/**
* 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)
}