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#ifndef SO3_MATH_H | ||
#define SO3_MATH_H | ||
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#include <math.h> | ||
#include <Eigen/Core> | ||
#include <opencv/cv.h> | ||
// #include <common_lib.h> | ||
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#define SKEW_SYM_MATRX(v) 0.0,-v[2],v[1],v[2],0.0,-v[0],-v[1],v[0],0.0 | ||
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template<typename T> | ||
Eigen::Matrix<T, 3, 3> Exp(const Eigen::Matrix<T, 3, 1> &&ang) | ||
{ | ||
T ang_norm = ang.norm(); | ||
Eigen::Matrix<T, 3, 3> Eye3 = Eigen::Matrix<T, 3, 3>::Identity(); | ||
if (ang_norm > 0.0000001) | ||
{ | ||
Eigen::Matrix<T, 3, 1> r_axis = ang / ang_norm; | ||
Eigen::Matrix<T, 3, 3> K; | ||
K << SKEW_SYM_MATRX(r_axis); | ||
/// Roderigous Tranformation | ||
return Eye3 + std::sin(ang_norm) * K + (1.0 - std::cos(ang_norm)) * K * K; | ||
} | ||
else | ||
{ | ||
return Eye3; | ||
} | ||
} | ||
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template<typename T, typename Ts> | ||
Eigen::Matrix<T, 3, 3> Exp(const Eigen::Matrix<T, 3, 1> &ang_vel, const Ts &dt) | ||
{ | ||
T ang_vel_norm = ang_vel.norm(); | ||
Eigen::Matrix<T, 3, 3> Eye3 = Eigen::Matrix<T, 3, 3>::Identity(); | ||
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if (ang_vel_norm > 0.0000001) | ||
{ | ||
Eigen::Matrix<T, 3, 1> r_axis = ang_vel / ang_vel_norm; | ||
Eigen::Matrix<T, 3, 3> K; | ||
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K << SKEW_SYM_MATRX(r_axis); | ||
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T r_ang = ang_vel_norm * dt; | ||
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/// Roderigous Tranformation | ||
return Eye3 + std::sin(r_ang) * K + (1.0 - std::cos(r_ang)) * K * K; | ||
} | ||
else | ||
{ | ||
return Eye3; | ||
} | ||
} | ||
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template<typename T> | ||
Eigen::Matrix<T, 3, 3> Exp(const T &v1, const T &v2, const T &v3) | ||
{ | ||
T &&norm = sqrt(v1 * v1 + v2 * v2 + v3 * v3); | ||
Eigen::Matrix<T, 3, 3> Eye3 = Eigen::Matrix<T, 3, 3>::Identity(); | ||
if (norm > 0.00001) | ||
{ | ||
T r_ang[3] = {v1 / norm, v2 / norm, v3 / norm}; | ||
Eigen::Matrix<T, 3, 3> K; | ||
K << SKEW_SYM_MATRX(r_ang); | ||
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/// Roderigous Tranformation | ||
return Eye3 + std::sin(norm) * K + (1.0 - std::cos(norm)) * K * K; | ||
} | ||
else | ||
{ | ||
return Eye3; | ||
} | ||
} | ||
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/* Logrithm of a Rotation Matrix */ | ||
template<typename T> | ||
Eigen::Matrix<T,3,1> Log(const Eigen::Matrix<T, 3, 3> &R) | ||
{ | ||
T theta = (R.trace() > 3.0 - 1e-6) ? 0.0 : std::acos(0.5 * (R.trace() - 1)); | ||
Eigen::Matrix<T,3,1> K(R(2,1) - R(1,2), R(0,2) - R(2,0), R(1,0) - R(0,1)); | ||
return (std::abs(theta) < 0.001) ? (0.5 * K) : (0.5 * theta / std::sin(theta) * K); | ||
} | ||
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template<typename T> | ||
Eigen::Matrix<T, 3, 1> RotMtoEuler(const Eigen::Matrix<T, 3, 3> &rot) | ||
{ | ||
T sy = sqrt(rot(0,0)*rot(0,0) + rot(1,0)*rot(1,0)); | ||
bool singular = sy < 1e-6; | ||
T x, y, z; | ||
if(!singular) | ||
{ | ||
x = atan2(rot(2, 1), rot(2, 2)); | ||
y = atan2(-rot(2, 0), sy); | ||
z = atan2(rot(1, 0), rot(0, 0)); | ||
} | ||
else | ||
{ | ||
x = atan2(-rot(1, 2), rot(1, 1)); | ||
y = atan2(-rot(2, 0), sy); | ||
z = 0; | ||
} | ||
Eigen::Matrix<T, 3, 1> ang(x, y, z); | ||
return ang; | ||
} | ||
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#endif |
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