Rot3.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

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

// \callgraph

#pragma once

#include <gtsam/geometry/Unit3.h>
#include <gtsam/geometry/Quaternion.h>
#include <gtsam/geometry/SO3.h>
#include <gtsam/base/concepts.h>
#include <gtsam/config.h> // Get GTSAM_USE_QUATERNIONS macro

#include <random>

// You can override the default coordinate mode using this flag
#ifndef ROT3_DEFAULT_COORDINATES_MODE
  #ifdef GTSAM_USE_QUATERNIONS
    // Exponential map is very cheap for quaternions
    #define ROT3_DEFAULT_COORDINATES_MODE Rot3::EXPMAP
  #else
    // If user doesn't require GTSAM_ROT3_EXPMAP in cmake when building
    #ifndef GTSAM_ROT3_EXPMAP
      // For rotation matrices, the Cayley transform is a fast retract alternative
      #define ROT3_DEFAULT_COORDINATES_MODE Rot3::CAYLEY
    #else
      #define ROT3_DEFAULT_COORDINATES_MODE Rot3::EXPMAP
    #endif
  #endif
#endif

namespace gtsam {

  class GTSAM_EXPORT Rot3 : public LieGroup<Rot3,3> {

  private:

#ifdef GTSAM_USE_QUATERNIONS

    gtsam::Quaternion quaternion_;
#else
    SO3 rot_;
#endif

  public:


    Rot3();

    Rot3(const Point3& col1, const Point3& col2, const Point3& col3);

    Rot3(double R11, double R12, double R13,
        double R21, double R22, double R23,
        double R31, double R32, double R33);

    template <typename Derived>
#ifdef GTSAM_USE_QUATERNIONS
    explicit Rot3(const Eigen::MatrixBase<Derived>& R) {
      quaternion_ = Matrix3(R);
    }
#else
    explicit Rot3(const Eigen::MatrixBase<Derived>& R) : rot_(R) {
    }
#endif

#ifdef GTSAM_USE_QUATERNIONS
    explicit Rot3(const Matrix3& R) : quaternion_(R) {}
#else
    explicit Rot3(const Matrix3& R) : rot_(R) {}
#endif

#ifdef GTSAM_USE_QUATERNIONS
    explicit Rot3(const SO3& R) : quaternion_(R.matrix()) {}
#else
    explicit Rot3(const SO3& R) : rot_(R) {}
#endif

    Rot3(const Quaternion& q);
    Rot3(double w, double x, double y, double z) : Rot3(Quaternion(w, x, y, z)) {}

    static Rot3 Random(std::mt19937 & rng);

    virtual ~Rot3() {}

    /* Static member function to generate some well known rotations */

    static Rot3 Rx(double t);

    static Rot3 Ry(double t);

    static Rot3 Rz(double t);

    static Rot3 RzRyRx(double x, double y, double z,
                       OptionalJacobian<3, 1> Hx = boost::none,
                       OptionalJacobian<3, 1> Hy = boost::none,
                       OptionalJacobian<3, 1> Hz = boost::none);

    inline static Rot3 RzRyRx(const Vector& xyz,
                              OptionalJacobian<3, 3> H = boost::none) {
      assert(xyz.size() == 3);
      Rot3 out;
      if (H) {
        Vector3 Hx, Hy, Hz;
        out = RzRyRx(xyz(0), xyz(1), xyz(2), Hx, Hy, Hz);
        (*H) << Hx, Hy, Hz;
      } else
        out = RzRyRx(xyz(0), xyz(1), xyz(2));
      return out;
    }

    static Rot3 Yaw  (double t) { return Rz(t); }

    static Rot3 Pitch(double t) { return Ry(t); }

    static Rot3 Roll (double t) { return Rx(t); }

    static Rot3 Ypr(double y, double p, double r,
                    OptionalJacobian<3, 1> Hy = boost::none,
                    OptionalJacobian<3, 1> Hp = boost::none,
                    OptionalJacobian<3, 1> Hr = boost::none) {
      return RzRyRx(r, p, y, Hr, Hp, Hy);
    }

    static Rot3 Quaternion(double w, double x, double y, double z) {
      gtsam::Quaternion q(w, x, y, z);
      return Rot3(q);
    }

    static Rot3 AxisAngle(const Point3& axis, double angle) {
      // Convert to unit vector.
      Vector3 unitAxis = Unit3(axis).unitVector();
#ifdef GTSAM_USE_QUATERNIONS
      return gtsam::Quaternion(Eigen::AngleAxis<double>(angle, unitAxis));
#else
      return Rot3(SO3::AxisAngle(unitAxis,angle));
#endif
    }

    static Rot3 AxisAngle(const Unit3& axis, double angle) {
      return AxisAngle(axis.unitVector(),angle);
    }

    static Rot3 Rodrigues(const Vector3& w) {
      return Rot3::Expmap(w);
    }

    static Rot3 Rodrigues(double wx, double wy, double wz) {
      return Rodrigues(Vector3(wx, wy, wz));
    }

    static Rot3 AlignPair(const Unit3& axis, const Unit3& a_p, const Unit3& b_p);

    static Rot3 AlignTwoPairs(const Unit3& a_p, const Unit3& b_p,  //
                              const Unit3& a_q, const Unit3& b_q);

    static Rot3 ClosestTo(const Matrix3& M) { return Rot3(SO3::ClosestTo(M)); }

    Rot3 normalized() const;


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

    bool equals(const Rot3& p, double tol = 1e-9) const;


    inline static Rot3 identity() {
      return Rot3();
    }

    Rot3 operator*(const Rot3& R2) const;

    Rot3 inverse() const {
#ifdef GTSAM_USE_QUATERNIONS
      return Rot3(quaternion_.inverse());
#else
      return Rot3(rot_.matrix().transpose());
#endif
    }

    Rot3 conjugate(const Rot3& cRb) const {
      // TODO: do more efficiently by using Eigen or quaternion properties
      return cRb * (*this) * cRb.inverse();
    }


    enum CoordinatesMode {
      EXPMAP, 
#ifndef GTSAM_USE_QUATERNIONS
      CAYLEY, 
#endif
      };

#ifndef GTSAM_USE_QUATERNIONS

    // Cayley chart around origin
    struct CayleyChart {
    static Rot3 Retract(const Vector3& v, OptionalJacobian<3, 3> H = boost::none);
    static Vector3 Local(const Rot3& r, OptionalJacobian<3, 3> H = boost::none);
    };

    Rot3 retractCayley(const Vector& omega) const {
      return compose(CayleyChart::Retract(omega));
    }

    Vector3 localCayley(const Rot3& other) const {
      return CayleyChart::Local(between(other));
    }

#endif


    static Rot3 Expmap(const Vector3& v, OptionalJacobian<3,3> H = boost::none) {
      if(H) *H = Rot3::ExpmapDerivative(v);
#ifdef GTSAM_USE_QUATERNIONS
      return traits<gtsam::Quaternion>::Expmap(v);
#else
      return Rot3(traits<SO3>::Expmap(v));
#endif
    }

    static Vector3 Logmap(const Rot3& R, OptionalJacobian<3,3> H = boost::none);

    static Matrix3 ExpmapDerivative(const Vector3& x);

    static Matrix3 LogmapDerivative(const Vector3& x);

    Matrix3 AdjointMap() const { return matrix(); }

    // Chart at origin, depends on compile-time flag ROT3_DEFAULT_COORDINATES_MODE
    struct ChartAtOrigin {
      static Rot3 Retract(const Vector3& v, ChartJacobian H = boost::none);
      static Vector3 Local(const Rot3& r, ChartJacobian H = boost::none);
    };

    using LieGroup<Rot3, 3>::inverse; // version with derivative


    Point3 rotate(const Point3& p, OptionalJacobian<3,3> H1 = boost::none,
        OptionalJacobian<3,3> H2 = boost::none) const;

    Point3 operator*(const Point3& p) const;

    Point3 unrotate(const Point3& p, OptionalJacobian<3,3> H1 = boost::none,
        OptionalJacobian<3,3> H2=boost::none) const;


    Unit3 rotate(const Unit3& p, OptionalJacobian<2,3> HR = boost::none,
        OptionalJacobian<2,2> Hp = boost::none) const;

    Unit3 unrotate(const Unit3& p, OptionalJacobian<2,3> HR = boost::none,
        OptionalJacobian<2,2> Hp = boost::none) const;

    Unit3 operator*(const Unit3& p) const;


    Matrix3 matrix() const;

    Matrix3 transpose() const;

    Point3 column(int index) const;

    Point3 r1() const; 
    Point3 r2() const; 
    Point3 r3() const; 

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

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

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

    double roll(OptionalJacobian<1, 3> H = boost::none) const;

    double pitch(OptionalJacobian<1, 3> H = boost::none) const;

    double yaw(OptionalJacobian<1, 3> H = boost::none) const;


    std::pair<Unit3, double> axisAngle() const;

    gtsam::Quaternion toQuaternion() const;

    Vector quaternion() const;

    Rot3 slerp(double t, const Rot3& other) const;

    GTSAM_EXPORT friend std::ostream &operator<<(std::ostream &os, const Rot3& p);


   private:
    friend class boost::serialization::access;
    template <class ARCHIVE>
    void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
#ifndef GTSAM_USE_QUATERNIONS
      Matrix3& M = rot_.matrix_;
      ar& boost::serialization::make_nvp("rot11", M(0, 0));
      ar& boost::serialization::make_nvp("rot12", M(0, 1));
      ar& boost::serialization::make_nvp("rot13", M(0, 2));
      ar& boost::serialization::make_nvp("rot21", M(1, 0));
      ar& boost::serialization::make_nvp("rot22", M(1, 1));
      ar& boost::serialization::make_nvp("rot23", M(1, 2));
      ar& boost::serialization::make_nvp("rot31", M(2, 0));
      ar& boost::serialization::make_nvp("rot32", M(2, 1));
      ar& boost::serialization::make_nvp("rot33", M(2, 2));
#else
      ar& boost::serialization::make_nvp("w", quaternion_.w());
      ar& boost::serialization::make_nvp("x", quaternion_.x());
      ar& boost::serialization::make_nvp("y", quaternion_.y());
      ar& boost::serialization::make_nvp("z", quaternion_.z());
#endif
    }

#ifdef GTSAM_USE_QUATERNIONS
  // only align if quaternion, Matrix3 has no alignment requirements
  public:
    GTSAM_MAKE_ALIGNED_OPERATOR_NEW
#endif
  };

  GTSAM_EXPORT std::pair<Matrix3, Vector3> RQ(
      const Matrix3& A, OptionalJacobian<3, 9> H = boost::none);

  template<>
  struct traits<Rot3> : public internal::LieGroup<Rot3> {};

  template<>
  struct traits<const Rot3> : public internal::LieGroup<Rot3> {};
}