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#ifndef __OPENCV_CORE_AFFINE3_HPP__
#define __OPENCV_CORE_AFFINE3_HPP__
#ifdef __cplusplus
#include <opencv2/core/core.hpp>
namespace cv
{
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;
Affine3();
//Augmented affine matrix
Affine3(const Mat4& affine);
//Rotation matrix
Affine3(const Mat3& R, const Vec3& t = Vec3::all(0));
//Rodrigues vector
Affine3(const Vec3& rvec, const Vec3& t = Vec3::all(0));
//Combines all contructors above. Supports 4x4, 4x3, 3x3, 1x3, 3x1 sizes of data matrix
explicit Affine3(const Mat& data, const Vec3& t = Vec3::all(0));
//From 16th element array
explicit Affine3(const float_type* vals);
static Affine3 Identity();
//Rotation matrix
void rotation(const Mat3& R);
//Rodrigues vector
void rotation(const Vec3& rvec);
//Combines rotation methods above. Suports 3x3, 1x3, 3x1 sizes of data matrix;
void rotation(const Mat& data);
void linear(const Mat3& L);
void translation(const Vec3& t);
Mat3 rotation() const;
Mat3 linear() const;
Vec3 translation() const;
//Rodrigues vector
Vec3 rvec() const;
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(R) is equivalent to Affine(rvec, 0) * a;
Affine3 rotate(const Vec3& rvec) const;
// a.translate(t) is equivalent to Affine(E, t) * a;
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);
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,
depth = DataType<channel_type>::depth,
channels = 16,
fmt = DataType<channel_type>::fmt + ((channels - 1) << 8),
type = CV_MAKETYPE(depth, channels)
};
typedef Vec<channel_type, channels> vec_type;
};
}
///////////////////////////////////////////////////////////////////////////////////
/// Implementaiton
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::DataType<T>::type);
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)));
return;
}
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 rx = _rvec[0], ry = _rvec[1], rz = _rvec[2];
double theta = std::sqrt(rx*rx + ry*ry + rz*rz);
if (theta < DBL_EPSILON)
rotation(Mat3::eye());
else
{
const double I[] = { 1, 0, 0, 0, 1, 0, 0, 0, 1 };
double c = std::cos(theta);
double s = std::sin(theta);
double c1 = 1. - c;
double itheta = theta ? 1./theta : 0.;
rx *= itheta; ry *= itheta; rz *= itheta;
double rrt[] = { rx*rx, rx*ry, rx*rz, rx*ry, ry*ry, ry*rz, rx*rz, ry*rz, rz*rz };
double _r_x_[] = { 0, -rz, ry, rz, 0, -rx, -ry, rx, 0 };
Mat3 R;
// 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]
for(int k = 0; k < 9; ++k)
R.val[k] = static_cast<float_type>(c*I[k] + c1*rrt[k] + s*_r_x_[k]);
rotation(R);
}
}
//Combines rotation methods above. Suports 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::DataType<T>::type);
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 marix can 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::DataType<T>::type, 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::DataType<T>::type, 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::DataType<T>::type, 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 */
#endif /* __cplusplus */
#endif /* __OPENCV_CORE_AFFINE3_HPP__ */
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