Before revision:  For a given ray, using the support of unit basis function, we derive the sufficient and necessary condition of non-vanishing intersectability , and obtain the analytic formula for the intersection length, which can be used to distinguish the units that produce valid intersections with the given ray, and then perform simple calculations only for those units  .
After revision:  For a given ray, using the support of unit basis function, we derive the sufficient and necessary condition for non-vanishing intersectability , and obtain the analytic formula for the intersection length, which can be used to distinguish the units that produce valid intersections with the given ray, and then perform simple calculations only for those units .