#include "library.h"

struct complex
{ double real, imag; };

struct point
{ double x, y; };

const double win_width = 500, win_height = 500;
const double range = 5;
const double x_scale = 0.5 * win_width / range;
const double y_scale = 0.5 * win_height / range;

complex point_to_complex(point p)
{ complex c;
  c.real = (p.x - win_width/2) / x_scale;
  c.imag = - (p.y - win_height/2) / y_scale;
  return c; }

point complex_to_point(complex c)
{ point p;
  p.x = c.real * x_scale + win_width/2;
  p.y = (- c.imag * y_scale) + win_height/2;
  return p; }

void print(complex c)
{ cout <<  c.real << " + " << c.imag << "i\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 draw_axes()
{ set_pen_width(1);
  set_pen_color(color::grey);
  complex c;
  point p;
  for (c.real = -range; c.real <= range; c.real += 1)
  { c.imag = - range;
    p = complex_to_point(c);
    move_to(p.x, p.y);
    c.imag = range;
    p = complex_to_point(c);
    draw_to(p.x, p.y); }
  for (c.imag = -range; c.imag <= range; c.imag += 1)
  { c.real = - range;
    p = complex_to_point(c);
    move_to(p.x, p.y);
    c.real = range;
    p = complex_to_point(c);
    draw_to(p.x, p.y); }
  set_pen_color(color::black);
  move_to(0.0, win_height/2);
  draw_to(win_width, win_height/2);
  move_to(win_width/2, 0.0);
  draw_to(win_width/2, win_height); }

void main()
{ make_window(win_width, win_height);
  draw_axes();
  while (true)
  {  wait_for_mouse_click();
     point p;
     p.x = get_click_x();
     p.y = get_click_y();
     complex c = point_to_complex(p);
     print(c);
     point q = complex_to_point(c);
     set_pen_width(4);
     draw_point(q.x, q.y); } }


// v = 0; c = point; v = v * v + c