CPose3D.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/config.h>                                     // for HAVE_SINCOS
#include <mrpt/utils/types_math.h>                           // for CVectorD...
#include <mrpt/math/CMatrix.h>                               // for CMatrix
#include <mrpt/math/geometry.h>                              // for skew_sym...
#include <mrpt/math/matrix_serialization.h>                  // for operator>>
#include <mrpt/math/wrap2pi.h>                               // for wrapToPi
#include <mrpt/poses/CPoint2D.h>                             // for CPoint2D
#include <mrpt/poses/CPoint3D.h>                             // for CPoint3D
#include <mrpt/poses/CPose2D.h>                              // for CPose2D
#include <mrpt/poses/CPose3D.h>                              // for CPose3D
#include <mrpt/poses/CPose3DQuat.h>                          // for CPose3DQuat
#include <mrpt/poses/CPose3DRotVec.h>                        // for CPose3DR...
#include <mrpt/utils/CStream.h>                              // for CStream
#include <algorithm>                                         // for move
#include <cmath>                                             // for fabs
#include <iomanip>                                           // for operator<<
#include <limits>                                            // for numeric_...
#include <ostream>                                           // for operator<<
#include <string>                                            // for allocator
#include <mrpt/math/CArrayNumeric.h>                         // for CArrayDo...
#include <mrpt/math/CMatrixFixedNumeric.h>                   // for CMatrixF...
#include <mrpt/math/CMatrixTemplateNumeric.h>                // for CMatrixD...
#include <mrpt/math/CQuaternion.h>                           // for CQuatern...
#include <mrpt/math/homog_matrices.h>                        // for homogene...
#include <mrpt/math/lightweight_geom_data.h>                 // for TPoint3D
#include <mrpt/math/ops_containers.h>                        // for dotProduct
#include <mrpt/utils/CSerializable.h>                        // for CSeriali...
#include <mrpt/utils/bits.h>                                 // for square
#include <mrpt/math/utils_matlab.h>
#include <mrpt/otherlibs/sophus/so3.hpp>
#include <mrpt/otherlibs/sophus/se3.hpp>
 
using namespace mrpt;
using namespace mrpt::math;
using namespace mrpt::utils;
using namespace mrpt::poses;
 
 
IMPLEMENTS_SERIALIZABLE(CPose3D, CSerializable ,mrpt::poses)
 
/*---------------------------------------------------------------
        Constructors
  ---------------------------------------------------------------*/
CPose3D::CPose3D()
        : m_ypr_uptodate(true), m_yaw(0),m_pitch(0),m_roll(0)
{
        m_coords[0] =
        m_coords[1] =
        m_coords[2] = 0;
        m_ROT.unit(3,1.0);
}
 
CPose3D::CPose3D(const double x,const double y,const double z, const double yaw, const double pitch, const double roll)
        : m_ROT(UNINITIALIZED_MATRIX), m_ypr_uptodate(false)
{
        setFromValues(x,y,z,yaw,pitch,roll);
}
 
CPose3D::CPose3D(const mrpt::math::TPose3D &o)
        : m_ypr_uptodate(false)
{
        setFromValues(o.x,o.y,o.z,o.yaw,o.pitch,o.roll);
}
 
CPose3D::CPose3D(const CPose2D &p)
        : m_ypr_uptodate(false)
{
        setFromValues(p.x(),p.y(),0, p.phi(),0,0);
}
 
CPose3D::CPose3D(const CPoint3D &p)
        : m_ypr_uptodate(false), m_yaw(),m_pitch(),m_roll()
{
        setFromValues(p.x(),p.y(),p.z());
}
 
CPose3D::CPose3D(const math::CMatrixDouble & m)
        : m_ROT( UNINITIALIZED_MATRIX ), m_ypr_uptodate(false)
{
        ASSERT_ABOVEEQ_(mrpt::math::size(m,1),3);
        ASSERT_ABOVEEQ_(mrpt::math::size(m,2),4);
        for (int r=0;r<3;r++)
                for (int c=0;c<3;c++)
                        m_ROT(r,c)=m.get_unsafe(r,c);
        for (int r=0;r<3;r++)
                m_coords[r] = m.get_unsafe(r,3);
}
 
 
CPose3D::CPose3D(const math::CMatrixDouble44 &m)
        : m_ROT( UNINITIALIZED_MATRIX ), m_ypr_uptodate(false)
{
        for (int r=0;r<3;r++)
                for (int c=0;c<3;c++)
                        m_ROT(r,c)=m.get_unsafe(r,c);
        for (int r=0;r<3;r++)
                m_coords[r] = m.get_unsafe(r,3);
}
 
/** Constructor from a quaternion (which only represents the 3D rotation part) and a 3D displacement. */
CPose3D::CPose3D(const mrpt::math::CQuaternionDouble &q, const double _x, const double _y, const double _z )
        : m_ROT( UNINITIALIZED_MATRIX ), m_ypr_uptodate(false)
{
        double yaw,pitch,roll;
        q.rpy(roll,pitch,yaw);
        this->setFromValues(_x,_y,_z,yaw,pitch,roll);
}
 
/** Constructor from a quaternion-based full pose. */
CPose3D::CPose3D(const CPose3DQuat &p )
        : m_ROT( UNINITIALIZED_MATRIX ), m_ypr_uptodate(false)
{
        // Extract XYZ + ROT from quaternion:
        m_coords[0] = p.x();
        m_coords[1] = p.y();
        m_coords[2] = p.z();
        p.quat().rotationMatrixNoResize(m_ROT);
}
 
/** Constructor from a rotation vector-based full pose. */
CPose3D::CPose3D(const CPose3DRotVec &p )
    : m_ROT( UNINITIALIZED_MATRIX ), m_ypr_uptodate(false)
{
    m_coords[0] = p.m_coords[0];
    m_coords[1] = p.m_coords[1];
    m_coords[2] = p.m_coords[2];
 
    this->setRotationMatrix( this->exp_rotation( p.m_rotvec ) );
}
 
/*---------------------------------------------------------------
   Implements the writing to a CStream capability of
     CSerializable objects
  ---------------------------------------------------------------*/
void  CPose3D::writeToStream(mrpt::utils::CStream &out,int *version) const
{
        if (version)
                *version = 2;
        else
        {
                const CPose3DQuat  q(*this);
                // The coordinates:
                out << q[0] << q[1] << q[2] << q[3] << q[4] << q[5] << q[6];
        }
}
 
/*---------------------------------------------------------------
        Implements the reading from a CStream capability of
                CSerializable objects
  ---------------------------------------------------------------*/
void  CPose3D::readFromStream(mrpt::utils::CStream &in,int version)
{
        switch(version)
        {
        case 0:
                {
                        // The coordinates:
                        CMatrix  HM2;
                        in >> HM2;
                        ASSERT_(mrpt::math::size(HM2,1)==4 && HM2.isSquare())
 
                        m_ROT = HM2.block(0,0,3,3).cast<double>();
 
                        m_coords[0] = HM2.get_unsafe(0,3);
                        m_coords[1] = HM2.get_unsafe(1,3);
                        m_coords[2] = HM2.get_unsafe(2,3);
                        m_ypr_uptodate = false;
                } break;
        case 1:
                {
                        // The coordinates:
                        CMatrixDouble44 HM;
                        in >> HM;
 
                        m_ROT = HM.block(0,0,3,3);
 
                        m_coords[0] = HM.get_unsafe(0,3);
                        m_coords[1] = HM.get_unsafe(1,3);
                        m_coords[2] = HM.get_unsafe(2,3);
                        m_ypr_uptodate = false;
                } break;
        case 2:
                {
                        // An equivalent CPose3DQuat
                        CPose3DQuat p(UNINITIALIZED_QUATERNION);
                        in >>p[0]>>p[1]>>p[2]>>p[3]>>p[4]>>p[5]>>p[6];
 
                        // Extract XYZ + ROT from quaternion:
                        m_ypr_uptodate = false;
                        m_coords[0] = p.x();
                        m_coords[1] = p.y();
                        m_coords[2] = p.z();
                        p.quat().rotationMatrixNoResize(m_ROT);
                } break;
        default:
                MRPT_THROW_UNKNOWN_SERIALIZATION_VERSION(version)
 
        };
}
 
/**  Textual output stream function.
 */
std::ostream& mrpt::poses::operator << (std::ostream& o, const CPose3D& p)
{
        const std::streamsize old_pre = o.precision();
        const std::ios_base::fmtflags old_flags = o.flags();
        o << "(x,y,z,yaw,pitch,roll)=(" << std::fixed << std::setprecision(4) << p.m_coords[0] << "," << p.m_coords[1] << "," << p.m_coords[2] <<  ","
                << std::setprecision(2) << RAD2DEG(p.yaw()) << "deg," << RAD2DEG(p.pitch()) << "deg," << RAD2DEG(p.roll()) << "deg)";
        o.flags(old_flags);
        o.precision(old_pre);
        return o;
}
 
/*---------------------------------------------------------------
  Implements the writing to a mxArray for Matlab
 ---------------------------------------------------------------*/
#if MRPT_HAS_MATLAB
// Add to implement mexplus::from template specialization
IMPLEMENTS_MEXPLUS_FROM( mrpt::poses::CPose3D )
 
mxArray* CPose3D::writeToMatlab() const
{
        const char* fields[] = {"R","t"};
        mexplus::MxArray pose_struct( mexplus::MxArray::Struct(sizeof(fields)/sizeof(fields[0]),fields) );
        pose_struct.set("R", mrpt::math::convertToMatlab(this->m_ROT));
        pose_struct.set("t", mrpt::math::convertToMatlab(this->m_coords));
        return pose_struct.release();
}
#endif
 
/*---------------------------------------------------------------
                                normalizeAngles
---------------------------------------------------------------*/
void  CPose3D::normalizeAngles()
{
        updateYawPitchRoll();
}
 
 
/*---------------------------------------------------------------
 Set the pose from 3D point and yaw/pitch/roll angles, in radians.
---------------------------------------------------------------*/
void  CPose3D::setFromValues(
        const double            x0,
        const double            y0,
        const double            z0,
        const double            yaw,
        const double            pitch,
        const double            roll)
{
        m_coords[0] = x0;
        m_coords[1] = y0;
        m_coords[2] = z0;
        this->m_yaw = mrpt::math::wrapToPi(yaw);
        this->m_pitch = mrpt::math::wrapToPi(pitch);
        this->m_roll = mrpt::math::wrapToPi(roll);
 
        m_ypr_uptodate = true;
 
        rebuildRotationMatrix();
}
 
/*---------------------------------------------------------------
 Set the pose from 3D point and yaw/pitch/roll angles, in radians.
---------------------------------------------------------------*/
void  CPose3D::rebuildRotationMatrix()
{
#ifdef HAVE_SINCOS
        double  cy,sy;
        ::sincos(m_yaw,&sy,&cy);
        double  cp,sp;
        ::sincos(m_pitch,&sp,&cp);
        double  cr,sr;
        ::sincos(m_roll,&sr,&cr);
#else
        const double    cy = cos(m_yaw);
        const double    sy = sin(m_yaw);
        const double    cp = cos(m_pitch);
        const double    sp = sin(m_pitch);
        const double    cr = cos(m_roll);
        const double    sr = sin(m_roll);
#endif
 
        MRPT_ALIGN16 const double rot_vals[] = {
                cy*cp,      cy*sp*sr-sy*cr,     cy*sp*cr+sy*sr,
                sy*cp,      sy*sp*sr+cy*cr,     sy*sp*cr-cy*sr,
                -sp,        cp*sr,              cp*cr
                };
        m_ROT.loadFromArray(rot_vals);
}
 
/*---------------------------------------------------------------
                Scalar multiplication.
---------------------------------------------------------------*/
void CPose3D::operator *=(const double s)
{
        updateYawPitchRoll();
        m_coords[0]*=s;
        m_coords[1]*=s;
        m_coords[2]*=s;
        m_yaw*=s;
        m_pitch*=s;
        m_roll*=s;
        rebuildRotationMatrix();
}
 
/*---------------------------------------------------------------
                getYawPitchRoll
---------------------------------------------------------------*/
void  CPose3D::getYawPitchRoll( double &yaw, double &pitch, double &roll ) const
{
        ASSERTDEBMSG_( std::abs(sqrt(square(m_ROT(0,0))+square(m_ROT(1,0))+square(m_ROT(2,0))) - 1 ) < 3e-3, "Homogeneous matrix is not orthogonal & normalized!: "+m_ROT.inMatlabFormat() )
        ASSERTDEBMSG_( std::abs(sqrt(square(m_ROT(0,1))+square(m_ROT(1,1))+square(m_ROT(2,1))) - 1 ) < 3e-3, "Homogeneous matrix is not orthogonal & normalized!: "+m_ROT.inMatlabFormat() )
        ASSERTDEBMSG_( std::abs(sqrt(square(m_ROT(0,2))+square(m_ROT(1,2))+square(m_ROT(2,2))) - 1 ) < 3e-3, "Homogeneous matrix is not orthogonal & normalized!: "+m_ROT.inMatlabFormat() )
 
        // Pitch is in the range [-pi/2, pi/2 ], so this calculation is enough:
        pitch =  atan2( - m_ROT(2,0), hypot( m_ROT(0,0),m_ROT(1,0) ) ); //asin( - m_ROT(2,0) );
 
        // Roll:
        if ( (fabs(m_ROT(2,1))+fabs(m_ROT(2,2)))<10*std::numeric_limits<double>::epsilon() )
        {
                //Gimbal lock between yaw and roll. This one is arbitrarily forced to be zero.
                //Check http://reference.mrpt.org/devel/classmrpt_1_1poses_1_1_c_pose3_d.html. If cos(pitch)==0, the homogeneous matrix is:
                //When sin(pitch)==1:
                //  /0  cysr-sycr cycr+sysr x\   /0  sin(r-y) cos(r-y)  x\.
                //  |0  sysr+cycr sycr-cysr y| = |0  cos(r-y) -sin(r-y) y|
                //  |-1     0         0     z|   |-1    0         0     z|
                //  \0      0         0     1/   \0     0         0     1/
                //
                //And when sin(pitch)=-1:
                //  /0 -cysr-sycr -cycr+sysr x\   /0 -sin(r+y) -cos(r+y) x\.
                //  |0 -sysr+cycr -sycr-cysr y| = |0 cos(r+y)  -sin(r+y) y|
                //  |1      0          0     z|   |1    0          0     z|
                //  \0      0          0     1/   \0    0          0     1/
                //
                //Both cases are in a "gimbal lock" status. This happens because pitch is vertical.
 
                roll = 0.0;
                if (pitch>0) yaw=atan2(m_ROT(1,2),m_ROT(0,2));
                else yaw=atan2(-m_ROT(1,2),-m_ROT(0,2));
        }
        else
        {
                roll = atan2( m_ROT(2,1), m_ROT(2,2) );
                // Yaw:
                yaw = atan2( m_ROT(1,0), m_ROT(0,0) );
        }
}
 
 
/*---------------------------------------------------------------
                sphericalCoordinates
---------------------------------------------------------------*/
void CPose3D::sphericalCoordinates(
    const TPoint3D &point,
    double &out_range,
    double &out_yaw,
    double &out_pitch ) const
{
    // Pass to coordinates as seen from this 6D pose:
        TPoint3D local;
        this->inverseComposePoint(point.x,point.y,point.z, local.x,local.y,local.z);
 
    // 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;
 
}
 
 
/*---------------------------------------------------------------
                addComponents
---------------------------------------------------------------*/
void CPose3D::addComponents(const CPose3D &p)
{
        updateYawPitchRoll();
        m_coords[0]+=p.m_coords[0];
        m_coords[1]+=p.m_coords[1];
        m_coords[2]+=p.m_coords[2];
        m_yaw+=p.m_yaw;
        m_pitch+=p.m_pitch;
        m_roll+=p.m_roll;
        rebuildRotationMatrix();
}
 
 
/*---------------------------------------------------------------
                distanceEuclidean6D
---------------------------------------------------------------*/
double CPose3D::distanceEuclidean6D( const CPose3D &o ) const
{
        updateYawPitchRoll();
        o.updateYawPitchRoll();
        return sqrt(
                square( o.m_coords[0] - m_coords[0] ) +
                square( o.m_coords[1] - m_coords[1] ) +
                square( o.m_coords[2] - m_coords[2] ) +
                square( wrapToPi( o.m_yaw - m_yaw ) ) +
                square( wrapToPi( o.m_pitch - m_pitch ) ) +
                square( wrapToPi( o.m_roll - m_roll ) ) );
}
 
 
/*---------------------------------------------------------------
                composePoint
---------------------------------------------------------------*/
void CPose3D::composePoint(double lx,double ly,double lz, double &gx, double &gy, double &gz,
        mrpt::math::CMatrixFixedNumeric<double,3,3>  *out_jacobian_df_dpoint,
        mrpt::math::CMatrixFixedNumeric<double,3,6>  *out_jacobian_df_dpose,
        mrpt::math::CMatrixFixedNumeric<double,3,6>  *out_jacobian_df_dse3,
        bool use_small_rot_approx ) const
{
        // Jacob: df/dpoint
        if (out_jacobian_df_dpoint)
                *out_jacobian_df_dpoint = m_ROT;
 
        // Jacob: df/dpose
        if (out_jacobian_df_dpose)
        {
                if (use_small_rot_approx)
                {
                        // Linearized Jacobians around (yaw,pitch,roll)=(0,0,0):
                        MRPT_ALIGN16 const double nums[3*6] = {
                                1, 0, 0, -ly, lz,   0,
                                0, 1, 0,  lx,  0, -lz,
                                0, 0, 1,   0, -lx,  ly };
                        out_jacobian_df_dpose->loadFromArray(nums);
                }
                else
                {
                        // Exact Jacobians:
                        updateYawPitchRoll();
        #       ifdef HAVE_SINCOS
                        double  cy,sy;
                        ::sincos(m_yaw,&sy,&cy);
                        double  cp,sp;
                        ::sincos(m_pitch,&sp,&cp);
                        double  cr,sr;
                        ::sincos(m_roll,&sr,&cr);
        #       else
                        const double    cy = cos(m_yaw);
                        const double    sy = sin(m_yaw);
                        const double    cp = cos(m_pitch);
                        const double    sp = sin(m_pitch);
                        const double    cr = cos(m_roll);
                        const double    sr = sin(m_roll);
        #       endif
 
                        MRPT_ALIGN16 const double nums[3*6] = {
                                1, 0, 0,
                                        -lx*sy*cp+ly*(-sy*sp*sr-cy*cr)+lz*(-sy*sp*cr+cy*sr),   // d_x'/d_yaw
                                        -lx*cy*sp+ly*(cy*cp*sr       )+lz*(cy*cp*cr      ),   // d_x'/d_pitch
                                                          ly*(cy*sp*cr+sy*sr)+lz*(-cy*sp*sr+sy*cr),   // d_x'/d_roll
                                0, 1, 0,
                                         lx*cy*cp+ly*(cy*sp*sr-sy*cr)+lz*(cy*sp*cr+sy*sr),   // d_y'/d_yaw
                                        -lx*sy*sp+ly*(sy*cp*sr)      +lz*(sy*cp*cr      ),   // d_y'/d_pitch
                                                          ly*(sy*sp*cr-cy*sr)+lz*(-sy*sp*sr-cy*cr),   // d_y'/d_roll
                                0, 0, 1,
                                        0,  // d_z' / d_yaw
                                        -lx*cp-ly*sp*sr-lz*sp*cr,  // d_z' / d_pitch
                                        ly*cp*cr-lz*cp*sr  // d_z' / d_roll
                                };
                        out_jacobian_df_dpose->loadFromArray(nums);
                }
        }
 
        gx=m_ROT(0,0)*lx+m_ROT(0,1)*ly+m_ROT(0,2)*lz+m_coords[0];
        gy=m_ROT(1,0)*lx+m_ROT(1,1)*ly+m_ROT(1,2)*lz+m_coords[1];
        gz=m_ROT(2,0)*lx+m_ROT(2,1)*ly+m_ROT(2,2)*lz+m_coords[2];
 
        // Jacob: df/dse3
        if (out_jacobian_df_dse3)
        {
                MRPT_ALIGN16 const double nums[3*6] = {
                        1, 0, 0,   0, gz, -gy,
                        0, 1, 0, -gz,  0,  gx,
                        0, 0, 1,  gy,-gx,   0 };
                out_jacobian_df_dse3->loadFromArray(nums);
        }
}
 
 
// TODO: Use SSE2? OTOH, this forces mem align...
#if MRPT_HAS_SSE2 && defined(MRPT_USE_SSE2)
/*static inline __m128 transformSSE(const __m128* matrix, const __m128& in)
{
    ASSERT_(((size_t)matrix & 15) == 0);
    __m128 a0 = _mm_mul_ps(_mm_load_ps((float*)(matrix+0)), _mm_shuffle_ps(in,in,_MM_SHUFFLE(0,0,0,0)));
    __m128 a1 = _mm_mul_ps(_mm_load_ps((float*)(matrix+1)), _mm_shuffle_ps(in,in,_MM_SHUFFLE(1,1,1,1)));
    __m128 a2 = _mm_mul_ps(_mm_load_ps((float*)(matrix+2)), _mm_shuffle_ps(in,in,_MM_SHUFFLE(2,2,2,2)));
 
    return _mm_add_ps(_mm_add_ps(a0,a1),a2);
}*/
#endif // SSE2
 
/*---------------------------------------------------------------
                getAsVector
---------------------------------------------------------------*/
void CPose3D::getAsVector(CVectorDouble &r) const
{
        updateYawPitchRoll();
        r.resize(6);
        r[0]=m_coords[0];
        r[1]=m_coords[1];
        r[2]=m_coords[2];
        r[3]=m_yaw;
        r[4]=m_pitch;
        r[5]=m_roll;
}
 
void CPose3D::getAsVector(mrpt::math::CArrayDouble<6> &r) const
{
        updateYawPitchRoll();
        r[0]=m_coords[0];
        r[1]=m_coords[1];
        r[2]=m_coords[2];
        r[3]=m_yaw;
        r[4]=m_pitch;
        r[5]=m_roll;
}
 
 
/*---------------------------------------------------------------
                unary -
---------------------------------------------------------------*/
CPose3D mrpt::poses::operator -(const CPose3D &b)
{
        CMatrixDouble44 B_INV(UNINITIALIZED_MATRIX);
        b.getInverseHomogeneousMatrix( B_INV );
        return CPose3D(B_INV);
}
 
void CPose3D::getAsQuaternion(mrpt::math::CQuaternionDouble &q, mrpt::math::CMatrixFixedNumeric<double,4,3>   *out_dq_dr ) const
{
        updateYawPitchRoll();
        mrpt::math::TPose3D(0, 0, 0, m_yaw, m_pitch, m_roll).getAsQuaternion(q, out_dq_dr);
}
 
bool mrpt::poses::operator==(const CPose3D &p1,const CPose3D &p2)
{
        return (p1.m_coords==p2.m_coords)&&(p1.getRotationMatrix()==p2.getRotationMatrix());
}
 
bool mrpt::poses::operator!=(const CPose3D &p1,const CPose3D &p2)
{
        return (p1.m_coords!=p2.m_coords)||(p1.getRotationMatrix()!=p2.getRotationMatrix());
}
 
/*---------------------------------------------------------------
                                point3D = pose3D + point3D
  ---------------------------------------------------------------*/
CPoint3D  CPose3D::operator + (const CPoint3D& b) const
{
        return CPoint3D(
                m_coords[0] + m_ROT(0,0)*b.x() + m_ROT(0,1)*b.y() +m_ROT(0,2)*b.z(),
                m_coords[1] + m_ROT(1,0)*b.x() + m_ROT(1,1)*b.y() +m_ROT(1,2)*b.z(),
                m_coords[2] + m_ROT(2,0)*b.x() + m_ROT(2,1)*b.y() +m_ROT(2,2)*b.z());
}
 
/*---------------------------------------------------------------
                                point3D = pose3D + point2D
  ---------------------------------------------------------------*/
CPoint3D  CPose3D::operator + (const CPoint2D& b) const
{
        return CPoint3D(
                m_coords[0] + m_ROT(0,0)*b.x() + m_ROT(0,1)*b.y(),
                m_coords[1] + m_ROT(1,0)*b.x() + m_ROT(1,1)*b.y(),
                m_coords[2] + m_ROT(2,0)*b.x() + m_ROT(2,1)*b.y());
}
 
 
/*---------------------------------------------------------------
                                this = A + B
  ---------------------------------------------------------------*/
void CPose3D::composeFrom(const CPose3D& A, const CPose3D& B )
{
        // The translation part HM(0:3,3)
        if (this==&B)
        {
                // we need to make a temporary copy of the vector:
                const CArrayDouble<3>  B_coords = B.m_coords;
                for (int r=0;r<3;r++)
                        m_coords[r] = A.m_coords[r] + A.m_ROT(r,0)*B_coords[0]+A.m_ROT(r,1)*B_coords[1]+A.m_ROT(r,2)*B_coords[2];
        }
        else
        {
                for (int r=0;r<3;r++)
                        m_coords[r] = A.m_coords[r] + A.m_ROT(r,0)*B.m_coords[0]+A.m_ROT(r,1)*B.m_coords[1]+A.m_ROT(r,2)*B.m_coords[2];
        }
 
        // Important: Make this multiplication AFTER the translational part, to cope with the case when A==this
        m_ROT.multiply_AB( A.m_ROT, B.m_ROT );
 
        m_ypr_uptodate=false;
}
 
/** Convert this pose into its inverse, saving the result in itself. */
void CPose3D::inverse()
{
        CMatrixDouble33  inv_rot(UNINITIALIZED_MATRIX);
        CArrayDouble<3>  inv_xyz;
 
        mrpt::math::homogeneousMatrixInverse(m_ROT,m_coords, inv_rot, inv_xyz);
 
        m_ROT = inv_rot;
        m_coords = inv_xyz;
        m_ypr_uptodate=false;
}
 
/*---------------------------------------------------------------
                                                isHorizontal
 ---------------------------------------------------------------*/
bool CPose3D::isHorizontal( const double tolerance  ) const
{
        updateYawPitchRoll();
        return (fabs(m_pitch)<=tolerance || M_PI-fabs(m_pitch) <=tolerance ) &&
               ( fabs(m_roll)<=tolerance || fabs(mrpt::math::wrapToPi( m_roll-M_PI))<=tolerance );
}
 
 
/**  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, composePoint
  */
void CPose3D::inverseComposeFrom(const CPose3D& A, const CPose3D& B )
{
        // this    =    A  (-)  B
        // HM_this = inv(HM_B) * HM_A
        //
        // [  R_b  | t_b ] -1   [  R_a  | t_a ]    [ R_b^t * Ra |    ..    ]
        // [ ------+-----]    * [ ------+-----]  = [ ---------- +----------]
        // [ 0 0 0 |  1  ]      [ 0 0 0 |  1  ]    [  0  0   0  |      1   ]
        //
 
        // XYZ part:
        CMatrixDouble33  R_b_inv(UNINITIALIZED_MATRIX);
        CArrayDouble<3>  t_b_inv;
        mrpt::math::homogeneousMatrixInverse(B.m_ROT,B.m_coords,  R_b_inv,t_b_inv);
 
        for (int i=0;i<3;i++)
                m_coords[i] = t_b_inv[i] + R_b_inv(i,0)*A.m_coords[0]+ R_b_inv(i,1)*A.m_coords[1]+ R_b_inv(i,2)*A.m_coords[2];
 
        // Rot part:
        m_ROT.multiply_AB( R_b_inv, A.m_ROT );
        m_ypr_uptodate=false;
}
 
/**  Computes the 3D point L such as \f$ L = G \ominus this \f$.
  * \sa composePoint, composeFrom
  */
void CPose3D::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,3,6>  *out_jacobian_df_dpose,
        mrpt::math::CMatrixFixedNumeric<double,3,6>  *out_jacobian_df_dse3
        )const
{
        CMatrixDouble33  R_inv(UNINITIALIZED_MATRIX);
        CArrayDouble<3>  t_inv;
        mrpt::math::homogeneousMatrixInverse(m_ROT,m_coords,  R_inv,t_inv);
 
        // Jacob: df/dpoint
        if (out_jacobian_df_dpoint)
                *out_jacobian_df_dpoint = R_inv;
 
        // Jacob: df/dpose
        if (out_jacobian_df_dpose)
        {
                // TODO: Perhaps this and the sin/cos's can be avoided if all needed terms are already in m_ROT ???
                updateYawPitchRoll();
 
#       ifdef HAVE_SINCOS
                double  cy,sy;
                ::sincos(m_yaw,&sy,&cy);
                double  cp,sp;
                ::sincos(m_pitch,&sp,&cp);
                double  cr,sr;
                ::sincos(m_roll,&sr,&cr);
#       else
                const double    cy = cos(m_yaw);
                const double    sy = sin(m_yaw);
                const double    cp = cos(m_pitch);
                const double    sp = sin(m_pitch);
                const double    cr = cos(m_roll);
                const double    sr = sin(m_roll);
#       endif
 
                const double m11_dy = -sy*cp;   const double m12_dy = cy*cp;    const double m13_dy = 0;
                const double m11_dp = -cy*sp;   const double m12_dp = -sy*sp;   const double m13_dp = -cp;
                const double m11_dr = 0;                const double m12_dr = 0;                const double m13_dr = 0;
 
                const double m21_dy = (-sy*sp*sr-cy*cr);        const double m22_dy = (cy*sp*sr-sy*cr);         const double m23_dy = 0;
                const double m21_dp = (cy*cp*sr );              const double m22_dp = (sy*cp*sr );                      const double m23_dp = -sp*sr;
                const double m21_dr = (cy*sp*cr+sy*sr);         const double m22_dr = (sy*sp*cr-cy*sr);         const double m23_dr = cp*cr;
 
                const double m31_dy = (-sy*sp*cr+cy*sr);        const double m32_dy = (cy*sp*cr+sy*sr);         const double m33_dy = 0;
                const double m31_dp = (cy*cp*cr );              const double m32_dp = (sy*cp*cr );                      const double m33_dp = -sp*cr;
                const double m31_dr = (-cy*sp*sr+sy*cr);        const double m32_dr = (-sy*sp*sr-cy*cr);        const double m33_dr = -cp*sr;
 
                const double Ax = gx-m_coords[0];
                const double Ay = gy-m_coords[1];
                const double Az = gz-m_coords[2];
 
                MRPT_ALIGN16 const double nums[3*6] = {
                        -m_ROT(0,0), -m_ROT(1,0), -m_ROT(2,0),
                                Ax*m11_dy + Ay*m12_dy + Az*m13_dy ,  // d_x'/d_yaw
                                Ax*m11_dp + Ay*m12_dp + Az*m13_dp,  // d_x'/d_pitch
                                Ax*m11_dr + Ay*m12_dr + Az*m13_dr,  // d_x'/d_roll
 
                        -m_ROT(0,1), -m_ROT(1,1), -m_ROT(2,1),
                                Ax*m21_dy + Ay*m22_dy + Az*m23_dy,  // d_x'/d_yaw
                                Ax*m21_dp + Ay*m22_dp + Az*m23_dp,  // d_x'/d_pitch
                                Ax*m21_dr + Ay*m22_dr + Az*m23_dr,  // d_x'/d_roll
 
                        -m_ROT(0,2), -m_ROT(1,2), -m_ROT(2,2),
                                Ax*m31_dy + Ay*m32_dy + Az*m33_dy,  // d_x'/d_yaw
                                Ax*m31_dp + Ay*m32_dp + Az*m33_dp,  // d_x'/d_pitch
                                Ax*m31_dr + Ay*m32_dr + Az*m33_dr,  // d_x'/d_roll
                        };
                out_jacobian_df_dpose->loadFromArray(nums);
        }
 
        lx = t_inv[0] +  R_inv(0,0) * gx + R_inv(0,1) * gy + R_inv(0,2) * gz;
        ly = t_inv[1] +  R_inv(1,0) * gx + R_inv(1,1) * gy + R_inv(1,2) * gz;
        lz = t_inv[2] +  R_inv(2,0) * gx + R_inv(2,1) * gy + R_inv(2,2) * gz;
 
        // Jacob: df/dse3
        if (out_jacobian_df_dse3)
        {
                MRPT_ALIGN16 const double nums[3*6] = {
                        -1, 0, 0,   0,-lz,  ly,
                        0, -1, 0,  lz,  0, -lx,
                        0, 0, -1, -ly, lx,   0 };
                out_jacobian_df_dse3->loadFromArray(nums);
        }
}
 
CPose3D CPose3D::exp(const mrpt::math::CArrayNumeric<double,6> & mu,bool pseudo_exponential )
{
        CPose3D P(UNINITIALIZED_POSE);
        CPose3D::exp(mu,P,pseudo_exponential);
        return P;
}
 
void CPose3D::exp(const mrpt::math::CArrayNumeric<double,6> & mu, CPose3D &out_pose, bool pseudo_exponential)
{
        if (pseudo_exponential)
        {
                auto R = Sophus::SO3<double>::exp( mu.block<3,1>(3,0) );
                out_pose.setRotationMatrix(R.matrix());
                out_pose.x(mu[0]);
                out_pose.y(mu[1]);
                out_pose.z(mu[2]);
        }
        else
        {
                auto R = Sophus::SE3<double>::exp(mu);
                out_pose = CPose3D( CMatrixDouble44(R.matrix()));
        }
}
 
CArrayDouble<3> CPose3D::ln_rotation() const
{
        Sophus::SO3<double> R(this->m_ROT);
        return R.log();
}
 
CMatrixDouble33 CPose3D::exp_rotation(const mrpt::math::CArrayNumeric<double,3> & w)
{
        auto R = Sophus::SO3<double>::exp(w);
        return R.matrix();
}
 
void CPose3D::ln(CArrayDouble<6> &result) const
{
        const Sophus::SE3<double> RT(m_ROT, m_coords);
        result = RT.log();
}
 
/* The following code fragments are based on formulas originally reported in the TooN and RobotVision packages */
namespace mrpt
{
        namespace poses
        {
                template <class VEC3,class MAT33>
                inline void deltaR(const MAT33& R, VEC3 &v)
                {
                        v[0]=R(2,1)-R(1,2);
                        v[1]=R(0,2)-R(2,0);
                        v[2]=R(1,0)-R(0,1);
                }
 
                template <typename VEC3,typename MAT3x3,typename MAT3x9>
                inline void M3x9(
                        const VEC3   &a,
                        const MAT3x3 &B,
                        MAT3x9       &RES)
                {
                        MRPT_ALIGN16 const double vals[] = {
                                a[0], -B(0,2), B(0,1), B(0,2), a[0], -B(0,0),-B(0,1), B(0,0), a[0],
                                a[1], -B(1,2), B(1,1), B(1,2), a[1], -B(1,0),-B(1,1), B(1,0), a[1],
                                a[2], -B(2,2), B(2,1), B(2,2), a[2], -B(2,0),-B(2,1), B(2,0), a[2]
                                };
                        RES.loadFromArray(vals);
                }
 
                inline CMatrixDouble33 ddeltaRt_dR(const CPose3D & P)
                {
                        const CMatrixDouble33 &R = P.getRotationMatrix();
                        const CArrayDouble<3> &t = P.m_coords;
 
                        CArrayDouble<3>  abc;
                        deltaR(R,abc);
                        double a = abc[0];
                        double b = abc[1];
                        double c = abc[2];
 
                        MRPT_ALIGN16 const double vals[] = {
                                -b*t[1]-c*t[2], 2*b*t[0]-a*t[1], 2*c*t[0]-a*t[2],
                                -b*t[0]+2*a*t[1],-a*t[0]-c*t[2], 2*c*t[1]-b*t[2],
                                -c*t[0]+2*a*t[2],-c*t[1]+2*b*t[2],-a*t[0]-b*t[1]
                                };
                        return CMatrixDouble33(vals);
                }
 
 
                inline void dVinvt_dR(const CPose3D &P, CMatrixFixedNumeric<double,3,9> &J)
                {
                        CArrayDouble<3>  a;
                        CMatrixDouble33  B(UNINITIALIZED_MATRIX);
 
                        const CMatrixDouble33 &R = P.getRotationMatrix();
                        const CArrayDouble<3> &t = P.m_coords;
 
                        const double d = 0.5*( R(0,0)+R(1,1)+R(2,2)-1);
 
                        if (d>0.9999)
                        {
                                a[0]=a[1]=a[2]=0;
                                B.zeros();
                        }
                        else
                        {
                                const double theta = acos(d);
                                const double theta2 = square(theta);
                                const double oned2 = (1-square(d));
                                const double sq = std::sqrt(oned2);
                                const double cot = 1./tan(0.5*theta);
                                const double csc2 = square(1./sin(0.5*theta));
 
                                CMatrixDouble33 skewR(UNINITIALIZED_MATRIX);
                                CArrayDouble<3>  vr;
                                deltaR(R,vr);
                                mrpt::math::skew_symmetric3(vr,skewR);
 
                                CArrayDouble<3> skewR_t;
                                skewR.multiply_Ab(t,skewR_t);
 
                                skewR_t*= -(d*theta-sq)/(8*pow(sq,3));
                                a = skewR_t;
 
                                CMatrixDouble33  skewR2(UNINITIALIZED_MATRIX);
                                skewR2.multiply_AB(skewR,skewR);
 
                                CArrayDouble<3> skewR2_t;
                                skewR2.multiply_Ab(t,skewR2_t);
                                skewR2_t*= (((theta*sq-d*theta2)*(0.5*theta*cot-1))-theta*sq*((0.25*theta*cot)+0.125*theta2*csc2-1))/(4*theta2*square(oned2));
                                a += skewR2_t;
 
                                mrpt::math::skew_symmetric3(t,B);
                                B *=-0.5*theta/(2*sq);
 
                                B += -(theta*cot-2)/(8*oned2) * ddeltaRt_dR(P);
                        }
                        M3x9(a,B,J);
                }
        }
}
 
void CPose3D::ln_jacob(mrpt::math::CMatrixFixedNumeric<double,6,12> &J) const
{
        J.zeros();
        // Jacobian structure 6x12:
        // (3rows, for t)       [       d_Vinvt_dR (3x9)    |  Vinv (3x3)  ]
        //                      [  -------------------------+------------- ]
        // (3rows, for \omega)  [       d_lnR_dR   (3x9)    |    0 (3x3)   ]
        //
        //          derivs wrt:     R_col1 R_col2  R_col3   |       t
        //
        // (Will be explained better in: http://www.mrpt.org/6D_poses:equivalences_compositions_and_uncertainty )
        //
        {
                CMatrixFixedNumeric<double,3,9> M(UNINITIALIZED_MATRIX);
                ln_rot_jacob(m_ROT, M);
                J.insertMatrix(3,0, M);
        }
        {
                CMatrixFixedNumeric<double,3,9> M(UNINITIALIZED_MATRIX);
                dVinvt_dR(*this,M);
                J.insertMatrix(0,0, M);
        }
 
        const CMatrixDouble33 & R = m_ROT;
        CArrayDouble<3> omega;
        CMatrixDouble33 Omega(UNINITIALIZED_MATRIX);
 
        CMatrixDouble33 V_inv(UNINITIALIZED_MATRIX);
        V_inv.unit(3,1.0); // Start with the identity_3
 
        const double d = 0.5*( R(0,0)+R(1,1)+R(2,2)-1);
        if (d>0.99999)
        {
                mrpt::poses::deltaR(R,omega);
                omega*=0.5;
                mrpt::math::skew_symmetric3(omega,Omega);
                CMatrixDouble33 Omega2(UNINITIALIZED_MATRIX);
                Omega2.multiply_AAt(Omega);
                Omega2*=1.0/12.0;
 
                Omega*=0.5;
 
                V_inv -= Omega;
                V_inv -= Omega2;
        }
        else
        {
                mrpt::poses::deltaR(R,omega);
 
                const double theta = acos(d);
                omega *=theta/(2*std::sqrt(1-d*d));
 
                mrpt::math::skew_symmetric3(omega,Omega);
 
                CMatrixDouble33 Omega2(UNINITIALIZED_MATRIX);
                Omega2.multiply_AAt(Omega);
 
                Omega2 *= (1-theta/(2*std::tan(theta*0.5)))/square(theta);
                Omega  *= 0.5;
 
                V_inv -= Omega;
                V_inv += Omega2;
        }
        J.insertMatrix(0,9, V_inv);
}
 
void CPose3D::ln_rot_jacob(const CMatrixDouble33 &R, CMatrixFixedNumeric<double,3,9> &M)
{
        const double d = 0.5*(R(0,0)+R(1,1)+R(2,2)-1);
        CArrayDouble<3>  a;
        CMatrixDouble33  B(UNINITIALIZED_MATRIX);
        if(d>0.99999)
        {
                a[0]=a[1]=a[2]=0;
                B.unit(3,-0.5);
        }
        else
        {
                const double theta = acos(d);
                const double d2 = square(d);
                const double sq = std::sqrt(1-d2);
                deltaR(R,a);
                a *= (d*theta-sq)/(4*(sq*sq*sq));
                B.unit(3, -theta/(2*sq) );
        }
        M3x9(a,B, M);
}
 
// Eq. 10.3.5 in tech report http://ingmec.ual.es/~jlblanco/papers/jlblanco2010geometry3D_techrep.pdf
void CPose3D::jacob_dexpeD_de(const CPose3D &D, Eigen::Matrix<double,12,6> & jacob)
{
        jacob.block<9,3>(0,0).setZero();
        jacob.block<3,3>(9,0).setIdentity();
        for (int i=0;i<3;i++) {
                Eigen::Block< Eigen::Matrix<double,12,6>,3,3,false> trg_blc = jacob.block<3,3>(3*i,3);
                mrpt::math::skew_symmetric3_neg( D.m_ROT.block<3,1>(0,i), trg_blc );
        }
        {
                Eigen::Block< Eigen::Matrix<double,12,6>,3,3,false> trg_blc = jacob.block<3,3>(9,3);
                mrpt::math::skew_symmetric3_neg( D.m_coords, trg_blc );
        }
}
 
// Eq. 10.3.7 in tech report http://ingmec.ual.es/~jlblanco/papers/jlblanco2010geometry3D_techrep.pdf
void CPose3D::jacob_dAexpeD_de(const CPose3D &A, const CPose3D &D, Eigen::Matrix<double,12,6> & jacob)
{
        jacob.block<9,3>(0,0).setZero();
        jacob.block<3,3>(9,0) = A.getRotationMatrix();
        Eigen::Matrix<double,3,3> aux;
        for (int i=0;i<3;i++) {
                mrpt::math::skew_symmetric3_neg( D.getRotationMatrix().block<3,1>(0,i),aux );
                jacob.block<3,3>(3*i,3) = A.m_ROT * aux;
        }
        mrpt::math::skew_symmetric3_neg( D.m_coords, aux );
        jacob.block<3,3>(9,3) = A.m_ROT * aux;
}
 
void CPose3D::setToNaN()
{
        for (int i=0;i<3;i++)
                for (int j=0;j<3;j++)
                        m_ROT(i,j) = std::numeric_limits<double>::quiet_NaN();
 
        for (int i=0;i<3;i++)
                m_coords[i] = std::numeric_limits<double>::quiet_NaN();
}