CPose3DQuat.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 "base-precomp.h"  // Precompiled headers
#include <mrpt/poses/CPose3D.h>
#include <mrpt/poses/CPose3DQuat.h>
#include <mrpt/utils/CStream.h>
#include <iomanip>
#include <limits>

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

IMPLEMENTS_SERIALIZABLE(CPose3DQuat, CSerializable, mrpt::poses)

/** Constructor from a CPose3D */
CPose3DQuat::CPose3DQuat(const CPose3D& p)
{
        x() = p.x();
        y() = p.y();
        z() = p.z();
        p.getAsQuaternion(m_quat);
}

/** Constructor from a 4x4 homogeneous transformation matrix.
  */
CPose3DQuat::CPose3DQuat(const CMatrixDouble44& M)
        : m_quat(UNINITIALIZED_QUATERNION)
{
        m_coords[0] = M.get_unsafe(0, 3);
        m_coords[1] = M.get_unsafe(1, 3);
        m_coords[2] = M.get_unsafe(2, 3);
        CPose3D p(M);
        p.getAsQuaternion(m_quat);
}

/** Returns the corresponding 4x4 homogeneous transformation matrix for the
 * point(translation) or pose (translation+orientation).
  * \sa getInverseHomogeneousMatrix
  */
void CPose3DQuat::getHomogeneousMatrix(CMatrixDouble44& out_HM) const
{
        m_quat.rotationMatrixNoResize(out_HM);
        out_HM.get_unsafe(0, 3) = m_coords[0];
        out_HM.get_unsafe(1, 3) = m_coords[1];
        out_HM.get_unsafe(2, 3) = m_coords[2];
        out_HM.get_unsafe(3, 0) = out_HM.get_unsafe(3, 1) =
                out_HM.get_unsafe(3, 2) = 0;
        out_HM.get_unsafe(3, 3) = 1;
}

/** Returns a 1x7 vector with [x y z qr qx qy qz] */
void CPose3DQuat::getAsVector(CVectorDouble& v) const
{
        v.resize(7);
        v[0] = m_coords[0];
        v[1] = m_coords[1];
        v[2] = m_coords[2];
        v[3] = m_quat[0];
        v[4] = m_quat[1];
        v[5] = m_quat[2];
        v[6] = m_quat[3];
}

/**  Makes "this = A (+) B"; this method is slightly more efficient than "this=
 * A + B;" since it avoids the temporary object.
  *  \note A or B can be "this" without problems.
  */
void CPose3DQuat::composeFrom(const CPose3DQuat& A, const CPose3DQuat& B)
{
        // The 3D point:
        double gx, gy, gz;
        A.m_quat.rotatePoint(
                B.m_coords[0], B.m_coords[1], B.m_coords[2], gx, gy, gz);
        this->m_coords[0] = A.m_coords[0] + gx;
        this->m_coords[1] = A.m_coords[1] + gy;
        this->m_coords[2] = A.m_coords[2] + gz;

        // The 3D rotation:
        this->m_quat.crossProduct(A.m_quat, B.m_quat);
}

/**  Makes \f$ this = A \ominus B \f$ this method is slightly more efficient
 * than "this= A - B;" since it avoids the temporary object.
  *  \note A or B can be "this" without problems.
  * \sa composeFrom
  */
void CPose3DQuat::inverseComposeFrom(const CPose3DQuat& A, const CPose3DQuat& B)
{
        // The 3D point:
        const CQuaternionDouble B_conj(
                B.m_quat.r(), -B.m_quat.x(), -B.m_quat.y(), -B.m_quat.z());
        B_conj.rotatePoint(
                A.m_coords[0] - B.m_coords[0], A.m_coords[1] - B.m_coords[1],
                A.m_coords[2] - B.m_coords[2], this->m_coords[0], this->m_coords[1],
                this->m_coords[2]);
        // The 3D rotation:
        this->m_quat.crossProduct(B_conj, A.m_quat);
}

/**  Computes the 3D point G such as \f$ G = this \oplus L \f$.
  * \sa inverseComposeFrom
  */
void CPose3DQuat::composePoint(
        const double lx, const double ly, const double lz, double& gx, double& gy,
        double& gz,
        mrpt::math::CMatrixFixedNumeric<double, 3, 3>* out_jacobian_df_dpoint,
        mrpt::math::CMatrixFixedNumeric<double, 3, 7>* out_jacobian_df_dpose) const
{
        if (out_jacobian_df_dpoint || out_jacobian_df_dpose)
        {
                const double qx2 = square(m_quat.x());
                const double qy2 = square(m_quat.y());
                const double qz2 = square(m_quat.z());

                // Jacob: df/dpoint
                if (out_jacobian_df_dpoint)
                {
                        // 3x3:  df_{qr} / da

                        alignas(16) const double vals[3 * 3] = {
                                1 - 2 * (qy2 + qz2),
                                2 * (m_quat.x() * m_quat.y() - m_quat.r() * m_quat.z()),
                                2 * (m_quat.r() * m_quat.y() + m_quat.x() * m_quat.z()),

                                2 * (m_quat.r() * m_quat.z() + m_quat.x() * m_quat.y()),
                                1 - 2 * (qx2 + qz2),
                                2 * (m_quat.y() * m_quat.z() - m_quat.r() * m_quat.x()),

                                2 * (m_quat.x() * m_quat.z() - m_quat.r() * m_quat.y()),
                                2 * (m_quat.r() * m_quat.x() + m_quat.y() * m_quat.z()),
                                1 - 2 * (qx2 + qy2)};
                        out_jacobian_df_dpoint->loadFromArray(vals);
                }

                // Jacob: df/dpose
                if (out_jacobian_df_dpose)
                {
                        // 3x7:  df_{qr} / dp
                        alignas(16) const double vals1[3 * 7] = {
                                1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0};
                        out_jacobian_df_dpose->loadFromArray(vals1);

                        alignas(16) const double vals[3 * 4] = {
                                2 * (-m_quat.z() * ly + m_quat.y() * lz),
                                2 * (m_quat.y() * ly + m_quat.z() * lz),
                                2 * (-2 * m_quat.y() * lx + m_quat.x() * ly + m_quat.r() * lz),
                                2 * (-2 * m_quat.z() * lx - m_quat.r() * ly + m_quat.x() * lz),

                                2 * (m_quat.z() * lx - m_quat.x() * lz),
                                2 * (m_quat.y() * lx - 2 * m_quat.x() * ly - m_quat.r() * lz),
                                2 * (m_quat.x() * lx + m_quat.z() * lz),
                                2 * (m_quat.r() * lx - 2 * m_quat.z() * ly + m_quat.y() * lz),

                                2 * (-m_quat.y() * lx + m_quat.x() * ly),
                                2 * (m_quat.z() * lx + m_quat.r() * ly - 2 * m_quat.x() * lz),
                                2 * (-m_quat.r() * lx + m_quat.z() * ly - 2 * m_quat.y() * lz),
                                2 * (m_quat.x() * lx + m_quat.y() * ly)};

                        CMatrixDouble44 norm_jacob(UNINITIALIZED_MATRIX);
                        this->quat().normalizationJacobian(norm_jacob);

                        out_jacobian_df_dpose->insertMatrix(
                                0, 3,
                                (CMatrixFixedNumeric<double, 3, 4>(vals) * norm_jacob).eval());
                }
        }

        // function itself:
        m_quat.rotatePoint(lx, ly, lz, gx, gy, gz);
        gx += m_coords[0];
        gy += m_coords[1];
        gz += m_coords[2];
}

/**  Computes the 3D point G such as \f$ L = G \ominus this \f$.
  * \sa composeFrom
  */
void CPose3DQuat::inverseComposePoint(
        const double gx, const double gy, const double gz, double& lx, double& ly,
        double& lz,
        mrpt::math::CMatrixFixedNumeric<double, 3, 3>* out_jacobian_df_dpoint,
        mrpt::math::CMatrixFixedNumeric<double, 3, 7>* out_jacobian_df_dpose) const
{
        if (out_jacobian_df_dpoint || out_jacobian_df_dpose)
        {
                const double qx2 = square(m_quat.x());
                const double qy2 = square(m_quat.y());
                const double qz2 = square(m_quat.z());

                // Jacob: df/dpoint
                if (out_jacobian_df_dpoint)
                {
                        // 3x3:  df_{m_quat.r()} / da
                        //              inv_df_da =
                        //              [ - 2*qy^2 - 2*qz^2 + 1,     2*qx*qy - 2*qr*qz,     2*qr*qy
                        //+
                        // 2*qx*qz]
                        //              [     2*qr*qz + 2*qx*qy, - 2*qx^2 - 2*qz^2 + 1,     2*qy*qz
                        //-
                        // 2*qr*qx]
                        //              [     2*qx*qz - 2*qr*qy,     2*qr*qx + 2*qy*qz, - 2*qx^2 -
                        // 2*qy^2 + 1]
                        //

                        alignas(16) const double vals[3 * 3] = {
                                1 - 2 * (qy2 + qz2),
                                2 * (m_quat.x() * m_quat.y() + m_quat.r() * m_quat.z()),
                                2 * (-m_quat.r() * m_quat.y() + m_quat.x() * m_quat.z()),

                                2 * (-m_quat.r() * m_quat.z() + m_quat.x() * m_quat.y()),
                                1 - 2 * (qx2 + qz2),
                                2 * (m_quat.y() * m_quat.z() + m_quat.r() * m_quat.x()),

                                2 * (m_quat.x() * m_quat.z() + m_quat.r() * m_quat.y()),
                                2 * (-m_quat.r() * m_quat.x() + m_quat.y() * m_quat.z()),
                                1 - 2 * (qx2 + qy2)};
                        out_jacobian_df_dpoint->loadFromArray(vals);
                }

                // Jacob: df/dpose
                if (out_jacobian_df_dpose)
                {
                        // 3x7:  df_{m_quat.r()} / dp
                        //              inv_df_dp =
                        //[ 2*qy^2 + 2*qz^2 - 1, - 2*qr*qz - 2*qx*qy,   2*qr*qy - 2*qx*qz,
                        // 2*qz*(ay - y) - 2*qy*(az - z),                 2*qy*(ay - y) +
                        // 2*qz*(az - z), 2*qx*(ay - y) - 4*qy*(ax - x) - 2*qr*(az - z),
                        // 2*qr*(ay - y) - 4*qz*(ax - x) + 2*qx*(az - z)]
                        //[   2*qr*qz - 2*qx*qy, 2*qx^2 + 2*qz^2 - 1, - 2*qr*qx - 2*qy*qz,
                        // 2*qx*(az - z) - 2*qz*(ax - x), 2*qy*(ax - x) - 4*qx*(ay - y) +
                        // 2*qr*(az - z),                 2*qx*(ax - x) + 2*qz*(az - z),
                        // 2*qy*(az - z) - 4*qz*(ay - y) - 2*qr*(ax - x)]
                        //[ - 2*qr*qy - 2*qx*qz,   2*qr*qx - 2*qy*qz, 2*qx^2 + 2*qy^2 - 1,
                        // 2*qy*(ax - x) - 2*qx*(ay - y), 2*qz*(ax - x) - 2*qr*(ay - y) -
                        // 4*qx*(az - z), 2*qr*(ax - x) + 2*qz*(ay - y) - 4*qy*(az - z),
                        // 2*qx*(ax - x) + 2*qy*(ay - y)]
                        //
                        const double qr = m_quat.r();
                        const double qx = m_quat.x();
                        const double qy = m_quat.y();
                        const double qz = m_quat.z();

                        alignas(16) const double vals1[3 * 7] = {
                                2 * qy2 + 2 * qz2 - 1,
                                -2 * qr * qz - 2 * qx * qy,
                                2 * qr * qy - 2 * qx * qz,
                                0,
                                0,
                                0,
                                0,

                                2 * qr * qz - 2 * qx * qy,
                                2 * qx2 + 2 * qz2 - 1,
                                -2 * qr * qx - 2 * qy * qz,
                                0,
                                0,
                                0,
                                0,

                                -2 * qr * qy - 2 * qx * qz,
                                2 * qr * qx - 2 * qy * qz,
                                2 * qx2 + 2 * qy2 - 1,
                                0,
                                0,
                                0,
                                0,
                        };

                        out_jacobian_df_dpose->loadFromArray(vals1);

                        const double Ax = 2 * (gx - m_coords[0]);
                        const double Ay = 2 * (gy - m_coords[1]);
                        const double Az = 2 * (gz - m_coords[2]);

                        alignas(16)
                                const double vals[3 * 4] = {-qy * Az + qz * Ay,
                                                                                        qy * Ay + qz * Az,
                                                                                        qx * Ay - 2 * qy * Ax - qr * Az,
                                                                                        qx * Az + qr * Ay - 2 * qz * Ax,

                                                                                        qx * Az - qz * Ax,
                                                                                        qy * Ax - 2 * qx * Ay + qr * Az,
                                                                                        qx * Ax + qz * Az,
                                                                                        qy * Az - 2 * qz * Ay - qr * Ax,

                                                                                        qy * Ax - qx * Ay,
                                                                                        qz * Ax - qr * Ay - 2 * qx * Az,
                                                                                        qr * Ax + qz * Ay - 2 * qy * Az,
                                                                                        qx * Ax + qy * Ay};

                        CMatrixDouble44 norm_jacob(UNINITIALIZED_MATRIX);
                        this->quat().normalizationJacobian(norm_jacob);

                        out_jacobian_df_dpose->insertMatrix(
                                0, 3,
                                (CMatrixFixedNumeric<double, 3, 4>(vals) * norm_jacob).eval());
                }
        }

        // function itself:
        m_quat.inverseRotatePoint(
                gx - m_coords[0], gy - m_coords[1], gz - m_coords[2], lx, ly, lz);
}

/*---------------------------------------------------------------
        *=
  ---------------------------------------------------------------*/
void CPose3DQuat::operator*=(const double s)
{
        m_coords[0] *= s;
        m_coords[1] *= s;
        m_coords[2] *= s;
        m_quat[0] *= s;
        m_quat[1] *= s;
        m_quat[2] *= s;
        m_quat[3] *= s;
}

/*---------------------------------------------------------------
   Implements the writing to a CStream capability of
         CSerializable objects
  ---------------------------------------------------------------*/
void CPose3DQuat::writeToStream(mrpt::utils::CStream& out, int* version) const
{
        if (version)
                *version = 0;
        else
        {
                out << m_coords[0] << m_coords[1] << m_coords[2] << m_quat[0]
                        << m_quat[1] << m_quat[2] << m_quat[3];
        }
}

/*---------------------------------------------------------------
        Implements the reading from a CStream capability of
                CSerializable objects
  ---------------------------------------------------------------*/
void CPose3DQuat::readFromStream(mrpt::utils::CStream& in, int version)
{
        switch (version)
        {
                case 0:
                {
                        in >> m_coords[0] >> m_coords[1] >> m_coords[2] >> m_quat[0] >>
                                m_quat[1] >> m_quat[2] >> m_quat[3];
                }
                break;
                default:
                        MRPT_THROW_UNKNOWN_SERIALIZATION_VERSION(version)
        };
}

/*---------------------------------------------------------------
                sphericalCoordinates
---------------------------------------------------------------*/
void CPose3DQuat::sphericalCoordinates(
        const TPoint3D& point, double& out_range, double& out_yaw,
        double& out_pitch,
        mrpt::math::CMatrixFixedNumeric<double, 3, 3>* out_jacob_dryp_dpoint,
        mrpt::math::CMatrixFixedNumeric<double, 3, 7>* out_jacob_dryp_dpose) const
{
        const bool comp_jacobs =
                out_jacob_dryp_dpoint != nullptr || out_jacob_dryp_dpose != nullptr;

        // Pass to coordinates as seen from this 6D pose:
        CMatrixFixedNumeric<double, 3, 3> jacob_dinv_dpoint,
                *ptr_ja1 = comp_jacobs ? &jacob_dinv_dpoint : nullptr;
        CMatrixFixedNumeric<double, 3, 7> jacob_dinv_dpose,
                *ptr_ja2 = comp_jacobs ? &jacob_dinv_dpose : nullptr;

        TPoint3D local;
        this->inverseComposePoint(
                point.x, point.y, point.z, local.x, local.y, local.z, ptr_ja1, ptr_ja2);

        // Range:
        out_range = local.norm();

        // Yaw:
        if (local.y != 0 || local.x != 0)
                out_yaw = atan2(local.y, local.x);
        else
                out_yaw = 0;

        // Pitch:
        if (out_range != 0)
                out_pitch = -asin(local.z / out_range);
        else
                out_pitch = 0;

        // Jacobians are:
        //  dryp_dpoint = dryp_dlocalpoint  * dinv_dpoint
        //  dryp_dpose  = dryp_dlocalpoint  * dinv_dpose
        if (comp_jacobs)
        {
                if (out_range == 0)
                        THROW_EXCEPTION("Jacobians are undefined for range=0")

                /* MATLAB:
                        syms H h_range h_yaw h_pitch real;
                        syms xi_ yi_ zi_ real;
                        h_range = sqrt(xi_^2+yi_^2+zi_^2);
                        h_yaw   = atan(yi_/xi_);
                        % h_pitch = -asin(zi_/ sqrt( xi_^2 + yi_^2 + zi_^2 ) );
                        h_pitch = -atan(zi_, sqrt( xi_^2 + yi_^2) );
                        H=[ h_range ; h_yaw ; h_pitch ];
                        jacob_fesf_xyz=jacobian(H,[xi_ yi_ zi_])
                */
                const double _r = 1.0 / out_range;
                const double x2 = square(local.x);
                const double y2 = square(local.y);

                const double t2 = std::sqrt(x2 + y2);
                const double _K = 1.0 / (t2 * square(out_range));

                double vals[3 * 3] = {local.x * _r,
                                                          local.y * _r,
                                                          local.z * _r,
                                                          -local.y / (x2 * (y2 / x2 + 1)),
                                                          1.0 / (local.x * (y2 / x2 + 1)),
                                                          0,
                                                          (local.x * local.z) * _K,
                                                          (local.y * local.z) * _K,
                                                          -t2 / square(out_range)};

                const CMatrixDouble33 dryp_dlocalpoint(vals);
                if (out_jacob_dryp_dpoint)
                        out_jacob_dryp_dpoint->multiply(
                                dryp_dlocalpoint, jacob_dinv_dpoint);
                if (out_jacob_dryp_dpose)
                        out_jacob_dryp_dpose->multiply(dryp_dlocalpoint, jacob_dinv_dpose);
        }
}

/**  Textual output stream function.
 */
std::ostream& mrpt::poses::operator<<(std::ostream& o, const CPose3DQuat& p)
{
        const std::streamsize old_pre = o.precision();
        const ios_base::fmtflags old_flags = o.flags();
        o << "(x,y,z,qr,qx,qy,qz)=(" << std::fixed << std::setprecision(4)
          << p.m_coords[0] << "," << p.m_coords[1] << "," << p.m_coords[2] << ","
          << p.quat()[0] << "," << p.quat()[1] << "," << p.quat()[2] << ","
          << p.quat()[3] << ")";
        o.flags(old_flags);
        o.precision(old_pre);
        return o;
}

/** Unary - operator: return the inverse pose "-p" (Note that is NOT the same
 * than a pose with all its arguments multiplied by "-1") */
CPose3DQuat mrpt::poses::operator-(const CPose3DQuat& p)
{
        CPose3DQuat ret = p;
        ret.inverse();
        return ret;
}

/** Convert this pose into its inverse, saving the result in itself. \sa
 * operator- */
void CPose3DQuat::inverse()
{
        // Invert translation:
        this->inverseComposePoint(0, 0, 0, m_coords[0], m_coords[1], m_coords[2]);

        // Invert rotation: [qr qx qy qz] ==> [qr -qx -qy -qz]
        m_quat[1] = -m_quat[1];
        m_quat[2] = -m_quat[2];
        m_quat[3] = -m_quat[3];
}

void CPose3DQuat::setToNaN()
{
        for (int i = 0; i < 3; i++)
                m_coords[i] = std::numeric_limits<double>::quiet_NaN();

        for (int i = 0; i < 4; i++)
                quat()[i] = std::numeric_limits<double>::quiet_NaN();
}

bool mrpt::poses::operator==(const CPose3DQuat& p1, const CPose3DQuat& p2)
{
        return p1.quat() == p2.quat() && p1.x() == p2.x() && p1.y() == p2.y() &&
                   p1.z() == p2.z();
}

bool mrpt::poses::operator!=(const CPose3DQuat& p1, const CPose3DQuat& p2)
{
        return !(p1 == p2);
}

CPoint3D mrpt::poses::operator-(const CPoint3D& G, const CPose3DQuat& p)
{
        CPoint3D L;
        p.inverseComposePoint(G[0], G[1], G[2], L[0], L[1], L[2]);
        return L;
}

mrpt::math::TPoint3D mrpt::poses::operator-(
        const mrpt::math::TPoint3D& G, const CPose3DQuat& p)
{
        mrpt::math::TPoint3D L;
        p.inverseComposePoint(G[0], G[1], G[2], L[0], L[1], L[2]);
        return L;
}