static void Main(string[] args)
{
try {
EllipticFunction ell = new EllipticFunction(0.1, 1.0); // parameter m = 0.1
// See Abramowitz and Stegun, table 17.1
Console.WriteLine( String.Format( "{0} {1}", ell.K(), ell.E()));
double phi = 20 * Math.Acos(-1.0) / 180.0;;
// See Abramowitz and Stegun, table 17.6 with
// alpha = asin(sqrt(m)) = 18.43 deg and phi = 20 deg
Console.WriteLine( String.Format("{0} {1}", ell.E(phi),
ell.E(Math.Sin(phi), Math.Cos(phi),
Math.Sqrt(1 - ell.k2 * Math.Sin(phi) * Math.Sin(phi))) ) );
// See Carlson 1995, Sec 3.
Console.WriteLine(String.Format("RF(1,2,0) = {0}", EllipticFunction.RF(1,2)));
Console.WriteLine(String.Format("RF(2,3,4) = {0}", EllipticFunction.RF(2,3,4)));
Console.WriteLine(String.Format("RC(0,1/4) = {0}", EllipticFunction.RC(0,0.25)));
Console.WriteLine(String.Format("RC(9/4,2) = {0}", EllipticFunction.RC(2.25,2)));
Console.WriteLine(String.Format("RC(1/4,-2) = {0}", EllipticFunction.RC(0.25,-2)));
Console.WriteLine(String.Format("RJ(0,1,2,3) = {0}", EllipticFunction.RJ(0,1,2,3)));
Console.WriteLine(String.Format("RJ(2,3,4,5) = {0}", EllipticFunction.RJ(2,3,4,5)));
Console.WriteLine(String.Format("RD(0,2,1) = {0}", EllipticFunction.RD(0,2,1)));
Console.WriteLine(String.Format("RD(2,3,4) = {0}", EllipticFunction.RD(2,3,4)));
Console.WriteLine(String.Format("RG(0,16,16) = {0}", EllipticFunction.RG(16,16)));
Console.WriteLine(String.Format("RG(2,3,4) = {0}", EllipticFunction.RG(2,3,4)));
Console.WriteLine(String.Format("RG(0,0.0796,4) = {0}", EllipticFunction.RG(0.0796, 4)));
}
catch (GeographicErr e) {
Console.WriteLine( String.Format( "Caught exception: {0}", e.Message ) );
}
}
/// <summary>
/// Initialize a new <see cref="TransverseMercatorExact"/> instance with specified equatorial radius, flattening and central scale factor.
/// </summary>
/// <param name="a">equatorial radius (meters).</param>
/// <param name="f">flattening of ellipsoid.</param>
/// <param name="k0">central scale factor.</param>
/// <param name="extendp">use extended domain.</param>
/// <remarks>
/// <para>
/// The transverse Mercator projection has a branch point singularity at <i>lat</i> = 0 and <i>lon</i> − <i>lon0</i> = 90 (1 − <i>e</i>)
/// or (for <see cref="UTM"/>) <i>x</i> = 18381 km, <i>y</i> = 0m. The <paramref name="extendp"/> argument governs where the branch cut is placed.
/// With <paramref name="extendp"/> = <see langword="false"/>, the "standard" convention is followed, namely the cut is placed along
/// <i>x</i> > 18381 km, <i>y</i> = 0m.
/// <see cref="Forward(double, double, double)"/> can be called with any <i>lat</i> and <i>lon</i> then produces the transformation shown
/// in Lee, Fig 46.
/// <see cref="Reverse(double, double, double)"/> analytically continues this in the ± <i>x</i> direction.
/// As a consequence, Reverse may map multiple points to the same geographic location; for example, for <see cref="UTM"/>,
/// <i>x</i> = 22051449.037349 m, <i>y</i> = −7131237.022729 m and <i>x</i> = 29735142.378357 m, <i>y</i> = 4235043.607933 m both map to
/// <i>lat</i> = −2°, <i>lon</i> = 88°.
/// </para>
/// <para>
/// With <paramref name="extendp"/> = <see langword="true"/>, the branch cut is moved to the lower left quadrant.
/// The various symmetries of the transverse Mercator projection can be used to explore the projection on any sheet.
/// In this mode the domains of <i>lat</i>, <i>lon</i>, <i>x</i>, and <i>y</i> are restricted to
/// <list type="bullet">
/// <item>
/// the union of
/// <list type="bullet">
/// <item><i>lat</i> in [0, 90] and <i>lon</i> − <i>lon0</i> in [0, 90]</item>
/// <item><i>lat</i> in (-90, 0] and <i>lon</i> − <i>lon0</i> in [90 (1 − e), 90]</item>
/// </list>
/// </item>
/// <item>
/// the union of
/// <list type="bullet">
/// <item><i>x</i>/(<i>k0</i> <i>a</i>) in [0, ∞) and <i>y</i>/(<i>k0</i> <i>a</i>) in [0, E(e2)]</item>
/// <item><i>x</i>/(<i>k0</i> <i>a</i>) in [K(1 − <i>e</i>^2) − E(1 − <i>e</i>^2), ∞) and <i>y</i>/(<i>k0</i> <i>a</i>) in (−∞, 0]</item>
/// </list>
/// </item>
/// </list>
/// See Sec. 5 of <a href="https://arxiv.org/abs/1002.1417">arXiv:1002.1417</a> for a full discussion of the treatment of the branch cut.
/// </para>
/// <para>
/// The method will work for all ellipsoids used in terrestrial geodesy.
/// The method cannot be applied directly to the case of a sphere (<i>f</i> = 0) because some the constants characterizing this method diverge in
/// that limit, and in practice, <i>f</i> should be larger than about <see cref="DBL_EPSILON"/>.
/// However, <see cref="TransverseMercator"/> treats the sphere exactly.
/// </para>
/// </remarks>
public TransverseMercatorExact(double a, double f, double k0, bool extendp = false)
{
_a = a;
_f = f;
_k0 = k0;
_mu = _f * (2 - _f);
_mv = 1 - _mu;
_e = Sqrt(_mu);
_extendp = extendp;
_Eu = new EllipticFunction(_mu);
_Ev = new EllipticFunction(_mv);
if (!(IsFinite(_a) && _a > 0))
{
throw new GeographicException("Equatorial radius is not positive");
}
if (!(_f > 0))
{
throw new GeographicException("Flattening is not positive");
}
if (!(_f < 1))
{
throw new GeographicException("Polar semi-axis is not positive");
}
if (!(IsFinite(_k0) && _k0 > 0))
{
throw new GeographicException("Scale is not positive");
}
}
private void OnSet(object sender, EventArgs e)
{
try
{
double k2 = Double.Parse(m_k2TextBox.Text);
double alpha2 = Double.Parse(m_alpha2TextBox.Text);
if (m_constructorComboBox.SelectedIndex == 0)
{
m_func = new EllipticFunction(k2, alpha2);
}
else
{
double kp2 = Double.Parse(m_kp2TextBox.Text);
double alphap2 = Double.Parse(m_alphap2TextBox.Text);
m_func = new EllipticFunction(k2, alpha2, kp2, alphap2);
}
m_KtextBox.Text = m_func.K().ToString();
m_EtextBox.Text = m_func.E().ToString();
m_DtextBox.Text = m_func.D().ToString();
m_KEtextBox.Text = m_func.KE().ToString();
m_PItextBox.Text = m_func.Pi().ToString();
m_GtextBox.Text = m_func.G().ToString();
m_HtextBox.Text = m_func.H().ToString();
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
}
static void Main(string[] args)
{
try {
EllipticFunction ell = new EllipticFunction(0.1, 1.0); // parameter m = 0.1
// See Abramowitz and Stegun, table 17.1
Console.WriteLine(String.Format("{0} {1}", ell.K(), ell.E()));
double phi = 20 * Math.Acos(-1.0) / 180.0;;
// See Abramowitz and Stegun, table 17.6 with
// alpha = asin(sqrt(m)) = 18.43 deg and phi = 20 deg
Console.WriteLine(String.Format("{0} {1}", ell.E(phi),
ell.E(Math.Sin(phi), Math.Cos(phi),
Math.Sqrt(1 - ell.k2 * Math.Sin(phi) * Math.Sin(phi)))));
// See Carlson 1995, Sec 3.
Console.WriteLine(String.Format("RF(1,2,0) = {0}", EllipticFunction.RF(1, 2)));
Console.WriteLine(String.Format("RF(2,3,4) = {0}", EllipticFunction.RF(2, 3, 4)));
Console.WriteLine(String.Format("RC(0,1/4) = {0}", EllipticFunction.RC(0, 0.25)));
Console.WriteLine(String.Format("RC(9/4,2) = {0}", EllipticFunction.RC(2.25, 2)));
Console.WriteLine(String.Format("RC(1/4,-2) = {0}", EllipticFunction.RC(0.25, -2)));
Console.WriteLine(String.Format("RJ(0,1,2,3) = {0}", EllipticFunction.RJ(0, 1, 2, 3)));
Console.WriteLine(String.Format("RJ(2,3,4,5) = {0}", EllipticFunction.RJ(2, 3, 4, 5)));
Console.WriteLine(String.Format("RD(0,2,1) = {0}", EllipticFunction.RD(0, 2, 1)));
Console.WriteLine(String.Format("RD(2,3,4) = {0}", EllipticFunction.RD(2, 3, 4)));
Console.WriteLine(String.Format("RG(0,16,16) = {0}", EllipticFunction.RG(16, 16)));
Console.WriteLine(String.Format("RG(2,3,4) = {0}", EllipticFunction.RG(2, 3, 4)));
Console.WriteLine(String.Format("RG(0,0.0796,4) = {0}", EllipticFunction.RG(0.0796, 4)));
}
catch (GeographicErr e) {
Console.WriteLine(String.Format("Caught exception: {0}", e.Message));
}
}
private void OnSet(object sender, EventArgs e)
{
try
{
double k2 = Double.Parse(m_k2TextBox.Text);
double alpha2 = Double.Parse(m_alpha2TextBox.Text);
if (m_constructorComboBox.SelectedIndex == 0)
m_func = new EllipticFunction(k2, alpha2);
else
{
double kp2 = Double.Parse(m_kp2TextBox.Text);
double alphap2 = Double.Parse(m_alphap2TextBox.Text);
m_func = new EllipticFunction(k2, alpha2, kp2, alphap2);
}
m_KtextBox.Text = m_func.K().ToString();
m_EtextBox.Text = m_func.E().ToString();
m_DtextBox.Text = m_func.D().ToString();
m_KEtextBox.Text = m_func.KE().ToString();
m_PItextBox.Text = m_func.Pi().ToString();
m_GtextBox.Text = m_func.G().ToString();
m_HtextBox.Text = m_func.H().ToString();
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
}
private void OnValidate(object sender, EventArgs e)
{
try
{
double phi = 0.8;
EllipticFunction f = new EllipticFunction(0.3, 0.4, 0.7, 0.6);
f.Reset(0.2, 0.3, 0.8, 0.7);
f = new EllipticFunction(0.3, 0.4);
f.Reset(0.2, 0.3);
double cn, sn, dn;
f.sncndn(0.3, out sn, out cn, out dn);
f.Delta(sn, cn);
f.D();
f.D(phi);
f.D(sn, cn, dn);
f.Pi();
f.Pi(phi);
f.Pi(sn, cn, dn);
f.KE();
f.K();
f.H();
f.H(phi);
f.H(sn, cn, dn);
f.G();
f.G(phi);
f.G(sn, cn, dn);
f.F(phi);
f.F(sn, cn, dn);
f.Einv(0.75);
f.Ed(60.0);
f.E();
f.E(phi);
f.E(sn, cn, dn);
double tau = 3.1415927 / 10.0;
f.deltaEinv(Math.Sin(tau), Math.Cos(tau));
f.deltaD(sn, cn, dn);
f.deltaE(sn, cn, dn);
f.deltaF(sn, cn, dn);
f.deltaG(sn, cn, dn);
f.deltaH(sn, cn, dn);
f.deltaPi(sn, cn, dn);
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
MessageBox.Show("No errors detected", "OK", MessageBoxButtons.OK, MessageBoxIcon.Information);
}
private void OnValidate(object sender, EventArgs e)
{
try
{
double phi = 0.8;
EllipticFunction f = new EllipticFunction(0.3, 0.4, 0.7, 0.6);
f.Reset(0.2, 0.3, 0.8, 0.7);
f = new EllipticFunction(0.3, 0.4);
f.Reset(0.2, 0.3);
double cn, sn, dn;
f.sncndn(0.3, out sn, out cn, out dn);
f.Delta(sn, cn);
f.D();
f.D(phi);
f.D(sn, cn, dn);
f.Pi();
f.Pi(phi);
f.Pi(sn, cn, dn);
f.KE();
f.K();
f.H();
f.H(phi);
f.H(sn, cn, dn);
f.G();
f.G(phi);
f.G(sn, cn, dn);
f.F(phi);
f.F(sn, cn, dn);
f.Einv(0.75);
f.Ed(60.0);
f.E();
f.E(phi);
f.E(sn, cn, dn);
double tau = 3.1415927 / 10.0;
f.deltaEinv(Math.Sin(tau), Math.Cos(tau));
f.deltaD(sn, cn, dn);
f.deltaE(sn, cn, dn);
f.deltaF(sn, cn, dn);
f.deltaG(sn, cn, dn);
f.deltaH(sn, cn, dn);
f.deltaPi(sn, cn, dn);
}
catch (Exception xcpt)
{
MessageBox.Show(xcpt.Message, "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
}
MessageBox.Show("No errors detected", "OK", MessageBoxButtons.OK, MessageBoxIcon.Information);
}
