struct control_point
{
   vec3 position, look_at, up;
};

...

void FlyPath::Animate()
{
   lerp = lerp + MY_CTIME;

   if (lerp > 1.0f)
   {
      lerp = 0.0f;

      if (++index >= count)
      {
         index = 0;
      }
   }

   vec3 p0 = step[(index - 1 + count) % count].position;
   vec3 p1 = step[(index    ) % count].position;
   vec3 p2 = step[(index + 1) % count].position;
   vec3 p3 = step[(index + 2) % count].position;

   current.position = 0.5f * ((2.0f * p1) + 
                              (-p0 + p2) * lerp +
                              (2.0f * p0 - 5.0f * p1 + 4.0f * p2 - p3) * pow(lerp, 2.0f) +
                              (-p0 + 3.0f * p1 - 3.0f * p2 + p3) * pow(lerp, 3.0f));

   p0 = step[(index - 1 + count) % count].look_at;
   p1 = step[(index    ) % count].look_at;
   p2 = step[(index + 1) % count].look_at;
   p3 = step[(index + 2) % count].look_at;

   current.look_at = 0.5f * ((2.0f * p1) + 
                             (-p0 + p2) * lerp +
                             (2.0f * p0 - 5.0f * p1 + 4.0f * p2 - p3) * pow(lerp, 2.0f) +
                             (-p0 + 3.0f * p1 - 3.0f * p2 + p3) * pow(lerp, 3.0f));

// current.up = ?????????????????????????????????????????????????????????

   return;
}

void FlyPath::Render()
{
   gluLookAt(current.position[x], current.position[y], current.position[z],
             current.look_at[x], current.look_at[y], current.look_at[z],
             current.up[x], current.up[y], current.up[z]);

   return;
}