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#ifndef OPENCV_CORE_AFFINE3_HPP
#define OPENCV_CORE_AFFINE3_HPP
#ifdef __cplusplus
#include <opencv2/core.hpp>
namespace cv
{
//! @addtogroup core
//! @{
/** @brief Affine transform
*
* It represents a 4x4 homogeneous transformation matrix \f$T\f$
*
* \f[T =
* \begin{bmatrix}
* R & t\\
* 0 & 1\\
* \end{bmatrix}
* \f]
*
* where \f$R\f$ is a 3x3 rotation matrix and \f$t\f$ is a 3x1 translation vector.
*
* You can specify \f$R\f$ either by a 3x3 rotation matrix or by a 3x1 rotation vector,
* which is converted to a 3x3 rotation matrix by the Rodrigues formula.
*
* To construct a matrix \f$T\f$ representing first rotation around the axis \f$r\f$ with rotation
* angle \f$|r|\f$ in radian (right hand rule) and then translation by the vector \f$t\f$, you can use
*
* @code
* cv::Vec3f r, t;
* cv::Affine3f T(r, t);
* @endcode
*
* If you already have the rotation matrix \f$R\f$, then you can use
*
* @code
* cv::Matx33f R;
* cv::Affine3f T(R, t);
* @endcode
*
* To extract the rotation matrix \f$R\f$ from \f$T\f$, use
*
* @code
* cv::Matx33f R = T.rotation();
* @endcode
*
* To extract the translation vector \f$t\f$ from \f$T\f$, use
*
* @code
* cv::Vec3f t = T.translation();
* @endcode
*
* To extract the rotation vector \f$r\f$ from \f$T\f$, use
*
* @code
* cv::Vec3f r = T.rvec();
* @endcode
*
* Note that since the mapping from rotation vectors to rotation matrices
* is many to one. The returned rotation vector is not necessarily the one
* you used before to set the matrix.
*
* If you have two transformations \f$T = T_1 * T_2\f$, use
*
* @code
* cv::Affine3f T, T1, T2;
* T = T2.concatenate(T1);
* @endcode
*
* To get the inverse transform of \f$T\f$, use
*
* @code
* cv::Affine3f T, T_inv;
* T_inv = T.inv();
* @endcode
*
*/
template<typename T>
class Affine3
{
public:
typedef T float_type;
typedef Matx<float_type, 3, 3> Mat3;
typedef Matx<float_type, 4, 4> Mat4;
typedef Vec<float_type, 3> Vec3;
//! Default constructor. It represents a 4x4 identity matrix.
Affine3();
//! Augmented affine matrix
Affine3(const Mat4& affine);
/**
* The resulting 4x4 matrix is
*
* \f[
* \begin{bmatrix}
* R & t\\
* 0 & 1\\
* \end{bmatrix}
* \f]
*
* @param R 3x3 rotation matrix.
* @param t 3x1 translation vector.
*/
Affine3(const Mat3& R, const Vec3& t = Vec3::all(0));
/**
* Rodrigues vector.
*
* The last row of the current matrix is set to [0,0,0,1].
*
* @param rvec 3x1 rotation vector. Its direction indicates the rotation axis and its length
* indicates the rotation angle in radian (using right hand rule).
* @param t 3x1 translation vector.
*/
Affine3(const Vec3& rvec, const Vec3& t = Vec3::all(0));
/**
* Combines all constructors above. Supports 4x4, 3x4, 3x3, 1x3, 3x1 sizes of data matrix.
*
* The last row of the current matrix is set to [0,0,0,1] when data is not 4x4.
*
* @param data 1-channel matrix.
* when it is 4x4, it is copied to the current matrix and t is not used.
* When it is 3x4, it is copied to the upper part 3x4 of the current matrix and t is not used.
* When it is 3x3, it is copied to the upper left 3x3 part of the current matrix.
* When it is 3x1 or 1x3, it is treated as a rotation vector and the Rodrigues formula is used
* to compute a 3x3 rotation matrix.
* @param t 3x1 translation vector. It is used only when data is neither 4x4 nor 3x4.
*/
explicit Affine3(const Mat& data, const Vec3& t = Vec3::all(0));
//! From 16-element array
explicit Affine3(const float_type* vals);
//! Create an 4x4 identity transform
static Affine3 Identity();
/**
* Rotation matrix.
*
* Copy the rotation matrix to the upper left 3x3 part of the current matrix.
* The remaining elements of the current matrix are not changed.
*
* @param R 3x3 rotation matrix.
*
*/
void rotation(const Mat3& R);
/**
* Rodrigues vector.
*
* It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.
*
* @param rvec 3x1 rotation vector. The direction indicates the rotation axis and
* its length indicates the rotation angle in radian (using the right thumb convention).
*/
void rotation(const Vec3& rvec);
/**
* Combines rotation methods above. Supports 3x3, 1x3, 3x1 sizes of data matrix.
*
* It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.
*
* @param data 1-channel matrix.
* When it is a 3x3 matrix, it sets the upper left 3x3 part of the current matrix.
* When it is a 1x3 or 3x1 matrix, it is used as a rotation vector. The Rodrigues formula
* is used to compute the rotation matrix and sets the upper left 3x3 part of the current matrix.
*/
void rotation(const Mat& data);
/**
* Copy the 3x3 matrix L to the upper left part of the current matrix
*
* It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.
*
* @param L 3x3 matrix.
*/
void linear(const Mat3& L);
/**
* Copy t to the first three elements of the last column of the current matrix
*
* It sets the upper right 3x1 part of the matrix. The remaining part is unaffected.
*
* @param t 3x1 translation vector.
*/
void translation(const Vec3& t);
//! @return the upper left 3x3 part
Mat3 rotation() const;
//! @return the upper left 3x3 part
Mat3 linear() const;
//! @return the upper right 3x1 part
Vec3 translation() const;
//! Rodrigues vector.
//! @return a vector representing the upper left 3x3 rotation matrix of the current matrix.
//! @warning Since the mapping between rotation vectors and rotation matrices is many to one,
//! this function returns only one rotation vector that represents the current rotation matrix,
//! which is not necessarily the same one set by `rotation(const Vec3& rvec)`.
Vec3 rvec() const;
//! @return the inverse of the current matrix.
Affine3 inv(int method = cv::DECOMP_SVD) const;
//! a.rotate(R) is equivalent to Affine(R, 0) * a;
Affine3 rotate(const Mat3& R) const;
//! a.rotate(rvec) is equivalent to Affine(rvec, 0) * a;
Affine3 rotate(const Vec3& rvec) const;
//! a.translate(t) is equivalent to Affine(E, t) * a, where E is an identity matrix
Affine3 translate(const Vec3& t) const;
//! a.concatenate(affine) is equivalent to affine * a;
Affine3 concatenate(const Affine3& affine) const;
template <typename Y> operator Affine3<Y>() const;
template <typename Y> Affine3<Y> cast() const;
Mat4 matrix;
#if defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H
Affine3(const Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>& affine);
Affine3(const Eigen::Transform<T, 3, Eigen::Affine>& affine);
operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>() const;
operator Eigen::Transform<T, 3, Eigen::Affine>() const;
#endif
};
template<typename T> static
Affine3<T> operator*(const Affine3<T>& affine1, const Affine3<T>& affine2);
//! V is a 3-element vector with member fields x, y and z
template<typename T, typename V> static
V operator*(const Affine3<T>& affine, const V& vector);
typedef Affine3<float> Affine3f;
typedef Affine3<double> Affine3d;
static Vec3f operator*(const Affine3f& affine, const Vec3f& vector);
static Vec3d operator*(const Affine3d& affine, const Vec3d& vector);
template<typename _Tp> class DataType< Affine3<_Tp> >
{
public:
typedef Affine3<_Tp> value_type;
typedef Affine3<typename DataType<_Tp>::work_type> work_type;
typedef _Tp channel_type;
enum { generic_type = 0,
channels = 16,
fmt = traits::SafeFmt<channel_type>::fmt + ((channels - 1) << 8)
#ifdef OPENCV_TRAITS_ENABLE_DEPRECATED
,depth = DataType<channel_type>::depth
,type = CV_MAKETYPE(depth, channels)
#endif
};
typedef Vec<channel_type, channels> vec_type;
};
namespace traits {
template<typename _Tp>
struct Depth< Affine3<_Tp> > { enum { value = Depth<_Tp>::value }; };
template<typename _Tp>
struct Type< Affine3<_Tp> > { enum { value = CV_MAKETYPE(Depth<_Tp>::value, 16) }; };
} // namespace
//! @} core
}
//! @cond IGNORED
///////////////////////////////////////////////////////////////////////////////////
// Implementation
template<typename T> inline
cv::Affine3<T>::Affine3()
: matrix(Mat4::eye())
{}
template<typename T> inline
cv::Affine3<T>::Affine3(const Mat4& affine)
: matrix(affine)
{}
template<typename T> inline
cv::Affine3<T>::Affine3(const Mat3& R, const Vec3& t)
{
rotation(R);
translation(t);
matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
matrix.val[15] = 1;
}
template<typename T> inline
cv::Affine3<T>::Affine3(const Vec3& _rvec, const Vec3& t)
{
rotation(_rvec);
translation(t);
matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
matrix.val[15] = 1;
}
template<typename T> inline
cv::Affine3<T>::Affine3(const cv::Mat& data, const Vec3& t)
{
CV_Assert(data.type() == cv::traits::Type<T>::value);
CV_Assert(data.channels() == 1);
if (data.cols == 4 && data.rows == 4)
{
data.copyTo(matrix);
return;
}
else if (data.cols == 4 && data.rows == 3)
{
rotation(data(Rect(0, 0, 3, 3)));
translation(data(Rect(3, 0, 1, 3)));
}
else
{
rotation(data);
translation(t);
}
matrix.val[12] = matrix.val[13] = matrix.val[14] = 0;
matrix.val[15] = 1;
}
template<typename T> inline
cv::Affine3<T>::Affine3(const float_type* vals) : matrix(vals)
{}
template<typename T> inline
cv::Affine3<T> cv::Affine3<T>::Identity()
{
return Affine3<T>(cv::Affine3<T>::Mat4::eye());
}
template<typename T> inline
void cv::Affine3<T>::rotation(const Mat3& R)
{
linear(R);
}
template<typename T> inline
void cv::Affine3<T>::rotation(const Vec3& _rvec)
{
double theta = norm(_rvec);
if (theta < DBL_EPSILON)
rotation(Mat3::eye());
else
{
double c = std::cos(theta);
double s = std::sin(theta);
double c1 = 1. - c;
double itheta = (theta != 0) ? 1./theta : 0.;
Point3_<T> r = _rvec*itheta;
Mat3 rrt( r.x*r.x, r.x*r.y, r.x*r.z, r.x*r.y, r.y*r.y, r.y*r.z, r.x*r.z, r.y*r.z, r.z*r.z );
Mat3 r_x( 0, -r.z, r.y, r.z, 0, -r.x, -r.y, r.x, 0 );
// R = cos(theta)*I + (1 - cos(theta))*r*rT + sin(theta)*[r_x]
// where [r_x] is [0 -rz ry; rz 0 -rx; -ry rx 0]
Mat3 R = c*Mat3::eye() + c1*rrt + s*r_x;
rotation(R);
}
}
//Combines rotation methods above. Supports 3x3, 1x3, 3x1 sizes of data matrix;
template<typename T> inline
void cv::Affine3<T>::rotation(const cv::Mat& data)
{
CV_Assert(data.type() == cv::traits::Type<T>::value);
CV_Assert(data.channels() == 1);
if (data.cols == 3 && data.rows == 3)
{
Mat3 R;
data.copyTo(R);
rotation(R);
}
else if ((data.cols == 3 && data.rows == 1) || (data.cols == 1 && data.rows == 3))
{
Vec3 _rvec;
data.reshape(1, 3).copyTo(_rvec);
rotation(_rvec);
}
else
CV_Assert(!"Input matrix can only be 3x3, 1x3 or 3x1");
}
template<typename T> inline
void cv::Affine3<T>::linear(const Mat3& L)
{
matrix.val[0] = L.val[0]; matrix.val[1] = L.val[1]; matrix.val[ 2] = L.val[2];
matrix.val[4] = L.val[3]; matrix.val[5] = L.val[4]; matrix.val[ 6] = L.val[5];
matrix.val[8] = L.val[6]; matrix.val[9] = L.val[7]; matrix.val[10] = L.val[8];
}
template<typename T> inline
void cv::Affine3<T>::translation(const Vec3& t)
{
matrix.val[3] = t[0]; matrix.val[7] = t[1]; matrix.val[11] = t[2];
}
template<typename T> inline
typename cv::Affine3<T>::Mat3 cv::Affine3<T>::rotation() const
{
return linear();
}
template<typename T> inline
typename cv::Affine3<T>::Mat3 cv::Affine3<T>::linear() const
{
typename cv::Affine3<T>::Mat3 R;
R.val[0] = matrix.val[0]; R.val[1] = matrix.val[1]; R.val[2] = matrix.val[ 2];
R.val[3] = matrix.val[4]; R.val[4] = matrix.val[5]; R.val[5] = matrix.val[ 6];
R.val[6] = matrix.val[8]; R.val[7] = matrix.val[9]; R.val[8] = matrix.val[10];
return R;
}
template<typename T> inline
typename cv::Affine3<T>::Vec3 cv::Affine3<T>::translation() const
{
return Vec3(matrix.val[3], matrix.val[7], matrix.val[11]);
}
template<typename T> inline
typename cv::Affine3<T>::Vec3 cv::Affine3<T>::rvec() const
{
cv::Vec3d w;
cv::Matx33d u, vt, R = rotation();
cv::SVD::compute(R, w, u, vt, cv::SVD::FULL_UV + cv::SVD::MODIFY_A);
R = u * vt;
double rx = R.val[7] - R.val[5];
double ry = R.val[2] - R.val[6];
double rz = R.val[3] - R.val[1];
double s = std::sqrt((rx*rx + ry*ry + rz*rz)*0.25);
double c = (R.val[0] + R.val[4] + R.val[8] - 1) * 0.5;
c = c > 1.0 ? 1.0 : c < -1.0 ? -1.0 : c;
double theta = acos(c);
if( s < 1e-5 )
{
if( c > 0 )
rx = ry = rz = 0;
else
{
double t;
t = (R.val[0] + 1) * 0.5;
rx = std::sqrt(std::max(t, 0.0));
t = (R.val[4] + 1) * 0.5;
ry = std::sqrt(std::max(t, 0.0)) * (R.val[1] < 0 ? -1.0 : 1.0);
t = (R.val[8] + 1) * 0.5;
rz = std::sqrt(std::max(t, 0.0)) * (R.val[2] < 0 ? -1.0 : 1.0);
if( fabs(rx) < fabs(ry) && fabs(rx) < fabs(rz) && (R.val[5] > 0) != (ry*rz > 0) )
rz = -rz;
theta /= std::sqrt(rx*rx + ry*ry + rz*rz);
rx *= theta;
ry *= theta;
rz *= theta;
}
}
else
{
double vth = 1/(2*s);
vth *= theta;
rx *= vth; ry *= vth; rz *= vth;
}
return cv::Vec3d(rx, ry, rz);
}
template<typename T> inline
cv::Affine3<T> cv::Affine3<T>::inv(int method) const
{
return matrix.inv(method);
}
template<typename T> inline
cv::Affine3<T> cv::Affine3<T>::rotate(const Mat3& R) const
{
Mat3 Lc = linear();
Vec3 tc = translation();
Mat4 result;
result.val[12] = result.val[13] = result.val[14] = 0;
result.val[15] = 1;
for(int j = 0; j < 3; ++j)
{
for(int i = 0; i < 3; ++i)
{
float_type value = 0;
for(int k = 0; k < 3; ++k)
value += R(j, k) * Lc(k, i);
result(j, i) = value;
}
result(j, 3) = R.row(j).dot(tc.t());
}
return result;
}
template<typename T> inline
cv::Affine3<T> cv::Affine3<T>::rotate(const Vec3& _rvec) const
{
return rotate(Affine3f(_rvec).rotation());
}
template<typename T> inline
cv::Affine3<T> cv::Affine3<T>::translate(const Vec3& t) const
{
Mat4 m = matrix;
m.val[ 3] += t[0];
m.val[ 7] += t[1];
m.val[11] += t[2];
return m;
}
template<typename T> inline
cv::Affine3<T> cv::Affine3<T>::concatenate(const Affine3<T>& affine) const
{
return (*this).rotate(affine.rotation()).translate(affine.translation());
}
template<typename T> template <typename Y> inline
cv::Affine3<T>::operator Affine3<Y>() const
{
return Affine3<Y>(matrix);
}
template<typename T> template <typename Y> inline
cv::Affine3<Y> cv::Affine3<T>::cast() const
{
return Affine3<Y>(matrix);
}
template<typename T> inline
cv::Affine3<T> cv::operator*(const cv::Affine3<T>& affine1, const cv::Affine3<T>& affine2)
{
return affine2.concatenate(affine1);
}
template<typename T, typename V> inline
V cv::operator*(const cv::Affine3<T>& affine, const V& v)
{
const typename Affine3<T>::Mat4& m = affine.matrix;
V r;
r.x = m.val[0] * v.x + m.val[1] * v.y + m.val[ 2] * v.z + m.val[ 3];
r.y = m.val[4] * v.x + m.val[5] * v.y + m.val[ 6] * v.z + m.val[ 7];
r.z = m.val[8] * v.x + m.val[9] * v.y + m.val[10] * v.z + m.val[11];
return r;
}
static inline
cv::Vec3f cv::operator*(const cv::Affine3f& affine, const cv::Vec3f& v)
{
const cv::Matx44f& m = affine.matrix;
cv::Vec3f r;
r.val[0] = m.val[0] * v[0] + m.val[1] * v[1] + m.val[ 2] * v[2] + m.val[ 3];
r.val[1] = m.val[4] * v[0] + m.val[5] * v[1] + m.val[ 6] * v[2] + m.val[ 7];
r.val[2] = m.val[8] * v[0] + m.val[9] * v[1] + m.val[10] * v[2] + m.val[11];
return r;
}
static inline
cv::Vec3d cv::operator*(const cv::Affine3d& affine, const cv::Vec3d& v)
{
const cv::Matx44d& m = affine.matrix;
cv::Vec3d r;
r.val[0] = m.val[0] * v[0] + m.val[1] * v[1] + m.val[ 2] * v[2] + m.val[ 3];
r.val[1] = m.val[4] * v[0] + m.val[5] * v[1] + m.val[ 6] * v[2] + m.val[ 7];
r.val[2] = m.val[8] * v[0] + m.val[9] * v[1] + m.val[10] * v[2] + m.val[11];
return r;
}
#if defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H
template<typename T> inline
cv::Affine3<T>::Affine3(const Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>& affine)
{
cv::Mat(4, 4, cv::traits::Type<T>::value, affine.matrix().data()).copyTo(matrix);
}
template<typename T> inline
cv::Affine3<T>::Affine3(const Eigen::Transform<T, 3, Eigen::Affine>& affine)
{
Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)> a = affine;
cv::Mat(4, 4, cv::traits::Type<T>::value, a.matrix().data()).copyTo(matrix);
}
template<typename T> inline
cv::Affine3<T>::operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>() const
{
Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)> r;
cv::Mat hdr(4, 4, cv::traits::Type<T>::value, r.matrix().data());
cv::Mat(matrix, false).copyTo(hdr);
return r;
}
template<typename T> inline
cv::Affine3<T>::operator Eigen::Transform<T, 3, Eigen::Affine>() const
{
return this->operator Eigen::Transform<T, 3, Eigen::Affine, (Eigen::RowMajor)>();
}
#endif /* defined EIGEN_WORLD_VERSION && defined EIGEN_GEOMETRY_MODULE_H */
//! @endcond
#endif /* __cplusplus */
#endif /* OPENCV_CORE_AFFINE3_HPP */