static int numit0_ = 20; // Newton iterations in Init
/**
* ructor with a single standard parallel.
*
* @param[in] a equatorial radius of ellipsoid (meters).
* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
* Negative \e f gives a prolate ellipsoid.
* @param[in] stdlat standard parallel (degrees), the circle of tangency.
* @param[in] k0 azimuthal scale on the standard parallel.
* @exception new GeographicException if \e a, (1 − \e f) \e a, or \e k0 is
* not positive.
* @exception new GeographicException if \e stdlat is not in [−90°,
* 90°].
**********************************************************************/
public AlbersEqualArea(double a, double f, double stdlat, double k0)
{
InitVars(a, f);
if (!(GeoMath.IsFinite(_a) && _a > 0))
{
throw new GeographicException("Equatorial radius is not positive");
}
if (!(GeoMath.IsFinite(_f) && _f < 1))
{
throw new GeographicException("Polar semi-axis is not positive");
}
if (!(GeoMath.IsFinite(k0) && k0 > 0))
{
throw new GeographicException("Scale is not positive");
}
if (!(Math.Abs(stdlat) <= 90))
{
throw new GeographicException("Standard latitude not in [-90d, 90d]");
}
double sphi, cphi;
GeoMath.Sincosd(stdlat, out sphi, out cphi);
Init(sphi, cphi, sphi, cphi, k0);
}
/**
* Set the azimuthal scale for the projection.
*
* @param[in] lat (degrees).
* @param[in] k azimuthal scale at latitude \e lat (default 1).
* @exception new GeographicException \e k is not positive.
* @exception new GeographicException if \e lat is not in (−90°,
* 90°).
*
* This allows a "latitude of conformality" to be specified.
**********************************************************************/
public void SetScale(double lat, double k = 1)
{
if (!(GeoMath.IsFinite(k) && k > 0))
{
throw new GeographicException("Scale is not positive");
}
if (!(Math.Abs(lat) < 90))
{
throw new GeographicException("Latitude for SetScale not in (-90d, 90d)");
}
double x, y, gamma, kold;
Forward(0, lat, 0, out x, out y, out gamma, out kold);
k /= kold;
_k0 *= k;
_k2 = GeoMath.Square(_k0);
}
/**
* ructor with two standard parallels.
*
* @param[in] a equatorial radius of ellipsoid (meters).
* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
* Negative \e f gives a prolate ellipsoid.
* @param[in] stdlat1 first standard parallel (degrees).
* @param[in] stdlat2 second standard parallel (degrees).
* @param[in] k1 azimuthal scale on the standard parallels.
* @exception new GeographicException if \e a, (1 − \e f) \e a, or \e k1 is
* not positive.
* @exception new GeographicException if \e stdlat1 or \e stdlat2 is not in
* [−90°, 90°], or if \e stdlat1 and \e stdlat2 are
* opposite poles.
**********************************************************************/
public AlbersEqualArea(double a, double f, double stdlat1, double stdlat2, double k1)
{
InitVars(a, f);
eps_ = GeoMath.Epsilon;
epsx_ = GeoMath.Square(eps_);
epsx2_ = GeoMath.Square(epsx_);
tol_ = GeoMath.Square(eps_);
tol0_ = (tol_ * GeoMath.Square(GeoMath.Square(eps_)));
_a = a;
_f = f;
_fm = 1 - _f;
_e2 = _f * (2 - _f);
_e = GeoMath.Square(Math.Abs(_e2));
_e2m = 1 - _e2;
_qZ = 1 + _e2m * atanhee(1);
_qx = _qZ / (2 * _e2m);
if (!(GeoMath.IsFinite(_a) && _a > 0))
{
throw new GeographicException("Equatorial radius is not positive");
}
if (!(GeoMath.IsFinite(_f) && _f < 1))
{
throw new GeographicException("Polar semi-axis is not positive");
}
if (!(GeoMath.IsFinite(k1) && k1 > 0))
{
throw new GeographicException("Scale is not positive");
}
if (!(Math.Abs(stdlat1) <= 90))
{
throw new GeographicException("Standard latitude 1 not in [-90d, 90d]");
}
if (!(Math.Abs(stdlat2) <= 90))
{
throw new GeographicException("Standard latitude 2 not in [-90d, 90d]");
}
double sphi1, cphi1, sphi2, cphi2;
GeoMath.Sincosd(stdlat1, out sphi1, out cphi1);
GeoMath.Sincosd(stdlat2, out sphi2, out cphi2);
Init(sphi1, cphi1, sphi2, cphi2, k1);
}
/**
* Constructor for a ellipsoid with
*
* @param[in] a equatorial radius (meters).
* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
* Negative \e f gives a prolate ellipsoid.
* @exception GeographicErr if \e a or (1 − \e f) \e a is not
* positive.
**********************************************************************/
public Geocentric(double a, double f)
{
_a = a;
_f = f;
_e2 = _f * (2 - _f);
_e2m = GeoMath.Square(1 - _f);
_e2a = Math.Abs(_e2);
_e4a = GeoMath.Square(_e2);
_maxrad = 2 * _a / GeoMath.Epsilon;
if (!(GeoMath.IsFinite(_a) && _a > 0))
{
throw new GeographicException("Equatorial radius is not positive");
}
if (!(GeoMath.IsFinite(_f) && _f < 1))
{
throw new GeographicException("Polar semi-axis is not positive");
}
}
/**
* ructor with two standard parallels specified by sines and cosines.
*
* @param[in] a equatorial radius of ellipsoid (meters).
* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
* Negative \e f gives a prolate ellipsoid.
* @param[in] sinlat1 sine of first standard parallel.
* @param[in] coslat1 cosine of first standard parallel.
* @param[in] sinlat2 sine of second standard parallel.
* @param[in] coslat2 cosine of second standard parallel.
* @param[in] k1 azimuthal scale on the standard parallels.
* @exception new GeographicException if \e a, (1 − \e f) \e a, or \e k1 is
* not positive.
* @exception new GeographicException if \e stdlat1 or \e stdlat2 is not in
* [−90°, 90°], or if \e stdlat1 and \e stdlat2 are
* opposite poles.
*
* This allows parallels close to the poles to be specified accurately.
* This routine computes the latitude of origin and the azimuthal scale at
* this latitude. If \e dlat = abs(\e lat2 − \e lat1) ≤ 160°,
* then the error in the latitude of origin is less than 4.5 ×
* 10<sup>−14</sup>d;.
**********************************************************************/
public AlbersEqualArea(double a, double f,
double sinlat1, double coslat1,
double sinlat2, double coslat2,
double k1)
{
InitVars(a, f);
if (!(GeoMath.IsFinite(_a) && _a > 0))
{
throw new GeographicException("Equatorial radius is not positive");
}
if (!(GeoMath.IsFinite(_f) && _f < 1))
{
throw new GeographicException("Polar semi-axis is not positive");
}
if (!(GeoMath.IsFinite(k1) && k1 > 0))
{
throw new GeographicException("Scale is not positive");
}
if (!(coslat1 >= 0))
{
throw new GeographicException("Standard latitude 1 not in [-90d, 90d]");
}
if (!(coslat2 >= 0))
{
throw new GeographicException("Standard latitude 2 not in [-90d, 90d]");
}
if (!(Math.Abs(sinlat1) <= 1 && coslat1 <= 1) || (coslat1 == 0 && sinlat1 == 0))
{
throw new GeographicException("Bad sine/cosine of standard latitude 1");
}
if (!(Math.Abs(sinlat2) <= 1 && coslat2 <= 1) || (coslat2 == 0 && sinlat2 == 0))
{
throw new GeographicException("Bad sine/cosine of standard latitude 2");
}
if (coslat1 == 0 && coslat2 == 0 && sinlat1 * sinlat2 <= 0)
{
throw new GeographicException
("Standard latitudes cannot be opposite poles");
}
Init(sinlat1, coslat1, sinlat2, coslat2, k1);
}
/**
* Constructor for a ellipsoid with
*
* @param[in] a equatorial radius (meters).
* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
* Negative \e f gives a prolate ellipsoid.
* @param[in] k0 central scale factor.
* @exception GeographicErr if \e a, (1 − \e f) \e a, or \e k0 is
* not positive.
**********************************************************************/
public TransverseMercator(double a, double f, double k0)
{
_a = a;
_f = f;
_k0 = k0;
_e2 = _f * (2 - _f);
_es = (f < 0 ? -1 : 1) * Math.Sqrt(Math.Abs(_e2));
_e2m = 1 - _e2;
// _c = Math.Sqrt( pow(1 + _e, 1 + _e) * pow(1 - _e, 1 - _e) ) )
// See, for example, Lee (1976), p 100.
_c = Math.Sqrt(_e2m) * Math.Exp(GeoMath.Eatanhe(1, _es));
_n = _f / (2 - _f);
if (!(GeoMath.IsFinite(_a) && _a > 0))
{
throw new GeographicException("Equatorial radius is not positive");
}
if (!(GeoMath.IsFinite(_f) && _f < 1))
{
throw new GeographicException("Polar semi-axis is not positive");
}
if (!(GeoMath.IsFinite(_k0) && _k0 > 0))
{
throw new GeographicException("Scale is not positive");
}
double[] b1coeff =
{
// b1*(n+1), polynomial in n2 of order 3
1, 4, 64, 256, 256,
};
double[] alpcoeff =
{
// alp[1]/n^1, polynomial in n of order 5
31564, -66675, 34440, 47250, -100800, 75600, 151200,
// alp[2]/n^2, polynomial in n of order 4
-1983433, 863232, 748608, -1161216, 524160, 1935360,
// alp[3]/n^3, polynomial in n of order 3
670412, 406647, -533952, 184464, 725760,
// alp[4]/n^4, polynomial in n of order 2
6601661, -7732800, 2230245, 7257600,
// alp[5]/n^5, polynomial in n of order 1
-13675556, 3438171, 7983360,
// alp[6]/n^6, polynomial in n of order 0
212378941, 319334400,
}; // count = 27
double[] betcoeff =
{
// bet[1]/n^1, polynomial in n of order 5
384796, -382725, -6720, 932400, -1612800, 1209600, 2419200,
// bet[2]/n^2, polynomial in n of order 4
-1118711, 1695744, -1174656, 258048, 80640, 3870720,
// bet[3]/n^3, polynomial in n of order 3
22276, -16929, -15984, 12852, 362880,
// bet[4]/n^4, polynomial in n of order 2
-830251, -158400, 197865, 7257600,
// bet[5]/n^5, polynomial in n of order 1
-435388, 453717, 15966720,
// bet[6]/n^6, polynomial in n of order 0
20648693, 638668800,
}; // count = 27
int m = maxpow_ / 2;
_b1 = GeoMath.PolyVal(m, b1coeff, 0, GeoMath.Square(_n)) / (b1coeff[m + 1] * (1 + _n));
// _a1 is the equivalent radius for computing the circumference of
// ellipse.
_a1 = _b1 * _a;
int o = 0;
double d = _n;
for (int l = 1; l <= maxpow_; ++l)
{
m = maxpow_ - l;
_alp[l] = d * GeoMath.PolyVal(m, alpcoeff, o, _n) / alpcoeff[o + m + 1];
_bet[l] = d * GeoMath.PolyVal(m, betcoeff, o, _n) / betcoeff[o + m + 1];
o += m + 2;
d *= _n;
}
// Post condition: o == sizeof(alpcoeff) / sizeof(double) &&
// o == sizeof(betcoeff) / sizeof(double)
}