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 <vector>
 
#include <gtsam/geometry/Point2.h>
#include <gtsam/geometry/Point3.h>
#include <gtsam/base/Manifold.h>
#include <gtsam/base/Vector.h>
#include <gtsam/base/VectorSerialization.h>
#include <gtsam/base/Matrix.h>
#include <gtsam/dllexport.h>
 
 
#include <random>
#include <string>
 
#ifdef GTSAM_USE_TBB
#include <mutex> // std::mutex
#endif
 
namespace gtsam {

class GTSAM_EXPORT Unit3 {
 
private:
 
  Vector3 p_; 
  mutable std::optional<Matrix32> B_; 
  mutable std::optional<Matrix62> H_B_; 
 
#ifdef GTSAM_USE_TBB
  mutable std::mutex B_mutex_; 
#endif
 
public:
 
  inline constexpr static auto dimension = 2;


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

  explicit Unit3(const Vector3& p);

  Unit3(double x, double y, double z);

  explicit Unit3(const Point2& p, double f);

  Unit3(const Unit3& u) : p_(u.p_) {}

  Unit3& operator=(const Unit3& u) {
    if (this == &u) return *this;
    p_ = u.p_;
 
    // Since p_ has changed, the old cached basis is no longer valid.
    B_.reset();
    H_B_.reset();
    return *this;
  }

  static Unit3 FromPoint3(const Point3& point, //
      OptionalJacobian<2, 3> H = {});

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


 
  GTSAM_EXPORT 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 = {}) const;

  Matrix3 skew() const;

  Point3 point3(OptionalJacobian<3, 2> H = {}) const;

  Vector3 unitVector(OptionalJacobian<3, 2> H = {}) const;

  Vector3 scaled(double magnitude, OptionalJacobian<3, 2> H_this = {},
                 OptionalJacobian<3, 1> H_magnitude = {}) const;

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

  double dot(const Unit3& q, OptionalJacobian<1,2> H1 = {}, //
                             OptionalJacobian<1,2> H2 = {}) const;

  Vector2 errorVector(const Unit3& q, OptionalJacobian<2, 2> H_p = {}, //
                      OptionalJacobian<2, 2> H_q = {}) const;

  double distance(const Unit3& q, OptionalJacobian<1, 2> H = {}) const;

  Unit3 cross(const Unit3& q, OptionalJacobian<2, 2> H_p = {},
              OptionalJacobian<2, 2> H_q = {}) const;

  Point3 cross(const Point3& q, OptionalJacobian<3, 2> H_p = {},
               OptionalJacobian<3, 3> H_q = {}) const;


  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 = {}) const;

  Vector2 localCoordinates(const Unit3& s) const;

  Vector2 localCoordinates(const Unit3& s, OptionalJacobian<2, 2> H1,
                           OptionalJacobian<2, 2> H2 = {}) const;

 
#ifdef GTSAM_ALLOW_DEPRECATED_SINCE_V43
  Vector2 error(const Unit3& q, OptionalJacobian<2, 2> H_q = {}) const {
    return errorVector(q, {}, H_q);
  }
#endif
 
private:

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

};

GTSAM_EXPORT Unit3 cross(const Unit3& p, const Unit3& q,
                         OptionalJacobian<2, 2> H_p = {},
                         OptionalJacobian<2, 2> H_q = {});

GTSAM_EXPORT Point3 cross(const Unit3& p, const Point3& q,
                          OptionalJacobian<3, 2> H_p = {},
                          OptionalJacobian<3, 3> H_q = {});

GTSAM_EXPORT Point3 cross(const Point3& p, const Unit3& q,
                          OptionalJacobian<3, 3> H_p = {},
                          OptionalJacobian<3, 2> H_q = {});


template <>
struct traits<Unit3> : public internal::Manifold<Unit3> {
  inline constexpr static int QcqpVectorDim = 4;

  template <int D = 1>
  static Matrix QcqpValue(const Unit3& value) {
    if constexpr (D == 1) {
      Eigen::Matrix<double, 4, 1> X;
      X(0, 0) = 1.0;
      X.segment<3>(1) = value.unitVector();
      return X;
    } else if constexpr (D >= 3) {
      Matrix X = Matrix::Zero(1, D);
      X.block(0, 0, 1, 3) = value.unitVector().transpose();
      return X;
    } else {
      throw std::invalid_argument(
          "traits<Unit3>::QcqpValue supports D=1 and D>=3.");
    }
  }

  template <int D = 1>
  static std::vector<std::pair<Matrix, double>> QcqpConstraints() {
    if constexpr (D == 1) {
      // Homogenized: pin the leading coordinate and the direction's norm.
      std::vector<std::pair<Matrix, double>> constraints;
      Matrix A = Matrix::Zero(4, 4);
      A(0, 0) = 1.0;
      constraints.emplace_back(A, 1.0);
      A.setZero();
      A(1, 1) = A(2, 2) = A(3, 3) = 1.0;
      constraints.emplace_back(A, 1.0);
      return constraints;
    } else if constexpr (D >= 3) {
      return {{Matrix::Identity(1, 1), 1.0}};
    } else {
      throw std::invalid_argument(
          "traits<Unit3>::QcqpConstraints supports D=1 and D>=3.");
    }
  }

  template <int D = 1>
  static Unit3 FromQcqpValue(const Matrix& X) {
    if constexpr (D == 1) {
      if (X.rows() != QcqpVectorDim || X.cols() != 1) {
        throw std::invalid_argument(
            "traits<Unit3>::FromQcqpValue requires a 4-by-1 matrix.");
      }
      return Unit3(Point3(X.block(1, 0, 3, 1)));
    } else if constexpr (D >= 3) {
      if (X.rows() != 1 || X.cols() != D) {
        throw std::invalid_argument(
            "traits<Unit3>::FromQcqpValue requires a 1-by-D matrix.");
      }
      return Unit3(Point3(X.block(0, 0, 1, 3).transpose()));
    } else {
      throw std::invalid_argument(
          "traits<Unit3>::FromQcqpValue supports D=1 and D>=3.");
    }
  }
};
 
template<> struct traits<const Unit3> : public internal::Manifold<Unit3> {
};
 
} // namespace gtsam