se3quat.h

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// g2o - General Graph Optimization
// Copyright (C) 2011 H. Strasdat
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright notice,
//   this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
//   notice, this list of conditions and the following disclaimer in the
//   documentation and/or other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
// IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
// TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
// PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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#ifndef G2O_SE3QUAT_H_
#define G2O_SE3QUAT_H_
 
#include <Eigen/Core>
#include <Eigen/Geometry>
#include <cassert>
 
#include "g2o/stuff/misc.h"
#include "se3_ops.h"
 
namespace g2o {
 
class G2O_TYPES_SLAM3D_API SE3Quat {
 public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
 
 protected:
  Quaternion _r;
  Vector3 _t;
 
 public:
  SE3Quat() {
    _r.setIdentity();
    _t.setZero();
  }
 
  SE3Quat(const Matrix3& R, const Vector3& t) : _r(Quaternion(R)), _t(t) {
    normalizeRotation();
  }
 
  SE3Quat(const Quaternion& q, const Vector3& t) : _r(q), _t(t) {
    normalizeRotation();
  }

  template <typename Derived>
  explicit SE3Quat(const Eigen::MatrixBase<Derived>& v) {
    assert((v.size() == 6 || v.size() == 7) &&
           "Vector dimension does not match");
    if (v.size() == 6) {
      for (int i = 0; i < 3; i++) {
        _t[i] = v[i];
        _r.coeffs()(i) = v[i + 3];
      }
      _r.w() = 0.;  // recover the positive w
      if (_r.norm() > 1.) {
        _r.normalize();
      } else {
        double w2 = cst(1.) - _r.squaredNorm();
        _r.w() = (w2 < cst(0.)) ? cst(0.) : std::sqrt(w2);
      }
    } else if (v.size() == 7) {
      int idx = 0;
      for (int i = 0; i < 3; ++i, ++idx) _t(i) = v(idx);
      for (int i = 0; i < 4; ++i, ++idx) _r.coeffs()(i) = v(idx);
      normalizeRotation();
    }
  }
 
  inline const Vector3& translation() const { return _t; }
 
  inline void setTranslation(const Vector3& t_) { _t = t_; }
 
  inline const Quaternion& rotation() const { return _r; }
 
  void setRotation(const Quaternion& r_) { _r = r_; }
 
  inline SE3Quat operator*(const SE3Quat& tr2) const {
    SE3Quat result(*this);
    result._t += _r * tr2._t;
    result._r *= tr2._r;
    result.normalizeRotation();
    return result;
  }
 
  inline SE3Quat& operator*=(const SE3Quat& tr2) {
    _t += _r * tr2._t;
    _r *= tr2._r;
    normalizeRotation();
    return *this;
  }
 
  inline Vector3 operator*(const Vector3& v) const { return _t + _r * v; }
 
  inline SE3Quat inverse() const {
    SE3Quat ret;
    ret._r = _r.conjugate();
    ret._t = ret._r * (_t * -cst(1.));
    return ret;
  }
 
  inline double operator[](int i) const {
    assert(i < 7);
    if (i < 3) return _t[i];
    return _r.coeffs()[i - 3];
  }
 
  inline Vector7 toVector() const {
    Vector7 v;
    v[0] = _t(0);
    v[1] = _t(1);
    v[2] = _t(2);
    v[3] = _r.x();
    v[4] = _r.y();
    v[5] = _r.z();
    v[6] = _r.w();
    return v;
  }
 
  inline void fromVector(const Vector7& v) {
    _r = Quaternion(v[6], v[3], v[4], v[5]);
    _t = Vector3(v[0], v[1], v[2]);
  }
 
  inline Vector6 toMinimalVector() const {
    Vector6 v;
    v[0] = _t(0);
    v[1] = _t(1);
    v[2] = _t(2);
    v[3] = _r.x();
    v[4] = _r.y();
    v[5] = _r.z();
    return v;
  }
 
  inline void fromMinimalVector(const Vector6& v) {
    double w = cst(1.) - v[3] * v[3] - v[4] * v[4] - v[5] * v[5];
    if (w > 0) {
      _r = Quaternion(std::sqrt(w), v[3], v[4], v[5]);
    } else {
      _r = Quaternion(0, -v[3], -v[4], -v[5]);
    }
    _t = Vector3(v[0], v[1], v[2]);
  }
 
  Vector6 log() const {
    Vector6 res;
    Matrix3 _R = _r.toRotationMatrix();
    double d = cst(0.5) * (_R(0, 0) + _R(1, 1) + _R(2, 2) - 1);
    Vector3 omega;
    Vector3 upsilon;
 
    Vector3 dR = deltaR(_R);
    Matrix3 V_inv;
 
    if (std::abs(d) > cst(0.99999)) {
      omega = 0.5 * dR;
      Matrix3 Omega = skew(omega);
      V_inv = Matrix3::Identity() - cst(0.5) * Omega +
              (cst(1.) / cst(12.)) * (Omega * Omega);
    } else {
      double theta = std::acos(d);
      omega = theta / (2 * std::sqrt(1 - d * d)) * dR;
      Matrix3 Omega = skew(omega);
      V_inv = (Matrix3::Identity() - cst(0.5) * Omega +
               (1 - theta / (2 * std::tan(theta / 2))) / (theta * theta) *
                   (Omega * Omega));
    }
 
    upsilon = V_inv * _t;
    for (int i = 0; i < 3; i++) {
      res[i] = omega[i];
    }
    for (int i = 0; i < 3; i++) {
      res[i + 3] = upsilon[i];
    }
 
    return res;
  }
 
  Vector3 map(const Vector3& xyz) const { return _r * xyz + _t; }
 
  static SE3Quat exp(const Vector6& update) {
    Vector3 omega;
    for (int i = 0; i < 3; i++) omega[i] = update[i];
    Vector3 upsilon;
    for (int i = 0; i < 3; i++) upsilon[i] = update[i + 3];
 
    double theta = omega.norm();
    Matrix3 Omega = skew(omega);
 
    Matrix3 R;
    Matrix3 V;
    if (theta < cst(0.00001)) {
      Matrix3 Omega2 = Omega * Omega;
 
      R = (Matrix3::Identity() + Omega + cst(0.5) * Omega2);
 
      V = (Matrix3::Identity() + cst(0.5) * Omega + cst(1.) / cst(6.) * Omega2);
    } else {
      Matrix3 Omega2 = Omega * Omega;
 
      R = (Matrix3::Identity() + std::sin(theta) / theta * Omega +
           (1 - std::cos(theta)) / (theta * theta) * Omega2);
 
      V = (Matrix3::Identity() +
           (1 - std::cos(theta)) / (theta * theta) * Omega +
           (theta - std::sin(theta)) / (std::pow(theta, 3)) * Omega2);
    }
    return SE3Quat(Quaternion(R), V * upsilon);
  }
 
  Eigen::Matrix<double, 6, 6, Eigen::ColMajor> adj() const {
    Matrix3 R = _r.toRotationMatrix();
    Eigen::Matrix<double, 6, 6, Eigen::ColMajor> res;
    res.block(0, 0, 3, 3) = R;
    res.block(3, 3, 3, 3) = R;
    res.block(3, 0, 3, 3) = skew(_t) * R;
    res.block(0, 3, 3, 3) = Matrix3::Zero(3, 3);
    return res;
  }
 
  Eigen::Matrix<double, 4, 4, Eigen::ColMajor> to_homogeneous_matrix() const {
    Eigen::Matrix<double, 4, 4, Eigen::ColMajor> homogeneous_matrix;
    homogeneous_matrix.setIdentity();
    homogeneous_matrix.block(0, 0, 3, 3) = _r.toRotationMatrix();
    homogeneous_matrix.col(3).head(3) = translation();
 
    return homogeneous_matrix;
  }
 
  void normalizeRotation() {
    if (_r.w() < 0) {
      _r.coeffs() *= -1;
    }
    _r.normalize();
  }

  operator Isometry3() const {
    Isometry3 result = (Isometry3)rotation();
    result.translation() = translation();
    return result;
  }
};
 
inline std::ostream& operator<<(std::ostream& out_str, const SE3Quat& se3) {
  out_str << se3.to_homogeneous_matrix() << std::endl;
  return out_str;
}
 
// G2O_TYPES_SLAM3D_API Quaternion euler_to_quat(double yaw, double pitch,
// double roll); G2O_TYPES_SLAM3D_API void quat_to_euler(const Quaternion& q,
// double& yaw, double& pitch, double& roll); G2O_TYPES_SLAM3D_API void
// jac_quat3_euler3(Eigen::Matrix<double, 6, 6, Eigen::ColMajor>& J, const
// SE3Quat& t);
 
}  // namespace g2o
 
#endif