Assume two line segments [p, p+r] and [q, q+s], and test if they intersect.

line_seg_intersect.c

#define CROSS_Z(a, b) ((a.x*b.y) - (a.y*b.x))
 
 bool LinesIntersect(GLKVector2 p, GLKVector2 p_plus_r, GLKVector2 q, GLKVector2 q_plus_s) {  
  /* Calculate q - p */
  GLKVector2 q_p	= {
   q.x - p.x,
   q.y - p.y
  };
  
  /* Calculate r */
  GLKVector2 r = {
   p_plus_r.x - p.x,
   p_plus_r.y - p.y
  };
  
  /* Calculate s */
  GLKVector2 s = {
   q_plus_s.x - q.x,
   q_plus_s.y - q.y
  };
  
  /* Calculate (q-p) x r */
  float q_pxr = CROSS_Z(q_p, r);
  
  /* Calculate (q-p) x s */
  float q_pxs = CROSS_Z(q_p, s);
  
  /* Calculate (r x s) */
  float rxs = CROSS_Z(r,s);
  
  if (q_pxr == 0.0f) {
   // Lines are collinear, and so intersect if they have any overlap.
   // Assume edge case as failure
   return false;
  }
  
  if (rxs == 0.0f) {
   // Lines are parallel.
   return false;
  }
  
  /* Calculate 1 / (rxs) */
  float one_div_rxs = 1.0f / rxs;
  
  /* Calculate t */
  float t = q_pxs * one_div_rxs;
  
  /* Calculate u */
  float u = q_pxr * one_div_rxs;
  
  return (t >= 0.0f) && (t <= 1.0f) && (u >= 0.0f) && (u <= 1.0f);
 }