// Copyright (C) 2014 The Regents of the University of California (Regents).
// 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.
//
//     * Neither the name of The Regents or University of California 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 HOLDERS 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.
//
// Please contact the author of this library if you have any questions.
// Author: Chris Sweeney (cmsweeney@cs.ucsb.edu)

// BSD 3-Clause License

// Copyright (c) 2021, Chenyu
// All rights reserved.

// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:

// 1. Redistributions of source code must retain the above copyright notice, this
//    list of conditions and the following disclaimer.

// 2. 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.

// 3. Neither the name of the copyright holder 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 HOLDER 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.

#ifndef GEOMETRY_ROTATION_UTILS_H_
#define GEOMETRY_ROTATION_UTILS_H_

#include <algorithm>
#include <cmath>
#include <vector>
#include <unordered_map>

#include <Eigen/Core>
#include <Eigen/Eigenvalues>
#include <Eigen/Geometry>

#include "utils/random.h"
#include "utils/types.h"

#ifndef M_PI
#define M_PI 3.14159265358979323846264338327950288
#endif

namespace gopt {
namespace geometry {
static RandomNumberGenerator rng(56);
static const double kRadToDeg = 180.0 / M_PI;
static const double kDegToRad = M_PI / 180.0;

double RadToDeg(double angle_radians);

double DegToRad(double angle_degrees);

double Clamp(const double val, const double min, const double max);

Eigen::MatrixXd ProjectToSOd(const Eigen::MatrixXd &M);

// Rotates the "rotation" set of orientations such that the orientations are
// most closely aligned in an L2 sense. That is, "rotation" is transformed such
// that R_rotation * R_gt_rotation^t is minimized.
void AlignRotations(const std::vector<Eigen::Vector3d>& gt_rotation,
                    std::vector<Eigen::Vector3d>* rotation);

// Aligns rotations to the ground truth rotations via a similarity
// transformation.
void AlignOrientations(
    const std::unordered_map<image_t, Eigen::Vector3d>& gt_rotations,
    std::unordered_map<image_t, Eigen::Vector3d>* rotations);

// Use Ceres to perform a stable composition of rotations. This is not as
// efficient as directly composing angle axis vectors (see the old
// implementation commented above) but is more stable.
Eigen::Vector3d MultiplyRotations(const Eigen::Vector3d& rotation1,
                                  const Eigen::Vector3d& rotation2);

// Computes R_ij = R_j * R_i^t.
Eigen::Vector3d RelativeRotationFromTwoRotations(
    const Eigen::Vector3d& rotation1, const Eigen::Vector3d& rotation2,
    const double noise);

// Computes R_ij = R_j * R_i^t.
Eigen::Vector3d RelativeRotationFromTwoRotations(
    const Eigen::Vector3d& rotation1, const Eigen::Vector3d& rotation2);

// return R_j = R_ij * R_i.
Eigen::Vector3d ApplyRelativeRotation(
    const Eigen::Vector3d& rotation1,
    const Eigen::Vector3d& relative_rotation);

Eigen::Vector3d RelativeTranslationFromTwoPositions(
    const Eigen::Vector3d& position1, const Eigen::Vector3d& position2,
    const Eigen::Vector3d& rotation1);

Eigen::Vector3d RelativeTranslationFromTwoPositions(
    const Eigen::Vector3d& position1,
    const Eigen::Vector3d& position2,
    const Eigen::Vector3d& rotation1,
    const Eigen::Vector3d& random_axis,
    const double noise);

Eigen::Vector3d RelativeTranslationFromTwoPositions(
    const Eigen::Vector3d relative_translation,
    const Eigen::Vector3d& random_axis,
    const double noise);

Eigen::Matrix3d CrossProductMatrix(const Eigen::Vector3d& vector);

}  // namespace geometry
}  // namespace gopt

#endif  // GEOMETRY_ROTATION_UTILS_H_
