#ifndef __geom_h
#define __geom_h


#include <vector>

using namespace std; 

typedef struct _point3d {
  int x,y,z; 
} point3d;

typedef struct _triangle3d {
  point3d *a,*b,*c; 
  //to avoid duplication of points, a triangle stores pointers to the
  //points (which are stored in the vector of points)
} triangle3d;


/* returns 2 times the signed area of triangle abc. The area is positive if c
   is to the left of ab, and negative if c is to the right of ab
 */
int signed_area3D(point3d a, point3d b, point3d c, point3d d);

/* return 1 if p,q,r, t on same plane, and 0 otherwise */
int collinear(point3d p, point3d q, point3d r, point3d t);


/* return 1 if d is  strictly left of abc; 0 otherwise */
int left (point3d a, point3d b, point3d c, point3d d); 


/* compute and return the convex hull of the points */
vector<triangle3d> brute_force_hull(vector<point3d> points);


#endif