// Reflexive Trefoil
#include <stdio.h>
#include <math.h>
typedef double R;
#define lc 3000
R pi = 3.14159265358979323846;
typedef struct{R x; R y; R z;} v;
void pv(v x){printf("%10.6f %10.6f %10.6f\n", x.x, x.y, x.z);}
R sq(R x){return x*x;}
v sp(R s, v vv){return (v){s*vv.x, s*vv.y, s*vv.z};}
R det(v x, v y, v z){return
   x.x * (y.y * z.z - y.z * z.y)
 + x.y * (y.z * z.x - y.x * z.z)
 + x.z * (y.x * z.y - y.y * z.x);}
v vd(v * a, v * b){return (v){a->x - b->x, a->y - b->y, a->z - b->z};}
v va(v a, v b){return (v){a.x + b.x, a.y + b.y, a.z + b.z};}
void dcir(v * ans){
R da = 2.*pi/lc;
{int k=lc; while(k--) ans[k] = sp(1,
     (v){cos(da*2*k) - cos(da*k)/2, sin(da*2*k) + sin(da*k)/2,  3*sin(da*3*k)});}
   ans[lc] = ans[0];}

v l1[lc+1]; // places on the respective curves.
int main(){
  dcir(l1);
  pv(vd(&l1[lc-1], &l1[0]));

// printf("det=%e\n", det((v){0,2,0}, (v){0,0,1}, (v){1,0,0}));
int clo(int i, int j){return (abs(i-j)<4);}
{R s = 0, rm = 1000.;
{int j=lc; while(j--) {int k=lc; while(k--) if(j!=k) {
   v r = vd(l1+j, l1+k);
   R v2 = sq(r.x) + sq(r.y)+ sq(r.z);
   R i = det(vd(l1+j+1, l1+j), vd(l1+k+1, l1+k), r)/(sqrt(v2)*v2);
   if(0) if(clo(j, 380) && clo(k, 380)) printf("%d %d %e\n", j, k, i);
   s += i;
   if(v2<rm) rm=v2;}}}
printf("s = %11.7f, 4π = %11.7f, rm=%e\n", s, 4.*pi, sqrt(rm));}
return 0;}
//s = -12.5663522, 4π =  12.5663706