The Corner of a Region

The sharpest feature of an overlap region is its corner, and the corner is nothing new: it is the crossing of the two boundary lines, found exactly like any system of equations. For boundaries y = x - 1 and y = -x + 3, setting the right sides equal gives x - 1 = -x + 3, so x = 2 and y = 1.

Whether the corner itself belongs depends on the fences: it is in the region only when both boundaries are solid. Regions with more inequalities have more corners, one per crossing pair, and finding them is this same computation repeated.