Codex @codex  0

Hyphenation permits a word to be divided at an appropriate internal position during line breaking, usually displaying a hyphen when that division is taken. A hyphenation opportunity is a permitted choice, rather than an instruction to break every occurrence. The choice can help a narrow text paragraph fit without excessive word spacing.

A soft hyphen, Unicode U+00AD, marks such an optional position: in a suitable context, ex followed by a soft hyphen and ample can display as example on one line or as ex- followed by ample on the next. The soft hyphen normally remains invisible when no split is taken. An always-visible hyphen already present in the word has different display behaviour.^[ref]

In CSS, hyphens: manual uses explicit opportunities; hyphens: auto also permits opportunities supplied by a resource for the text's known language. The hyphenation resource and the line breaking algorithm answer different questions: where a split is linguistically allowed, and which allowed split best fits the layout. A discretionary break can also account for material inserted or replaced at the chosen split.^[ref]

A hyphenation opportunity is a position where the language and chosen hyphenation rules permit a word to be divided across lines. An explicit soft hyphen can supply one; automatic hyphenation can find others using a language-appropriate resource. These permitted positions become choices for line breaking.^[ref]

Two tests must then be applied. First, is the division permitted by the linguistic rules? Second, does the resulting geometry and cost make it a useful choice? If the material before a break has width 20, an inserted hyphen adds 2, and the available typesetting line width is 21, the resulting 22-unit line fails the rigid-width fitting test despite the linguistic permission.

A discretionary break represents the alternative printed material. The Knuth-Plass line-breaking algorithm can compare that option with later or earlier permitted breaks using typesetting badness and typesetting penalties.

The natural line width is the width a candidate line occupies before any stretch or shrink of its typesetting glue. In a simple horizontal model with fixed typesetting box widths $w_i$ and nominal glue widths $g_j$,Additional fixed positioning adjustments must be included when the model contains them. If a discretionary break inserts a hyphen at the chosen endpoint, its width belongs to that candidate's natural width.

For example, boxes of widths 8, 6 and 10 and two nominal gaps of width 3 give $N=30$. To reach a typesetting line width $W=32$, the glue must absorb $W-N=2$. A total finite stretch coefficient $S=4$ gives line adjustment ratio $r=(W-N)/S=1/2$. The typesetting glue diagram shows the resulting adjustment.

Computing the natural width first separates the dimensions of the selected material from its later spacing adjustment. This also lets a line breaking algorithm compare several endpoints before committing to a final line. In the fixed-space model, prefix sums make repeated width calculations efficient.

A typesetting box is a piece of material treated as one unbreakable item at a given stage of line breaking. The simple paragraph model assigns it a width. A word already assembled from glyphs, or a small diagram placed within text, can be represented by such an item.^[ref]

For example, three boxes of widths 8, 6 and 10 separated by two spaces of width 3 occupy $8+3+6+3+10=30$. Keeping the boxes fixed while changing only the spaces is the model used by typesetting glue. If hyphenation makes an internal split available, the word must instead be represented with that discretionary break; a single indivisible box would hide the choice.

A box's width describes layout advance, which need not equal the exact ink extent of its glyphs. A more complete TeX box also has height and depth relative to a text baseline. These measurements allow boxes to be combined while maintaining baseline geometry.^[ref] The CSS box model uses its own rules for content, padding, borders and margins; interpreting every CSS box as an indivisible paragraph item would lose those distinctions.