sentences:  After having recursively gone through all the trouble of solving the problem for the guessed half-space, now compare the distance returned by this result with the shortest distance from the query point to the partitioning plane.This latter distance is that between the query point and the closest possible point that could exist in the half-space not searched.If this distance is greater than that returned in the earlier result, then clearly there is no need to search the other half-space.