Once the ambiguous case for has been eliminated by the definition of the function, there might be zero or one values (and corresponding points ) for a given , , and .
(If the distance between and is zero, then a single point of interception exists at the shared pointor an infinite number of points of interception over time if in addition . These special cases are excluded from all the considerations below.)
Equation (1) is undefined when is zero. If happens to be headed directly for with a nonzero velocity (that is, , which means is zero, and is nonzero), then a point of interception will exist at point . Otherwise, no point of interception will exist. In either case, the value of is irrelevant to the physical problem since point does not move.
Equation (1) is undefined when the parameter of the function is less than or greater than . Consider the parameter of the function: is a number between and which will modify the speed ratio to determine how far has to turn from its line of sight in order to try to intercept : a faster and a close to lead to a more radical turn. If, for instance, is headed directly toward or directly away from , then or , , and the relative speeds of and are irrelevant to : the intercept angle will be 0 (i.e. should run directly towards to try to intercept). If, on the other hand, is running directly broadside to 's line of sight, , then is going to have to turn quite a ways from its line of sight to try and intercept : how far, exactly, is determined only by the ratio of their speeds, since will be .
So, when the ratio of the velocities modified by the relative angle of their vectors is less than or greater than , will escape from off to one side or the other, and no point is defined. This doesn't describe all possible escapes of ; rather, it describes the escapes where is running obliquelyat something like a right angleacross 's line of sight. Such an escape has an understandable representation when is less than , as shown by in Figure 4: is moving so fast (relative to ) that even though is headed in the general direction of , still can't close the gap, even with a maximum of . (Because of the ambiguity expressed by , a similar escape where is greater than is not easily picturedsee in the figure.

A description of all possible escapes cannot use equation (1) as its sole criterion, since in many cases the equation will happily yield an even though an interception is impossible (and even though the reprentation expressed by the formula has long since stopped having any correspondence with the physical situation). The reflection case ( ) of the previous paragaph begins to illustrate the failure of the representation (that is, the failure of the formulaic solution for ) when is not large enough for an interception.
Figure 5 further clarifies the potential difficulty, and combines a physical representation (at a certain point in time) in black, and the corresponding mathematical representation (for the equation) in red.

Consider, on the other hand, a representation of the problem when is greater than but is at least as large as , as shown in Figure 6.

The two illustrations in Figure 7, then, are the physical representations of the general case for noninterception.
When , then formula (1) will be undefined. When , either formula (1) will be undefined, or will be greater than , or both. In either situation, an interception is impossible according to the assumptions of the problem; but otherwise, formula (1) will give a correct interception value.