conversions.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          https://www.mrpt.org/                         |
   |                                                                        |
   | Copyright (c) 2005-2019, Individual contributors, see AUTHORS file     |
   | See: https://www.mrpt.org/Authors - All rights reserved.               |
   | Released under BSD License. See: https://www.mrpt.org/License          |
   +------------------------------------------------------------------------+ */

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

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

using namespace std;
using namespace mrpt;
using namespace mrpt::math;
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
using precnum_t = long double;
#else
using precnum_t = double;
#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 = CPose3D(HM).asTPose();
}

//*---------------------------------------------------------------
//          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::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::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;
}