How to devise multicategory classifiers employing linear discriminant functions?

1. We might reduce the problem to $c$ two-class problems, where the $i^{th}$ problem is solved by a linear discriminant function that separates points assigned to $w_i$ from those not assigned to $w_1$.

2. A more extravagant approach would be to use $\frac{c(c-1)}{2}$ linear discriminants, one for every pair of classes.

For these two methods, I don't understand how they divide the area. If we remove all the lines in Figure 9.3, how should we start?