#include "library.h"

const int screen_size = 600;
const double function_max = 20.0;

// the window will be 600 x 600
// the window's pixel coordinates ranging from (0,0) to (600,600)
// will represent complex numbers running from (-20-20i) to (20+20i)

struct complex
{ double real, imag; };

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

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

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

void screen_pos_to_function(int scrx, int scry, double & x, double & y)
{ x = (scrx-screen_size/2.0)/(screen_size/2.0)*function_max;
  y = (screen_size/2.0-scry)/(screen_size/2.0)*function_max; }

void function_to_screen_pos(double x, double y, int & scrx, int & scry)
{ scrx = (int)(x/function_max*(screen_size/2)+screen_size/2);
  scry = screen_size/2-(int)(y/function_max*(screen_size/2)); }

complex get_complex()     // wait for the user to click the mouse
                          // then work out which complex number
                          // the mouse-click position corresponds to.
{ wait_for_mouse_click();
  int x = get_click_x(), y = get_click_y();
  double r, i;
  screen_pos_to_function(x, y, r, i);
  return make_complex(r, i); }

void main()
{ make_window(screen_size, screen_size);

  set_pen_color(color::grey);   // draw in the axes so we can see where zero is
  move_to(0, screen_size/2);
  draw_to(screen_size, screen_size/2);
  move_to(screen_size/2, 0);
  draw_to(screen_size/2, screen_size);
  set_pen_color(color::black);
  
  while (true)
  { complex c = get_complex();  // let the user select a starting position, c
    print(c);
    cout << " size = " << size(c) << "\n";
    int sx, sy;
    function_to_screen_pos(c.real, c.imag, sx, sy);
    move_to(sx, sy);
    complex v = make_complex(0, 0);
    for (int i=0 ; i<1000; i+=1)
                                // repeat a thousand times the complex number
                                // calculation v = v*v + c and see what happens
    { v = add(mul(v, v), c);
      function_to_screen_pos(v.real, v.imag, sx, sy);
      draw_to(sx, sy); } } }