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/geometry/SOn.h>
 
#include <gtsam/base/Lie.h>
#include <gtsam/base/Matrix.h>
#include <gtsam/dllexport.h>
 
#include <cmath>
#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 <>
Matrix3 SO3::AdjointMap() const;

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, 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, ChartJacobian H);
 
template <>
GTSAM_EXPORT
Vector3 SO3::ChartAtOrigin::Local(const SO3& R, ChartJacobian H);
 
template <>
GTSAM_EXPORT
Vector9 SO3::vec(OptionalJacobian<9, 3> H) const;

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));
}
 
namespace so3 {

GTSAM_EXPORT Matrix3 compose(const Matrix3& M, const SO3& R,
                OptionalJacobian<9, 9> H = boost::none);

GTSAM_EXPORT Matrix99 Dcompose(const SO3& R);
 
// Below are two functors that allow for saving computation when exponential map
// and its derivatives are needed at the same location in so<3>. The second
// functor also implements dedicated methods to apply dexp and/or inv(dexp).

class GTSAM_EXPORT ExpmapFunctor {
 protected:
  const double theta2;
  Matrix3 W, K, KK;
  bool nearZero;
  double theta, sin_theta, one_minus_cos;  // only defined if !nearZero
 
  void init(bool nearZeroApprox = false);
 
 public:
  explicit ExpmapFunctor(const Vector3& omega, bool nearZeroApprox = false);

  ExpmapFunctor(const Vector3& axis, double angle, bool nearZeroApprox = false);

  SO3 expmap() const;
};

class DexpFunctor : public ExpmapFunctor {
  const Vector3 omega;
  double a, b;
  Matrix3 dexp_;
 
 public:
  GTSAM_EXPORT explicit DexpFunctor(const Vector3& omega, bool nearZeroApprox = false);
 
  // NOTE(luca): Right Jacobian for Exponential map in SO(3) - equation
  // (10.86) and following equations in G.S. Chirikjian, "Stochastic Models,
  // Information Theory, and Lie Groups", Volume 2, 2008.
  //   expmap(omega + v) \approx expmap(omega) * expmap(dexp * v)
  // This maps a perturbation v in the tangent space to
  // a perturbation on the manifold Expmap(dexp * v) */
  const Matrix3& dexp() const { return dexp_; }

  GTSAM_EXPORT Vector3 applyDexp(const Vector3& v, OptionalJacobian<3, 3> H1 = boost::none,
                    OptionalJacobian<3, 3> H2 = boost::none) const;

  GTSAM_EXPORT Vector3 applyInvDexp(const Vector3& v,
                       OptionalJacobian<3, 3> H1 = boost::none,
                       OptionalJacobian<3, 3> H2 = boost::none) const;
};
}  //  namespace so3
 
/*
 * Define the traits. internal::LieGroup provides both Lie group and Testable
 */
 
template <>
struct traits<SO3> : public internal::LieGroup<SO3> {};
 
template <>
struct traits<const SO3> : public internal::LieGroup<SO3> {};
 
}  // end namespace gtsam