#include <string>
#include <fstream>
#include <iostream>
#include <cmath>
#include <cassert>
#include <cstring>

using namespace std;

template <typename T>
struct TPoint {
  T x;
  T y;

  TPoint(T a, T b)
  : x(a)
  , y(b)
  {}
};
typedef TPoint<unsigned int> Point;
typedef TPoint<int> APoint; // absolute point, can be negative
typedef TPoint<double> DPoint; // absolute point, can be negative
template<typename Elem, typename Traits, typename T>
std::basic_ostream<Elem, Traits>& operator << (std::basic_ostream<Elem, Traits>& o, TPoint<T> const& p)
{
  o << "(" << p.x << ", " << p.y << ")";
  return o;
}

struct Image {
  unsigned int width;
  unsigned int height;
  uint8_t* r_chan;
  uint8_t* g_chan;
  uint8_t* b_chan;

  Image()
  : width(0)
  , height(0)
  , r_chan(NULL)
  , g_chan(NULL)
  , b_chan(NULL)
  {}

  Image(unsigned int w, unsigned int h)
  {
    this->width = w;
    this->height = h;
    r_chan = new uint8_t[width * height];
    memset(r_chan, 0, width * height * sizeof (uint8_t));
    g_chan = new uint8_t[width * height];
    memset(g_chan, 0, width * height * sizeof (uint8_t));
    b_chan = new uint8_t[width * height];
    memset(b_chan, 0, width * height * sizeof (uint8_t));
  }

  Image(string const& path)
  : Image()
  {
    ifstream is(path);
    if (!is.is_open())
    {
      cerr << "Cannot open file '" << path << "'" << endl;
      abort();
    }

    if (!this->read_header(is))
    {
      cerr << "Invalid header." << endl;
      abort();
    }

    if (!this->read_body(is))
    {
      delete r_chan;
      r_chan = nullptr;
      delete g_chan;
      r_chan = nullptr;
      delete b_chan;
      r_chan = nullptr;

      cerr << "Invalid header." << endl;
      abort();
    }
  }

  bool save(string const& path)
  {
    ofstream os(path);
    if (!os.is_open())
    {
      cerr << "Cannot open file '" << path << "'" << endl;
      return false;
    }
    this->write_header(os);
    this->write_body(os);
    return true;
  }

  void set_pixel(unsigned int x, unsigned int y, uint8_t r, uint8_t g, uint8_t b)
  {
    int const index = y * width + x;
    r_chan[index] = r;
    g_chan[index] = g;
    b_chan[index] = b;
  }

  private:
    bool read_header(std::ifstream& istr)
    {
      // check magic
      if (istr.get() != 'P' )
      {
        return false;
      }

      char type = static_cast<char>(istr.get());
      if (type != '6')
      {
        return false;
      }

      if (istr.get() != '\n')
      {
        return false;
      }

      // skip comments
      while (istr.peek() == '#')
      {
        std::string line;
        std::getline(istr, line);
      }

      // get size
      istr >> width >> height;
      if (width == 0 || height == 0)
      {
        return false;
      }

      // get maxvalue
      if (istr.get() != '\n')
      {
        return false;
      }

      int max_value = -1;
      istr >> max_value;
      if (max_value > 255)
      {
        return false;
      }

      if (istr.get() != '\n')
      {
        return false;
      }

      cout << "width: " << width << endl;
      cout << "height: " << height << endl;

      return true;
    }

    bool write_header(std::ofstream& ostr)
    {
      ostr << "P6" << endl;
      ostr << width << " " << height << endl;
      ostr << "255" << endl;
      return true;
    }

    bool read_body(std::ifstream& istr)
    {
      r_chan = new uint8_t[width * height];
      g_chan = new uint8_t[width * height];
      b_chan = new uint8_t[width * height];

      for (unsigned int row = 0; row < height; ++row)
      {
        for (unsigned int col = 0; col < width; ++col)
        {
          int index = row * width + col;
          r_chan[index] = istr.get();
          g_chan[index] = istr.get();
          b_chan[index] = istr.get();
        }
      }

      return true;
    }

    bool write_body(std::ofstream& ostr)
    {
      for (unsigned int row = 0; row < height; ++row)
      {
        for (unsigned int col = 0; col < width; ++col)
        {
          int index = row * width + col;
          ostr << (char) r_chan[index];
          ostr << (char) g_chan[index];
          ostr << (char) b_chan[index];
        }
      }
      return true;
    }
};


//
//
// Drawing
//

void draw_line(Image& img, unsigned int x1, unsigned int y1, unsigned int x2, unsigned int y2)
{
  if (x1 > x2)
  {
    swap(x1, x2);
    swap(y1, y2);
  }
  double const slope = ((double) y2 - y1) / ((double) x2 - x1);
  cout << "draw slope = " << slope << endl;
  unsigned int previous_y = y1;
  for (unsigned int i = x1; i <= x2; ++i)
  {
    unsigned int y = slope * (i - x1) + y1;
    int inc = slope > 0 ? 1 : -1;
    for (unsigned int runner = previous_y; runner != y; runner+= inc)
      img.set_pixel(i, runner, 255, 0, 0); // set line to red
    previous_y = y;
  }
}

void draw_line(Image& img, Point const& p1, Point const& p2)
{
  draw_line(img, p1.x, p1.y, p2.x, p2.y);
}


//
//
// Trigonometry
//

double convert_radian(Image const& img, Point const& p, double const ratio)
{
  double const centered_x = p.x - (img.width / 2.0f);
  double const centered_y = (- (int) p.y) + (img.height / 2.0f);
  double const cos_value = centered_x * ratio;
  double const sin_value = centered_y * ratio;
  double angle = acos(cos_value);
  if (sin_value < 0)
    angle = 2 * M_PI - angle;

  return angle;
}

APoint convert_abs_coord(double const angle, double const ratio)
{
  return APoint((int) ceil(cos(angle) / ratio), (int) ceil(sin(angle) / ratio));
}

Point convert_img_coord(Image const& img, APoint const& p)
{
  return Point(p.x + img.width / 2.0f, - p.y + img.height / 2.0f);
}

double compute_ratio(Image const& img)
{
  unsigned int const nb_points = img.width * img.height;
  double const square_side = sqrt(nb_points) - 1;
  double const half_side = square_side / 2;
  unsigned int const trigo_length = (unsigned int) ceil(half_side * sqrt(2));
  return 1.0f / trigo_length;
}

inline
bool fequal(float a, float b, float sigma)
{
  return abs(a - b) < sigma;
}

void compute_output_size(Image const& src, double const rotation, unsigned int& width, unsigned int& height)
{
  double const ratio = compute_ratio(src);
  int min_w = 0;
  int max_w = 0;
  int min_h = 0;
  int max_h = 0;

  //cout << "Image dimensions: " << src.width << " x " << src.height << endl;
  Point p(0, 0);
  double angle = convert_radian(src, p, ratio);
  APoint tl = convert_abs_coord(angle + rotation, ratio);
  min_w = min(min_w, tl.x);
  max_w = max(max_w, tl.x);
  min_h = min(min_h, tl.y);
  max_h = max(max_h, tl.y);
  //cout << "Rotated " << p << " (" << angle << ") = " << tl << "(" << angle + rotation << ")" << endl << endl;

  p = Point(src.width - 1, 0);
  angle = convert_radian(src, p, ratio);
  APoint tr = convert_abs_coord(angle + rotation, ratio);
  min_w = min(min_w, tr.x);
  max_w = max(max_w, tr.x);
  min_h = min(min_h, tr.y);
  max_h = max(max_h, tr.y);
  //cout << "Rotated " << p << " (" << angle << ") = " << tr << "(" << angle + rotation << ")" << endl << endl;

  p = Point(0, src.height - 1);
  angle = convert_radian(src, p, ratio);
  APoint bl = convert_abs_coord(angle + rotation, ratio);
  min_w = min(min_w, bl.x);
  max_w = max(max_w, bl.x);
  min_h = min(min_h, bl.y);
  max_h = max(max_h, bl.y);
  //cout << "Rotated " << p << " (" << angle << ") = " << bl << "(" << angle + rotation << ")" << endl << endl;

  p = Point(src.width - 1, src.height - 1);
  angle = convert_radian(src, p, ratio);
  APoint br = convert_abs_coord(angle + rotation, ratio);
  min_w = min(min_w, br.x);
  max_w = max(max_w, br.x);
  min_h = min(min_h, br.y);
  max_h = max(max_h, br.y);
  //cout << "Rotated " << p << " (" << angle << ") = " << br << "(" << angle + rotation << ")" << endl << endl;

  width = max_w - min_w + 1;
  height = max_h - min_h + 1;
}


//
//
// Rotation
//

Point rotate(Image const& src, Point const& p, double const ratio, double const rotation, Image const& rotated)
{
  double angle = convert_radian(src, p, ratio);
  APoint a_point = convert_abs_coord(angle + rotation, ratio);
  return convert_img_coord(rotated, a_point);
}

Image rotate(Image const& src, double angle)
{
  // FIXME
  Image rot(0, 0);
  cout << angle << src.width << endl; // to remove warnings
  return rot;
}


//
//
// Check
//

bool check_trigo()
{
  Image square(500, 500);
  double const ratio = compute_ratio(square);

  // Check that the origin of a square image is at sqrt(2) / 2
  double const angle = convert_radian(square, Point(0, 0), ratio);

  double const sigma = 1.0e-2;
  if (abs(angle - (3 * M_PI / 4)) > sigma)
  {
    cout << "Invalid angle value: " << angle << " != " << 3 * M_PI / 4 << endl;
    return false;
  }

  // Check that we can reverse the origin point.
  APoint const abs_reverse_point = convert_abs_coord(angle, ratio);
  cout << "reversed abs origin: " << abs_reverse_point << endl;
  Point const reverse_point = convert_img_coord(square, abs_reverse_point);
  cout << "reversed origin in square: " << reverse_point << endl;
  if (abs(0.0 - reverse_point.x) > sigma)
  {
    cerr << "Reverse origin:" << endl;
    cout << "Invalid x value: " << reverse_point.x << " != " << 0 << endl;
    return false;
  }
  if (abs(0.0 - reverse_point.y) > sigma)
  {
    cerr << "Reverse origin:" << endl;
    cout << "Invalid y value: " << reverse_point.y << " != " << 0 << endl;
    return false;
  }

  // Check that when rotating the origin by 45 degrees
  double const rotation = M_PI / 4; // 45 degrees
  unsigned int w = 0;
  unsigned int h = 0;
  compute_output_size(square, rotation, w, h);

  // failed check: is precision an issue?
  if (false)
  {
    if (!fequal(w, square.width * sqrt(2), sigma)
        || !fequal(h, square.height * sqrt(2), sigma))
    {
      cerr << "Invalid rotated image dimensions " << w << " x " << h << endl;
      cerr << " expected " << (int) ceil(square.width * sqrt(2)) << " x " << (int) ceil(square.height * sqrt(2)) << endl;
      return false;
    }


    Image rotated(w, h);

    APoint const a_p45 = convert_abs_coord(angle + rotation, ratio);
    Point const p45 = convert_img_coord(rotated, a_p45);
    if (abs((float) (0) - p45.x) > sigma)
    {
      cerr << "Rotation origin by 45 degrees:" << endl;
      cerr << " invalid x value: " << p45.x << " != " << 0 << endl;
      cerr << " absolute point: " << a_p45 << endl;
      cerr << " relative point: " << p45 << endl;
      return false;
    }
    if (abs(0.0 - p45.y) > sigma)
    {
      cerr << "Rotation origin by 45 degrees:" << endl;
      cerr << "Invalid y value: " << p45.y << " != " << 0 << endl;
      return false;
    }
  }

  return true;
}

void check_lines()
{
  Image const square(500, 500);
  double const ratio = compute_ratio(square);
  unsigned int w = 0;
  unsigned int h = 0;
  {
    double const rotation = M_PI / 8; // 22 degrees
    compute_output_size(square, rotation, w, h);
    Image rotated(w, h);

    Point tl = rotate(square, Point(0, 0), ratio, rotation, rotated);
    Point tr = rotate(square, Point(square.width - 1, 0), ratio, rotation, rotated);
    Point bl = rotate(square, Point(0, square.height - 1), ratio, rotation, rotated);
    Point br = rotate(square, Point(square.width - 1, square.height - 1), ratio, rotation, rotated);

    draw_line(rotated, tl, tr);
    draw_line(rotated, tr, br);
    draw_line(rotated, br, bl);
    draw_line(rotated, bl, tl);

    rotated.save("check_lines_01.ppm");
  }
  {
    double const rotation = M_PI / 6; // 33 degrees
    compute_output_size(square, rotation, w, h);
    Image rotated(w, h);

    Point tl = rotate(square, Point(0, 0), ratio, rotation, rotated);
    Point tr = rotate(square, Point(square.width - 1, 0), ratio, rotation, rotated);
    Point bl = rotate(square, Point(0, square.height - 1), ratio, rotation, rotated);
    Point br = rotate(square, Point(square.width - 1, square.height - 1), ratio, rotation, rotated);

    draw_line(rotated, tl, tr);
    draw_line(rotated, tr, br);
    draw_line(rotated, br, bl);
    draw_line(rotated, bl, tl);

    rotated.save("check_lines_02.ppm");
  }
  {
    double const rotation = M_PI / 4; // 45 degrees
    compute_output_size(square, rotation, w, h);
    Image rotated(w, h);

    Point tl = rotate(square, Point(0, 0), ratio, rotation, rotated);
    Point tr = rotate(square, Point(square.width - 1, 0), ratio, rotation, rotated);
    Point bl = rotate(square, Point(0, square.height - 1), ratio, rotation, rotated);
    Point br = rotate(square, Point(square.width - 1, square.height - 1), ratio, rotation, rotated);

    draw_line(rotated, tl, tr);
    draw_line(rotated, tr, br);
    draw_line(rotated, br, bl);
    draw_line(rotated, bl, tl);

    rotated.save("check_lines_03.ppm");
  }
  {
    double const rotation = M_PI / 2; // 90 degrees
    compute_output_size(square, rotation, w, h);
    Image rotated(w, h);

    Point tl = rotate(square, Point(0, 0), ratio, rotation, rotated);
    Point tr = rotate(square, Point(square.width - 1, 0), ratio, rotation, rotated);
    Point bl = rotate(square, Point(0, square.height - 1), ratio, rotation, rotated);
    Point br = rotate(square, Point(square.width - 1, square.height - 1), ratio, rotation, rotated);

    draw_line(rotated, tl, tr);
    draw_line(rotated, tr, br);
    draw_line(rotated, br, bl);
    draw_line(rotated, bl, tl);

    rotated.save("check_lines_04.ppm");
  }
}


//
//
// Main
//

int main()
{
  if (!check_trigo())
    return 1;

  check_lines();

  return 0;

  Image img("img/luigi.ppm");

  Image rotated = rotate(img, 30);
  rotated.save("rotated.ppm");

  return 0;
}