#include "library.h"

const double pi = acos(-1.0);

double power(const double y, const int p)
{ if (p==0)
    return 1;
  else
  { const double prev = power(y, p-1);
    return y*prev; } }

double factorial(const int n)
{ if (n==0)
    return 1;
  else
  { const double prev = factorial(n-1);
    return n*prev; } }

int multiplier(const int n)
{ if (n%2==0)
    return 0;
  else if (n%4==1)
    return 1;
  else
    return -1; }

double term(const double x, const int n)
{ return multiplier(n) * power(x, n) / factorial(n); }

double sum_of_terms(const int first, const int last, const double x)
{ const double first_term = term(x, first);
  if (first==last)
    return first_term;
  const double other_terms = sum_of_terms(first+1, last, x);
  return first_term + other_terms; }

double sine(const double angle, const int terms)
{ const double x = angle*pi/180;
  return sum_of_terms(0, terms, x); }

const int winw=720, winh=500;

void setup()
{ make_window(winw, winh);
  set_pen_color(color::green);
  move_to(0, 1*winh/4);
  draw_to(winw, 1*winh/4);
  move_to(0, 2*winh/4);
  draw_to(winw, 2*winh/4);
  move_to(0, 3*winh/4);
  draw_to(winw, 3*winh/4);
  move_to(1*winw/4, 0);
  draw_to(1*winw/4, winh);
  move_to(2*winw/4, 0);
  draw_to(2*winw/4, winh);
  move_to(3*winw/4, 0);
  draw_to(3*winw/4, winh); }

void plot_graph(const double min_x, const double max_x, const int num_terms)
{ if (max_x-min_x <= 1)
  { const double min_sine = sine(min_x, num_terms);
    const double max_sine = sine(max_x, num_terms);
    move_to(min_x, winh/2-min_sine*winh/4);
    draw_to(max_x, winh/2-max_sine*winh/4); }
  else
  { const double mid_x = (min_x+max_x)/2;
    plot_graph(min_x, mid_x, num_terms);
    plot_graph(mid_x, max_x, num_terms); } }

void plot_many_graphs(const int first_test, const int last_test)
{ if (first_test<=last_test)
  { const double redness = (first_test-1.0)/(last_test-1.0);
    set_pen_color(redness, 0, 1-redness); 
    plot_graph(0, winw, first_test);
    plot_many_graphs(first_test+1, last_test); } }

void main()
{ setup();
  plot_many_graphs(1, 49); }