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math/example/HSO4.hpp

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/********************************************************************************************/
/* */
/* HSO4.hpp header file */
/* */
/* This file is not currently part of the Boost library. It is simply an example of the use */
/* quaternions can be put to. Hopefully it will be usefull too. */
/* */
/* This file provides tools to convert between quaternions and R^4 rotation matrices. */
/* */
/********************************************************************************************/
// (C) Copyright Hubert Holin 2001.
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
#ifndef TEST_HSO4_HPP
#define TEST_HSO4_HPP
#include <utility>
#include "HSO3.hpp"
template<typename TYPE_FLOAT>
struct R4_matrix
{
TYPE_FLOAT a11, a12, a13, a14;
TYPE_FLOAT a21, a22, a23, a24;
TYPE_FLOAT a31, a32, a33, a34;
TYPE_FLOAT a41, a42, a43, a44;
};
// Note: the input quaternions need not be of norm 1 for the following function
template<typename TYPE_FLOAT>
R4_matrix<TYPE_FLOAT> quaternions_to_R4_rotation(::std::pair< ::boost::math::quaternion<TYPE_FLOAT> , ::boost::math::quaternion<TYPE_FLOAT> > const & pq)
{
using ::std::numeric_limits;
TYPE_FLOAT a0 = pq.first.R_component_1();
TYPE_FLOAT b0 = pq.first.R_component_2();
TYPE_FLOAT c0 = pq.first.R_component_3();
TYPE_FLOAT d0 = pq.first.R_component_4();
TYPE_FLOAT norme_carre0 = a0*a0+b0*b0+c0*c0+d0*d0;
if (norme_carre0 <= numeric_limits<TYPE_FLOAT>::epsilon())
{
::std::string error_reporting("Argument to quaternions_to_R4_rotation is too small!");
::std::underflow_error bad_argument(error_reporting);
throw(bad_argument);
}
TYPE_FLOAT a1 = pq.second.R_component_1();
TYPE_FLOAT b1 = pq.second.R_component_2();
TYPE_FLOAT c1 = pq.second.R_component_3();
TYPE_FLOAT d1 = pq.second.R_component_4();
TYPE_FLOAT norme_carre1 = a1*a1+b1*b1+c1*c1+d1*d1;
if (norme_carre1 <= numeric_limits<TYPE_FLOAT>::epsilon())
{
::std::string error_reporting("Argument to quaternions_to_R4_rotation is too small!");
::std::underflow_error bad_argument(error_reporting);
throw(bad_argument);
}
TYPE_FLOAT prod_norm = norme_carre0*norme_carre1;
TYPE_FLOAT a0a1 = a0*a1;
TYPE_FLOAT a0b1 = a0*b1;
TYPE_FLOAT a0c1 = a0*c1;
TYPE_FLOAT a0d1 = a0*d1;
TYPE_FLOAT b0a1 = b0*a1;
TYPE_FLOAT b0b1 = b0*b1;
TYPE_FLOAT b0c1 = b0*c1;
TYPE_FLOAT b0d1 = b0*d1;
TYPE_FLOAT c0a1 = c0*a1;
TYPE_FLOAT c0b1 = c0*b1;
TYPE_FLOAT c0c1 = c0*c1;
TYPE_FLOAT c0d1 = c0*d1;
TYPE_FLOAT d0a1 = d0*a1;
TYPE_FLOAT d0b1 = d0*b1;
TYPE_FLOAT d0c1 = d0*c1;
TYPE_FLOAT d0d1 = d0*d1;
R4_matrix<TYPE_FLOAT> out_matrix;
out_matrix.a11 = (+a0a1+b0b1+c0c1+d0d1)/prod_norm;
out_matrix.a12 = (+a0b1-b0a1-c0d1+d0c1)/prod_norm;
out_matrix.a13 = (+a0c1+b0d1-c0a1-d0b1)/prod_norm;
out_matrix.a14 = (+a0d1-b0c1+c0b1-d0a1)/prod_norm;
out_matrix.a21 = (-a0b1+b0a1-c0d1+d0c1)/prod_norm;
out_matrix.a22 = (+a0a1+b0b1-c0c1-d0d1)/prod_norm;
out_matrix.a23 = (-a0d1+b0c1+c0b1-d0a1)/prod_norm;
out_matrix.a24 = (+a0c1+b0d1+c0a1+d0b1)/prod_norm;
out_matrix.a31 = (-a0c1+b0d1+c0a1-d0b1)/prod_norm;
out_matrix.a32 = (+a0d1+b0c1+c0b1+d0a1)/prod_norm;
out_matrix.a33 = (+a0a1-b0b1+c0c1-d0d1)/prod_norm;
out_matrix.a34 = (-a0b1-b0a1+c0d1+d0c1)/prod_norm;
out_matrix.a41 = (-a0d1-b0c1+c0b1+d0a1)/prod_norm;
out_matrix.a42 = (-a0c1+b0d1-c0a1+d0b1)/prod_norm;
out_matrix.a43 = (+a0b1+b0a1+c0d1+d0c1)/prod_norm;
out_matrix.a44 = (+a0a1-b0b1-c0c1+d0d1)/prod_norm;
return(out_matrix);
}
template<typename TYPE_FLOAT>
inline bool is_R4_rotation_matrix(R4_matrix<TYPE_FLOAT> const & mat)
{
using ::std::abs;
using ::std::numeric_limits;
return (
!(
(abs(mat.a11*mat.a11+mat.a21*mat.a21+mat.a31*mat.a31+mat.a41*mat.a41 - static_cast<TYPE_FLOAT>(1)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a11*mat.a12+mat.a21*mat.a22+mat.a31*mat.a32+mat.a41*mat.a42 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a11*mat.a13+mat.a21*mat.a23+mat.a31*mat.a33+mat.a41*mat.a43 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a11*mat.a14+mat.a21*mat.a24+mat.a31*mat.a34+mat.a41*mat.a44 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
//(abs(mat.a11*mat.a12+mat.a21*mat.a22+mat.a31*mat.a32+mat.a41*mat.a42 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a12*mat.a12+mat.a22*mat.a22+mat.a32*mat.a32+mat.a42*mat.a42 - static_cast<TYPE_FLOAT>(1)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a12*mat.a13+mat.a22*mat.a23+mat.a32*mat.a33+mat.a42*mat.a43 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a12*mat.a14+mat.a22*mat.a24+mat.a32*mat.a34+mat.a42*mat.a44 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
//(abs(mat.a11*mat.a13+mat.a21*mat.a23+mat.a31*mat.a33+mat.a41*mat.a43 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
//(abs(mat.a12*mat.a13+mat.a22*mat.a23+mat.a32*mat.a33+mat.a42*mat.a43 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a13*mat.a13+mat.a23*mat.a23+mat.a33*mat.a33+mat.a43*mat.a43 - static_cast<TYPE_FLOAT>(1)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a13*mat.a14+mat.a23*mat.a24+mat.a33*mat.a34+mat.a43*mat.a44 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
//(abs(mat.a11*mat.a14+mat.a21*mat.a24+mat.a31*mat.a34+mat.a41*mat.a44 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
//(abs(mat.a12*mat.a14+mat.a22*mat.a24+mat.a32*mat.a34+mat.a42*mat.a44 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
//(abs(mat.a13*mat.a14+mat.a23*mat.a24+mat.a33*mat.a34+mat.a43*mat.a44 - static_cast<TYPE_FLOAT>(0)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())||
(abs(mat.a14*mat.a14+mat.a24*mat.a24+mat.a34*mat.a34+mat.a44*mat.a44 - static_cast<TYPE_FLOAT>(1)) > static_cast<TYPE_FLOAT>(10)*numeric_limits<TYPE_FLOAT>::epsilon())
)
);
}
template<typename TYPE_FLOAT>
::std::pair< ::boost::math::quaternion<TYPE_FLOAT> , ::boost::math::quaternion<TYPE_FLOAT> > R4_rotation_to_quaternions( R4_matrix<TYPE_FLOAT> const & rot,
::std::pair< ::boost::math::quaternion<TYPE_FLOAT> , ::boost::math::quaternion<TYPE_FLOAT> > const * hint = 0)
{
if (!is_R4_rotation_matrix(rot))
{
::std::string error_reporting("Argument to R4_rotation_to_quaternions is not an R^4 rotation matrix!");
::std::range_error bad_argument(error_reporting);
throw(bad_argument);
}
R3_matrix<TYPE_FLOAT> mat;
mat.a11 = -rot.a31*rot.a42+rot.a32*rot.a41+rot.a22*rot.a11-rot.a21*rot.a12;
mat.a12 = -rot.a31*rot.a43+rot.a33*rot.a41+rot.a23*rot.a11-rot.a21*rot.a13;
mat.a13 = -rot.a31*rot.a44+rot.a34*rot.a41+rot.a24*rot.a11-rot.a21*rot.a14;
mat.a21 = -rot.a31*rot.a12-rot.a22*rot.a41+rot.a32*rot.a11+rot.a21*rot.a42;
mat.a22 = -rot.a31*rot.a13-rot.a23*rot.a41+rot.a33*rot.a11+rot.a21*rot.a43;
mat.a23 = -rot.a31*rot.a14-rot.a24*rot.a41+rot.a34*rot.a11+rot.a21*rot.a44;
mat.a31 = +rot.a31*rot.a22-rot.a12*rot.a41+rot.a42*rot.a11-rot.a21*rot.a32;
mat.a32 = +rot.a31*rot.a23-rot.a13*rot.a41+rot.a43*rot.a11-rot.a21*rot.a33;
mat.a33 = +rot.a31*rot.a24-rot.a14*rot.a41+rot.a44*rot.a11-rot.a21*rot.a34;
::boost::math::quaternion<TYPE_FLOAT> q = R3_rotation_to_quaternion(mat);
::boost::math::quaternion<TYPE_FLOAT> p =
::boost::math::quaternion<TYPE_FLOAT>(rot.a11,rot.a12,rot.a13,rot.a14)*q;
if ((hint != 0) && (abs(hint->second+q) < abs(hint->second-q)))
{
return(::std::make_pair(-p,-q));
}
return(::std::make_pair(p,q));
}
#endif /* TEST_HSO4_HPP */
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