#include "library.h"

struct complex
{ double real, imag; };

complex make_complex(double r, double im)
{ complex x;
  x.real = r;
  x.imag = im;
  return x; }

void print(complex x)
{ if (x.imag >= 0)
    cout << x.real << " + " << x.imag << "i";
  else
    cout << x.real << " - " << -x.imag << "i"; }


complex read_complex()
{ complex x;
  cout << "Enter the real part: ";
  cin >> x.real;
  cout << "Enter imaginary part: ";
  cin >> x.imag;
  return x; }

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

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

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

complex div(complex a, complex b)
{ double bot = b.real*b.real + b.imag*b.imag;
  double topreal = a.real*b.real + a.imag*b.imag;
  double topimag = a.imag*b.real - a.real*b.imag;
  return make_complex(topreal/bot, topimag/bot);
}

const double minreal = -2, maxreal = 2, minimag = -2, maximag = 2;
const double maxx = 600, maxy = 600;

double real_to_x(double r)
{
  return (r - minreal) / (maxreal - minreal) * maxx;
}

double imag_to_y(double i)
{
  return maxy - (i - minimag) / (maximag - minimag) * maxy;
}

void plot_complex(complex x)
{ double sx = real_to_x(x.real);
  double sy = imag_to_y(x.imag);
  move_to(sx-10, sy-10);
  draw_to(sx+10, sy+10);
  move_to(sx-10, sy+10);
  draw_to(sx+10, sy-10); }

double x_to_real(double x)
{ return x/maxx * (maxreal - minreal) + minreal; }

double y_to_imag(double y)
{ y = maxy - y;
  return y/maxy * (maximag - minimag) + minimag; }

complex read_click()
{ wait_for_mouse_click();
  double sx = get_click_x(),
         sy = get_click_y();
  return make_complex(x_to_real(sx), y_to_imag(sy)); }

void move_to(complex x)
{
  double sx = real_to_x(x.real);
  double sy = imag_to_y(x.imag);
  move_to(sx, sy);
}

void draw_to(complex x)
{
  double sx = real_to_x(x.real);
  double sy = imag_to_y(x.imag);
  draw_to(sx, sy);
}

void draw_axes()
{ double yzero = imag_to_y(0);
  move_to(0.0, yzero);
  draw_to(maxx, yzero);
  double xzero = real_to_x(0);
  move_to(xzero, 0.0);
  draw_to(xzero, maxy); }

void main()
{
  make_window(maxx, maxy);
  draw_axes();
  while (true)
  { cout << "Enter C:\n";
    complex C = read_click();
    complex Z = make_complex(0.0, 0.0);
    move_to(C);
    for (int i = 0; i < 100; i += 1)
    { Z = add(mul(Z, Z), C);
      draw_to(Z); } } }



/*
void main()
{ cout << "Enter A:\n";
  complex a = read_complex();
  cout << "Enter B:\n";
  complex b = read_complex();
  complex plus = add(a, b);
  complex min = sub(a, b);
  complex tim = mul(a, b);
  complex divi = div(a, b);
  cout << "A+B = "; print(plus); cout << "\n";
  cout << "A-B = "; print(min); cout << "\n";
  cout << "A*B = "; print(tim); cout << "\n";
  cout << "A/B = "; print(divi); cout << "\n";
}
*/