dcovector_small.hpp File Reference

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Classes
class	dcovector_small< l >
	Samll Real Double-precision Column Vector Class. More...

Functions
double	operator/ (const dcovec2 &, const dcovec2 &)
dcovec2	rotate (const dcovec2 &, const double &)
dcovec3	operator/ (const dcovec3 &, const dcovec3 &)
dcovec3	operator/= (dcovec3 &, const dcovec3 &)
dquater	vr2q (const dcovec3 &, const double &)
dquater	vt2q (const dcovec3 &, const double &)
dcovec3	rotate (const dcovec3 &, const dquater &)
dquater	conj (const dquater &)
dcovec3	imag (const dquater &)
dquater	inv (const dquater &)
dquater	operator* (const dquater &, const dquater &)
dquater	operator/ (const dquater &, const dquater &)
dquater	operator*= (dquater &, const dquater &)
dquater	operator/= (dquater &, const dquater &)
dcovec3	q2vt (const dquater &)
dgemat3	q2m (const dquater &)

Function Documentation

double operator/ ( const dcovec2 &  A, const dcovec2 &  B  )

inline

calculate vector product only for 2D vector

Definition at line 3 of file dcovector_small-specialized.hpp.

{CPPL_VERBOSE_REPORT;
  return A(0)*B(1) -A(1)*B(0);
}

dcovec2 rotate ( const dcovec2 &  v, const double &  t  )

inline

rotate 2D vector by theta [rad]

Definition at line 17 of file dcovector_small-specialized.hpp.

{CPPL_VERBOSE_REPORT;
  dcovec2 w;
  w(0) =v(0)*std::cos(t) -v(1)*std::sin(t);
  w(1) =v(0)*std::sin(t) +v(1)*std::cos(t);
  return w;
}

dcovec3 operator/ ( const dcovec3 &  A, const dcovec3 &  B  )

inline

calculate vector product only for 3D vector

Definition at line 37 of file dcovector_small-specialized.hpp.

{CPPL_VERBOSE_REPORT;
  dcovec3 C;
  C(0) =A(1)*B(2) -A(2)*B(1);
  C(1) =A(2)*B(0) -A(0)*B(2);
  C(2) =A(0)*B(1) -A(1)*B(0);
  return C;
}

dcovec3 operator/= ( dcovec3 &  A, const dcovec3 &  B  )

inline

calculate vector product only for 3D vector

Definition at line 48 of file dcovector_small-specialized.hpp.

{CPPL_VERBOSE_REPORT;
  A =A/B;
  return A;
}

dquater vr2q ( const dcovec3 &  v, const double &  r  )

inline

make quaternion from imag vector and real value

Definition at line 56 of file dcovector_small-specialized.hpp.

Referenced by rotate(), and vt2q().

{CPPL_VERBOSE_REPORT;
  return dquater(v(0),v(1),v(2),r);
}

dquater vt2q ( const dcovec3 &  v, const double &  theta  )

inline

make quaternion from directional vector and rotational angle

Definition at line 63 of file dcovector_small-specialized.hpp.

References nrm2(), and vr2q().

Referenced by m2q().

{CPPL_VERBOSE_REPORT;
  return vr2q( v/(nrm2(v)+DBL_MIN)*std::sin(0.5*theta), std::cos(0.5*theta) );
}

dcovec3 rotate ( const dcovec3 &  v, const dquater &  q  )

inline

rotate 3D vector by quaternion

Definition at line 70 of file dcovector_small-specialized.hpp.

References conj(), imag(), and vr2q().

{CPPL_VERBOSE_REPORT;
  return imag( q*vr2q(v,0.)*conj(q) );
}

dquater conj ( const dquater &  q )

inline

conjuction

Definition at line 87 of file dcovector_small-specialized.hpp.

Referenced by inv(), q2m(), and rotate().

{CPPL_VERBOSE_REPORT;
  return dquater(-q(0),-q(1),-q(2), q(3));
}

dcovec3 imag ( const dquater &  q )

inline

imag

Definition at line 94 of file dcovector_small-specialized.hpp.

Referenced by zhsmatrix::checkup(), zhematrix::complete(), operator<<(), rotate(), _zhematrix::write(), and zhematrix::write().

{CPPL_VERBOSE_REPORT;
  return dcovec3(q(0),q(1),q(2));
}

dquater inv ( const dquater &  q )

inline

inverse

Definition at line 101 of file dcovector_small-specialized.hpp.

References conj(), and nrm2().

Referenced by operator/().

{CPPL_VERBOSE_REPORT;
  return conj(q)/std::pow(nrm2(q),2);
}

dquater operator* ( const dquater &  q1, const dquater &  q2  )

inline

dquater*dquater operator

Definition at line 108 of file dcovector_small-specialized.hpp.

{CPPL_VERBOSE_REPORT;
  return dquater(q1(3)*q2(0) +q1(0)*q2(3) +q1(1)*q2(2) -q1(2)*q2(1),
                 q1(3)*q2(1) -q1(0)*q2(2) +q1(1)*q2(3) +q1(2)*q2(0),
                 q1(3)*q2(2) +q1(0)*q2(1) -q1(1)*q2(0) +q1(2)*q2(3),
                 q1(3)*q2(3) -q1(0)*q2(0) -q1(1)*q2(1) -q1(2)*q2(2) );
}

dquater operator/ ( const dquater &  q1, const dquater &  q2  )

inline

dquater/dquater operator

Definition at line 118 of file dcovector_small-specialized.hpp.

References inv().

{CPPL_VERBOSE_REPORT;
  return q1*inv(q2);
}

dquater operator*= ( dquater &  q1, const dquater &  q2  )

inline

dquater*=dquater operator

Definition at line 125 of file dcovector_small-specialized.hpp.

{CPPL_VERBOSE_REPORT;
  q1 =q1*q2;
  return q1;
}

dquater operator/= ( dquater &  q1, const dquater &  q2  )

inline

dquater/=dquater operator

Definition at line 133 of file dcovector_small-specialized.hpp.

{CPPL_VERBOSE_REPORT;
  q1 =q1/q2;
  return q1;
}

dcovec3 q2vt ( const dquater &  q )

inline

return vector from quaternion (|vector|=theta)

Definition at line 141 of file dcovector_small-specialized.hpp.

{CPPL_VERBOSE_REPORT;
  double sin_theta_half;
  double theta( 2.*std::acos(q(3)) );
  
  if(theta<M_PI){
    sin_theta_half =std::sin(0.5*theta);
  }
  else{
    theta -=2.*M_PI;
    sin_theta_half =-std::sin(0.5*theta);
  }
  
  return dcovec3( theta*q(0)/sin_theta_half,
                  theta*q(1)/sin_theta_half,
                  theta*q(2)/sin_theta_half );
}

dgemat3 q2m ( const dquater &  q )

inline

return rotational matrix made of quaternion

Definition at line 161 of file dcovector_small-specialized.hpp.

References conj().

Referenced by rotate().

{CPPL_VERBOSE_REPORT;
  dquater cq( conj(q) );
  dquater X( dquater(+q(3),+q(2),-q(1),-q(0))*cq );
  dquater Y( dquater(-q(2),+q(3),+q(0),-q(1))*cq );
  dquater Z( dquater(+q(1),-q(0),+q(3),-q(2))*cq );
  dgemat3 mat;
  mat(0,0)=X(0); mat(0,1)=Y(0); mat(0,2)=Z(0);
  mat(1,0)=X(1); mat(1,1)=Y(1); mat(1,2)=Z(1);
  mat(2,0)=X(2); mat(2,1)=Y(2); mat(2,2)=Z(2);
  return mat;
}