diff --git a/devel/source/maths.en.tm b/devel/source/maths.en.tm index 8d90c56..f4ec7a4 100644 --- a/devel/source/maths.en.tm +++ b/devel/source/maths.en.tm @@ -1,19 +1,19 @@ - + - +> <\body> - + - In this chapter we describe the algorithms used by in order - to typeset mathematical formulas. This is a difficult subject, because - esthetics and effectiveness do not always go hand in hand. Until now, - is widely accepted for having achieved an optimal compromise in - this respect. Nevertheless, we thought that several improvements could - still be made, which have now been implemented in . We will - shortly describe the motivations behind them. + In this chapter we describe the algorithms used by in order to + typeset mathematical formulas. This is a difficult subject, because + esthetics and effectiveness do not always go hand in hand. Until now, + is widely accepted for having achieved an optimal compromise in this + respect. Nevertheless, we thought that several improvements could still be + made, which have now been implemented in . We will shortly + describe the motivations behind them. In order to obtain esthetic formulas, what criteria should we use? It is often stressed that good typesetting allows the reader to concentrate on @@ -22,22 +22,19 @@ typesetted in a non uniform way: <\description> - The eye expects text of a similar - nature to be typesetted with respect to a same base line. For instance, - in , the bottoms of the and - should be at the same height as the bottom of the - -part in the . This should again be - the case in +2+2>. + The eye expects text of a similar nature to + be typesetted with respect to a same base line. For instance, in + , the bottoms of the and should be at the + same height as the bottom of the -part in the . This + should again be the case in +2+2>. - Different components of text with - approximately the same function should be separated by equal amounts of - space. For instance, in +f>, the - typesetter should notice the hangover of the . This - should again be the case in +e+e\ - >. Similarly, the distance between the baselines of the - and the in - > should not be disproportially large with - respect to the height of an . + Different components of text with approximately + the same function should be separated by equal amounts of space. For + instance, in +f>, the typesetter should notice the + hangover of the . This should again be the case in + +e+e>. Similarly, the distance between the + baselines of the and the in > should not + be disproportially large with respect to the height of an . Additional difficulties may arise when considering automatically generated @@ -46,58 +43,57 @@ Unfortunately, the different esthetic criteria may enter into conflict with each other. For instance, consider the formula - +x>. On the one hand, the - baselines of the scripts should be the same, but the other hand, the first - subscript should not be ``disproportionally low'' with respect to the - . Unfortunately, this dilemma can not been solved in a - completely satisfactory way without the help of a human for the simple - reason that the computer has no way to know whether the - > and > are - ``related''. Indeed, if the > and - > are close (like in - +x>), then it is natural to opt - for a common base line. However, if they are further away from each other - (like in +>cx>), then we might want to opt for different base lines - and locally optimize the rendering of the first >. + +x>. On the one hand, the baselines of the + scripts should be the same, but the other hand, the first subscript should + not be ``disproportionally low'' with respect to the . + Unfortunately, this dilemma can not been solved in a completely + satisfactory way without the help of a human for the simple reason that the + computer has no way to know whether the > and + > are ``related''. Indeed, if the > + and > are close (like in + +x>), then it is natural to opt for a common + base line. However, if they are further away from each other (like in + +>cx>), + then we might want to opt for different base lines and locally optimize the + rendering of the first >. - Consequently, should offer a reasonable compromise for the - most frequent cases, while offering methods for the user to make finer - adjustments in the remaining ones. Currently, we just provided the - and - constructs to move and resize boxes in order to perform such adjustments. - For instance, if the brackets around the two sums + Consequently, should offer a reasonable compromise for the most + frequent cases, while offering methods for the user to make finer + adjustments in the remaining ones. We provide the constructs + and to move and + resize boxes in order to perform such adjustments. For instance, if the + brackets around the two sums - <\expand|equation*> - \ax=\by - + <\equation*> + \ax|)>=\>by|)> + have different sizes, then one may resize the bottom of the subscript - of the second sum to . Alternatively, one - may resize the bottoms of both the and - subscripts to (say) . + of the second sum to . Alternatively, one may resize + the bottoms of both the and subscripts to (say) + . For easier adjustments you may use + and to automatically + adjust the size of the contents to the height of the character ``x'' and + the largest one in the font respectively. Notice that one should adjust by preference in a structural and not visual way. For instance, one should prefer to in the above example, because the second option disallows you to switch to another font size for your document. Similarly, you should try not change the semantics of the formula. For instance, in the above example, you might - have added a ``dummy subscript'' to the subscript of the - sum. However, this would alter the meaning of the formula (whence make it - non suitable as input to a computer algebra system) In the future, we plan - to provide additional constructs in order to facilitate structural - adjusting. For instance, in the case of a formula like + have added a ``dummy subscript'' to the subscript of the sum. + However, this would alter the meaning of the formula (whence make it non + suitable as input to a computer algebra system) In the future, we plan to + provide additional constructs in order to facilitate structural adjusting. + For instance, in the case of a formula like - <\expand|equation*> - 1+x+x+\+x+xx+xx+\x+xx+xx+\, - + <\equation*> + 1+x+x+\+x+xx+xx+\x+xx+xx+\, + one might think of a construct to enclose the entire formula into an area, where all scripts are forced to be double (using dummy superscripts - whereever necessary). + wherever necessary). @@ -105,49 +101,46 @@ different components. The following are often needed: <\description> - .>The main font reference space - , which can be taken as the distance between successive - lines of text. + >The main font reference space , + which can be taken as the distance between successive lines of text. - and .>The bottom and top level - for the font (we have ). + and >The bottom and top level for the + font (we have ). - .>The reference minimal space between - distinct components, like the minimal distance between a subscript and a + >The reference minimal space between distinct + components, like the minimal distance between a subscript and a superscript. In fact, . - .>The width of several types of lines, like - the fraction and square root bars, wide accents, etc. + >The width of several types of lines, like the + fraction and square root bars, wide accents, etc. - .>The height of the fraction bar, which is - needed for the positioning of fractions and big delimiters. Usually, + >The height of the fraction bar, which is needed + for the positioning of fractions and big delimiters. Usually, is almost equal to below. The following parameters are mainly needed in order to deal with scripts: <\description> - .>The height of the - character, which is needed for the positioning of scripts. All the - remaining parameters are actually computed as a function of - . + >The height of the character, which is + needed for the positioning of scripts. All the remaining parameters are + actually computed as a function of . - .>Logical base line for subscripts. + >Logical base line for subscripts. - .>Subscripts may never physically - exceed this top height. + >Subscripts may never physically exceed this + top height. - .>Logical base line for + >Logical base line for superscripts. + + >Superscripts may never physically exceed + this bottom height. + + >Suggestion for a physical top line for superscripts. - .>Superscripts may never physically - exceed this bottom height. - - .>Suggestion for a physical top line - for superscripts. - - .>Possible shift of the base lines when we - are inside fractions or scripts. + >Possible shift of the base lines when we are + inside fractions or scripts. The individual strings in a font also have several important positioning @@ -196,7 +189,7 @@ The root itself is typesetted like a large delimiter. The positioning of a potential script works only is very dependent on the - usage of fonts. + usage of fonts. The upper bar has a overhang of at the right and the logical right limit of the root is situated another @@ -224,12 +217,12 @@ The following heuristics are used: <\itemize> - We use fonts for small accents and an algorithm for the wider ones. + We use fonts for small accents and an + algorithm for the wider ones. The distance between the main argument and the accent is at least - (or a distance which depends on the font for - small accents). + (or a distance which depends on the font for small + accents). The accent is positioned horizintally according to the right slope of the main argument. @@ -253,7 +246,7 @@ <\enumerate> Always pretend that the subscript has height at least in the script font (actually we should use the - height of an instead). + height of an instead). Try to position the script at the base line given by the main argument. @@ -271,7 +264,7 @@ Move the superscript up to the logical base line if necessary. This will usually occur: most of the time, the logical base line is the just - the height of an -script below the suggested top line. + the height of an -script below the suggested top line. If the superscript physically descends below the physical under limit given by the main box, then we move the superscript further @@ -303,92 +296,60 @@ again complicated because of potential conflicts between locally and globally optimal esthetics. - First of all, fonts come only with a discrete set of possible - sizes for large delimiters. This is an advantage from the point of view - that it favorites delimiters around slightly different expressions to have - the same baselines. However, it has the disadvantage that delimiters are - easily made ``one size to large''. For this reason, we actually diminish - the height and the depth of the delimited expression by the small amount - , before computing the sizes of the delimiters. + First of all, fonts come only with a discrete set of possible sizes + for large delimiters. This is an advantage from the point of view that it + favorites delimiters around slightly different expressions to have the same + baselines. However, it has the disadvantage that delimiters are easily made + ``one size to large''. For this reason, we actually diminish the height and + the depth of the delimited expression by the small amount , + before computing the sizes of the delimiters. Secondly, it is best when the vertical middles of big delimiters occur at the height of fraction bars. However, in a formula like - <\expand|equation*> - f>>>, - + <\equation*> + f>>>|)>, + it may be worth it to descend the delimiters a bit. On the other hand, slight vertical shifts in the middles of the delimiters potentially have a bad effect on base lines, like in - <\expand|equation*> - fX+g\ - Y. - + <\equation*> + fX|)>+gY|)>. + - In , we use the following compromise: we start with the - middle of the delimited expression as a first approximation to the middle - of the delimiters. The real middle is obtained by shifting this middle - towards the height of fraction bars by an amount which cannot exceed - . + In , we use the following compromise: we start with the middle of + the delimited expression as a first approximation to the middle of the + delimiters. The real middle is obtained by shifting this middle towards the + height of fraction bars by an amount which cannot exceed . From a horizontal point of view, we finally have to notice that we adapted the metrics of the big delimiters in a way that potential scripts are - positioned in a better way. For instance, according to the + positioned in a better way. For instance, according to the file, in a formula like - <\expand|equation*> - A+B<\ - right|)>, - + <\equation*> + B|)>|)>, + the square rather seems to be a left superscript of the second closing bracket than a right superscript of the first one. This is particularly annoying in the case of automatically generated formulas, where this situation occurs quite often. - + - + <\initial> <\collection> - - - - - - - - - - - - - + - - -<\references> - <\collection> - > - |?>> - |?>> - |?>> - |?>> - |?>> - |?>> - |?>> - |?>> - |?>> - |?>> - > - - + \ No newline at end of file diff --git a/main/editing/man-structured-geometry.en.tm b/main/editing/man-structured-geometry.en.tm index ea50b6d..209947a 100644 --- a/main/editing/man-structured-geometry.en.tm +++ b/main/editing/man-structured-geometry.en.tm @@ -55,8 +55,8 @@ tag for the shortcuts to apply. The tags , , - and from the - menu. + , , , , + from the menu. The durations of animations can be modified using and . @@ -78,4 +78,4 @@ <\collection> - \ No newline at end of file + diff --git a/main/math/keyboard/man-large.en.tm b/main/math/keyboard/man-large.en.tm index 4227e76..45c8009 100644 --- a/main/math/keyboard/man-large.en.tm +++ b/main/math/keyboard/man-large.en.tm @@ -54,7 +54,7 @@ Sometimes you may want large delimiters of a particular size, instead of self-adjusting ones. This can be achieved by resizing the expression in - between the brackets using . + between the brackets using the items in . Notice that it is possible to insert a pair of invisible brackets using . This is for instance useful in @@ -77,4 +77,4 @@ <\collection> - \ No newline at end of file +