#include "library.h"

struct complex
{ double real, imag; };

struct point
{ double x, y; };

const double win_width = 700, win_height = 700;
double range_min_real = -2, range_max_real = 2;
double range_min_imag = -2, range_max_imag = 2;
double x_scale = 0.5 * win_width / (range_max_real - range_min_real);
double y_scale = 0.5 * win_height / (range_max_imag - range_min_imag);

complex make_complex(double r, double i)
{ complex c;
  c.real = r;
  c.imag = i;
  return c; }

point make_point(double x, double y)
{ point p;
  p.x = x;
  p.y = y;
  return p; }

complex point_to_complex(point p)
{ complex c;
  c.real = p.x / win_width * (range_max_real - range_min_real) + range_min_real;
  c.imag = (win_height - p.y) / win_height * (range_max_imag - range_min_imag) + range_min_imag;
  return c; }

point complex_to_point(complex c)
{ point p;
  p.x = (c.real - range_min_real) / (range_max_real - range_min_real) * win_width;
  p.y = win_height - (c.imag - range_min_imag) / (range_max_imag - range_min_imag) * win_height;
  return p; }

void print(complex c)
{ cout <<  c.real << " + " << c.imag << "i\n"; }

void print(point p)
{ cout <<  p.x << ", " << p.y << "\n"; }

complex add(complex a, complex b)
{ complex c;
  c.real = a.real + b.real;
  c.imag = a.imag + b.imag;
  return c; }

complex sub(complex a, complex b)
{ complex c;
  c.real = a.real - b.real;
  c.imag = a.imag - b.imag;
  return c; }

complex mul(complex a, complex b)
{ complex c;
  c.real = a.real * b.real - a.imag * b.imag;
  c.imag = a.real * b.imag + a.imag * b.real;
  return c; }

complex div(complex a, complex b)
{ complex c;
  double bottom = b.real * b.real + b.imag * b.imag;
  if (bottom==0.0)
    cout << "Error, division by zero!\n";
  else
  { c.real = (a.real * b.real + a.imag * b.imag) / bottom;
    c.imag = (b.real * a.imag - a.real * b.imag) / bottom; }
  return c; }

double magnitude(complex a)
{ return sqrt(a.real*a.real + a.imag*a.imag); }

void move_to(complex c)
{ point p = complex_to_point(c);
  move_to(p.x, p.y); }

void draw_to(complex c)
{ point p = complex_to_point(c);
  draw_to(p.x, p.y); }

void draw_point(complex c)
{ point q = complex_to_point(c);
  draw_point(q.x, q.y); }

void draw_axes()
{ set_pen_width(1);
  set_pen_color(color::white);
  fill_rectangle(0, 0, (int)win_width+1, (int)win_height+1, color::white);
  set_pen_color(color::grey);
  complex c;
  for (c.real = range_min_real; c.real <= range_max_real; c.real += 1)
  { c.imag = range_min_real;
    move_to(c);
    c.imag = range_max_real;
    draw_to(c); }
  for (c.imag = range_min_imag; c.imag <= range_max_imag; c.imag += 1)
  { c.real = range_min_imag;
    move_to(c);
    c.real = range_max_imag;
    draw_to(c); }
  set_pen_color(color::black);
  move_to(make_complex(0.0, range_max_imag));
  draw_to(make_complex(0.0, range_min_imag));
  move_to(make_complex(range_max_real, 0.0));
  draw_to(make_complex(range_min_real, 0.0)); }

complex click_to_complex()
{ wait_for_mouse_click();
  point p;
  p.x = get_click_x();
  p.y = get_click_y();
  return point_to_complex(p); }

void zoom_in_on(complex centre, double zoom_factor)
{ double whole = range_max_real - range_min_real;
  range_min_real = centre.real - whole/(2*zoom_factor);
  range_max_real = centre.real + whole/(2*zoom_factor);
  whole = range_max_imag - range_min_imag;
  range_min_imag = centre.imag - whole/(2*zoom_factor);
  range_max_imag = centre.imag + whole/(2*zoom_factor);
  x_scale = win_width / (range_max_real - range_min_real);
  y_scale = win_height / (range_max_imag - range_min_imag); }

void main()
{ make_window(win_width, win_height);
  draw_axes();
  set_pen_width(4);
  point p;
  while (true)
  {  for (p.x = 0; p.x < win_width; p.x += 1)
     { for (p.y = 0; p.y < win_height; p.y += 1)
       { complex c = point_to_complex(p);
         complex v = c;
         double m = 0;
         for (int i=0; i<1000 && m < 3; i+=1)
         { c = add(mul(c, c), v);
           m = magnitude(c); }
         if (m<3)
           set_pixel_color(p.x, p.y, color::red);
         else
           set_pixel_color(p.x, p.y, color::yellow); } }
     complex c = click_to_complex();
     zoom_in_on(c, 2); } }