lB. There are two classes of qualitatively distinguishable configurations for

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

(dA rrrr dB): We can see that lB intersects lA either in front of or behind dA. If the intersection

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

point lies in front of dA, we are in a situation like where S is the intersection point. We can further see that the angle from lA to lB lies clearly in the interval (π, 2 · π). Furthermore, lB can be rotated in the whole interval (π, 2 · π) without changing the DRAf relation. Using this, we obtain the DRAfp-relation rrrr- between dA and dB if the point of intersection S lies in front of dA. For any qcc belonging to such a scenario, the rest of the proof follows from Prop. 37 and Prop. 38 as well as the inspection of the extended classifiers:

SˆAB > ed(dpA) ∧ dir(dpA) = + *−→ −*
SˆAB < ed(dpA) ∧ dir(dpA) = *− −→ −*
But these also yield (dpA rrrr- dpB). By the same arguments, we show that
(dA rrrr+ dB) if the point of intersection of lA and lB lies behind dA. The proof for all other cases is analogous.

Corollary 47. *The 72 relations in Fig. 3 are those out of the 2401 formal* combinations of four LR *letters that are geometrically possible.*
Proof. By an exhaustive inspection of the primitive classifiers which occur in the basic classifiers for all pqccs. For the decomposition, we refer to the proof of Thm. 45.

Theorem 48. Given a qcc Q and an arbitrary geometric realization R(Q) *of it,*
the DRAfp relation in R(Q) is the same as that computed by the basic classifiers on Q. Proof. Follows from Thm. 45 and Prop. 46.