diff options
Diffstat (limited to 'doc')
| -rw-r--r-- | doc/dw-line-breaking.doc | 92 |
1 files changed, 59 insertions, 33 deletions
diff --git a/doc/dw-line-breaking.doc b/doc/dw-line-breaking.doc index 54d03d19..ac4f61d6 100644 --- a/doc/dw-line-breaking.doc +++ b/doc/dw-line-breaking.doc @@ -151,9 +151,12 @@ So we need the following values: - \f$w_i\f$ (the width of the word \f$i\f$ itself); - \f$s_i\f$ (the width of the space following the word \f$i\f$); - the stretchability \f$y_i\f$, a value denoting how much the space - after word\f$i\f$ can be stretched (typically \f${1\over 2} s_i\f$); + after word\f$i\f$ can be stretched (typically \f${1\over 2} s_i\f$ + for justified text; otherwise 0, since the spaces are not + stretched); - the shrinkability \f$y_i\f$, a value denoting how much the space - after word\f$i\f$ can be shrunken (typically \f${1\over 3} s_i\f$); + after word\f$i\f$ can be shrunken (typically \f${1\over 3} s_i\f$ + for justified text; otherwise 0, since the spaces are not shrinked); - the penalty \f$p_i\f$, if the line is broken after word \f$i\f$; - a width \f$h_i\f$, which is added, when the line is broken after word \f$i\f$. @@ -171,13 +174,16 @@ We define: \f[W_a^b = \sum_{i=a}^{b} w_i + \sum_{i=a}^{b-1} s_i + h_b\f] -\f[Y_a^b = \sum_{i=a}^{b-1} y_i\f] +\f[Y_a^b = {Y_0}_a^b + \sum_{i=a}^{b-1} y_i\f] -\f[Z_a^b = \sum_{i=a}^{b-1} z_i\f] +\f[Z_a^b = {Z_0}_a^b + \sum_{i=a}^{b-1} z_i\f] -\f$W_a^b\f$ is the total width, \f$Y_a^b\f$ the total stretchability, and -\f$Z_a^b\f$ the total shrinkability. +\f$W_a^b\f$ is the total width, \f$Y_a^b\f$ the total stretchability, +and \f$Z_a^b\f$ the total shrinkability. \f${Y_0}_a^b\f$ and +\f${Z_0}_a^b\f$ are the stretchability and shrinkability defined per +line, and applied at the borders; they are 0 for justified text, but +\f${Y_0}_a^b\f$ has a positive value otherwise, see below for details. Furthermore the *adjustment ratio* \f$r_a^b\f$: @@ -217,6 +223,53 @@ integer arithmetic is used for performance, which make the actual code more complicated. See dw::Textblock::BadnessAndPenalty for details.) +Ragged Borders +-------------- + +For other than justified text (left-, right-aligned and centered), the +spaces between the words are not shrinked or stretched (so \f$y_i\f$ +and \f$z_i\f$ are 0), but additional space is added to the left or +right border or to both. For this reason, an additional stretchability +\f${Y_0}_a^b\f$ is added (see definition above). Since this space at +the border is 0 in an ideal case (\f$W_a^b = l\f$), it cannot be +shrunken, so \f${Z_0}_a^b\f$ is 0. + +This is not equivalent to the calculation of the total stretchability +as done for justified text, since in this case, the stretchability +depends on the number of words: consider the typical case that all +spaces and stretchabilities are equal (\f$y_a = y_{a + 1} = \ldots = +y_b\f$). With \f$n\f$ words, the total strechability would be \f$n +\cdot y_a\f$, so increase with an increasing number of words +(\f$y_a\f$ is constant). This is correct for justified text, but for +other alignments, where only one space (or two, for centered text) is +changed, this would mean that a line with many narrow words is more +stretchable than a line with few wide words. + +It is obvious that left-aligned text can be handled in the same way as +right-aligned text. [... Centered text? ...] + +The default value for the stretchability is the line height without +the space between the lines (more precisely: the maximum of all word +heights). The exact value not so important when comparing different +possible values for the badness \f$\beta_a^b\f$, when \f${Y_0}_a^b\f$ +is nearly constant for different \f$b\f$ (which is the case for the +actual value), but it is important for the comparison with penalties, +which are constant. To be considered is also that for non-justified +text, hyphenation is differently (less) desirable; this effect can be +achieved by enlarging the stretchability, which will lead to a smaller +badness, and so make hyphenation less likely. The user can configure +the stretchability by changing the preference value +*stretchability_factor* (default: 1.0). + +(Comparison to T<sub>E</sub>X: Knuth and Plass describe a method for +ragged borders, which is effectively the same as described here (Knuth +1999, pp. 93--94). The value for the stretchability of the line +is slightly less, 1&nsbp;em (ibid., see also p.&nsbp;72 for the +definition of the units). However, this article suggests a value for +the hyphenation penalty, which is ten times larger than the value for +justified text; this would suggest a larger value for +*stretchability_factor*.) + Hyphens ======= @@ -336,33 +389,6 @@ Low Priority be used? Currently, this is redundant to dw::Textblock::BadnessAndPenalty. -**Other than justified text:** The calculation of badness is designed -for justified text. For other alignments, it may be modified. The -point is the definition of stretchability and for the line. - -Consider left-aligned text. Most importantly, not the spaces between -the words, but the space on the right border is adjusted. If the -actual line width (sum of words and normal spaces, \f$W_a^b\f$ above) -equals the the ideal width (e. g. given by the browser window -width, \f$l\f$ above), this space is zero, so it is not possible to -shrink it further. For this reason, the shrinkability is now already -set to 0. - -On the other hand, there should be a stretchability for the space on -the right border. However, only the spaces between the words have a -stretchability; later, the differences are summed up and used to fill -the space on the right. This works, but is a bit imprecise, since the -stretchability of the space on the right depends on the number of words -in the line. - -(Likewise, if you modify the code to assign a positive value for the -shrinkability for left-aligned text, the difference is summed up and -used for the right border; since this difference is negative, the -lines will, when spaces are shrunken, get too long!) - -Analogous considerations must be made for right-aligned and centered -text. (For centered texts, there are two adjustable spaces.) - Solved (Must Be Documented) --------------------------- |