (;;)
{
SphericalHarmonic.spherical_harmonic_values(ref n_data, ref l, ref m, ref theta, ref phi, ref yr,
ref yi);
if (n_data == 0)
{
break;
}
Console.WriteLine(" "
+ l.ToString().PadLeft(2) + " "
+ m.ToString().PadLeft(2) + " "
+ theta.ToString("0.####").PadLeft(8) + " "
+ phi.ToString("0.####").PadLeft(8) + " "
+ yr.ToString("0.################").PadLeft(24) + " "
+ yi.ToString("0.################").PadLeft(24) + "");
}
}
public SphericalHarmonicsPanel()
{
InitializeComponent();
try
{
m_sh0 = new SphericalHarmonic(C, S, N, a, SphericalHarmonic.Normalization.SCHMIDT);
m_sh1 = new SphericalHarmonic1(C, S, N, C1, S1, N1, a, SphericalHarmonic1.Normalization.FULL);
m_sh2 = new SphericalHarmonic2(C, S, N, C1, S1, N1, C2, S2, N2, a, SphericalHarmonic2.Normalization.FULL);
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
m_classComboBox.SelectedIndex = 0;
}
public SphericalHarmonicsPanel()
{
InitializeComponent();
try
{
m_sh0 = new SphericalHarmonic(C, S, N, a, SphericalHarmonic.Normalization.SCHMIDT);
m_sh1 = new SphericalHarmonic1(C, S, N, C1, S1, N1, a, SphericalHarmonic1.Normalization.FULL);
m_sh2 = new SphericalHarmonic2(C, S, N, C1, S1, N1, C2, S2, N2, a, SphericalHarmonic2.Normalization.FULL);
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
m_classComboBox.SelectedIndex = 0;
}
static void Main(string[] args)
{
try {
int N = 3; // The maximum degree
double[] ca = { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }; // cosine coefficients
double[] sa = { 6, 5, 4, 3, 2, 1 }; // sine coefficients
double a = 1;
SphericalHarmonic h = new SphericalHarmonic(ca, sa, N, a, SphericalHarmonic.Normalization.SCHMIDT);
double x = 2, y = 3, z = 1;
double v, vx, vy, vz;
v = h.HarmonicSum(x, y, z, out vx, out vy, out vz);
Console.WriteLine(String.Format("{0} {1} {2} {3}", v, vx, vy, vz));
}
catch (GeographicErr e) {
Console.WriteLine(String.Format("Caught exception: {0}", e.Message));
}
}
static void Main(string[] args)
{
try {
int N = 3; // The maximum degree
double[] ca = {10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; // cosine coefficients
double[] sa = {6, 5, 4, 3, 2, 1}; // sine coefficients
double a = 1;
SphericalHarmonic h = new SphericalHarmonic(ca, sa, N, a, SphericalHarmonic.Normalization.SCHMIDT);
double x = 2, y = 3, z = 1;
double v, vx, vy, vz;
v = h.HarmonicSum(x, y, z, out vx, out vy, out vz);
Console.WriteLine(String.Format("{0} {1} {2} {3}", v, vx, vy, vz));
}
catch (GeographicErr e) {
Console.WriteLine(String.Format("Caught exception: {0}", e.Message));
}
}
static void Main(string[] args)
{
// This computes the same value as example-SphericalHarmonic.cpp using a
// CircularEngine (which will be faster if many values on a circle of
// latitude are to be found).
try {
int N = 3; // The maxium degree
double[] ca = { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 }; // cosine coefficients
double[] sa = { 6, 5, 4, 3, 2, 1 }; // sine coefficients
double a = 1;
SphericalHarmonic h = new SphericalHarmonic(ca, sa, N, a, SphericalHarmonic.Normalization.SCHMIDT);
double x = 2, y = 3, z = 1, p = Math.Sqrt(x * x + y * y);
CircularEngine circ = h.Circle(p, z, true);
double v, vx, vy, vz;
v = circ.LongitudeSum(x / p, y / p, out vx, out vy, out vz);
Console.WriteLine(String.Format("{0} {1} {2} {3}", v, vx, vy, vz));
}
catch (GeographicErr e) {
Console.WriteLine(String.Format("Caught exception: {0}", e.Message));
}
}
static void Main(string[] args)
{
// This computes the same value as example-SphericalHarmonic.cpp using a
// CircularEngine (which will be faster if many values on a circle of
// latitude are to be found).
try {
int N = 3; // The maxium degree
double[] ca = {10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; // cosine coefficients
double[] sa = {6, 5, 4, 3, 2, 1}; // sine coefficients
double a = 1;
SphericalHarmonic h = new SphericalHarmonic(ca, sa, N, a, SphericalHarmonic.Normalization.SCHMIDT);
double x = 2, y = 3, z = 1, p = Math.Sqrt(x*x+y*y);
CircularEngine circ = h.Circle(p, z, true);
double v, vx, vy, vz;
v = circ.LongitudeSum(x/p, y/p, out vx, out vy, out vz);
Console.WriteLine(String.Format("{0} {1} {2} {3}", v, vx, vy, vz));
}
catch (GeographicErr e) {
Console.WriteLine(String.Format("Caught exception: {0}", e.Message));
}
}
/// <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);
}
}
}
private void OnValidate(object sender, EventArgs e)
{
try
{
const double DEG_TO_RAD = 3.1415926535897932384626433832795 / 180.0;
double gradx, grady, gradz;
SphericalHarmonic s0 = new SphericalHarmonic(C, S, N, N - 1, 0, a, SphericalHarmonic.Normalization.SCHMIDT);
s0 = new SphericalHarmonic(C, S, N, a, SphericalHarmonic.Normalization.SCHMIDT);
double sum = s0.HarmonicSum(1.0, 2.0, 3.0);
double test = s0.HarmonicSum(1.0, 2.0, 3.0, out gradx, out grady, out grady);
if (sum != test)
{
throw new Exception("Error in SphericalHarmonic.HarmonicSum");
}
SphericalCoefficients sc = s0.Coefficients();
CircularEngine ce = s0.Circle(1.0, 0.5, true);
sum = ce.LongitudeSum(60.0);
test = ce.LongitudeSum(Math.Cos(60.0 * DEG_TO_RAD), Math.Sin(60.0 * DEG_TO_RAD));
if (sum != test)
{
throw new Exception("Error in CircularEngine.LongitudeSum 1");
}
test = ce.LongitudeSum(60.0, out gradx, out grady, out gradz);
if (sum != test)
{
throw new Exception("Error in CircularEngine.LongitudeSum 2");
}
ce.LongitudeSum(Math.Cos(60.0 * DEG_TO_RAD), Math.Sin(60.0 * DEG_TO_RAD), out gradx, out grady, out gradz);
if (sum != test)
{
throw new Exception("Error in CircularEngine.LongitudeSum 3");
}
SphericalHarmonic1 s1 = new SphericalHarmonic1(C, S, N, N - 1, 1, C1, S1, N1, N1 - 1, 0, a, SphericalHarmonic1.Normalization.SCHMIDT);
s1 = new SphericalHarmonic1(C, S, N, C1, S1, N1, a, SphericalHarmonic1.Normalization.SCHMIDT);
sum = s1.HarmonicSum(0.95, 1.0, 2.0, 3.0);
test = s1.HarmonicSum(0.95, 1.0, 2.0, 3.0, out gradx, out grady, out gradz);
if (sum != test)
{
throw new Exception("Error in SphericalHarmonic1.HarmonicSum 3");
}
ce = s1.Circle(0.95, 1.0, 0.5, true);
sc = s1.Coefficients();
sc = s1.Coefficients1();
SphericalHarmonic2 s2 = new SphericalHarmonic2(C, S, N, N - 1, 2, C1, S1, N1, N1 - 1, 1,
C2, S2, N2, N2 - 1, 0, a, SphericalHarmonic2.Normalization.SCHMIDT);
s2 = new SphericalHarmonic2(C, S, N, C1, S1, N1, C2, S2, N2, a, SphericalHarmonic2.Normalization.SCHMIDT);
sum = s2.HarmonicSum(0.95, 0.8, 1.0, 2.0, 3.0);
test = s2.HarmonicSum(0.95, 0.8, 1.0, 2.0, 3.0, out gradx, out grady, out gradz);
if (sum != test)
{
throw new Exception("Error in SphericalHarmonic2.HarmonicSum 3");
}
ce = s2.Circle(0.95, 0.8, 1.0, 0.5, true);
sc = s2.Coefficients();
sc = s2.Coefficients1();
sc = s2.Coefficients2();
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
return;
}
MessageBox.Show("No errors found", "OK", MessageBoxButtons.OK, MessageBoxIcon.Information);
}
/// <summary>
/// Construct a gravity model.
/// </summary>
/// <param name="name">the name of the model.</param>
/// <param name="path">directory for data file.</param>
/// <param name="Nmax">if non-negative, truncate the degree of the model this value.</param>
/// <param name="Mmax">if non-negative, truncate the order of the model this value.</param>
/// <remarks>
/// A filename is formed by appending ".egm" (World Gravity Model) to the <paramref name="name"/>.
/// If <paramref name="path"/> is specified (and is non-empty), then the file is loaded from directory, <paramref name="path"/>.
/// Otherwise the <paramref name="path"/> is given by <see cref="DefaultGravityPath"/>.
/// <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 ".egm.cof").
/// </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 GravityModel(string name, string path = "", int Nmax = -1, int Mmax = -1)
{
_name = name;
_dir = path;
_description = "NONE";
_amodel = double.NaN;
_GMmodel = double.NaN;
_zeta0 = 0;
_corrmult = 1;
_nmx = -1;
_mmx = -1;
_norm = Normalization.Full;
if (string.IsNullOrWhiteSpace(path))
{
_dir = DefaultGravityPath;
}
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 _name, ref _description, ref _date, ref _amodel, ref _GMmodel,
ref _zeta0, ref _corrmult, ref _norm, ref _id, ref _earth);
double[] _Cx, _Sx;
string coeff = _filename + ".cof";
using (var coeffstr = File.OpenRead(coeff))
{
Span <byte> id = stackalloc byte[idlength_];
if (coeffstr.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())}");
}
int N = 0, M = 0;
if (truncate)
{
N = Nmax; M = Mmax;
}
var scoeff = SphericalEngine.Coeff.FromStream(coeffstr, ref N, ref M, truncate);
_Cx = new double[scoeff.Cnm.Length];
_Sx = new double[scoeff.Snm.Length];
scoeff.Cnm.CopyTo(_Cx);
scoeff.Snm.CopyTo(_Sx);
if (!(N >= 0 && M >= 0))
{
throw new GeographicException("Degree and order must be at least 0");
}
if (_Cx[0] != 0)
{
throw new GeographicException("The degree 0 term should be zero");
}
_Cx[0] = 1; // Include the 1/r term in the sum
_gravitational = new SphericalHarmonic(_Cx, _Sx, N, N, M, _amodel, _norm);
if (truncate)
{
N = Nmax; M = Mmax;
}
scoeff = SphericalEngine.Coeff.FromStream(coeffstr, ref N, ref M, truncate);
double[] _CC, _CS;
if (N < 0)
{
N = M = 0;
_CC = new[] { 0d };
}
else
{
_CC = new double[scoeff.Cnm.Length];
scoeff.Cnm.CopyTo(_CC);
}
_CS = new double[scoeff.Snm.Length];
scoeff.Snm.CopyTo(_CS);
_CC[0] += _zeta0 / _corrmult;
_correction = new SphericalHarmonic(_CC, _CS, N, N, M, 1, _norm);
var pos = (int)coeffstr.Position;
coeffstr.Seek(0, SeekOrigin.End);
if (pos != coeffstr.Position)
{
throw new GeographicException("Extra data in " + coeff);
}
}
int nmx = _gravitational.Coefficients.Nmx;
_nmx = Max(nmx, _correction.Coefficients.Nmx);
_mmx = Max(_gravitational.Coefficients.Mmx,
_correction.Coefficients.Mmx);
// Adjust the normalization of the normal potential to match the model.
var mult = _earth._GM / _GMmodel;
var amult = Sq(_earth._a / _amodel);
// The 0th term in _zonal should be is 1 + _dzonal0. Instead set it to 1
// to give exact cancellation with the (0,0) term in the model and account
// for _dzonal0 separately.
var _zonal = new List <double> {
1
};
_dzonal0 = (_earth.MassConstant - _GMmodel) / _GMmodel;
for (int n = 2; n <= nmx; n += 2)
{
// Only include as many normal zonal terms as matter. Figuring the limit
// in this way works because the coefficients of the normal potential
// (which is smooth) decay much more rapidly that the corresponding
// coefficient of the model potential (which is bumpy). Typically this
// goes out to n = 18.
mult *= amult;
double
r = _Cx[n], // the model term
s = -mult *_earth.Jn(n) / Sqrt(2 * n + 1), // the normal term
t = r - s; // the difference
if (t == r) // the normal term is negligible
{
break;
}
_zonal.Add(0); // index = n - 1; the odd terms are 0
_zonal.Add(s);
}
int nmx1 = _zonal.Count - 1;
var za = _zonal.ToArray();
_disturbing = new SphericalHarmonic1(_Cx, _Sx,
_gravitational.Coefficients.N,
nmx, _gravitational.Coefficients.Mmx,
za,
za, // This is not accessed!
nmx1, nmx1, 0,
_amodel,
_norm);
}
private void OnValidate(object sender, EventArgs e)
{
try
{
const double DEG_TO_RAD = 3.1415926535897932384626433832795 / 180.0;
double gradx, grady, gradz;
SphericalHarmonic s0 = new SphericalHarmonic(C, S, N, N - 1, 0, a, SphericalHarmonic.Normalization.SCHMIDT);
s0 = new SphericalHarmonic(C, S, N, a, SphericalHarmonic.Normalization.SCHMIDT);
double sum = s0.HarmonicSum(1.0, 2.0, 3.0);
double test = s0.HarmonicSum(1.0, 2.0, 3.0, out gradx, out grady, out grady);
if (sum != test)
throw new Exception("Error in SphericalHarmonic.HarmonicSum");
SphericalCoefficients sc = s0.Coefficients();
CircularEngine ce = s0.Circle(1.0, 0.5, true);
sum = ce.LongitudeSum(60.0);
test = ce.LongitudeSum(Math.Cos(60.0 * DEG_TO_RAD), Math.Sin(60.0 * DEG_TO_RAD));
if ( sum != test )
throw new Exception("Error in CircularEngine.LongitudeSum 1");
test = ce.LongitudeSum(60.0, out gradx, out grady, out gradz);
if ( sum != test )
throw new Exception("Error in CircularEngine.LongitudeSum 2");
ce.LongitudeSum(Math.Cos(60.0 * DEG_TO_RAD), Math.Sin(60.0 * DEG_TO_RAD), out gradx, out grady, out gradz);
if (sum != test)
throw new Exception("Error in CircularEngine.LongitudeSum 3");
SphericalHarmonic1 s1 = new SphericalHarmonic1(C, S, N, N - 1, 1, C1, S1, N1, N1 - 1, 0, a, SphericalHarmonic1.Normalization.SCHMIDT);
s1 = new SphericalHarmonic1(C, S, N, C1, S1, N1, a, SphericalHarmonic1.Normalization.SCHMIDT);
sum = s1.HarmonicSum(0.95, 1.0, 2.0, 3.0);
test = s1.HarmonicSum(0.95, 1.0, 2.0, 3.0, out gradx, out grady, out gradz);
if (sum != test)
throw new Exception("Error in SphericalHarmonic1.HarmonicSum 3");
ce = s1.Circle(0.95, 1.0, 0.5, true);
sc = s1.Coefficients();
sc = s1.Coefficients1();
SphericalHarmonic2 s2 = new SphericalHarmonic2(C, S, N, N - 1, 2, C1, S1, N1, N1 - 1, 1,
C2, S2, N2, N2 - 1, 0, a, SphericalHarmonic2.Normalization.SCHMIDT);
s2 = new SphericalHarmonic2(C, S, N, C1, S1, N1, C2, S2, N2, a, SphericalHarmonic2.Normalization.SCHMIDT);
sum = s2.HarmonicSum(0.95, 0.8, 1.0, 2.0, 3.0);
test = s2.HarmonicSum(0.95, 0.8, 1.0, 2.0, 3.0, out gradx, out grady, out gradz);
if (sum != test)
throw new Exception("Error in SphericalHarmonic2.HarmonicSum 3");
ce = s2.Circle(0.95, 0.8, 1.0, 0.5, true);
sc = s2.Coefficients();
sc = s2.Coefficients1();
sc = s2.Coefficients2();
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
return;
}
MessageBox.Show("No errors found", "OK", MessageBoxButtons.OK, MessageBoxIcon.Information);
}
public static void spherical_harmonic_test()
//****************************************************************************80
//
// Purpose:
//
// SPHERICAL_HARMONIC_TEST tests SPHERICAL_HARMONIC.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 02 June 2007
//
// Author:
//
// John Burkardt
//
{
const int N_MAX = 20;
double[] c = new double[N_MAX + 1];
int l = 0;
int m = 0;
double phi = 0;
double[] s = new double[N_MAX + 1];
double theta = 0;
double yi = 0;
double yr = 0;
Console.WriteLine("");
Console.WriteLine("SPHERICAL_HARMONIC_TEST:");
Console.WriteLine(" SPHERICAL_HARMONIC evaluates spherical harmonic functions.");
Console.WriteLine("");
Console.WriteLine(
" N M THETA PHI YR YI");
Console.WriteLine("");
int n_data = 0;
for (;;)
{
Burkardt.Values.SphericalHarmonic.spherical_harmonic_values(ref n_data, ref l, ref m, ref theta,
ref phi, ref yr, ref yi);
if (n_data == 0)
{
break;
}
SphericalHarmonic.spherical_harmonic(l, m, theta, phi, ref c, ref s);
double yr2 = c[l];
double yi2 = s[l];
Console.WriteLine(" "
+ l.ToString(CultureInfo.InvariantCulture).PadLeft(8) + " "
+ m.ToString(CultureInfo.InvariantCulture).PadLeft(8) + " "
+ theta.ToString(CultureInfo.InvariantCulture).PadLeft(8) + " "
+ phi.ToString(CultureInfo.InvariantCulture).PadLeft(8) + " "
+ yr.ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ yi.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
Console.WriteLine(" "
+ " " + " "
+ " " + " "
+ " " + " "
+ " " + " "
+ yr2.ToString(CultureInfo.InvariantCulture).PadLeft(14) + " "
+ yi2.ToString(CultureInfo.InvariantCulture).PadLeft(14) + "");
}
}
