How two segments meet #
Two segments meet in nothing, or in a segment. The blueprint says "the empty set, one point, or one closed interval" (Lemma 3.7, polygonal overlay); a point is a segment with equal endpoints, so the statement folds to a dichotomy, and that is the form the overlay wants — it subdivides at the endpoints of whatever the meet turns out to be, and a degenerate meet contributes one subdivision point.
No case analysis on whether the segments are parallel, and no determinant. The meet is
compact and convex, so its preimage under the parametrization lineMap a b is a compact
convex subset of ℝ, hence a closed interval; pushing that interval forward is a segment.
Blueprint #
segment_inter_segment— the meet dichotomy used by Lemma 3.7.