text: // Ceres Solver - A fast non-linear least squares minimizer
  // Copyright 2016 Google Inc. All rights reserved.
  // http://ceres-solver.org/
  //
  // 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.
  // * Neither the name of Google Inc. nor the names of its contributors may be
  //   used to endorse or promote products derived from this software without
  //   specific prior written permission.
  //
  // 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 OWNER OR CONTRIBUTORS BE
  // LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
  // CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
  // SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
  // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
  // CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  // ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  // POSSIBILITY OF SUCH DAMAGE.
  //
  // Author: vitus@google.com (Michael Vitus)
  //
  // Defines the types used in the 2D pose graph SLAM formulation. Each vertex of
  // the graph has a unique integer ID with a position and orientation. There are
  // delta transformation constraints between two vertices.
  
  #ifndef CERES_EXAMPLES_POSE_GRAPH_2D_TYPES_H_
  #define CERES_EXAMPLES_POSE_GRAPH_2D_TYPES_H_
  
  #include <fstream>
  
  #include "Eigen/Core"
  #include "normalize_angle.h"
  
  namespace ceres::examples {
  
  // The state for each vertex in the pose graph.
  struct Pose2d {
    double x;
    double y;
    double yaw_radians;
  
    // The name of the data type in the g2o file format.
    static std::string name() { return "VERTEX_SE2"; }
  };
  
  inline std::istream& operator>>(std::istream& input, Pose2d& pose) {
    input >> pose.x >> pose.y >> pose.yaw_radians;
    // Normalize the angle between -pi to pi.
    pose.yaw_radians = NormalizeAngle(pose.yaw_radians);
    return input;
  }
  
  // The constraint between two vertices in the pose graph. The constraint is the
  // transformation from vertex id_begin to vertex id_end.
  struct Constraint2d {
    int id_begin;
    int id_end;
  
    double x;
    double y;
    double yaw_radians;
  
    // The inverse of the covariance matrix for the measurement. The order of the
    // entries are x, y, and yaw.
    Eigen::Matrix3d information;
  
    // The name of the data type in the g2o file format.
    static std::string name() { return "EDGE_SE2"; }
  };
  
  inline std::istream& operator>>(std::istream& input, Constraint2d& constraint) {
    input >> constraint.id_begin >> constraint.id_end >> constraint.x >>
        constraint.y >> constraint.yaw_radians >> constraint.information(0, 0) >>
        constraint.information(0, 1) >> constraint.information(0, 2) >>
        constraint.information(1, 1) >> constraint.information(1, 2) >>
        constraint.information(2, 2);
  
    // Set the lower triangular part of the information matrix.
    constraint.information(1, 0) = constraint.information(0, 1);
    constraint.information(2, 0) = constraint.information(0, 2);
    constraint.information(2, 1) = constraint.information(1, 2);
  
    // Normalize the angle between -pi to pi.
    constraint.yaw_radians = NormalizeAngle(constraint.yaw_radians);
    return input;
  }
  
  }  // namespace ceres::examples
  
  #endif  // CERES_EXAMPLES_POSE_GRAPH_2D_TYPES_H_
  