/**
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This file is part of the Basalt project.
https://gitlab.com/VladyslavUsenko/basalt-headers.git

Copyright (c) 2019, Vladyslav Usenko and Nikolaus Demmel.
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@file
@brief Implementation of unified camera model
*/

#pragma once

#include <basalt/camera/camera_static_assert.hpp>

#include <basalt/utils/sophus_utils.hpp>

namespace basalt {

using std::sqrt;

/// @brief Camera model used in the paper "Bundle Adjustment in the Large".
///
/// See https://grail.cs.washington.edu/projects/bal/ for details.
/// This model has N=3 parameters \f$ \mathbf{i} = \left[f, k_1, k_2
/// \right]^T \f$.
///
/// Unlike the original formulation we assume that the POSITIVE z-axis
/// points in camera direction and thus don't include the "minus" in the
/// perspective projection. You need to consider this when loading BAL data.
///
/// Specifically, for the camera frame we assume the positive z axis pointing
/// forward in view direction and in the image, y is poiting down, x to the
/// right. In the original BAL formulation, the camera points in negative z
/// axis, y is up in the image. Thus when loading the data, we invert the y and
/// z camera axes (y also in the image) in the perspective projection, we don't
/// have the "minus" like in the original Snavely model.
///
/// A 3D point P in camera coordinates is mapped to pixel coordinates p':
/// p  = [P / P.z]_xy    (perspective division)
/// p' =  f * r(p) * p   (conversion to pixel coordinates)
/// r(p) = 1.0 + k1 * ||p||^2 + k2 * ||p||^4.
///
/// See \ref project and \ref unproject functions for more details.
template <typename Scalar_ = double>
class BalCamera {
 public:
  using Scalar = Scalar_;
  static constexpr int N = 3;  ///< Number of intrinsic parameters.

  using Vec2 = Eigen::Matrix<Scalar, 2, 1>;
  using Vec4 = Eigen::Matrix<Scalar, 4, 1>;

  using VecN = Eigen::Matrix<Scalar, N, 1>;

  using Mat2 = Eigen::Matrix<Scalar, 2, 2>;
  using Mat24 = Eigen::Matrix<Scalar, 2, 4>;
  using Mat2N = Eigen::Matrix<Scalar, 2, N>;

  using Mat42 = Eigen::Matrix<Scalar, 4, 2>;
  using Mat4N = Eigen::Matrix<Scalar, 4, N>;

  /// @brief Default constructor with zero intrinsics
  BalCamera() { param_.setZero(); }

  /// @brief Construct camera model with given vector of intrinsics
  ///
  /// @param[in] p vector of intrinsic parameters [f, k1, k2]
  explicit BalCamera(const VecN& p) { param_ = p; }

  /// @brief Cast to different scalar type
  template <class Scalar2>
  BalCamera<Scalar2> cast() const {
    return BalCamera<Scalar2>(param_.template cast<Scalar2>());
  }

  /// @brief Camera model name
  ///
  /// @return "bal"
  static std::string getName() { return "bal"; }

  /// @brief Project the point and optionally compute Jacobians
  ///
  /// @param[in] p3d point to project
  /// @param[out] proj result of projection
  /// @param[out] d_proj_d_p3d if not nullptr computed Jacobian of projection
  /// with respect to p3d
  /// @param[out] d_proj_d_param point if not nullptr computed Jacobian of
  /// projection with respect to intrinsic parameters
  /// @return if projection is valid
  template <class DerivedPoint3D, class DerivedPoint2D,
            class DerivedJ3D = std::nullptr_t,
            class DerivedJparam = std::nullptr_t>
  inline bool project(const Eigen::MatrixBase<DerivedPoint3D>& p3d,
                      Eigen::MatrixBase<DerivedPoint2D>& proj,
                      DerivedJ3D d_proj_d_p3d = nullptr,
                      DerivedJparam d_proj_d_param = nullptr) const {
    checkProjectionDerivedTypes<DerivedPoint3D, DerivedPoint2D, DerivedJ3D,
                                DerivedJparam, N>();

    const typename EvalOrReference<DerivedPoint3D>::Type p3d_eval(p3d);

    const Scalar& f = param_[0];
    const Scalar& k1 = param_[1];
    const Scalar& k2 = param_[2];

    const Scalar& x = p3d_eval[0];
    const Scalar& y = p3d_eval[1];
    const Scalar& z = p3d_eval[2];

    const Scalar mx = x / z;
    const Scalar my = y / z;

    const Scalar mx2 = mx * mx;
    const Scalar my2 = my * my;

    const Scalar r2 = mx2 + my2;
    const Scalar r4 = r2 * r2;

    const Scalar rp = Scalar(1) + k1 * r2 + k2 * r4;

    proj = Vec2(f * mx * rp, f * my * rp);

    const bool is_valid = z >= Sophus::Constants<Scalar>::epsilonSqrt();

    if constexpr (!std::is_same_v<DerivedJ3D, std::nullptr_t>) {
      BASALT_ASSERT(d_proj_d_p3d);
      d_proj_d_p3d->setZero();

      const Scalar tmp = k1 + k2 * Scalar(2) * r2;

      (*d_proj_d_p3d)(0, 0) = f * (rp + Scalar(2) * mx2 * tmp) / z;
      (*d_proj_d_p3d)(1, 1) = f * (rp + Scalar(2) * my2 * tmp) / z;

      (*d_proj_d_p3d)(1, 0) = (*d_proj_d_p3d)(0, 1) =
          f * my * mx * Scalar(2) * tmp / z;

      (*d_proj_d_p3d)(0, 2) = -f * mx * (rp + Scalar(2) * tmp * r2) / z;
      (*d_proj_d_p3d)(1, 2) = -f * my * (rp + Scalar(2) * tmp * r2) / z;
    } else {
      UNUSED(d_proj_d_p3d);
    }

    if constexpr (!std::is_same_v<DerivedJparam, std::nullptr_t>) {
      BASALT_ASSERT(d_proj_d_param);
      (*d_proj_d_param).setZero();
      (*d_proj_d_param)(0, 0) = mx * rp;
      (*d_proj_d_param)(1, 0) = my * rp;
      (*d_proj_d_param)(0, 1) = f * mx * r2;
      (*d_proj_d_param)(1, 1) = f * my * r2;
      (*d_proj_d_param)(0, 2) = f * mx * r4;
      (*d_proj_d_param)(1, 2) = f * my * r4;
    } else {
      UNUSED(d_proj_d_param);
    }

    return is_valid;
  }

  /// @brief Unproject the point and optionally compute Jacobians
  ///
  ///
  /// @param[in] proj point to unproject
  /// @param[out] p3d result of unprojection
  /// @param[out] d_p3d_d_proj if not nullptr computed Jacobian of unprojection
  /// with respect to proj
  /// @param[out] d_p3d_d_param point if not nullptr computed Jacobian of
  /// unprojection with respect to intrinsic parameters
  /// @return if unprojection is valid
  template <class DerivedPoint2D, class DerivedPoint3D,
            class DerivedJ2D = std::nullptr_t,
            class DerivedJparam = std::nullptr_t>
  inline bool unproject(const Eigen::MatrixBase<DerivedPoint2D>& proj,
                        Eigen::MatrixBase<DerivedPoint3D>& p3d,
                        DerivedJ2D d_p3d_d_proj = nullptr,
                        DerivedJparam d_p3d_d_param = nullptr) const {
    checkUnprojectionDerivedTypes<DerivedPoint2D, DerivedPoint3D, DerivedJ2D,
                                  DerivedJparam, N>();

    const typename EvalOrReference<DerivedPoint2D>::Type proj_eval(proj);

    const Scalar& f = param_[0];
    const Scalar& k1 = param_[1];
    const Scalar& k2 = param_[2];

    const Scalar& u = proj_eval[0];
    const Scalar& v = proj_eval[1];

    const Vec2 pp(u / f, v / f);

    Vec2 p = pp;

    for (int i = 0; i < 3; i++) {
      const Scalar r2 = p.squaredNorm();

      const Scalar rp = (Scalar(1) + k1 * r2 + k2 * r2 * r2);
      const Vec2 pp_computed = p * rp;

      const Scalar tmp = k1 + k2 * Scalar(2) * r2;

      Mat2 J_p;
      J_p(0, 0) = (rp + Scalar(2) * p[0] * p[0] * tmp);
      J_p(1, 1) = (rp + Scalar(2) * p[1] * p[1] * tmp);
      J_p(1, 0) = J_p(0, 1) = p[0] * p[1] * Scalar(2) * tmp;

      const Vec2 dp = (J_p.transpose() * J_p).inverse() * J_p.transpose() *
                      (pp_computed - pp);

      p -= dp;
    }

    p3d.setZero();
    p3d[0] = p[0];
    p3d[1] = p[1];
    p3d[2] = 1;

    p3d.normalize();

    BASALT_ASSERT_STREAM(d_p3d_d_proj == nullptr && d_p3d_d_param == nullptr,
                         "Jacobians for unprojection are not implemented");
    UNUSED(d_p3d_d_proj);
    UNUSED(d_p3d_d_param);

    return true;
  }

  /// @brief Set parameters from initialization
  ///
  /// Initializes the camera model to  \f$ \left[f_x, 0, 0 \right]^T \f$
  ///
  /// @param[in] init vector [fx, fy, cx, cy]
  inline void setFromInit(const Vec4& init) {
    param_[0] = init[0];
    param_[1] = 0;
    param_[2] = 0;
  }

  /// @brief Increment intrinsic parameters by inc and clamp the values to the
  /// valid range
  ///
  /// @param[in] inc increment vector
  void operator+=(const VecN& inc) { param_ += inc; }

  /// @brief Returns a const reference to the intrinsic parameters vector
  ///
  /// The order is following: \f$ \left[f, k1, k2 \right]^T \f$
  /// @return const reference to the intrinsic parameters vector
  const VecN& getParam() const { return param_; }

  /// @brief Projections used for unit-tests
  static Eigen::aligned_vector<BalCamera> getTestProjections() {
    Eigen::aligned_vector<BalCamera> res;

    VecN vec1;

    vec1 << 399.752, -3.78048e-05, 5.37738e-07;
    res.emplace_back(vec1);

    return res;
  }

  /// @brief Resolutions used for unit-tests
  static Eigen::aligned_vector<Eigen::Vector2i> getTestResolutions() {
    Eigen::aligned_vector<Eigen::Vector2i> res;

    res.emplace_back(640, 480);

    return res;
  }

  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
 private:
  VecN param_;
};

}  // namespace basalt