Fishes are generally vigorous animals that move around constantly. If at some instant the sight of one fish is blocked by another fish passing by, the occlusion will most likely be cleared soon after--since both fish are in motion. The temporary blocking of sight should not result in abrupt changes in a fish's behavior. Therefore, occlusion tests against another fish tend to be unessential. To increase computational efficiency, the artificial fish performs occlusion tests only against large static environmental objects. In the current implementation, this includes cylindrical objects. Note that, for obstacles with more complex geometric shapes, cylinders can serve as their bounding boxes.
The algorithm for testing the intersection of a ray with a cylinder is
simple, especially since the axis of each cylinder is parallel to the
z-axis of the world coordinate system (see Fig. 
).
Let the coordinates of O and P in the world
coordinate system be denoted by 
and 
, respectively. Then line 
can be represented by
the parametric equation
where 
, 
, 
and 
. Let r denote the radius and h the height
of the cylinder C under consideration. Its projection onto the
XY-plane is a circle A which can be represented by the parametric
equation
where (a,b,0) denotes the center of A. The occlusion-test algorithm we develop can be outlined as follows (all calculations are performed in the world coordinate system):
intersects with circle A:
Substitute the x and y in Eq. () with those in
Eq. () and solve for t. If the solutions 
and
( 
) have real values and at least one of them is
in [0,1], then do step 2; Otherwise, stop (P is not occluded
by cylinder C).
intersects with
cylinder C:
Substitute the t in Eq. () with and to get
the points of intersection. In fact, one only needs to calculate
, i=1,2. If 
for i=1 or
i=2, then point P is occluded. Otherwise, P is visible.
| Xiaoyuan Tu | January 1996 |
