Unit3.h

/* ----------------------------------------------------------------------------

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

 * See LICENSE for the license information

 * -------------------------------------------------------------------------- */

/*
 * @file Unit3.h
 * @date Feb 02, 2011
 * @author Can Erdogan
 * @author Frank Dellaert
 * @author Alex Trevor
 * @brief Develop a Unit3 class - basically a point on a unit sphere
 */

#pragma once

#include <gtsam/geometry/Point2.h>
#include <gtsam/geometry/Point3.h>
#include <gtsam/base/Manifold.h>
#include <gtsam/base/Matrix.h>
#include <gtsam/dllexport.h>

#include <boost/optional.hpp>
#include <boost/random/mersenne_twister.hpp>
#include <boost/serialization/nvp.hpp>

#include <string>

#ifdef GTSAM_USE_TBB
#include <tbb/mutex.h>
#endif

namespace gtsam {

class GTSAM_EXPORT Unit3 {

private:

  Vector3 p_; 
  mutable boost::optional<Matrix32> B_; 
  mutable boost::optional<Matrix62> H_B_; 

#ifdef GTSAM_USE_TBB
  mutable tbb::mutex B_mutex_; 
#endif

public:

  enum {
    dimension = 2
  };


  Unit3() :
      p_(1.0, 0.0, 0.0) {
  }

  explicit Unit3(const Vector3& p) :
      p_(p.normalized()) {
  }

  Unit3(double x, double y, double z) :
      p_(x, y, z) {
    p_.normalize();
  }

  explicit Unit3(const Point2& p, double f) : p_(p.x(), p.y(), f) {
    p_.normalize();
  }

  Unit3(const Unit3& u) {
    p_ = u.p_;
  }

  Unit3& operator=(const Unit3 & u) {
    p_ = u.p_;
    return *this;
  }

  static Unit3 FromPoint3(const Point3& point, //
      OptionalJacobian<2, 3> H = boost::none);

  static Unit3 Random(boost::mt19937 & rng);



  friend std::ostream& operator<<(std::ostream& os, const Unit3& pair);

  void print(const std::string& s = std::string()) const;

  bool equals(const Unit3& s, double tol = 1e-9) const {
    return equal_with_abs_tol(p_, s.p_, tol);
  }


  const Matrix32& basis(OptionalJacobian<6, 2> H = boost::none) const;

  Matrix3 skew() const;

  Point3 point3(OptionalJacobian<3, 2> H = boost::none) const;

  Vector3 unitVector(OptionalJacobian<3, 2> H = boost::none) const;

  friend Point3 operator*(double s, const Unit3& d) {
    return Point3(s * d.p_);
  }

  double dot(const Unit3& q, OptionalJacobian<1,2> H1 = boost::none, //
                             OptionalJacobian<1,2> H2 = boost::none) const;

  Vector2 error(const Unit3& q, OptionalJacobian<2, 2> H_q = boost::none) const;

  Vector2 errorVector(const Unit3& q, OptionalJacobian<2, 2> H_p = boost::none, //
                      OptionalJacobian<2, 2> H_q = boost::none) const;

  double distance(const Unit3& q, OptionalJacobian<1, 2> H = boost::none) const;

  Unit3 cross(const Unit3& q) const {
    return Unit3(p_.cross(q.p_));
  }

  Point3 cross(const Point3& q) const {
    return point3().cross(q);
  }



  inline static size_t Dim() {
    return 2;
  }

  inline size_t dim() const {
    return 2;
  }

  enum CoordinatesMode {
    EXPMAP, 
    RENORM 
  };

  Unit3 retract(const Vector2& v, OptionalJacobian<2,2> H = boost::none) const;

  Vector2 localCoordinates(const Unit3& s) const;


private:


  friend class boost::serialization::access;
  template<class ARCHIVE>
  void serialize(ARCHIVE & ar, const unsigned int /*version*/) {
    ar & BOOST_SERIALIZATION_NVP(p_);
  }


public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
};

// Define GTSAM traits
template<> struct traits<Unit3> : public internal::Manifold<Unit3> {
};

template<> struct traits<const Unit3> : public internal::Manifold<Unit3> {
};

} // namespace gtsam