conversions.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          http://www.mrpt.org/                          |
   |                                                                        |
   | Copyright (c) 2005-2017, Individual contributors, see AUTHORS file     |
   | See: http://www.mrpt.org/Authors - All rights reserved.                |
   | Released under BSD License. See details in http://www.mrpt.org/License |
   +------------------------------------------------------------------------+ */

#include "topography-precomp.h"  // Precompiled headers

#include <mrpt/topography/conversions.h>
#include <mrpt/poses/CPoint3D.h>
#include <mrpt/poses/CPose3D.h>
#include <mrpt/math/utils.h>
#include <mrpt/math/geometry.h>

using namespace std;
using namespace mrpt;
using namespace mrpt::math;
using namespace mrpt::utils;
using namespace mrpt::poses;

bool mrpt::topography::operator==(const TCoords& a, const TCoords& o)
{
        return a.decimal_value == o.decimal_value;
}
bool mrpt::topography::operator!=(const TCoords& a, const TCoords& o)
{
        return !(a == o);
}
bool mrpt::topography::operator==(
        const TGeodeticCoords& a, const TGeodeticCoords& o)
{
        return a.lat == o.lat && a.lon == o.lon && a.height == o.height;
}
bool mrpt::topography::operator!=(
        const TGeodeticCoords& a, const TGeodeticCoords& o)
{
        return !(a == o);
}

//#define M_PI_TOPO 3.141592653589793
// inline double DEG2RAD(const double x) { return x*M_PI_TOPO/180.0;    }

// Define a generic type for "precission numbers":
#ifdef HAVE_LONG_DOUBLE
typedef long double precnum_t;
#else
typedef double precnum_t;
#endif

std::ostream& mrpt::topography::operator<<(std::ostream& out, const TCoords& o)
{
        return out << o.getAsString();
}

/*---------------------------------------------------------------
                                geocentricToENU_WGS84
 ---------------------------------------------------------------*/
void mrpt::topography::geocentricToENU_WGS84(
        const mrpt::math::TPoint3D& P_geocentric_,
        mrpt::math::TPoint3D& out_ENU_point,
        const TGeodeticCoords& in_coords_origin)
{
        // Generate reference 3D point:
        TPoint3D P_geocentric_ref;
        geodeticToGeocentric_WGS84(in_coords_origin, P_geocentric_ref);

        const double clat = cos(DEG2RAD(in_coords_origin.lat)),
                                 slat = sin(DEG2RAD(in_coords_origin.lat));
        const double clon = cos(DEG2RAD(in_coords_origin.lon)),
                                 slon = sin(DEG2RAD(in_coords_origin.lon));

        // Compute the resulting relative coordinates:
        // For using smaller numbers:
        const mrpt::math::TPoint3D P_geocentric = P_geocentric_ - P_geocentric_ref;

        // Optimized calculation: Local transformed coordinates of P_geo(x,y,z)
        //   after rotation given by the transposed rotation matrix from ENU ->
        //   ECEF.
        out_ENU_point.x = -slon * P_geocentric.x + clon * P_geocentric.y;
        out_ENU_point.y = -clon * slat * P_geocentric.x -
                                          slon * slat * P_geocentric.y + clat * P_geocentric.z;
        out_ENU_point.z = clon * clat * P_geocentric.x +
                                          slon * clat * P_geocentric.y + slat * P_geocentric.z;
}

void mrpt::topography::geocentricToENU_WGS84(
        const std::vector<mrpt::math::TPoint3D>& in_geocentric_points,
        std::vector<mrpt::math::TPoint3D>& out_ENU_points,
        const TGeodeticCoords& in_coords_origin)
{
        // Generate reference 3D point:
        TPoint3D P_geocentric_ref;
        geodeticToGeocentric_WGS84(in_coords_origin, P_geocentric_ref);

        const double clat = cos(DEG2RAD(in_coords_origin.lat)),
                                 slat = sin(DEG2RAD(in_coords_origin.lat));
        const double clon = cos(DEG2RAD(in_coords_origin.lon)),
                                 slon = sin(DEG2RAD(in_coords_origin.lon));

        const size_t N = in_geocentric_points.size();
        out_ENU_points.resize(N);
        for (size_t i = 0; i < N; i++)
        {
                // Compute the resulting relative coordinates for using smaller numbers:
                const mrpt::math::TPoint3D P_geocentric =
                        in_geocentric_points[i] - P_geocentric_ref;

                // Optimized calculation: Local transformed coordinates of P_geo(x,y,z)
                //   after rotation given by the transposed rotation matrix from ENU ->
                //   ECEF.
                out_ENU_points[i].x = -slon * P_geocentric.x + clon * P_geocentric.y;
                out_ENU_points[i].y = -clon * slat * P_geocentric.x -
                                                          slon * slat * P_geocentric.y +
                                                          clat * P_geocentric.z;
                out_ENU_points[i].z = clon * clat * P_geocentric.x +
                                                          slon * clat * P_geocentric.y +
                                                          slat * P_geocentric.z;
        }
}

/*---------------------------------------------------------------
                                geodeticToENU_WGS84
 ---------------------------------------------------------------*/
void mrpt::topography::geodeticToENU_WGS84(
        const TGeodeticCoords& in_coords, mrpt::math::TPoint3D& out_ENU_point,
        const TGeodeticCoords& in_coords_origin)
{
        // --------------------------------------------------------------------
        //  Explanation: We compute the earth-centric coordinates first,
        //    then make a system transformation to local XYZ coordinates
        //    using a system of three orthogonal vectors as local reference.
        //
        // See: http://en.wikipedia.org/wiki/Reference_ellipsoid
        // (JLBC 21/DEC/2006)  (Fixed: JLBC 9/JUL/2008)
        // - Oct/2013, Emilio Sanjurjo: Fixed UP vector pointing exactly normal to
        // ellipsoid surface.
        // --------------------------------------------------------------------
        // Generate 3D point:
        TPoint3D P_geocentric;
        geodeticToGeocentric_WGS84(in_coords, P_geocentric);

        geocentricToENU_WGS84(P_geocentric, out_ENU_point, in_coords_origin);
}

/*---------------------------------------------------------------
                                        ENU_axes_from_WGS84
 ---------------------------------------------------------------*/
void mrpt::topography::ENU_axes_from_WGS84(
        double in_longitude_reference_degrees, double in_latitude_reference_degrees,
        double in_height_reference_meters, mrpt::math::TPose3D& out_ENU,
        bool only_angles)
{
        // See "coordinatesTransformation_WGS84" for more comments.
        TPoint3D PPref;
        mrpt::topography::geodeticToGeocentric_WGS84(
                TGeodeticCoords(
                        in_latitude_reference_degrees, in_longitude_reference_degrees,
                        in_height_reference_meters),
                PPref);

        const double clat = cos(DEG2RAD(in_latitude_reference_degrees)),
                                 slat = sin(DEG2RAD(in_latitude_reference_degrees));
        const double clon = cos(DEG2RAD(in_longitude_reference_degrees)),
                                 slon = sin(DEG2RAD(in_longitude_reference_degrees));

        CMatrixDouble44 HM;  // zeros by default
        HM(0, 0) = -slon;
        HM(0, 1) = -clon * slat;
        HM(0, 2) = clon * clat;
        HM(1, 0) = clon;
        HM(1, 1) = -slon * slat;
        HM(1, 2) = slon * clat;
        HM(2, 0) = 0;
        HM(2, 1) = clat;
        HM(2, 2) = slat;
        HM(3, 3) = 1;

        if (!only_angles)
        {
                HM(0, 3) = PPref.x;
                HM(1, 3) = PPref.y;
                HM(2, 3) = PPref.z;
        }

        out_ENU = mrpt::math::TPose3D(CPose3D(HM));
}

//*---------------------------------------------------------------
//                      geodeticToGeocentric_WGS84
// ---------------------------------------------------------------*/
void mrpt::topography::geodeticToGeocentric_WGS84(
        const TGeodeticCoords& in_coords, mrpt::math::TPoint3D& out_point)
{
        // --------------------------------------------------------------------
        // See: http://en.wikipedia.org/wiki/Reference_ellipsoid
        //  Constants are for WGS84
        // --------------------------------------------------------------------

        static const precnum_t a =
                6378137L;  // Semi-major axis of the Earth (meters)
        static const precnum_t b = 6356752.3142L;  // Semi-minor axis:

        static const precnum_t ae = acos(b / a);  // eccentricity:
        static const precnum_t cos2_ae_earth =
                square(cos(ae));  // The cos^2 of the angular eccentricity of the Earth:
        // // 0.993305619995739L;
        static const precnum_t sin2_ae_earth =
                square(sin(ae));  // The sin^2 of the angular eccentricity of the Earth:
        // // 0.006694380004261L;

        const precnum_t lon = DEG2RAD(precnum_t(in_coords.lon));
        const precnum_t lat = DEG2RAD(precnum_t(in_coords.lat));

        // The radius of curvature in the prime vertical:
        const precnum_t N = a / std::sqrt(1 - sin2_ae_earth * square(sin(lat)));

        // Generate 3D point:
        out_point.x = (N + in_coords.height) * cos(lat) * cos(lon);
        out_point.y = (N + in_coords.height) * cos(lat) * sin(lon);
        out_point.z = (cos2_ae_earth * N + in_coords.height) * sin(lat);
}

/*---------------------------------------------------------------
                        geodeticToGeocentric_WGS84
 ---------------------------------------------------------------*/
void mrpt::topography::geodeticToGeocentric(
        const TGeodeticCoords& in_coords, TGeocentricCoords& out_point,
        const TEllipsoid& ellip)
{
        static const precnum_t a =
                ellip.sa;  // Semi-major axis of the Earth (meters)
        static const precnum_t b = ellip.sb;  // Semi-minor axis:

        static const precnum_t ae = acos(b / a);  // eccentricity:
        static const precnum_t cos2_ae_earth =
                square(cos(ae));  // The cos^2 of the angular eccentricity of the Earth:
        // // 0.993305619995739L;
        static const precnum_t sin2_ae_earth =
                square(sin(ae));  // The sin^2 of the angular eccentricity of the Earth:
        // // 0.006694380004261L;

        const precnum_t lon = DEG2RAD(precnum_t(in_coords.lon));
        const precnum_t lat = DEG2RAD(precnum_t(in_coords.lat));

        // The radius of curvature in the prime vertical:
        const precnum_t N = a / std::sqrt(1 - sin2_ae_earth * square(sin(lat)));

        // Generate 3D point:
        out_point.x = (N + in_coords.height) * cos(lat) * cos(lon);
        out_point.y = (N + in_coords.height) * cos(lat) * sin(lon);
        out_point.z = (cos2_ae_earth * N + in_coords.height) * sin(lat);
}

/*---------------------------------------------------------------
                        geocentricToGeodetic
 ---------------------------------------------------------------*/
void mrpt::topography::geocentricToGeodetic(
        const TGeocentricCoords& in_point, TGeodeticCoords& out_coords,
        const TEllipsoid& ellip)
{
        const double sa2 = ellip.sa * ellip.sa;
        const double sb2 = ellip.sb * ellip.sb;

        const double e2 = (sa2 - sb2) / sa2;
        const double ep2 = (sa2 - sb2) / sb2;
        const double p = sqrt(in_point.x * in_point.x + in_point.y * in_point.y);
        const double theta = atan2(in_point.z * ellip.sa, p * ellip.sb);

        out_coords.lon = atan2(in_point.y, in_point.x);
        out_coords.lat = atan2(
                in_point.z + ep2 * ellip.sb * sin(theta) * sin(theta) * sin(theta),
                p - e2 * ellip.sa * cos(theta) * cos(theta) * cos(theta));

        const double clat = cos(out_coords.lat);
        const double slat = sin(out_coords.lat);
        const double N = sa2 / sqrt(sa2 * clat * clat + sb2 * slat * slat);

        out_coords.height = p / clat - N;

        out_coords.lon = RAD2DEG(out_coords.lon);
        out_coords.lat = RAD2DEG(out_coords.lat);
}

/*---------------------------------------------------------------
                                        UTMToGeodesic
 ---------------------------------------------------------------*/
void mrpt::topography::UTMToGeodetic(
        double X, double Y, int huso, char hem, double& out_lon /*degrees*/,
        double& out_lat /*degrees*/, const TEllipsoid& ellip)
{
        ASSERT_(hem == 's' || hem == 'S' || hem == 'n' || hem == 'N');

        X = X - 5e5;
        if (hem == 's' || hem == 'S') Y = Y - 1e7;

        const precnum_t lon0 = huso * 6 - 183;
        const precnum_t a2 = ellip.sa * ellip.sa;
        const precnum_t b2 = ellip.sb * ellip.sb;
        const precnum_t ep2 = (a2 - b2) / b2;
        const precnum_t c = a2 / ellip.sb;
        const precnum_t latp = Y / (6366197.724 * 0.9996);
        const precnum_t clp2 = square(cos(latp));

        const precnum_t v = c * 0.9996 / sqrt(1 + ep2 * clp2);
        const precnum_t na = X / v;
        const precnum_t A1 = sin(2 * latp);
        const precnum_t A2 = A1 * clp2;
        const precnum_t J2 = latp + A1 * 0.5;
        const precnum_t J4 = 0.75 * J2 + 0.25 * A2;
        const precnum_t J6 = (5 * J4 + A2 * clp2) / 3;

        const precnum_t alp = 0.75 * ep2;
        const precnum_t beta = (5.0 / 3.0) * alp * alp;
        const precnum_t gam = (35.0 / 27.0) * alp * alp * alp;
        const precnum_t B = 0.9996 * c * (latp - alp * J2 + beta * J4 - gam * J6);
        const precnum_t nb = (Y - B) / v;
        const precnum_t psi = (ep2 * square(na)) / 2 * clp2;
        const precnum_t eps = na * (1 - psi / 3);
        const precnum_t nu = nb * (1 - psi) + latp;
        const precnum_t she = (exp(eps) - exp(-eps)) / 2;
        const precnum_t dlon = atan2(she, cos(nu));
        const precnum_t tau = atan2(cos(dlon) * tan(nu), 1);

        out_lon = RAD2DEG(dlon) + lon0;
        out_lat = RAD2DEG(
                latp +
                (1 + ep2 * clp2 - 1.5 * ep2 * sin(latp) * cos(latp) * (tau - latp)) *
                        (tau - latp));
}

void mrpt::topography::geodeticToUTM(
        const TGeodeticCoords& GeodeticCoords, TUTMCoords& UTMCoords, int& UTMZone,
        char& UTMLatitudeBand, const TEllipsoid& ellip)
{
        const double la = GeodeticCoords.lat;
        char Letra;
        if (la < -72)
                Letra = 'C';
        else if (la < -64)
                Letra = 'D';
        else if (la < -56)
                Letra = 'E';
        else if (la < -48)
                Letra = 'F';
        else if (la < -40)
                Letra = 'G';
        else if (la < -32)
                Letra = 'H';
        else if (la < -24)
                Letra = 'J';
        else if (la < -16)
                Letra = 'K';
        else if (la < -8)
                Letra = 'L';
        else if (la < 0)
                Letra = 'M';
        else if (la < 8)
                Letra = 'N';
        else if (la < 16)
                Letra = 'P';
        else if (la < 24)
                Letra = 'Q';
        else if (la < 32)
                Letra = 'R';
        else if (la < 40)
                Letra = 'S';
        else if (la < 48)
                Letra = 'T';
        else if (la < 56)
                Letra = 'U';
        else if (la < 64)
                Letra = 'V';
        else if (la < 72)
                Letra = 'W';
        else
                Letra = 'X';

        const precnum_t lat = DEG2RAD(GeodeticCoords.lat);
        const precnum_t lon = DEG2RAD(GeodeticCoords.lon);
        const int Huso = mrpt::utils::fix((GeodeticCoords.lon / 6) + 31);
        const precnum_t lon0 = DEG2RAD(Huso * 6 - 183);

        const precnum_t sa = ellip.sa;
        const precnum_t sb = ellip.sb;
        //      const precnum_t e2              = (sa*sa-sb*sb)/(sa*sa);
        const precnum_t ep2 = (sa * sa - sb * sb) / (sb * sb);
        const precnum_t c = sa * sa / sb;
        //      const precnum_t alp             = (sa-sb)/sa;

        const precnum_t Dlon = lon - lon0;
        const precnum_t clat = cos(lat);
        const precnum_t sDlon = sin(Dlon);
        const precnum_t cDlon = cos(Dlon);

        const precnum_t A = clat * sDlon;
        const precnum_t eps = 0.5 * log((1 + A) / (1 - A));
        const precnum_t nu = atan2(tan(lat), cDlon) - lat;
        const precnum_t v = 0.9996 * c / sqrt(1 + ep2 * clat * clat);
        const precnum_t psi = 0.5 * ep2 * eps * eps * clat * clat;
        const precnum_t A1 = sin(2 * lat);
        const precnum_t A2 = A1 * clat * clat;
        const precnum_t J2 = lat + 0.5 * A1;
        const precnum_t J4 = 0.75 * J2 + 0.25 * A2;
        const precnum_t J6 = (5.0 * J4 + A2 * clat * clat) / 3;
        const precnum_t nalp = 0.75 * ep2;
        const precnum_t nbet = (5.0 / 3.0) * nalp * nalp;
        const precnum_t ngam = (35.0 / 27.0) * nalp * nalp * nalp;
        const precnum_t B = 0.9996 * c * (lat - nalp * J2 + nbet * J4 - ngam * J6);

        UTMCoords.x = eps * v * (1 + psi / 3.0) + 500000;
        UTMCoords.y = nu * v * (1 + psi) + B;
        UTMCoords.z = GeodeticCoords.height;

        UTMZone = Huso;
        UTMLatitudeBand = Letra;
}

/*---------------------------------------------------------------
                                        LatLonToUTM
 ---------------------------------------------------------------*/
void mrpt::topography::GeodeticToUTM(
        double la, double lo, double& xx, double& yy, int& out_UTM_zone,
        char& out_UTM_latitude_band, const TEllipsoid& ellip)
{
        // This method is based on public code by Gabriel Ruiz Martinez and Rafael
        // Palacios.
        //  http://www.mathworks.com/matlabcentral/fileexchange/10915

        const double sa = ellip.sa;
        const double sb = ellip.sb;
        const double e2 = (sqrt((sa * sa) - (sb * sb))) / sb;

        const double e2cuadrada = e2 * e2;

        const double c = (sa * sa) / sb;

        const double lat = DEG2RAD(la);
        const double lon = DEG2RAD(lo);

        const int Huso = mrpt::utils::fix((lo / 6) + 31);
        double S = ((Huso * 6) - 183);
        double deltaS = lon - DEG2RAD(S);

        char Letra;

        if (la < -72)
                Letra = 'C';
        else if (la < -64)
                Letra = 'D';
        else if (la < -56)
                Letra = 'E';
        else if (la < -48)
                Letra = 'F';
        else if (la < -40)
                Letra = 'G';
        else if (la < -32)
                Letra = 'H';
        else if (la < -24)
                Letra = 'J';
        else if (la < -16)
                Letra = 'K';
        else if (la < -8)
                Letra = 'L';
        else if (la < 0)
                Letra = 'M';
        else if (la < 8)
                Letra = 'N';
        else if (la < 16)
                Letra = 'P';
        else if (la < 24)
                Letra = 'Q';
        else if (la < 32)
                Letra = 'R';
        else if (la < 40)
                Letra = 'S';
        else if (la < 48)
                Letra = 'T';
        else if (la < 56)
                Letra = 'U';
        else if (la < 64)
                Letra = 'V';
        else if (la < 72)
                Letra = 'W';
        else
                Letra = 'X';

        const double a = cos(lat) * sin(deltaS);
        const double epsilon = 0.5 * log((1 + a) / (1 - a));
        const double nu = atan(tan(lat) / cos(deltaS)) - lat;
        const double v = (c / sqrt((1 + (e2cuadrada * square(cos(lat)))))) * 0.9996;
        const double ta = 0.5 * e2cuadrada * square(epsilon) * square(cos(lat));
        const double a1 = sin(2 * lat);
        const double a2 = a1 * square(cos(lat));
        const double j2 = lat + 0.5 * a1;
        const double j4 = ((3.0 * j2) + a2) / 4.0;
        const double j6 = ((5.0 * j4) + (a2 * square(cos(lat)))) / 3.0;
        const double alfa = 0.75 * e2cuadrada;
        const double beta = (5.0 / 3.0) * pow(alfa, 2.0);
        const double gama = (35.0 / 27.0) * pow(alfa, 3.0);
        const double Bm = 0.9996 * c * (lat - alfa * j2 + beta * j4 - gama * j6);

        xx = epsilon * v * (1 + (ta / 3.0)) + 500000;
        yy = nu * v * (1 + ta) + Bm;

        if (yy < 0) yy += 9999999;

        out_UTM_zone = Huso;
        out_UTM_latitude_band = Letra;
}

/**  7-parameter Bursa-Wolf transformation:
  *   [ X Y Z ]_WGS84 = [ dX dY dZ ] + ( 1 + dS ) [ 1 RZ -RY; -RZ 1 RX; RY -RX 1
 * ] [ X Y Z ]_local
  * \sa transform10params
  */
void mrpt::topography::transform7params(
        const mrpt::math::TPoint3D& p, const TDatum7Params& d,
        mrpt::math::TPoint3D& o)
{
        const double scale = (1 + d.dS);

        o.x = d.dX + scale * (p.x + p.y * d.Rz - p.z * d.Ry);
        o.y = d.dY + scale * (-p.x * d.Rz + p.y + p.z * d.Rx);
        o.z = d.dZ + scale * (p.x * d.Ry - p.y * d.Rx + p.z);
}

/**  7-parameter Bursa-Wolf transformation TOPCON:
  *   [ X Y Z ]_WGS84 = [ dX dY dZ ] + ( 1 + dS ) [ 1 RZ -RY; -RZ 1 RX; RY -RX 1
 * ] [ X Y Z ]_local
  * \sa transform10params
  */
void mrpt::topography::transform7params_TOPCON(
        const mrpt::math::TPoint3D& p, const TDatum7Params_TOPCON& d,
        mrpt::math::TPoint3D& o)
{
        const double scale = (1 + d.dS);

        o.x = d.dX + scale * (d.m11 * p.x + d.m12 * p.y + d.m13 * p.z);
        o.y = d.dY + scale * (d.m21 * p.x + d.m22 * p.y + d.m23 * p.z);
        o.z = d.dZ + scale * (d.m31 * p.x + d.m32 * p.y + d.m33 * p.z);
}

/**  10-parameter Molodensky-Badekas transformation:
  *   [ X Y Z ]_WGS84 = [ dX dY dZ ] + ( 1 + dS ) [ 1 RZ -RY; -RZ 1 RX; RY -RX 1
 * ] [ X-Xp Y-Yp Z-Zp ]_local + [Xp Yp Zp]
  * \sa transform7params
  */
void mrpt::topography::transform10params(
        const mrpt::math::TPoint3D& p, const TDatum10Params& d,
        mrpt::math::TPoint3D& o)
{
        const double scale = (1 + d.dS);

        const double px = p.x - d.Xp;
        const double py = p.y - d.Yp;
        const double pz = p.z - d.Zp;

        o.x = d.dX + scale * (px + py * d.Rz - pz * d.Ry) + d.Xp;
        o.y = d.dY + scale * (-px * d.Rz + py + pz * d.Rx) + d.Yp;
        o.z = d.dZ + scale * (px * d.Ry - py * d.Rx + pz) + d.Zp;
}

/**  Helmert 2D transformation:
  *   [ X Y ]_WGS84 = [ dX dY ] + ( 1 + dS ) [ cos(alpha) -sin(alpha);
 * sin(alpha) cos(alpha) ] [ X-Xp Y-Yp Z-Zp ]_local + [Xp Yp Zp]
  * \sa transformHelmert3D
  */
void mrpt::topography::transformHelmert2D(
        const mrpt::math::TPoint2D& p, const TDatumHelmert2D& d,
        mrpt::math::TPoint2D& o)
{
        const double scale = (1 + d.dS);

        const double px = p.x - d.Xp;
        const double py = p.y - d.Yp;

        o.x = d.dX + scale * (px * cos(d.alpha) - py * sin(d.alpha)) + d.Xp;
        o.y = d.dY + scale * (px * sin(d.alpha) + py * cos(d.alpha)) + d.Yp;
}

/**  Helmert 2D transformation:
  *   [ X Y ]_WGS84 = [ dX dY ] + ( 1 + dS ) [ cos(alpha) -sin(alpha);
 * sin(alpha) cos(alpha) ] [ X-Xp Y-Yp Z-Zp ]_local + [Xp Yp Zp]
  * \sa transformHelmert3D
  */
void mrpt::topography::transformHelmert2D_TOPCON(
        const mrpt::math::TPoint2D& p, const TDatumHelmert2D_TOPCON& d,
        mrpt::math::TPoint2D& o)
{
        o.x = d.a * p.x + d.b * p.y + d.c;
        o.y = -d.b * p.x + d.a * p.y + d.d;
}

/**  Helmert 3D transformation:
  *   [ X Y ]_WGS84 = [ dX dY ] + ( 1 + dS ) [ cos(alpha) -sin(alpha);
 * sin(alpha) cos(alpha) ] [ X-Xp Y-Yp Z-Zp ]_local + [Xp Yp Zp]
  * \sa transformHelmert3D
  */
void mrpt::topography::transformHelmert3D(
        const mrpt::math::TPoint3D& p, const TDatumHelmert3D& d,
        mrpt::math::TPoint3D& o)
{
        TDatum7Params d2(d.dX, d.dY, d.dZ, -1 * d.Rx, -1 * d.Ry, -1 * d.Rz, d.dS);
        transform7params(p, d2, o);
}

/**  Helmert 3D transformation:
  *   [ X Y ]_WGS84 = [ dX dY ] + ( 1 + dS ) [ cos(alpha) -sin(alpha);
 * sin(alpha) cos(alpha) ] [ X-Xp Y-Yp Z-Zp ]_local + [Xp Yp Zp]
  * \sa transformHelmert3D
  */
void mrpt::topography::transformHelmert3D_TOPCON(
        const mrpt::math::TPoint3D& p, const TDatumHelmert3D_TOPCON& d,
        mrpt::math::TPoint3D& o)
{
        o.x = d.a * p.x + d.b * p.y + d.c;
        o.y = d.d * p.x + d.e * p.y + d.f;
        o.z = p.z + d.g;
}

/**  1D transformation:
  *   [ Z ]_WGS84 = (dy * X - dx * Y + Z)*(1+e)+DZ
  * \sa transformHelmert3D
  */
void mrpt::topography::transform1D(
        const mrpt::math::TPoint3D& p, const TDatum1DTransf& d,
        mrpt::math::TPoint3D& o)
{
        o.x = p.x;
        o.y = p.y;
        o.z = (d.dY * p.x - d.dX * p.y + p.z) * (1 + d.dS) + d.DZ;
}

/**  1D transformation:
  *   [ X;Y ]_WGS84 = [X;Y]_locales+[1 -sin(d.beta);0
 * cos(d.beta)]*[x*d.dSx;y*d.dSy ]
  * \sa transformHelmert3D
  */
void mrpt::topography::transfInterpolation(
        const mrpt::math::TPoint3D& p, const TDatumTransfInterpolation& d,
        mrpt::math::TPoint3D& o)
{
        o.x = d.dX + p.x * d.dSx - p.y * d.dSy * sin(d.beta);
        o.y = d.dY + p.y * d.dSy * cos(d.beta);
        o.z = p.z;
}

/** ENU to geocentric coordinates.
  * \sa geodeticToENU_WGS84
  */
void mrpt::topography::ENUToGeocentric(
        const mrpt::math::TPoint3D& p, const TGeodeticCoords& in_coords_origin,
        TGeocentricCoords& out_coords, const TEllipsoid& ellip)
{
        // Generate reference 3D point:
        TPoint3D P_geocentric_ref;
        mrpt::topography::geodeticToGeocentric(
                in_coords_origin, P_geocentric_ref, ellip);

        CVectorDouble P_ref(3);
        P_ref[0] = P_geocentric_ref.x;
        P_ref[1] = P_geocentric_ref.y;
        P_ref[2] = P_geocentric_ref.z;

        // Z axis -> In direction out-ward the center of the Earth:
        CVectorDouble REF_X(3), REF_Y(3), REF_Z(3);
        math::normalize(P_ref, REF_Z);

        // 1st column: Starting at the reference point, move in the tangent
        // direction
        //   east-ward: I compute this as the derivative of P_ref wrt "longitude":
        //      A_east[0] =-(N+in_height_meters)*cos(lat)*sin(lon);  --> -Z[1]
        //      A_east[1] = (N+in_height_meters)*cos(lat)*cos(lon);  -->  Z[0]
        //      A_east[2] = 0;                                       -->  0
        // ---------------------------------------------------------------------------
        CVectorDouble AUX_X(3);
        AUX_X[0] = -REF_Z[1];
        AUX_X[1] = REF_Z[0];
        AUX_X[2] = 0;
        math::normalize(AUX_X, REF_X);

        // 2nd column: The cross product:
        math::crossProduct3D(REF_Z, REF_X, REF_Y);

        out_coords.x =
                REF_X[0] * p.x + REF_Y[0] * p.y + REF_Z[0] * p.z + P_geocentric_ref.x;
        out_coords.y =
                REF_X[1] * p.x + REF_Y[1] * p.y + REF_Z[1] * p.z + P_geocentric_ref.y;
        out_coords.z =
                REF_X[2] * p.x + REF_Y[2] * p.y + REF_Z[2] * p.z + P_geocentric_ref.z;
}