/* Initiallize the TM structure */
static void TMProj(ref TMProjection tm, double a, double rf, double cm, double sf, double lto, double fe, double fn, double utom)
{
tm = new TMProjection();
double f;
tm.meridian = cm;
tm.scalef = sf;
tm.orglat = lto;
tm.falsee = fe;
tm.falsen = fn;
tm.utom = utom;
if (rf != 0.0)
{
f = 1.0 / rf;
}
else
{
f = 0.0;
}
tm.a = a;
tm.rf = rf;
tm.f = f;
tm.e2 = (2.0 * f) - (f * f);
tm.ep2 = tm.e2 / (1.0 - tm.e2);
tm.om = meridian_arc(tm, tm.orglat);
}
/*************************************************************************/
/* */
/* foot_point_lat */
/* */
/* Calculates the foot point latitude from the meridional arc */
/* Method based on Redfearn's formulation as expressed in GDA technical*/
/* manual at http://www.anzlic.org.au/icsm/gdatm/index.html */
/* */
/* Takes parameters */
/* tm definition (for scale factor) */
/* meridional arc (metres) */
/* */
/* Returns the foot point latitude (radians) */
/* */
/*************************************************************************/
static double foot_point_lat(TMProjection tm, double m)
{
double f = tm.f;
double a = tm.a;
double n;
double n2;
double n3;
double n4;
double g;
double sig;
double phio;
n = f / (2.0 - f);
n2 = n * n;
n3 = n2 * n;
n4 = n2 * n2;
g = a * (1.0 - n) * (1.0 - n2) * (1 + 9.0 * n2 / 4.0 + 225.0 * n4 / 64.0);
sig = m / g;
phio = sig + (3.0 * n / 2.0 - 27.0 * n3 / 32.0) * Math.Sin(2.0 * sig)
+ (21.0 * n2 / 16.0 - 55.0 * n4 / 32.0) * Math.Sin(4.0 * sig)
+ (151.0 * n3 / 96.0) * Math.Sin(6.0 * sig)
+ (1097.0 * n4 / 512.0) * Math.Sin(8.0 * sig);
return(phio);
}
/// <summary>
/// Calculates the foot point latitude from the meridional arc
/// Method based on Redfearn's formulation as expressed in GDA technical
/// manual at http://www.anzlic.org.au/icsm/gdatm/index.html
/// </summary>
private static double FootPointLatitude(TMProjection projection, double meridianArc)
{
var f = projection.EllipsoidParams.F;
var a = projection.EllipsoidParams.A;
double n;
double n2;
double n3;
double n4;
double g;
double sig;
double phio;
n = f / (2.0 - f);
n2 = n * n;
n3 = n2 * n;
n4 = n2 * n2;
g = a * (1.0 - n) * (1.0 - n2) * (1 + 9.0 * n2 / 4.0 + 225.0 * n4 / 64.0);
sig = meridianArc / g;
phio = sig + (3.0 * n / 2.0 - 27.0 * n3 / 32.0) * Sin(2.0 * sig)
+ (21.0 * n2 / 16.0 - 55.0 * n4 / 32.0) * Sin(4.0 * sig)
+ (151.0 * n3 / 96.0) * Sin(6.0 * sig)
+ (1097.0 * n4 / 512.0) * Sin(8.0 * sig);
return(phio);
}
static TMProjection Get_NZTM_Projection()
{
if (!initiallized)
{
projection = new TMProjection();
TMProj(ref projection, NZTM_A, NZTM_RF, MathFunc.Deg2Rad(NZTM_CM), NZTM_SF, MathFunc.Deg2Rad(NZTM_OLAT), NZTM_FE, NZTM_FN, 1.0);
initiallized = true;
}
return(projection);
}
/***************************************************************************/
/* */
/* meridian_arc */
/* */
/* Returns the length of meridional arc (Helmert formula) */
/* Method based on Redfearn's formulation as expressed in GDA technical */
/* manual at http://www.anzlic.org.au/icsm/gdatm/index.html */
/* */
/* Parameters are */
/* projection */
/* latitude (radians) */
/* */
/* Return value is the arc length in metres */
/* */
/***************************************************************************/
public static double meridian_arc(TMProjection tm, double lt)
{
double e2 = tm.e2;
double a = tm.a;
double e4;
double e6;
double A0;
double A2;
double A4;
double A6;
e4 = e2 * e2;
e6 = e4 * e2;
A0 = 1 - (e2 / 4.0) - (3.0 * e4 / 64.0) - (5.0 * e6 / 256.0);
A2 = (3.0 / 8.0) * (e2 + e4 / 4.0 + 15.0 * e6 / 128.0);
A4 = (15.0 / 256.0) * (e4 + 3.0 * e6 / 4.0);
A6 = 35.0 * e6 / 3072.0;
return(a * (A0 * lt - A2 * Math.Sin(2 * lt) + A4 * Math.Sin(4 * lt) - A6 * Math.Sin(6 * lt)));
}
/// <summary>
/// Returns the length of meridional arc (Helmert formula)
/// Method based on Redfearn's formulation as expressed in GDA technical
/// manual at http://www.anzlic.org.au/icsm/gdatm/index.html
/// </summary>
private static double MeridianArc(TMProjection projection, double latitudeRad)
{
var e2 = projection.EllipsoidParams.E2;
var a = projection.EllipsoidParams.A;
var lt = latitudeRad;
double e4;
double e6;
double A0;
double A2;
double A4;
double A6;
e4 = e2 * e2;
e6 = e4 * e2;
A0 = 1 - (e2 / 4.0) - (3.0 * e4 / 64.0) - (5.0 * e6 / 256.0);
A2 = (3.0 / 8.0) * (e2 + e4 / 4.0 + 15.0 * e6 / 128.0);
A4 = (15.0 / 256.0) * (e4 + 3.0 * e6 / 4.0);
A6 = 35.0 * e6 / 3072.0;
return(a * (A0 * lt - A2 * Sin(2 * lt) + A4 * Sin(4 * lt) - A6 * Sin(6 * lt)));
}
public static void geod_nztm(double lt, double ln, ref double n, ref double e)
{
TMProjection nztm = Get_NZTM_Projection();
geod_tm(nztm, ln, lt, ref e, ref n);
}
/* Functions implementation the TM projection specifically for the
* NZTM coordinate system
*/
public static void nztm_geod(double n, double e, ref double lt, ref double ln)
{
TMProjection nztm = Get_NZTM_Projection();
tm_geod(nztm, e, n, ref ln, ref lt);
}
/***************************************************************************/
/* */
/* geodtm */
/* */
/* Routine to convert from latitude and longitude to Transverse Mercator.*/
/* Method based on Redfearn's formulation as expressed in GDA technical */
/* manual at http://www.anzlic.org.au/icsm/gdatm/index.html */
/* Loosely based on FORTRAN source code by J.Hannah and A.Broadhurst. */
/* */
/* Takes parameters */
/* input latitude (radians) */
/* input longitude (radians) */
/* output easting (metres) */
/* output northing (metres) */
/* */
/***************************************************************************/
static void geod_tm(TMProjection tm,
double ln, double lt, ref double ce, ref double cn)
{
double fn = tm.falsen;
double fe = tm.falsee;
double sf = tm.scalef;
double e2 = tm.e2;
double a = tm.a;
double cm = tm.meridian;
double om = tm.om;
double utom = tm.utom;
double dlon;
double m;
double slt;
double eslt;
double eta;
double rho;
double psi;
double clt;
double w;
double wc;
double wc2;
double t;
double t2;
double t4;
double t6;
double trm1;
double trm2;
double trm3;
double gce;
double trm4;
double gcn;
dlon = ln - cm;
while (dlon > Math.PI)
{
dlon -= TWOPI;
}
while (dlon < -Math.PI)
{
dlon += TWOPI;
}
m = meridian_arc(tm, lt);
slt = Math.Sin(lt);
eslt = (1.0 - e2 * slt * slt);
eta = a / Math.Sqrt(eslt);
rho = eta * (1.0 - e2) / eslt;
psi = eta / rho;
clt = Math.Cos(lt);
w = dlon;
wc = clt * w;
wc2 = wc * wc;
t = slt / clt;
t2 = t * t;
t4 = t2 * t2;
t6 = t2 * t4;
trm1 = (psi - t2) / 6.0;
trm2 = (((4.0 * (1.0 - 6.0 * t2) * psi
+ (1.0 + 8.0 * t2)) * psi
- 2.0 * t2) * psi + t4) / 120.0;
trm3 = (61 - 479.0 * t2 + 179.0 * t4 - t6) / 5040.0;
gce = (sf * eta * dlon * clt) * (((trm3 * wc2 + trm2) * wc2 + trm1) * wc2 + 1.0);
ce = gce / utom + fe;
trm1 = 1.0 / 2.0;
trm2 = ((4.0 * psi + 1) * psi - t2) / 24.0;
trm3 = ((((8.0 * (11.0 - 24.0 * t2) * psi
- 28.0 * (1.0 - 6.0 * t2)) * psi
+ (1.0 - 32.0 * t2)) * psi
- 2.0 * t2) * psi
+ t4) / 720.0;
trm4 = (1385.0 - 3111.0 * t2 + 543.0 * t4 - t6) / 40320.0;
gcn = (eta * t) * ((((trm4 * wc2 + trm3) * wc2 + trm2) * wc2 + trm1) * wc2);
cn = (gcn + m - om) * sf / utom + fn;
return;
}
/***************************************************************************/
/* */
/* tmgeod */
/* */
/* Routine to convert from Tranverse Mercator to latitude and longitude. */
/* Method based on Redfearn's formulation as expressed in GDA technical */
/* manual at http://www.anzlic.org.au/icsm/gdatm/index.html */
/* */
/* Takes parameters */
/* input easting (metres) */
/* input northing (metres) */
/* output latitude (radians) */
/* output longitude (radians) */
/* */
/***************************************************************************/
static void tm_geod(TMProjection tm,
double ce, double cn, ref double ln, ref double lt)
{
double fn = tm.falsen;
double fe = tm.falsee;
double sf = tm.scalef;
double e2 = tm.e2;
double a = tm.a;
double cm = tm.meridian;
double om = tm.om;
double utom = tm.utom;
double cn1;
double fphi;
double slt;
double clt;
double eslt;
double eta;
double rho;
double psi;
double E;
double x;
double x2;
double t;
double t2;
double t4;
double trm1;
double trm2;
double trm3;
double trm4;
cn1 = (cn - fn) * utom / sf + om;
fphi = foot_point_lat(tm, cn1);
slt = Math.Sin(fphi);
clt = Math.Cos(fphi);
eslt = (1.0 - e2 * slt * slt);
eta = a / Math.Sqrt(eslt);
rho = eta * (1.0 - e2) / eslt;
psi = eta / rho;
E = (ce - fe) * utom;
x = E / (eta * sf);
x2 = x * x;
t = slt / clt;
t2 = t * t;
t4 = t2 * t2;
trm1 = 1.0 / 2.0;
trm2 = ((-4.0 * psi
+ 9.0 * (1 - t2)) * psi
+ 12.0 * t2) / 24.0;
trm3 = ((((8.0 * (11.0 - 24.0 * t2) * psi
- 12.0 * (21.0 - 71.0 * t2)) * psi
+ 15.0 * ((15.0 * t2 - 98.0) * t2 + 15)) * psi
+ 180.0 * ((-3.0 * t2 + 5.0) * t2)) * psi + 360.0 * t4) / 720.0;
trm4 = (((1575.0 * t2 + 4095.0) * t2 + 3633.0) * t2 + 1385.0) / 40320.0;
lt = fphi + (t * x * E / (sf * rho)) * (((trm4 * x2 - trm3) * x2 + trm2) * x2 - trm1);
trm1 = 1.0;
trm2 = (psi + 2.0 * t2) / 6.0;
trm3 = (((-4.0 * (1.0 - 6.0 * t2) * psi
+ (9.0 - 68.0 * t2)) * psi
+ 72.0 * t2) * psi
+ 24.0 * t4) / 120.0;
trm4 = (((720.0 * t2 + 1320.0) * t2 + 662.0) * t2 + 61.0) / 5040.0;
ln = cm - (x / clt) * (((trm4 * x2 - trm3) * x2 + trm2) * x2 - trm1);
}
/// <summary>
/// Routine to convert from latitude and longitude to Transverse Mercator.
/// Method based on Redfearn's formulation as expressed in GDA technical
/// manual at http://www.anzlic.org.au/icsm/gdatm/index.html
/// Loosely based on FORTRAN source code by J.Hannah and A.Broadhurst.
/// </summary>
private static void LatLongToTransverseMercator(TMProjection projection, double latitudeRad, double longitudeRad, out double easting, out double northing)
{
var fn = projection.FalseNorthing;
var fe = projection.FalseEasting;
var sf = projection.ScaleFactor;
var e2 = projection.EllipsoidParams.E2;
var a = projection.EllipsoidParams.A;
var cm = projection.CentralMeridian;
var om = projection.IntermediateCalculation;
var utom = projection.UnitToMetreConversion;
double dlon;
double m;
double slt;
double eslt;
double eta;
double rho;
double psi;
double clt;
double w;
double wc;
double wc2;
double t;
double t2;
double t4;
double t6;
double trm1;
double trm2;
double trm3;
double gce;
double trm4;
double gcn;
dlon = longitudeRad - cm;
while (dlon > PI)
{
dlon -= (PI * 2);
}
while (dlon < -PI)
{
dlon += (PI * 2);
}
m = MeridianArc(projection, latitudeRad);
slt = Sin(latitudeRad);
eslt = (1.0 - e2 * slt * slt);
eta = a / Sqrt(eslt);
rho = eta * (1.0 - e2) / eslt;
psi = eta / rho;
clt = Cos(latitudeRad);
w = dlon;
wc = clt * w;
wc2 = wc * wc;
t = slt / clt;
t2 = t * t;
t4 = t2 * t2;
t6 = t2 * t4;
trm1 = (psi - t2) / 6.0;
trm2 = (((4.0 * (1.0 - 6.0 * t2) * psi
+ (1.0 + 8.0 * t2)) * psi
- 2.0 * t2) * psi + t4) / 120.0;
trm3 = (61 - 479.0 * t2 + 179.0 * t4 - t6) / 5040.0;
gce = (sf * eta * dlon * clt) * (((trm3 * wc2 + trm2) * wc2 + trm1) * wc2 + 1.0);
// out
easting = gce / utom + fe;
trm1 = 1.0 / 2.0;
trm2 = ((4.0 * psi + 1) * psi - t2) / 24.0;
trm3 = ((((8.0 * (11.0 - 24.0 * t2) * psi
- 28.0 * (1.0 - 6.0 * t2)) * psi
+ (1.0 - 32.0 * t2)) * psi
- 2.0 * t2) * psi
+ t4) / 720.0;
trm4 = (1385.0 - 3111.0 * t2 + 543.0 * t4 - t6) / 40320.0;
gcn = (eta * t) * ((((trm4 * wc2 + trm3) * wc2 + trm2) * wc2 + trm1) * wc2);
// out
northing = (gcn + m - om) * sf / utom + fn;
}
/// <summary>
/// Routine to convert from Tranverse Mercator to latitude and longitude.
/// Method based on Redfearn's formulation as expressed in GDA technical
/// manual at http://www.anzlic.org.au/icsm/gdatm/index.html
/// </summary>
private static void TransverseMercatorToLatLong(TMProjection projection, double easting, double northing, out double latitudeRad, out double longitudeRad)
{
var fn = projection.FalseNorthing;
var fe = projection.FalseEasting;
var sf = projection.ScaleFactor;
var e2 = projection.EllipsoidParams.E2;
var a = projection.EllipsoidParams.A;
var cm = projection.CentralMeridian;
var om = projection.IntermediateCalculation;
var utom = projection.UnitToMetreConversion;
double cn1;
double fphi;
double slt;
double clt;
double eslt;
double eta;
double rho;
double psi;
double E;
double x;
double x2;
double t;
double t2;
double t4;
double trm1;
double trm2;
double trm3;
double trm4;
cn1 = (northing - fn) * utom / sf + om;
fphi = FootPointLatitude(projection, cn1);
slt = Sin(fphi);
clt = Cos(fphi);
eslt = (1.0 - e2 * slt * slt);
eta = a / Sqrt(eslt);
rho = eta * (1.0 - e2) / eslt;
psi = eta / rho;
E = (easting - fe) * utom;
x = E / (eta * sf);
x2 = x * x;
t = slt / clt;
t2 = t * t;
t4 = t2 * t2;
trm1 = 1.0 / 2.0;
trm2 = ((-4.0 * psi
+ 9.0 * (1 - t2)) * psi
+ 12.0 * t2) / 24.0;
trm3 = ((((8.0 * (11.0 - 24.0 * t2) * psi
- 12.0 * (21.0 - 71.0 * t2)) * psi
+ 15.0 * ((15.0 * t2 - 98.0) * t2 + 15)) * psi
+ 180.0 * ((-3.0 * t2 + 5.0) * t2)) * psi + 360.0 * t4) / 720.0;
trm4 = (((1575.0 * t2 + 4095.0) * t2 + 3633.0) * t2 + 1385.0) / 40320.0;
// out
latitudeRad = fphi + (t * x * E / (sf * rho)) * (((trm4 * x2 - trm3) * x2 + trm2) * x2 - trm1);
trm1 = 1.0;
trm2 = (psi + 2.0 * t2) / 6.0;
trm3 = (((-4.0 * (1.0 - 6.0 * t2) * psi
+ (9.0 - 68.0 * t2)) * psi
+ 72.0 * t2) * psi
+ 24.0 * t4) / 120.0;
trm4 = (((720.0 * t2 + 1320.0) * t2 + 662.0) * t2 + 61.0) / 5040.0;
// out
longitudeRad = cm - (x / clt) * (((trm4 * x2 - trm3) * x2 + trm2) * x2 - trm1);
}
