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#include "LinearTransformations.h"
#include "utility.h"
#include <cstdlib>
#include <cmath>
namespace meow{
template<class Scalar>
inline void
Rotation3D<Scalar>::calcMatrix(){
Scalar sum(0.0);
for(size_t i = 0; i < 3u; i++){
sum = sum + squ(_theta(i, 0));
}
Scalar t(sqrt(double(sum)));
std::vector<Scalar> u(3);
for(size_t i = 0; i < 3u; i++){
u[i] = _theta[i] / t;
}
Scalar cs(cos(double(t)));
Scalar sn(sin(double(t)));
_matrix.entry(0, 0, cs + squ(u[0]) * ((1 - cs)));
_matrix.entry(1, 1, cs + squ(u[1]) * ((1 - cs)));
_matrix.entry(2, 2, cs + squ(u[2]) * ((1 - cs)));
_matrix.entry(0, 1, u[0] * u[1] * (1 - cs) - u[2] * sn);
_matrix.entry(1, 0, u[1] * u[0] * (1 - cs) + u[2] * sn);
_matrix.entry(0, 2, u[0] * u[2] * (1 - cs) + u[1] * sn);
_matrix.entry(2, 0, u[2] * u[0] * (1 - cs) - u[1] * sn);
_matrix.entry(1, 2, u[1] * u[2] * (1 - cs) - u[0] * sn);
_matrix.entry(2, 1, u[2] * u[1] * (1 - cs) + u[0] * sn);
}
template<class Scalar>
inline
Rotation3D<Scalar>::Rotation3D():
LinearTransformation(3u, 3u, 3u){
_theta[0] = _theta[1] = _theta[2] = Scalar(0);
_matrix.identitied();
}
template<class Scalar>
inline void
Rotation3D<Scalar>::axisTheta(Matrix<Scalar> const& __axis,
Scalar const& __theta){
Scalar sum(0.0);
for(size_t i = 0; i < 3u; i++)
sum = sum + squ(__axis(i, 0));
Scalar t(sqrt(double(sum)));
for(size_t i = 0; i < 3u; i++)
_theta[i] = __axis(i, 0) * __theta / t;
calcMatrix();
}
template<class Scalar>
inline Scalar
Rotation3D<Scalar>::parameter(size_t __i) const{
return _theta[__i];
}
template<class Scalar>
inline Scalar
Rotation3D<Scalar>::parameter(size_t __i, Scalar const& __s) const{
_theta[__i] = __s;
calcMatrix();
return _theta[__i];
}
template<class Scalar>
inline Matrix<Scalar>
Rotation3D<Scalar>::transformate(Matrix<Scalar> const& __x) const{
return _matrix * __x;
}
template<class Scalar>
inline Matrix<Scalar>
Rotation3D<Scalar>::jacobian(Matrix<Scalar> const& __x) const{
return _matrix;
}
template<class Scalar>
inline Matrix<Scalar>
Rotation3D<Scalar>::jacobian(Matrix<Scalar> const& __x,
size_t __i) const{
Matrix<Scalar> mid(3u, 3u, Scalar(0.0));
if(__i == 0){
mid.entry(1, 2, Scalar(-1.0));
mid.entry(2, 1, Scalar( 1.0));
}else if(__i == 1){
mid.entry(0, 2, Scalar( 1.0));
mid.entry(2, 0, Scalar(-1.0));
}else{
mid.entry(0, 1, Scalar(-1.0));
mid.entry(1, 0, Scalar( 1.0));
}
return _matrix * mid * __x;
}
template<class Scalar>
inline Matrix<Scalar>
Rotation3D<Scalar>::invTransformate(Matrix<Scalar> const& __x) const{
return _matrix.transpose() * __x;
}
template<class Scalar>
inline Matrix<Scalar>
Rotation3D<Scalar>::invJacobian(Matrix<Scalar> const& __x) const{
return _matrix.transpose();
}
template<class Scalar>
inline Matrix<Scalar>
Rotation3D<Scalar>::invJacobian(Matrix<Scalar> const& __x,
size_t __i) const{
Matrix<Scalar> mid(3u, 3u, Scalar(0.0));
if(__i == 0){
mid.entry(1, 2, Scalar(-1.0));
mid.entry(2, 1, Scalar( 1.0));
}else if(__i == 1){
mid.entry(0, 2, Scalar( 1.0));
mid.entry(2, 0, Scalar(-1.0));
}else{
mid.entry(0, 1, Scalar(-1.0));
mid.entry(1, 0, Scalar( 1.0));
}
return _matrix.transpose() * mid.transpose() * __x;
}
template<class Scalar>
inline Matrix<Scalar>
Rotation3D<Scalar>::invMatrix() const{
return _matrix.transpose();
}
}
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