
$$\begin{array}{l}{{d i r(d p_{A})=+}}\\ {{d i r(d p_{B})=-}}\\ {{d i r(d p_{C})=-}}\end{array}$$

In this case the assignment of <p is arbitrary.

This construction gives us the desired qcc and a realization of it.

## 3.3 Primitive Classifiers

The last and most crucial point is the computation of DRA relations between three dipoles. We can decompose this task into subtasks, since each DRAf relation comprises four LR relations between a dipole and point; these are obtained from a qualitative composition configuration using so-called *primitive* classifiers. The *basic classifiers* apply the *primitive classifiers* to the abstract dipoles in each qualitative composition configuration in an adequate manner.

For DRAfp relations an extension of the *basic classifiers* is used in cases where the qualitative angle between several dipoles has to be determined. Finally, the resulting data is collected in a (composition) table.

Definition 35 (Primitive Qualitative Composition Configuration). A primitive qualitative composition configuration (pqcc) is a sub-configuration of a qualitative composition configuration (see Def. 29) containing two abstract dipoles
(where for the second one, only the start or end point is used for classification).

All other data are the same as in Def. 29.

Notation 36. To simplify the explanation of large classifiers, we shall write:

$${\mathrm{instead~of~}}$$
$$\begin{array}{r c l}{{f(x)}}&{{=}}&{{\left\{\begin{array}{l l l}{{c o n d_{1}}}&{{\longrightarrow}}&{{v a l u e_{1}}}\\ {{c o n d_{2}}}&{{\longrightarrow}}&{{v a l u e_{2}}}\end{array}\right.}}\\ {{}}&{{}}&{{}}\\ {{}}&{{}}\\ {{}}&{{}}\\ {{f(x)}}&{{=}}&{{\left\{\begin{array}{l l l}{{v a l u e_{1}}}&{{\mathrm{if~}c o n d_{1}}}\\ {{v a l u e_{2}}}&{{\mathrm{if~}c o n d_{2}.}}\end{array}\right.}}\end{array}$$
it the "$ f(x)=$". 
If it is clear which function we are defining, we even omit the "f(x) =".

Given a primitive qualitative composition configuration Q, *primitive classifiers* map the qualitative locations of a dipole dp1 and a point pt (which is the start or end point of another dipole dp2) to a letter indicating the LR relation between the dipole and point. We say that the dipole has positive pos orientation if dir(dp) = +, otherwise the orientation is negative neg.

We need three different types of primitive classifiers for our algorithm.

Given two arbitrary dipoles dp1 and dp2, we construct a primitive classifier for a pqcc with intersecting carrier rays in its realization. The classifier itself only works on dp1 and pt, where pt is either the start or end point of dp2. A
and