#include <cmath>

#include "ceres/ceres.h"

#include "aos/util/math.h"
#include "y2019/vision/target_finder.h"

using ceres::CENTRAL;
using ceres::CostFunction;
using ceres::Problem;
using ceres::Solve;
using ceres::Solver;

namespace y2019 {
namespace vision {

static constexpr double kInchesToMeters = 0.0254;

using namespace aos::vision;
using aos::vision::Vector;

Target Target::MakeTemplate() {
  Target out;
  // This is how off-vertical the tape is.
  const double theta = 14.5 * M_PI / 180.0;

  const double tape_offset = 4 * kInchesToMeters;
  const double tape_width = 2 * kInchesToMeters;
  const double tape_length = 5.5 * kInchesToMeters;

  const double s = sin(theta);
  const double c = cos(theta);
  out.right.top = Vector<2>(tape_offset, 0.0);
  out.right.inside = Vector<2>(tape_offset + tape_width * c, tape_width * s);
  out.right.bottom = Vector<2>(tape_offset + tape_width * c + tape_length * s,
                               tape_width * s - tape_length * c);
  out.right.outside =
      Vector<2>(tape_offset + tape_length * s, -tape_length * c);

  out.right.is_right = true;
  out.left.top = Vector<2>(-out.right.top.x(), out.right.top.y());
  out.left.inside = Vector<2>(-out.right.inside.x(), out.right.inside.y());
  out.left.bottom = Vector<2>(-out.right.bottom.x(), out.right.bottom.y());
  out.left.outside = Vector<2>(-out.right.outside.x(), out.right.outside.y());
  return out;
}

std::array<Vector<2>, 8> Target::ToPointList() const {
  // Note, the even points are fit with the line solver in the 4 point solution
  // while the odds are fit with the point matcher.
  return std::array<Vector<2>, 8>{{right.top, right.outside, right.inside,
                                   right.bottom, left.top, left.outside,
                                   left.inside, left.bottom}};
}

Target Project(const Target &target, const IntrinsicParams &intrinsics,
               const ExtrinsicParams &extrinsics) {
  Target new_targ;
  new_targ.right.is_right = true;
  new_targ.right.top = Project(target.right.top, intrinsics, extrinsics);
  new_targ.right.inside = Project(target.right.inside, intrinsics, extrinsics);
  new_targ.right.bottom = Project(target.right.bottom, intrinsics, extrinsics);
  new_targ.right.outside =
      Project(target.right.outside, intrinsics, extrinsics);

  new_targ.left.top = Project(target.left.top, intrinsics, extrinsics);
  new_targ.left.inside = Project(target.left.inside, intrinsics, extrinsics);
  new_targ.left.bottom = Project(target.left.bottom, intrinsics, extrinsics);
  new_targ.left.outside = Project(target.left.outside, intrinsics, extrinsics);

  return new_targ;
}

// Used at runtime on a single image given camera parameters.
struct PointCostFunctor {
  PointCostFunctor(Vector<2> result, Vector<2> template_pt,
                   IntrinsicParams intrinsics)
      : result(result), template_pt(template_pt), intrinsics(intrinsics) {}

  template <typename T>
  bool operator()(const T *const x, T *residual) const {
    const auto extrinsics = TemplatedExtrinsicParams<T>::get(x);
    ::Eigen::Matrix<T, 2, 1> pt =
        Project<T>(ToEigenMatrix<T>(template_pt), intrinsics, extrinsics);
    residual[0] = result.x() - pt(0, 0);
    residual[1] = result.y() - pt(1, 0);
    return true;
  }

  Vector<2> result;
  Vector<2> template_pt;
  IntrinsicParams intrinsics;
};

// Find the distance from a lower target point to the 'vertical' line it should
// be on.
struct LineCostFunctor {
  LineCostFunctor(Vector<2> result, Segment<2> template_seg,
                  IntrinsicParams intrinsics)
      : result(result), template_seg(template_seg), intrinsics(intrinsics) {}

  template <typename T>
  bool operator()(const T *const x, T *residual) const {
    const auto extrinsics = TemplatedExtrinsicParams<T>::get(x);
    const ::Eigen::Matrix<T, 2, 1> p1 =
        Project<T>(ToEigenMatrix<T>(template_seg.A()), intrinsics, extrinsics);
    const ::Eigen::Matrix<T, 2, 1> p2 =
        Project<T>(ToEigenMatrix<T>(template_seg.B()), intrinsics, extrinsics);
    // Distance from line(P1, P2) to point result
    T dx = p2.x() - p1.x();
    T dy = p2.y() - p1.y();
    T denom = (p2 - p1).norm();
    residual[0] = ceres::abs(dy * result.x() - dx * result.y() +
                             p2.x() * p1.y() - p2.y() * p1.x()) /
                  denom;
    return true;
  }

  Vector<2> result;
  Segment<2> template_seg;
  IntrinsicParams intrinsics;
};

// Find the distance that the bottom point is outside the target and penalize
// that linearly.
class BottomPointCostFunctor {
 public:
  BottomPointCostFunctor(::Eigen::Vector2f bottom_point,
                         Segment<2> template_seg, IntrinsicParams intrinsics)
      : bottom_point_(bottom_point.x(), bottom_point.y()),
        template_seg_(template_seg),
        intrinsics_(intrinsics) {}

  template <typename T>
  bool operator()(const T *const x, T *residual) const {
    const auto extrinsics = TemplatedExtrinsicParams<T>::get(x);
    const ::Eigen::Matrix<T, 2, 1> p1 = Project<T>(
        ToEigenMatrix<T>(template_seg_.A()), intrinsics_, extrinsics);
    const ::Eigen::Matrix<T, 2, 1> p2 = Project<T>(
        ToEigenMatrix<T>(template_seg_.B()), intrinsics_, extrinsics);

    // Construct a vector pointed perpendicular to the line.  This vector is
    // pointed down out the bottom of the target.
    ::Eigen::Matrix<T, 2, 1> down_axis;
    down_axis << -(p1.y() - p2.y()), p1.x() - p2.x();
    down_axis.normalize();

    // Positive means out.
    const T component = down_axis.transpose() * (bottom_point_ - p1);

    if (component > T(0)) {
      residual[0] = component * 1.0;
    } else {
      residual[0] = T(0);
    }
    return true;
  }

 private:
  ::Eigen::Vector2d bottom_point_;
  Segment<2> template_seg_;

  IntrinsicParams intrinsics_;
};

IntermediateResult TargetFinder::ProcessTargetToResult(const Target &target,
                                                       bool verbose) {
  // Memory for the ceres solver.
  double params_8point[ExtrinsicParams::kNumParams];
  default_extrinsics_.set(&params_8point[0]);
  double params_4point[ExtrinsicParams::kNumParams];
  default_extrinsics_.set(&params_4point[0]);

  Problem::Options problem_options;
  problem_options.context = ceres_context_.get();
  Problem problem_8point(problem_options);
  Problem problem_4point(problem_options);

  ::std::array<aos::vision::Vector<2>, 8> target_value = target.ToPointList();
  ::std::array<aos::vision::Vector<2>, 8> template_value =
      target_template_.ToPointList();

  for (size_t i = 0; i < 8; ++i) {
    aos::vision::Vector<2> a = template_value[i];
    aos::vision::Vector<2> b = target_value[i];

    if (i % 2 == 1) {
      aos::vision::Vector<2> a2 = template_value[i - 1];
      aos::vision::Segment<2> line = Segment<2>(a, a2);

      problem_4point.AddResidualBlock(
          new ceres::AutoDiffCostFunction<LineCostFunctor, 1, 4>(
              new LineCostFunctor(b, line, intrinsics_)),
          NULL, &params_4point[0]);
    } else {
      problem_4point.AddResidualBlock(
          new ceres::AutoDiffCostFunction<PointCostFunctor, 2, 4>(
              new PointCostFunctor(b, a, intrinsics_)),
          NULL, &params_4point[0]);
    }

    problem_8point.AddResidualBlock(
        new ceres::AutoDiffCostFunction<PointCostFunctor, 2, 4>(
            new PointCostFunctor(b, a, intrinsics_)),
        NULL, &params_8point[0]);
  }

  Solver::Options options;
  options.minimizer_progress_to_stdout = false;
  Solver::Summary summary_8point;
  Solve(options, &problem_8point, &summary_8point);

  // So, let's sneak up on it.  Start by warm-starting it with where we got on
  // the 8 point solution.
  ExtrinsicParams::get(&params_8point[0]).set(&params_4point[0]);
  // Then solve without the bottom constraint.
  Solver::Summary summary_4point1;
  Solve(options, &problem_4point, &summary_4point1);

  // Now, add a large cost for the bottom point being below the bottom line.
  problem_4point.AddResidualBlock(
      new ceres::AutoDiffCostFunction<BottomPointCostFunctor, 1, 4>(
          new BottomPointCostFunctor(target.left.bottom_point,
                                     Segment<2>(target_template_.left.outside,
                                                target_template_.left.bottom),
                                     intrinsics_)),
      NULL, &params_4point[0]);
  // Make sure to point the segment the other way so when we do a -pi/2 rotation
  // on the line, it points down in target space.
  problem_4point.AddResidualBlock(
      new ceres::AutoDiffCostFunction<BottomPointCostFunctor, 1, 4>(
          new BottomPointCostFunctor(target.right.bottom_point,
                                     Segment<2>(target_template_.right.bottom,
                                                target_template_.right.outside),
                                     intrinsics_)),
      NULL, &params_4point[0]);

  // And then re-solve.
  Solver::Summary summary_4point2;
  Solve(options, &problem_4point, &summary_4point2);

  IntermediateResult IR;
  IR.extrinsics = ExtrinsicParams::get(&params_8point[0]);
  IR.solver_error = summary_8point.final_cost;
  IR.backup_extrinsics = ExtrinsicParams::get(&params_4point[0]);
  IR.backup_solver_error = summary_4point2.final_cost;

  // Normalize all angles to (-M_PI, M_PI]
  IR.extrinsics.r1 = ::aos::math::NormalizeAngle(IR.extrinsics.r1);
  IR.extrinsics.r2 = ::aos::math::NormalizeAngle(IR.extrinsics.r2);
  IR.backup_extrinsics.r1 =
      ::aos::math::NormalizeAngle(IR.backup_extrinsics.r1);
  IR.backup_extrinsics.r2 =
      ::aos::math::NormalizeAngle(IR.backup_extrinsics.r2);
  IR.target_width = target.width();

  // Ok, let's look at how perpendicular the corners are.
  // Vector from the outside to inside along the top on the left.
  const ::Eigen::Vector2d top_left_vector =
      (target.left.top.GetData() - target.left.inside.GetData())
          .transpose()
          .normalized();
  // Vector up the outside of the left target.
  const ::Eigen::Vector2d outer_left_vector =
      (target.left.top.GetData() - target.left.outside.GetData())
          .transpose()
          .normalized();
  // Vector up the inside of the left target.
  const ::Eigen::Vector2d inner_left_vector =
      (target.left.inside.GetData() - target.left.bottom.GetData())
          .transpose()
          .normalized();

  // Vector from the outside to inside along the top on the right.
  const ::Eigen::Vector2d top_right_vector =
      (target.right.top.GetData() - target.right.inside.GetData())
          .transpose()
          .normalized();
  // Vector up the outside of the right target.
  const ::Eigen::Vector2d outer_right_vector =
      (target.right.top.GetData() - target.right.outside.GetData())
          .transpose()
          .normalized();
  // Vector up the inside of the right target.
  const ::Eigen::Vector2d inner_right_vector =
      (target.right.inside.GetData() - target.right.bottom.GetData())
          .transpose()
          .normalized();

  // Now dot the vectors and use that to compute angles.
  // Left side, outside corner.
  const double left_outer_corner_dot =
      (outer_left_vector.transpose() * top_left_vector)(0);
  // Left side, inside corner.
  const double left_inner_corner_dot =
      (inner_left_vector.transpose() * top_left_vector)(0);
  // Right side, outside corner.
  const double right_outer_corner_dot =
      (outer_right_vector.transpose() * top_right_vector)(0);
  // Right side, inside corner.
  const double right_inner_corner_dot =
      (inner_right_vector.transpose() * top_right_vector)(0);

  constexpr double kCornerThreshold = 0.35;
  if (::std::abs(left_outer_corner_dot) < kCornerThreshold &&
      ::std::abs(left_inner_corner_dot) < kCornerThreshold &&
      ::std::abs(right_outer_corner_dot) < kCornerThreshold &&
      ::std::abs(right_inner_corner_dot) < kCornerThreshold) {
    IR.good_corners = true;
  } else {
    IR.good_corners = false;
  }

  if (verbose) {
    std::cout << "rup = " << intrinsics_.mount_angle * 180 / M_PI << ";\n";
    std::cout << "fl = " << intrinsics_.focal_length << ";\n";
    std::cout << "8 points:\n";
    std::cout << summary_8point.BriefReport() << "\n";
    std::cout << "error = " << summary_8point.final_cost << ";\n";
    std::cout << "y = " << IR.extrinsics.y / kInchesToMeters << ";\n";
    std::cout << "z = " << IR.extrinsics.z / kInchesToMeters << ";\n";
    std::cout << "r1 = " << IR.extrinsics.r1 * 180 / M_PI << ";\n";
    std::cout << "r2 = " << IR.extrinsics.r2 * 180 / M_PI << ";\n";
    std::cout << "4 points:\n";
    std::cout << summary_4point1.BriefReport() << "\n";
    std::cout << "error = " << summary_4point1.final_cost << ";\n\n";
    std::cout << "4 points:\n";
    std::cout << summary_4point2.BriefReport() << "\n";
    std::cout << "error = " << summary_4point2.final_cost << ";\n\n";
    std::cout << "y = " << IR.backup_extrinsics.y / kInchesToMeters << ";\n";
    std::cout << "z = " << IR.backup_extrinsics.z / kInchesToMeters << ";\n";
    std::cout << "r1 = " << IR.backup_extrinsics.r1 * 180 / M_PI << ";\n";
    std::cout << "r2 = " << IR.backup_extrinsics.r2 * 180 / M_PI << ";\n";

    printf("left upper outer corner angle: %f, top (%f, %f), outer (%f, %f)\n",
           (outer_left_vector.transpose() * top_left_vector)(0),
           top_left_vector(0, 0), top_left_vector(1, 0),
           outer_left_vector(0, 0), outer_left_vector(1, 0));
    printf("left upper inner corner angle: %f\n",
           (inner_left_vector.transpose() * top_left_vector)(0));

    printf("right upper outer corner angle: %f, top (%f, %f), outer (%f, %f)\n",
           (outer_right_vector.transpose() * top_right_vector)(0),
           top_right_vector(0, 0), top_right_vector(1, 0),
           outer_right_vector(0, 0), outer_right_vector(1, 0));
    printf("right upper inner corner angle: %f\n",
           (inner_right_vector.transpose() * top_right_vector)(0));
  }
  return IR;
}

}  // namespace vision
}  // namespace y2019