Quantum Boundaries for Last Line Adjustments

Aug 31, 2026·
Didier Verna
Didier Verna
· 1 min read
Type
Event
Date
Jul 17, 2024 — Jul 19, 2024
Location

Alt Hotel

635 Confluence Way SE, Calgary, Alberta T2G 0G1

Abstract
The glue model of TeX is a powerful and elegant abstraction allowing for many typographic applications. One such application is the typesetting of a paragraph’s last line, which requires special treatment. By adding infinitely stretchable glue at the end of a paragraph, the need for special-casing the final line is avoided, albeit at the cost of sub-optimal typesetting. In conscientious typography, optimally typesetting the last line of a paragraph turns out to be a non-trivial problem, especially if one wants to take into account such aesthetic concerns as runt or full-out lines. In this paper, we present an algorithm for optimal last line adjustment, introducing the concept of quantum boundaries: potential line breaks whose exact state remains unknown until an actual paragraph solution is observed.