#include <math.h>
#include <stdio.h>

#define N 6

static double p[N+1];

typedef struct xy XY;

struct xy {
  double x;
  double y;
  } ;

/*
 * Find the point at which the line a1-a2 intersects the line b1-b2,
 *  possibly after extending one or both lines enough that they
 *  intersect.  Return the fraction of the way from a1 to a2 this is
 *  (ie, 0 if a1, 1 if a2).
 *
 * In METAFONT-speak, if I haven't forgotten too much of it, this is
 *
 *	k1 = whatever    (k1 is the return value)
 *	k2 = whatever
 *	p = k1[a1,a2]
 *	p = k2[b1,b2]
 *
 * Since we don't care about p, we eliminate it:
 *
 *	k1[a1,a2] = k2[b1,b2]
 *
 * Expanding into individual equations,
 *
 *	(1-k1) a1x + k1 a2x = (1-k2) b1x + k2 b2x
 *	(1-k1) a1y + k1 a2y = (1-k2) b1y + k2 b2y
 *
 * This is two equations in two unknowns.  Isolating the unknowns,
 *
 *	k1 (a2x - a1x) + k2 (b1x - b2x) = b1x - a1x
 *	k1 (a2y - a1y) + k2 (b1y - b2y) = b1y - a1y
 *
 * This then gives, successively
 *
 *	k2 = ((b1y - a1y) - k1 (a2y - a1y)) / (b1y - b2y)
 *
 *	k1 = ((b1x - a1x) - k2 (b1x - b2x)) / (a2x - a1x)
 *
 *	                   (b1y - a1y) - k1 (a2y - a1y)
 *	     (b1x - a1x) - ---------------------------- (b1x - b2x)
 *	                            b1y - b2y
 *	k1 = ------------------------------------------------------
 *	                          a2x - a1x
 *
 *	     (b1x - a1x) (b1y - b2y) - (b1y - a1y) (b1x - b2x) + k1 (a2y - a1y) (b1x - b2x)
 *	k1 = ------------------------------------------------------------------------------
 *	                            (a2x - a1x) (b1y - b2y)
 *
 *	k1 (a2x - a1x) (b1y - b2y) = (b1x - a1x) (b1y - b2y) - (b1y - a1y) (b1x - b2x) + k1 (a2y - a1y) (b1x - b2x)
 *
 *	k1 [(a2x - a1x) (b1y - b2y) - (a2y - a1y) (b1x - b2x)] = (b1x - a1x) (b1y - b2y) - (b1y - a1y) (b1x - b2x)
 *
 *	     (b1x - a1x) (b1y - b2y) - (b1y - a1y) (b1x - b2x)
 *	k1 = -------------------------------------------------
 *	     (a2x - a1x) (b1y - b2y) - (a2y - a1y) (b1x - b2x)
 */
static double intersection(XY a1, XY a2, XY b1, XY b2)
{
 return( (((b1.x - a1.x) * (b1.y - b2.y)) - ((b1.y - a1.y) * (b1.x - b2.x))) /
	 (((a2.x - a1.x) * (b1.y - b2.y)) - ((a2.y - a1.y) * (b1.x - b2.x))) );
}

static void find_p(void)
{
 int i;

 for (i=N;i>=0;i--)
  { p[i] = intersection((XY){1,0},(XY){0,1},(XY){0,0},(XY){cos(i*M_PI/(2*N)),sin(i*M_PI/(2*N))});
  }
}

static XY alpha(XY p1, double a, XY p2)
{
 return((XY){ ((1-a)*p1.x) + (a*p2.x),
	      ((1-a)*p1.y) + (a*p2.y) });
}

static void print_line(XY p1, XY p2)
{
 printf("%g %g moveto %g %g lineto\n",p1.x*500,p1.y*500,p2.x*500,p2.y*500);
}

static void draw_lines(void)
{
 int i;
 XY p1;
 XY p2;
 XY p3;

 p1 = (XY){0,0};
 p2 = (XY){1,0};
 p3 = (XY){.5,sqrt(.75)};
 for (i=N;i>=0;i--)
  { print_line(alpha(p1,p[i],p2),alpha(p3,p[i],p2));
    print_line(alpha(p2,p[i],p3),alpha(p1,p[i],p3));
    print_line(alpha(p3,p[i],p1),alpha(p2,p[i],p1));
  }
}

int main(void);
int main(void)
{
 find_p();
 draw_lines();
 return(0);
}