SO3.h

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/* ----------------------------------------------------------------------------
 
 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
 * Atlanta, Georgia 30332-0415
 * All Rights Reserved
 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
 
 * See LICENSE for the license information
 
 * -------------------------------------------------------------------------- */

 
#pragma once
 
#include <gtsam/base/Lie.h>
#include <gtsam/base/Matrix.h>
#include <gtsam/base/MatrixConstants.h>
#include <gtsam/dllexport.h>
#include <gtsam/geometry/Kernel.h>
#include <gtsam/geometry/SOn.h>
 
#include <optional>
#include <vector>
 
namespace gtsam {
 
using SO3 = SO<3>;
 
// Below are all declarations of SO<3> specializations.
// They are *defined* in SO3.cpp.
 
template <>
GTSAM_EXPORT
SO3 SO3::AxisAngle(const Vector3& axis, double theta);
 
template <>
GTSAM_EXPORT
SO3 SO3::ClosestTo(const Matrix3& M);
 
template <>
GTSAM_EXPORT
SO3 SO3::ChordalMean(const std::vector<SO3>& rotations);
 
template <>
GTSAM_EXPORT
Matrix3 SO3::Hat(const Vector3& xi);  
 
template <>
GTSAM_EXPORT
Vector3 SO3::Vee(const Matrix3& X);  

template <>
inline Matrix3 SO3::AdjointMap() const{ return matrix_; }

template <>
GTSAM_EXPORT
SO3 SO3::Expmap(const Vector3& omega);
 
template <>
GTSAM_EXPORT
SO3 SO3::Expmap(const Vector3& omega, ChartJacobian H);

template <>
GTSAM_EXPORT
Matrix3 SO3::ExpmapDerivative(const Vector3& omega);

template <>
GTSAM_EXPORT
Vector3 SO3::Logmap(const SO3& R);
 
template <>
GTSAM_EXPORT
Vector3 SO3::Logmap(const SO3& R, ChartJacobian H);

template <>
GTSAM_EXPORT
Matrix3 SO3::LogmapDerivative(const Vector3& omega);
 
// Chart at origin for SO3 is *not* Cayley but actual Expmap/Logmap
template <>
GTSAM_EXPORT
SO3 SO3::ChartAtOrigin::Retract(const Vector3& omega);
 
template <>
GTSAM_EXPORT
SO3 SO3::ChartAtOrigin::Retract(const Vector3& omega, ChartJacobian H);
 
template <>
GTSAM_EXPORT
Vector3 SO3::ChartAtOrigin::Local(const SO3& R);
 
template <>
GTSAM_EXPORT
Vector3 SO3::ChartAtOrigin::Local(const SO3& R, ChartJacobian H);
 
template <>
GTSAM_EXPORT
Vector9 SO3::vec(OptionalJacobian<9, 3> H) const;
 
#if GTSAM_ENABLE_BOOST_SERIALIZATION
template <class Archive>
void serialize(Archive& ar, SO3& R, const unsigned int /*version*/) {
  Matrix3& M = R.matrix_;
  ar& boost::serialization::make_nvp("R11", M(0, 0));
  ar& boost::serialization::make_nvp("R12", M(0, 1));
  ar& boost::serialization::make_nvp("R13", M(0, 2));
  ar& boost::serialization::make_nvp("R21", M(1, 0));
  ar& boost::serialization::make_nvp("R22", M(1, 1));
  ar& boost::serialization::make_nvp("R23", M(1, 2));
  ar& boost::serialization::make_nvp("R31", M(2, 0));
  ar& boost::serialization::make_nvp("R32", M(2, 1));
  ar& boost::serialization::make_nvp("R33", M(2, 2));
}
#endif
 
namespace so3 {

GTSAM_EXPORT Matrix3 compose(const Matrix3& M, const SO3& R,
                OptionalJacobian<9, 9> H = {});

GTSAM_EXPORT Matrix99 Dcompose(const SO3& R);

struct GTSAM_EXPORT ExpmapFunctor {
  double theta2;  
  double theta;   
  Matrix3 W;      
  Matrix3 WW;     
  bool nearZero{false};  
 
  // Ethan Eade's constants:
  double A;  // A = sin(theta) / theta
  double B;  // B = (1 - cos(theta)) / theta^2

  explicit ExpmapFunctor(const Vector3& omega);

  ExpmapFunctor(double nearZeroThresholdSq, const Vector3& axis);

  ExpmapFunctor(const Vector3& axis, double angle);

  inline Matrix3 expmap() const { return I_3x3 + A * W + B * WW; }
 
protected:
  void init(double nearZeroThresholdSq);
};

struct GTSAM_EXPORT DexpFunctor : public ExpmapFunctor {
  Vector3 omega;       
  bool nearPi{false};  

  explicit DexpFunctor(const Vector3& omega);

  explicit DexpFunctor(const Vector3& omega, double nearZeroThresholdSq, double nearPiThresholdSq);
 
  // Rodrigues kernel: R_[l/r](ω) = I + A(θ) Ω + B(θ) Ω² (left).
  Kernel Rodrigues() const&;
 
  // Jacobian kernel J_[l/r](ω) = I +/0 B Ω + C Ω²  (left/right).
  Kernel Jacobian() const&;
 
  // Specialized kernel for inverse Jacobian, stable even for |ω| > π
  InvJKernel InvJacobian() const&;  // I +/- 1/2 Ω + D Ω²
 
  // Gamma kernel: Γ_[l/r](ω) = 0.5 I ± C Ω + E Ω² (left/right).
  Kernel Gamma() const&;
 
  // NOTE(luca): Right Jacobian for Exponential map in SO(3)
  // This maps a perturbation dxi=(w,v) in the tangent space to
  // a perturbation on the manifold Expmap(dexp * xi)
  Matrix3 rightJacobian() const;
 
  // Compute the left Jacobian for Exponential map in SO(3)
  Matrix3 leftJacobian() const;

  Vector3 tangentExpmap(const Vector3& v,
                        OptionalJacobian<6, 6> H = {}) const;

  Vector3 tangentExpmap(const Vector3& v, const Matrix3& rotation,
                        OptionalJacobian<6, 6> H = {}) const;
 
#ifdef GTSAM_ALLOW_DEPRECATED_SINCE_V43
  Matrix3 rightJacobianInverse() const;

  Matrix3 leftJacobianInverse() const;

  Vector3 applyRightJacobian(const Vector3& v,
    OptionalJacobian<3, 3> H1 = {}, OptionalJacobian<3, 3> H2 = {}) const;

  Vector3 applyRightJacobianInverse(const Vector3& v,
    OptionalJacobian<3, 3> H1 = {}, OptionalJacobian<3, 3> H2 = {}) const;

  Vector3 applyLeftJacobian(const Vector3& v,
    OptionalJacobian<3, 3> H1 = {}, OptionalJacobian<3, 3> H2 = {}) const;

  Vector3 applyLeftJacobianInverse(const Vector3& v,
    OptionalJacobian<3, 3> H1 = {}, OptionalJacobian<3, 3> H2 = {}) const;

  inline Matrix3 dexp() const { return rightJacobian(); }

  inline Matrix3 invDexp() const { return rightJacobianInverse(); }
#endif
 
  // access to (lazily evaluated) coefficients
  double C() const;
  double D() const;
  double E() const;
 
  // access to (lazily evaluated) radial derivatives c'(θ)/θ
  double dA() const;
  double dB() const;
  double dC() const;
  double dE() const;
 
 protected:
  // Lazy caches stored as std::optional
  mutable std::optional<double> C_, D_, E_;  
  mutable std::optional<double> dA_, dB_, dC_, dE_;  
};
}  //  namespace so3
 
/*
 * Define the traits. internal::MatrixLieGroup provides both Lie group and Testable
 */
 
template <>
struct traits<SO3> : public internal::MatrixLieGroup<SO3, 3> {};
 
template <>
struct traits<const SO3> : public internal::MatrixLieGroup<SO3, 3> {};
 
}  // end namespace gtsam