

![0_image_0.png](0_image_0.png)

realization of this pqcc is given in Fig. 17 for the reader's convenience, the actual dipoles are omitted from the figure, since they can be placed arbitrarily.

To realize the dipole, this classifier takes dipole dp1 and the start or end point of dp2 called pt as well as information on whether dp1 is pointing in the same direction as the ray (pos) or against it (neg) for both dipoles. The classifier returns an LR-relation determining the relation between dp1 and pt.

In this case, the classifier clix,y(dp1*, pt*) is given by:

![0_image_1.png](0_image_1.png)

st(dp1) < x ∧ ed(dp1) < x −→ F

st(dp1) < x ∧ ed(dp1) = x −→ E st(dp1) < x ∧ ed(dp1) > x −→ I

st(dp1) = x ∧ ed(dp1) > x −→ S st(dp1) > x ∧ ed(dp1) > x −→ B

st(dp1) > x ∧ ed(dp1) > x −→ F

st(dp1) > x ∧ ed(dp1) = x −→ E

st(dp1) > x ∧ ed(dp1) < x −→ I

st(dp1) = x ∧ ed(dp1) < x −→ S

st(dp1) < x ∧ ed(dp1) < x −→ B

The subscripts on the classifier denote the point of intersection of the two lines.

For the case shown in Fig. 17, we have x = y = S. We see that the table for neg is exactly the complement of pos. This primitive classifier assumes that, in the geometric realization, the second dipole (containing point pt) points to the right w.r.t. dipole d. If the second dipole points to the left in the realization, it is sufficient to apply an operation that interchanges L with R on this classifier, in order to obtain the correct results. We will call this operation com. This is the only primitive classifier needed for intersecting lines.

Secondly, we give a primitive classifier cls(dp1*, pt*) for two lines that coincide, see Fig. 18.