transform.h

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/*
 * Copyright 2016 The Cartographer Authors
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#ifndef CARTOGRAPHER_TRANSFORM_TRANSFORM_H_
#define CARTOGRAPHER_TRANSFORM_TRANSFORM_H_

#include <cmath>

#include "Eigen/Core"
#include "Eigen/Geometry"
#include "cartographer/common/math.h"
#include "cartographer/transform/proto/transform.pb.h"
#include "cartographer/transform/rigid_transform.h"

namespace cartographer {
namespace transform {

// Returns the non-negative rotation angle in radians of the 3D transformation
// 'transform'.
template <typename FloatType>
FloatType GetAngle(const Rigid3<FloatType>& transform) {
  return FloatType(2) * std::atan2(transform.rotation().vec().norm(),
                                   std::abs(transform.rotation().w()));
}

// Returns the yaw component in radians of the given 3D 'rotation'. Assuming
// 'rotation' is composed of three rotations around X, then Y, then Z, returns
// the angle of the Z rotation.
template <typename T>
T GetYaw(const Eigen::Quaternion<T>& rotation) {
  const Eigen::Matrix<T, 3, 1> direction =
      rotation * Eigen::Matrix<T, 3, 1>::UnitX();
  return atan2(direction.y(), direction.x());
}

// Returns the yaw component in radians of the given 3D transformation
// 'transform'.
template <typename T>
T GetYaw(const Rigid3<T>& transform) {
  return GetYaw(transform.rotation());
}

// Returns an angle-axis vector (a vector with the length of the rotation angle
// pointing to the direction of the rotation axis) representing the same
// rotation as the given 'quaternion'.
template <typename T>
Eigen::Matrix<T, 3, 1> RotationQuaternionToAngleAxisVector(
    const Eigen::Quaternion<T>& quaternion) {
  Eigen::Quaternion<T> normalized_quaternion = quaternion.normalized();
  // We choose the quaternion with positive 'w', i.e., the one with a smaller
  // angle that represents this orientation.
  if (normalized_quaternion.w() < 0.) {
    // Multiply by -1. http://eigen.tuxfamily.org/bz/show_bug.cgi?id=560
    normalized_quaternion.w() *= T(-1.);
    normalized_quaternion.x() *= T(-1.);
    normalized_quaternion.y() *= T(-1.);
    normalized_quaternion.z() *= T(-1.);
  }
  // We convert the normalized_quaternion into a vector along the rotation axis
  // with length of the rotation angle.
  const T angle = T(2.) * atan2(normalized_quaternion.vec().norm(),
                                normalized_quaternion.w());
  constexpr double kCutoffAngle = 1e-7;  // We linearize below this angle.
  const T scale = angle < kCutoffAngle ? T(2.) : angle / sin(angle / T(2.));
  return Eigen::Matrix<T, 3, 1>(scale * normalized_quaternion.x(),
                                scale * normalized_quaternion.y(),
                                scale * normalized_quaternion.z());
}

// Returns a quaternion representing the same rotation as the given 'angle_axis'
// vector.
template <typename T>
Eigen::Quaternion<T> AngleAxisVectorToRotationQuaternion(
    const Eigen::Matrix<T, 3, 1>& angle_axis) {
  T scale = T(0.5);
  T w = T(1.);
  constexpr double kCutoffAngle = 1e-8;  // We linearize below this angle.
  if (angle_axis.squaredNorm() > kCutoffAngle) {
    const T norm = angle_axis.norm();
    scale = sin(norm / 2.) / norm;
    w = cos(norm / 2.);
  }
  const Eigen::Matrix<T, 3, 1> quaternion_xyz = scale * angle_axis;
  return Eigen::Quaternion<T>(w, quaternion_xyz.x(), quaternion_xyz.y(),
                              quaternion_xyz.z());
}

// Projects 'transform' onto the XY plane.
template <typename T>
Rigid2<T> Project2D(const Rigid3<T>& transform) {
  return Rigid2<T>(transform.translation().template head<2>(),
                   GetYaw(transform));
}

// Embeds 'transform' into 3D space in the XY plane.
template <typename T>
Rigid3<T> Embed3D(const Rigid2<T>& transform) {
  return Rigid3<T>(
      {transform.translation().x(), transform.translation().y(), T(0)},
      Eigen::AngleAxis<T>(transform.rotation().angle(),
                          Eigen::Matrix<T, 3, 1>::UnitZ()));
}

// Conversions between Eigen and proto.
Rigid2d ToRigid2(const proto::Rigid2d& transform);
Eigen::Vector2d ToEigen(const proto::Vector2d& vector);
Eigen::Vector3f ToEigen(const proto::Vector3f& vector);
Eigen::Vector3d ToEigen(const proto::Vector3d& vector);
Eigen::Quaterniond ToEigen(const proto::Quaterniond& quaternion);
proto::Rigid2d ToProto(const Rigid2d& transform);
proto::Rigid2f ToProto(const Rigid2f& transform);
proto::Rigid3d ToProto(const Rigid3d& rigid);
Rigid3d ToRigid3(const proto::Rigid3d& rigid);
proto::Rigid3f ToProto(const Rigid3f& rigid);
proto::Vector2d ToProto(const Eigen::Vector2d& vector);
proto::Vector3f ToProto(const Eigen::Vector3f& vector);
proto::Vector3d ToProto(const Eigen::Vector3d& vector);
proto::Quaternionf ToProto(const Eigen::Quaternionf& quaternion);
proto::Quaterniond ToProto(const Eigen::Quaterniond& quaternion);

}  // namespace transform
}  // namespace cartographer

#endif  // CARTOGRAPHER_TRANSFORM_TRANSFORM_H_