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diff --git a/doc/context/sources/general/manuals/fonts/fonts-math.tex b/doc/context/sources/general/manuals/fonts/fonts-math.tex new file mode 100644 index 000000000..766204937 --- /dev/null +++ b/doc/context/sources/general/manuals/fonts/fonts-math.tex @@ -0,0 +1,1093 @@ +% language=uk + +% todo: + +% \starttext +% \setupbodyfont[cambria] +% \setupmathematics[kernpairs=yes] +% $abcd$ % 𝑎𝑏 +% \stoptext +% +% kernpairs = { +% [0x1D44E] = { +% [0x1D44F] = 1000, -- 𝑎𝑏 demo +% } +% }, + +\startcomponent fonts-math + +\environment fonts-environment + +\startchapter[title=Math][color=darkmix-3] + +\startsection[title=Introduction] + +As one can expect, math support in \CONTEXT\ is to some extend modelled after +what plain \TEX\ provides, plus what was later decided to be standard. This +mostly concerns the way fonts behave and what names are used to access glyphs or +special constructs. It means that when you come from another macro package you +can stick to coding math the way you did before, at least the basic coding. In +addition to this, \CONTEXT\ gives control over fonts, structure and rendering and +most of that was either driven by personal need or user demand. To be honest, +many of the options are probably of not much interest to the average user. + +As we focus on fonts we will only touch this aspect of math here. Right from when +we started with developing \LUATEX, cleaning op the math part of \CONTEXT\ was +part of the game. Some primitives were added that would make it possible to avoid +unnecessary complex macros to get certain glyphs rendered, like radicals, accents +and extensibles. This was made easy because we also support \OPENTYPE\ math and +because we knew that eventually the Latin Modern and Gyre fonts would also +support \OPENTYPE. In order to move forward and get rid of traditional eight bit +fonts \CONTEXT\ \MKIV\ can construct a virtual \OPENTYPE\ font from traditional +math fonts. It makes not much sense to discuss that here as by now this method is +only provided for reasons of compatibility and a reference to the past. As a lot +of time went into this it will always stay around if only to remind us of what +we went through to get where we are now. + +\stopsection + +\startsection[title=\UNICODE\ math] + +Due to the limited amount of glyphs in a \TYPEONE\ font a macro package has to +jump through loops in order to get traditional \TEX\ engines behave well. As a +practical consequence these fonts are often a mixture of characters, symbols, +punctuation and snippets that make up larger shapes. The font dimensions in these +files have often special meanings too. + +This has all changed considerably with math being part of \UNICODE. It was however +\MICROSOFT\ where the real action took place: the development of the first font that +combined \UNICODE\ with \OPENTYPE\ technology. The Cambria font can be considered +the benchmark for fonts that surfaced later. The characteristic of a math font are +the following: + +\startitemize[packed] + \startitem All math alphabets are present: latin as well as greek, in regular, + italic, bold, fraktur and script variants as well as some combinations of these. \stopitem + \startitem The symbols that make sense are present (read: the more obscure shapes + can be omited). \stopitem + \startitem For the characters that make sense, there are two variants that render well + at smaller sizes: script and scriptscript. In the font they have the same size but + the application will scale them down. This feature is named \type {ssty}. \stopitem + \startitem Characters that can extend horizontally (for instance accents and arrows) or vertically + (like radicals and fences) have associated larger variants and carries information about + how to grow indefinitely. \stopitem + \startitem There is a whole lot of special math dimensions. Most of the ones + already used in \TEX\ are present. \stopitem + \startitem Some glyphs come in variants in order to please special usage. There + can also be variants for script or fraktur alphabets. \stopitem +\stopitemize + +This means that in practice an \OPENTYPE\ math font is quite large. We easily +have thousands of glyphs. It also means that creating such a font involves some +expertise and this is one of the reasons why \TEX\ usergroups have joined forces +in developing a suite of fonts. There are also other initiatives in the \TEX\ +community, of which Xits is an example. \footnote {This is a useable +variant of Stix fonts with proper math features, some extra glyphs and +experimental right||to||left shapes.} The well known Lucida Bright math font +package has also been upgraded to a set of \OPENTYPE\ math fonts. + +The fact that there are not that many math fonts out there has a positive side as +well: \CONTEXT\ comes with them pre|-|configured. Because during the development +of \LUATEX\ we needed to have at least a couple of fonts for testing, and because +it makes no sense to waste time on traditional fonts, the Latin Modern, Palatino, +Times and a few more fonts were (and still are) provided as virtual \UNICODE\ +fonts. + +In a regular text font, what you key in is what you get out. So, when you've +chosen a font with an italic shape, you get italic shapes, even if the smallcaps +feature is enabled. In math, if you use the right unicodes you also get the shape +you expect. Because in this case italic shapes are situated in one of the +alphabets you explicitly choose a rendering. You can enter the right codepoints +directly, so for instance if you enter \UNICODE\ character \type {U+1D434} you +will get \mathematics {\utfchar {"1D434}}. In practice something like \type {$\bi +A$} should also give that character if only because that is what we have been +doing for over three decades. This means that the engine has to map a regular +\type {A} onto the bold italic alphabet. In a traditional approach you will use +math families for this, but in \CONTEXT\ \MKIV\ we simply use one font and one +family and let the \MKIV\ machinery do the rest. + +In text mode we switch fonts styles in the following way: + +\startbuffer +regular {\it italic} {\bf bold} {\bi bold italic} and so on +\stopbuffer + +\typebuffer + +The three commands shown here are shortcuts for font switches. This input is +converted into an internal representation and after whatever manipulations +are applied end up as: + +\blank \getbuffer \blank + +If we look at what fonts we end up with we get: + +\blank \markfonts{\getbuffer} \blank + +Now lets do the same in math mode: + +\startbuffer +$regular {\it italic} {\bf bold} {\bi bold italic} and so on$ +\stopbuffer + +\typebuffer + +This time we get a different result: + +\blank \getbuffer \blank + +If again we analyze the fonts you see this: + +\blank \markfonts{\getbuffer} \blank + +All glyphs come from the same font. Instead of regular we get italic simply because +math characters are italic by nature. The two character style switches are not +really font switches but just make sure that the given input is mapped onto the +right alphabet. + +A traditional approach using \TYPEONE\ fonts is to use a so called math family for +each alphabet. In that case each alphabet maps one||to||one onto the font: when +we switch to a bold family we just take the glyph that sits in that slot. In \MKIV\ +we have all characters in one family so behind the screens a given character is +remapped. + +Now take a look at the following example: + +\startbuffer +$text^{script^{scriptscript}}$ +\stopbuffer + +\typebuffer + +This renders to this, with the characters marked by font: + +\blank \markfonts{\getbuffer} \blank + +This time we have three different fonts: one for each of the three math sizes. +But this representation is not entirely honest, because indeed we have three font +instances for math, but the glyphs come from the same \OPENTYPE\ math font. We +just load the same font three times, once for each size. In fact we load the +font once, but use three copies, scaled accordingly to the relative scale the +font prescribes. + +There is a whole bunch of commands to choose specific characters in math mode +using a regular input. These are state switching commands. + +\def\SampleLine#1#2#3% + {\NC \type{#1}\space + \ifx#2\empty\else\type{#2}\fi\space + \ifx#3\empty\else\type{#3}\fi + \NC $#1 a$ + \NC $#1 A$ + \NC \NR} + +\starttabulate[|||||] +\HL +\SampleLine \mr \empty \empty +\HL +\SampleLine \mathdefault \empty \empty +\SampleLine \mathscript \empty \empty +\SampleLine \mathfraktur \empty \empty +\SampleLine \mathblackboard\empty \empty +\HL +\SampleLine \rm \mathrm \empty +\SampleLine \ss \mathss \empty +\SampleLine \tt \mathtt \empty +\HL +\SampleLine \tf \mathtf \tfmath +\SampleLine \sl \mathsl \slmath +\SampleLine \it \mathit \itmath +\HL +\SampleLine \bf \mathbf \bfmath +\SampleLine \bs \mathbs \bsmath +\SampleLine \bi \mathbi \bimath +\HL +\stoptabulate + +As you can see here, some commands have synonyms. The short commands adapt +themselves to text and mathmode, the longer ones are meant for use in math mode +only. + +In text mode distinctive shapes are either a font property (the whole font looks +that way) or a stylistic alternate (an extra feature of a font). In math mode we +can have alternates, but in addition to the previously mentioned alphabet +switchers we have a few more: + +\starttabulate[|||||] +\HL +\SampleLine \frak \empty \empty +\SampleLine \cal \empty \empty +\SampleLine \bbd \empty \empty +\SampleLine \blackboard \empty \empty +\SampleLine \fraktur \empty \empty +\SampleLine \gothic \empty \empty +\HL +\stoptabulate + +This chapter is not meant as an introduction to math but it is good to know +that math font support in \CONTEXT\ is rather flexible. There are several +mechanisms for remapping and converting characters and sequences into +others and more is possible. Here is one: + +\startbuffer +\startformula +\reals {\mathbf R} \utfchar{"0211D} \utfchar{"1D411} +\stopformula +\stopbuffer + +\typebuffer \blank \getbuffer \blank + +Compare this to: + +\startbuffer +\setupmathematics[symbolset=blackboard-to-bold] +\startformula +\reals {\mathbf R} \utfchar{"0211D} \utfchar{"1D411} +\stopformula +\stopbuffer + +\typebuffer \blank \start \getbuffer \stop \blank + +Greek is always troublesome because instead of regular text shapes math uses a +few variants. Because in \UNICODE\ characters are only included once, we have +gaps in the math alphabets but \MKIV\ will take care of this. \footnote {This is +a typical example of where exceptions in a standard force all applications that +deal with it have to implement tweaks.} Depending on the field an author has to +choose between upright and italic greek: + +\startbuffer +$\nabla \alpha \mathgreekupright \nabla \alpha \mathgreekitalic \nabla \alpha$ +\stopbuffer + +\typebuffer \blank \start \getbuffer \stop \blank + +By default \CONTEXT\ is set up as follows: + +\starttyping +\setupmathematics + [sygreek=normal, + lcgreek=italic, + ucgreek=normal] +\stoptyping + +Again, these are not features of a font. The font just provides the glyphs and +the \TEX\ engine, controlled by \CONTEXT\ takes care of mapping characters to +glyphs and building special constructs. The same is true for spacing. Although +math fonts do have kerning information, most of the math spacing is controlled +by properties of characters and not by the font. + +\unexpanded\def\SampleLine#1% + {\NC + \type{$a #1{+} b$} + \NC + \ruledhbox{$\mathsurround\zeropoint a#1{+}b$} + \NC \NR} + +\starttabulate[|||] +\SampleLine \mathord +\SampleLine \mathpunct +\SampleLine \mathinner +\SampleLine \mathop +\SampleLine \mathalpha +\SampleLine \mathnothing +\SampleLine \mathbin +\SampleLine \mathrel +\stoptabulate + +As a user you don't have to worry about these issues because characters are tagged +according to their usage. \footnote {There are a few more commands, like \type +{\mathlimop}, \type {\mathnolop} and \type {mathbox} but these are used +differently.} + +With \TEX\ being the oldest and still dominant math renderer it is no surprise +that \MICROSOFT\ modelled its math renderer after \TEX\ and Cambria quite well +suits the concept. In retrospect it is somewhat unfortunate that we're still +stuck with some left overs (or compromises) from the past with respect to spacing +built into the font. However, as long as this is consistent over fonts it's not +that relevant. You can always influence the spacing with the commands mentioned. + +If you look at the low level definitions in for instance plain \TEX\ but also in +\CONTEXT\ \MKII\ that relate to prime symbols it probably takes a while before you +figure out what happens there. For instance, the prime symbol is triggered by a +quote and multiple in a row results in primes that are spaced tightly. In +\UNICODE\ we have slots for single, double and tripple primes. Therefore, in +\MKIV\ we have a mechanism that accepts different kinds of input that eventually +all end up in one of these three glyphs. + +\unexpanded\def\SampleLine#1% + {\NC \type{#1} \NC #1 \NC \NR} + +\starttabulate[|||] +\SampleLine{$f^2$} +\SampleLine{$f\prime^2$} +\SampleLine{$f\prime\prime^2$} +\SampleLine{$f\prime\prime\prime^2$} +\SampleLine{$f{\prime}^2$} +\SampleLine{$f{\prime\prime}^2$} +\SampleLine{$f{\prime\prime\prime}^2$} +\SampleLine{$f'(x)$} +\SampleLine{$f''(x)$} +\SampleLine{$f'''(x)$} +\SampleLine{$f\utfchar{0x2032}(x)$} +\SampleLine{$f\utfchar{0x2033}(x)$} +\SampleLine{$f\utfchar{0x2034}(x)$} +\SampleLine{$f\utfchar{0x2032}\utfchar{0x2032}(x)$} +\SampleLine{$f\utfchar{0x2032}\utfchar{0x2032}\utfchar{0x2032}(x)$} +\SampleLine{$f\utfchar{0x2033}\utfchar{0x2032}(x)$} +\SampleLine{$f\utfchar{0x2032}\utfchar{0x2033}(x)$} +\stoptabulate + +Again, this is not the same as ligature building features in text fonts, but +handled in a different way. + +The \TEX\ engine understands the concept of italic correction. When an italic +shape is followed by for instance an upright shape, you can insert a \type {\/} +and the engine will add a correction as defined in the font. In \OPENTYPE\ we +don't have such corrections available but we can fake it, which is what the \type +{itlc} feature in \CONTEXT\ does. However, you need to enable this feature +explicitly. An example of a setup is: + +\starttyping +\definefontfeature + [default] + [default] + [itlc=yes,textitalics=yes] + +\setupitaliccorrection + [global,always] +\stoptyping + +This will make sure that the right amount of correction is added between +italic shapes and non italics or boxes. Using \type {text} instead of +\type {always} would limit the correction to glyphs only and leaving out +the \type {global} would permit selective (grouped) usage at the cost +of more runtime. There is no need for the \type {\/} here. + +In math we also can have italic correction but there it is built into the engine +and in traditional \TEX\ no directives are needed. Italic correction properties +in math fonts are somewhat troublesome as their application depends on what we're +dealing with: symbols, super- and subscripts, etc. Because early versions of +\LUATEX\ didn't handle all of it well, if only because the fonts were not yet okay, +the \MKIV\ math handler provides a bit of control. + +\def\SampleLine#1#2% + {\NC #1 + \NC \setupmathematics[italics=#1]\ruledhbox{$m$ t} + \NC \setupmathematics[italics=#1]\ruledhbox{$m$ {\it t}} + \NC \setupmathematics[italics=#1]\ruledhbox{t $m$ t $m$ {\it t}} + \NC #2 + \NC \NR} + +\starttabulate[||||||] +\SampleLine0{no correction} +\SampleLine1{only apply italics when the font carries them} +\SampleLine2{apply italics provided by the font or automatically calculated} +\SampleLine3{apply italics based on an emwidth and character properties} +\SampleLine4{use method 1 but fall back on 3 if needed} +\stoptabulate + +Because we cannot rely on fonts too much, we default to method~3 which in practice +works out well, so the setup is: + +\starttyping +\setupmathematics + [italics=3] +\stoptyping + +There are all kind of commands that can be used to build math constructs in such a +way that super- and subscripts are consistently rendered. It goes beyond this +chapter to discuss them and most users will never see or use those commands. The +main message of the examples above is that text and math use different fonts and +properties and therefore also different methods in rendering text or a formula. +Even if the names of mechanisms are the same (like italics) you cannot assume +that both modes do exactly the same. + +\stopsection + +\startsection[title=Bold math] + +If you look at what \UNICODE\ provides you will notice that there are quite some +bold characters. First of all there are a bunch of alphabets and because bold is +not present in the text part of \UNICODE\ these alphabets have no holes. Then +there are some symbols that have special meaning. + +\startluacode +local find = string.find +local NC, NR = context.NC, context.NR + +context.starttabulate { "|Tl||l|" } +for unicode, entry in table.sortedhash(characters.data) do + local description = entry.description + if find(description,"^MATHEMATICAL BOLD") then + NC() context("U+04X",unicode) + NC() context.mathematics(utf.char(unicode)) + NC() context(description) + NC() NR() + end +end +context.stoptabulate() +\stopluacode + +The biggest mistake one can make when discussing bold math is the assumption that +these bold alphabets are meant for section titles and other structural elements +that need some emphasis. This is not true, in that case we would expect the whole +formula to be bold and the bold symbols or variables would be even more bold. +Bold math boils down to {\em all} math being bold. The reason why we show the +list of bold characters on the previous pages is that it gives a good impression of +fact that we're mostly given alphabets in an otherwise regular font. + +As Latin Modern (being derived from Computer Modern) has some bold extras in +\MKII\ to some extend we do support a complete bold math switch but mixing bold +formulas with regular ones has some limitations. Math typesetting consists of two +phases: first the input is translated into a special list where references to +fonts are not yet resolved. Instead families are used and each family has three +sizes: text, script and scriptscript. In a second pass the formula is typeset and +the families get translated into fonts. So, if we change the definition of a +family, say math italic into bold math italic, then the definition that is actual +when the second pass takes place is used. + +Although \LUATEX\ provides for many more families and as a consequence we could +have replaced the \MKII\ mechanism with a more complete one, instead we just +forgot about it and stuck to one family for regular math and another one for bold +math. Okay, this is not entirely true as later on we added some more in order to +deal with bidirectional typesetting. + +Only a few math fonts come with a bold variant. One of the objectives of the \TEX +Gyre math font project is to explore the possibilities of bold math companions, +but such a font will probably have less coverage, simply because no real complex +math will end up in for instance section titles. + +When I wrote this down there were not that many math fonts that come with a real +(complete) bold variant. The \CONTEXT\ math font subsystem tries to fill this gap +as good as possible by using pseudo fonts. When a typeface doesn't define a math +bold variant a pseudo setup is used. When a real bold font is used, it could be +that not all alphabets are supported in which case a suitable alternative is +tried. + +The Xits font, assembed from Stix and enhanced by Khaled Hosny, comes with a bold +variant but the coverage is not complete, at least not when I wrote this +paragraph. This can go unnoticed because \CONTEXT\ tries to work around this. On +the other hand, it definitely has bold properties, which can be seen from the +next example. You switch between regular and bold math with the \type {\mr} and +\type {\mb} commands. + +\startbuffer +\switchtobodyfont[xitsbidi] + +$ \sqrt{x } \quad + \mb \sqrt{mb} \quad + \mathupright \sqrt{u } \quad + \mr \sqrt{mr} \quad + \mathupright \sqrt{u } \quad + \mathdefault \sqrt{d } +$ +\stopbuffer + +\typebuffer \blank \start \getbuffer \stop \blank + +You can track some of what happens with: + +\starttyping +\enabletrackers[math.remapping,math.families] +\stoptyping + +You will get some information about remapping or when it fails if fallback +remapping is used. But no matter what happens with glyphs, you will notice in +this example that the radical symbol is bold indeed. + +\stopsection + +\startsection[title=Bidirectional math] + +There is not that much to tell about bidirectional math typesetting, simply +because the fonts are still in development. However, Khaled Hosny added +some support to the Xits font. Of course you need to load this font first: + +\starttyping +\switchtobodyfont[xitsbidi] +\stoptyping + +In the previous chapter we mentioned bold math and as Xits also comes with +a bold variant which means that this command loads the whole lot (which is +fast enough anyway). + +Easiest is to just show a few examples. When in left to right mode we get what we +are accustomed to: + +\startbuffer +\setupmathematics[align=l2r] + +\startformula +\sqrt{x^2\over 4x} \eqno(1) +\stopformula + +\startformula +5 < 6 > 4 +\stopformula + +\startformula +5 \leq 6 \geq 7 +\stopformula +\stopbuffer + +\typebuffer \start \switchtobodyfont[xitsbidi] \getbuffer \stop + +However, when we go the other way, we automatically get digits converted to +arabic. + +\startbuffer +\setupmathematics[align=r2l,bidi=yes] + +\startformula +\sqrt{ف^2\over 4ب} \eqno(1) +\stopformula + +\startformula +5 < 6 > 4 +\stopformula + +\startformula +5 \leq 6 \geq 7 +\stopformula +\stopbuffer + +\typebuffer \start \switchtobodyfont[xitsbidi] \getbuffer \stop + +You don't have to worry about how the font is set up, but not that much is needed +because \CONTEXT\ does it for you and the Xits typescripts carries the right +definitions. Just to give you an idea, we show a feature definition: The magic is +in the \type {rtlm} feature combined with \type {locl}. + +\starttyping +\definefontfeature + [mathematics-r2l] + [mathematics] + [language=ara, + rtlm=yes, + locl=yes] +\stoptyping + +Some symbols are mirrored too: + +\startbuffer +\setupmathematics[align=r2l,bidi=yes] + +\startformula +\sum^\infty_{س=0} س^2 \eqno(2) +\stopformula +\stopbuffer + +\typebuffer \start \switchtobodyfont[xitsbidi] \getbuffer \stop + +And of course the extensible fences are done properly too: + +\startbuffer +\setupmathematics[align=r2l,bidi=yes] + +\startformula +\left(\root{2} \of{155}\right) +\stopformula + +\startformula +\left[\int^{55}_{123} 666^3\right] +\qquad\textstyle\left[\int^{55}_{123} 666^3\right] +\stopformula + +\startformula +\left\{\sum^{55}_{123} 666^3\right\} +\stopformula +\stopbuffer + +\typebuffer \start \switchtobodyfont[xitsbidi] \getbuffer \stop + +The real torture test is the radical sign. A mirrored shape is used +and it grows upwards as well as leftwards. + +\startbuffer +\setupmathematics[align=r2l,bidi=yes] + +\startformula +\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{55}}}}}}}}}} +\stopformula +\stopbuffer + +\typebuffer \start \switchtobodyfont[xitsbidi] \getbuffer \stop + +\stopsection + +\startsection[title=Styles] + +In text mode you use font switches like \type {\sl} that switches the current font +to a slanted one. In math mode it is an alphabet switch in the same font. In +fact, there isn't much to choose from fonts there, apart from a massive switch +to bold, in which case \type {\bf} is just a bolder alphabet in that bolder font. + +A lot of things in math mode happen automatically. There are for instance always +three instances of (the same) font active, each different in size: text, script +and the smallest, scriptscript and when you ask for instance for a superscript +the next smaller size is used. + +\starttabulate[|l|l|l|] +\NC normal \NC \type {\textstyle} \NC $\textstyle text^{script^{scriptscript}}$ \NC \NR +\NC smaller \NC \type {\scriptstyle} \NC $\scriptstyle text^{script^{scriptscript}}$ \NC \NR +\NC smallest \NC \type {\scriptscriptstyle} \NC $\scriptscriptstyle text^{script^{scriptscript}}$ \NC \NR +\stoptabulate + +In text style, superscripts can go twice smaller, but in script style only one +smaller size is left, and in scriptscript style you're stuck with one size. The +commands in the second column can be used to force a style. + +The math formula builder has an important property: the formula is typeset after +it has been scanned completely. In a traditional setup that has some +consequences. Take this: + +\starttyping +one \sl two \bf three \bi four +\stoptyping + +In a traditional setup four so called families are used and each character gets +tagged with a family number. So we have (for instance): + +\blank \start \tttf +o\low7n\low7e\low7 t\low6w\low6o\low6 t\low5h\low5r\low5e\low5e\low5 f\low9o\low9u\low9r\low9 +\stop \blank + +As the number of families was limited there could be at most 16 families. In +fact, the first four were traditionally reserved for math roman, math italic, +symbol and extensibles. Then, due to the limit of 256 characters per font, +another few were used for additional symbol fonts. So, adding a few more variants +could exhaust the family pool quite fast. You could argue that we could halfway +redefine a family but this will not work as there is a one to one relationship +between family numbers and fonts assigned to them when the formula has been +read in (the last value counts). And grouping won't help you either. + +The actual (plain) situation is even more complex. As we have a limited number of +characters per font, most symbols are accessed by name, and the name relates to a +mathematical character definition using for instance \type {\mathchardef}. Such a +definition refers to a slot in a specific family number and therefore font. It +also puts a character in a so called math class. One of these, the alphanumeric +class, with number~7, is special. Characters that are input directly on the +keyboard (like \type {a}||\type {z} can also be tagged this way using \type +{\mathcode}. + +When we switch a family, this will normally not affect a symbol defined as math +character, simply because we refer to a specific family|/|slot combination, but +when a character has class~7, then it will be taken from the current family. This +permits latin letters, digits and greek letters to be typeset in different +styles. So, in that traditional approach we have fonts that provide a bunch of +symbols as well as some alphabets. Think for instance of a font with additional +symbols where the regular alphabet slots contain blackboard shapes. The symbols +are accessed directly and the characters are accessed via the regular \type +{a}||\type {z} characters as these will adapt to the family and therefore font. +In practice users will not notice this complication as macro packages hide the +implementation details. + +In \MKIV\ the situation is different as there we have one family (or a few more +if we use a full bold switch and|/|or bidirectional math). Although we no longer +have the limit of 16 fonts we actually don't need that many families, at least +not in the way we've set up \MKIV \footnote{A technical note: in principle the +\MKIV\ approach can have a speed penalty compared to a multi||family approach but +we don't care too much about it. Also, as we load less fonts the extra overhead gets +compensated nicely.} + +\blank \start \tttf +o\low1n\low1e\low1 t\low1w\low1o\low1 t\low1h\low1r\low1e\low1e\low1 f\low1o\low1u\low1r\low1 +\stop \blank + +So how does this relate to styles? Each family has three fonts and we can use the +switch commands to choose any of these. In text mode we use the term style for a +font switch, while in math mode it's more than that: indeed we switch a font, but +only in size, but the spacing is also adapted. If a proper math font is used, the +smaller sizes are actually alternates in the font, visually adapted to suit their +use. + +In text mode we do this in order to limit the scope of a switch: + +\starttyping +normal {\bf bold {\it italic} bold} normalbracket +\stoptyping + +This is the same as: + +\starttyping +normal \bgroup \bf bold \bgroup \it italic\egroup + \ bold\egroup \ normalbracket +\stoptyping + +and: + +\starttyping +normal \begingroup \bf bold \begingroup \it italic\endgroup + \ bold\endgroup \ normalbracket +\stoptyping + +The \CONTEXT\ distribution ships with a plain math definition file that also uses +one family but reassigns some math codes when we switch to another style. As the +number of characters that this applies to this is efficient enough for a modern +computer. A peek into \type {luatex-math.tex} gives an impression of what we deal +with. However, keep in mind that the implementation in \MKIV\ goes it differently +and is therefore more powerful. We also have hardly any definitions at the \TEX\ +end and use information from \type {char-def.lua} instead. + +In math mode there is a subtle difference in the way grouping works with styles: + +\starttyping +text {\scriptstyle script} normal +\stoptyping + +This is the same as: + +\starttyping +text \bgroup\scriptstyle script\egroup\ normal +\stoptyping + +but different from: + +\starttyping +text \begingroup\scriptstyle script\endgroup\ script +\stoptyping + +This has to do with the fact that a style switch is explicitly registered in the +math list and grouping like this is not limiting the scope. In math mode the +braced grouping mode actually does create a math group and there the scope of the +switch is limited to that group. In practice users will not run into this but +they can use macros that use \type {\begingroup}. Among other reasons, this is +why we have a special mathstyle mechanism. + +\startbuffer +\ruledhbox{$x\begingroup\scriptstyle x\endgroup x$} \quad +\ruledhbox{$x\begingroup\setupmathstyle[script]x\endgroup x$} \quad +\ruledhbox{$x{\setupmathstyle[script]x}x$} \quad +\ruledhbox{$x\startmathstyle[script]x\stopmathstyle x$} +\stopbuffer + +\typebuffer + +This gives: + +\startlinecorrection[blank] \dontleavehmode \getbuffer \stoplinecorrection + +Mechanisms that support the \type {mathstyle} parameter know how to apply the +proper grouping so you don't have to worry there. You can best avoid using the +verbose grouping command and stick to braces or the \type {start}||\type {stop} +command. An example is the fence mechanism: + +\startbuffer +\definemathfence + [fancybracket] [bracket] + [color=darkblue] +\definemathfence + [smallbracket] [bracket] + [command=yes,color=darkgreen,mathstyle=small] +\definemathfence + [normalbracket] [bracket] + [command=yes,color=darkred] +\stopbuffer + +\typebuffer \getbuffer + +We apply this to an example: + +\startbuffer +$x \fenced[bar]{\frac{1}{x}} x$ \quad +$x \fenced[doublebar]{\frac{1}{x}} x$ \quad +$x \fenced[bracket]{\frac{1}{x}} x$ \quad +$x \fenced[fancybracket]{\frac{1}{x}} x$ \quad +$x \frac{1}{n} \normalbracket{\frac{1}{n}} \smallbracket{\frac{1}{s}} x$ +\stopbuffer + +\typebuffer + +Of course these somewhat weird examples are not real but at least they +demonstrate the principles. + +\startlinecorrection[blank] \dontleavehmode \getbuffer \stoplinecorrection + +A math style is a combination of the following keys. Their effect can depend on +the current state, for instance you can switch cramp or size indepently. + +\starttabulate[|T||] +\NC display \NC display style, like text style but somewhat more spacy \NC \NR +\NC text \NC text style, normally used inline \NC \NR +\NC script \NC smaller than text cq. display style \NC \NR +\NC scriptscript \NC smaller than script style \NC \NR +\NC cramped packed \NC more tightly positioned superscripts \NC \NR +\NC uncramped normal \NC normal positioned superscripts \NC \NR +\NC small \NC switch to the next smaller style but keep cramp state \NC \NR +\NC big \NC switch to the next larger style but keep cramp state \NC \NR +\stoptabulate + +Future versions of \MKIV\ will provide more features (like parameter sets driven +by keywords). As you might prefer a more symbolic approach we provide: + +\starttyping +\definemathstyle[default][text,cramped] +\stoptyping + +After this you can use the keyword \type {default} which has the advantage that +you only need to change one definition in order to get different rendering. + +\stopsection + +\startsection[title=Supported fonts] + +As in \CONTEXT\ MKIV\ I wanted to go ahead with \UNICODE\ math as soon as the +first version of \LUATEX\ showed up. Because at that time only Cambria was +available I decided to provide virtual \UNICODE\ math fonts as a prelude to +proper replacements for the popular \TYPEONE\ math fonts. In the meantime Xits +came around and in 2012 we had quite useable math companions for the public Latin +Modern, Pagella and Termes fonts and the \TEX\ user groups started shipping +\OPENTYPE\ variants of Lucida. The virtual variants will still around so that we +can compare them with the new implementations. As the official specification of +\OPENTYPE\ math is not always clear from the beginning the \OPENTYPE\ fonts get +improved over time. In fact, this is true not only for math fonts. Just think of +this: + +\startitemize + +\startitem As \UNICODE\ gets extended, fonts might get more glyphs and possibly +alternate shapes. \stopitem + +\startitem The more languages are supported, the more glyphs are to be available +and features have to get language dependent instances. \stopitem + +\startitem The larger the font, the bigger the chance that mistakes get unnoticed +especially when contextual subtitutions and positioning are used. \stopitem + +\startitem Math fonts can get more script and scriptscript alternates, more size +variants, more advanced extensibles, bidirectional support, etc. \stopitem + +\stopitemize + +So, like regular programs, \LUATEX\ and macro packages, we now have fonts as +component that needs occasional updating. Of course resources like hyphenation +patterns are also subjected to this, so it's not a new aspect. But still, best +keep en eye on font updates. + +While there are lots of text fonts, there are not that many math fonts, so you +can safely assume that \CONTEXT\ ships with the proper setup for those fonts. Of +course you have to choose a specific instance when you set up your own +combination of fonts, but a peek into the typescripts shows the way. + +In the font manual and on the wiki you can find more about typescript and what is +possible, so here we just take a look at one definition: + +\startnarrowtyping +\starttypescript [serif] [dejavu] [name] + \definefontsynonym [Serif] [name:dejavuserif] [features=default] + \definefontsynonym [SerifBold] [name:dejavuserifbold] [features=default] + \definefontsynonym [SerifItalic] [name:dejavuserifitalic] [features=default] + \definefontsynonym [SerifBoldItalic] [name:dejavuserifbolditalic] [features=default] +\stoptypescript + +\starttypescript [sans] [dejavu] [name] + \definefontsynonym [Sans] [name:dejavusans] [features=default] + \definefontsynonym [SansBold] [name:dejavusansbold] [features=default] + \definefontsynonym [SansItalic] [name:dejavusansoblique] [features=default] + \definefontsynonym [SansBoldItalic] [name:dejavusansboldoblique] [features=default] +\stoptypescript + +\starttypescript [mono] [dejavu] [name] + \definefontsynonym [Mono] [name:dejavusansmono] [features=none] + \definefontsynonym [MonoBold] [name:dejavusansmonobold] [features=none] + \definefontsynonym [MonoItalic] [name:dejavusansmonooblique] [features=none] + \definefontsynonym [MonoBoldItalic] [name:dejavusansmonoboldoblique] [features=none] +\stoptypescript + +\starttypescript[dejavu] + \definetypeface [dejavu] [rm] [serif] [dejavu] [default] + \definetypeface [dejavu] [ss] [sans] [dejavu] [default] + \definetypeface [dejavu] [tt] [mono] [dejavu] [default] + \definetypeface [dejavu] [mm] [math] [xits] [default] [scale=1.2] +\stoptypescript +\stopnarrowtyping + +So, in many cases you can just copy this blob and replace the font names by your +own. + +Loading a font, and Dejavu is a predefined one, is done as follows: + +\starttyping +\setupbodyfont[dejavu] +\stoptyping + +In a similar fashion you can enable \type {cambria}, \type {pagella}, \type +{termes}, \type {lucidaot}, etc.\ and if you don't use this command at all, you +get Latin Modern. These fonts are part of \TEX\ distributions, including +\CONTEXT\ stand||alone that can be downloaded from \CONTEXT\ garden. + +If you want to use Lucida, all you have to do when you have bought the fonts, is +to put the \OPENTYPE\ files in a place where they can be found, for instance: + +\starttyping +tex/texmf-fonts/fonts/data/lucida +\stoptyping + +Of course you need to run \type {mtxrun --generate} afterwards so that the files +can be found. + +\startnotabene + Tracing and characters coverage will be discussed here as soon as the styles + that are used for them are normalized. +\stopnotabene + +\stopsection + +\startsection[title={Stylistic alternates}] + +Some fonts provide stylistic alternates. These can be described in goodies files +and the Lucida setup is a good example. Here we demonstrate the effects. We +disable the default math rendering (which takes the italic variants). + +\startbuffer[sa:1] +\switchtobodyfont[lucidaot,14.4pt] +\setupmathrendering[lucidaot][it=] +$x + ^{i \leftarrow 0 = ∅} + _{i \leftarrow 0 = ∅} +$ +\stopbuffer + +\typebuffer[sa:1] + +The next code enabled three alternatives: + +\startbuffer[sa:2] +\switchtobodyfont[lucidaot,14.4pt] +\setupmathrendering[lucidaot][it=] +$x + ^{i \leftarrow 0 = ∅} + _{\setmathfontalternate{arrow} + \setmathfontalternate{dotless} + \setmathfontalternate{zero} + i \leftarrow 0 = ∅} +$ +\stopbuffer + +\typebuffer[sa:2] + +Here we set them in one go: + +\startbuffer[sa:3] +\switchtobodyfont[lucidaot,14.4pt] +\setupmathrendering[lucidaot][it=] +$x + ^{i \leftarrow 0 = ∅} + _{\setmathfontalternate{arrow,dotless,zero} + i \leftarrow 0 = ∅} +$ +\stopbuffer +\ +\typebuffer[sa:3] + +The last example shows how to enable these features globally: + +\startbuffer[sa:4] +\switchtobodyfont[lucidaot,14.4pt] +\setupmathrendering[lucidaot][it=] +\setupmathematics[stylealternative={arrow,dotless,zero}] +$x + ^{i \leftarrow 0 = ∅} + _{i \leftarrow 0 = ∅} +$ +\stopbuffer + +\typebuffer[sa:4] + +The results are collected here: + +\startlinecorrection[blank] +\startcombination[4*1] + {\vbox{\hsize.2\hsize\midaligned{\nospacing\getbuffer[sa:1]}}} {\bf nothing} + {\vbox{\hsize.2\hsize\midaligned{\nospacing\getbuffer[sa:2]}}} {\bf stepwise} + {\vbox{\hsize.2\hsize\midaligned{\nospacing\getbuffer[sa:3]}}} {\bf combined} + {\vbox{\hsize.2\hsize\midaligned{\nospacing\getbuffer[sa:4]}}} {\bf global} +\stopcombination +\stoplinecorrection + +\stopsection + +\startsection[title=Italics and limits] + +An \OPENTYPE\ font treats italic correction differently from traditional fonts. +Officially the italic correction is used for placement above and below limits +where the scripts shift left and right half of the correction from the center of +the shape. Advanced kerns are then to be used for anchoring the scripts when they +are placed at the right side (so far no fonts seem to do this). Because we cannot +foresee if fonts compensate for correction then we can control placement a bit. +There is a parameter \type {\mathnolimitsmode} that controls the correction. + +\definebodyfontenvironment[20pt] + +\startlinecorrection +\startcombination[5*1] + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[20pt]\mathnolimitsmode0$\displaystyle\int\nolimits^0_1$\hss}} {\tttf 0} + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[20pt]\mathnolimitsmode1$\displaystyle\int\nolimits^0_1$\hss}} {\tttf 1} + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[20pt]\mathnolimitsmode2$\displaystyle\int\nolimits^0_1$\hss}} {\tttf 2} + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[20pt]\mathnolimitsmode3$\displaystyle\int\nolimits^0_1$\hss}} {\tttf 3} + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[20pt]\mathnolimitsmode4$\displaystyle\int\nolimits^0_1$\hss}} {\tttf 4} +\stopcombination +\stoplinecorrection + +A value larger than 15 is interpreted as a factor (in the usual \TEX\ way 1000 +means 1.0). We have some values left for future use when correction is to be +combined with kerns. + +In \CONTEXT\ we set the value to 1 which means that the factors for super- and +subscript are set via math parameters (or constants in the font). We use a +default of \type {{0,800}} so we don't shift the superscript and the subscript we +shift less than the italic correction. This is driven by a feature but you can +change the values before loading a font, for instance with: + +\starttyping +\adaptfontfeature[*math*][mathnolimitsmode={100,700}] +\stoptyping + +The defaults come out as: + +\startlinecorrection +\startcombination[5*1] + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[modern, 20pt]$\displaystyle\int\nolimits^0_1$\hss}} {\tttf modern} + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[xits, 20pt]$\displaystyle\int\nolimits^0_1$\hss}} {\tttf xits} + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[lucidaot,20pt]$\displaystyle\int\nolimits^0_1$\hss}} {\tttf lucidaot} + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[pagella, 20pt]$\displaystyle\int\nolimits^0_1$\hss}} {\tttf pagella} + {\ruledhbox to .15\hsize{\hss\showglyphs\switchtobodyfont[cambria, 20pt]$\displaystyle\int\nolimits^0_1$\hss}} {\tttf cambria} +\stopcombination +\stoplinecorrection + +\stopsection + +\startsection[title=Kerning] + +Math kerns in \OPENTYPE\ are quite advanced and use a staircase model left +and|/|or right of characters. However, hardly any math font implements them +(extensively). Therefore we provide a way to fine tune your fonts to your +preferences. You can test this mechanism by patching \type {cambria-math.lfg} by +adding this to the mathematics subtable: + +\starttyping +kernpairs = { + [0x1D44E] = { + [0x1D44F] = 1000, -- 𝑎𝑏 demo + } +} +\stoptyping + +After that, the next example should work: + +\starttyping +\starttext + \setupbodyfont[cambria] + \setupmathematics[kernpairs=yes] + $abcd$ +\stoptext +\stoptyping + +There should be a gap between the $𝑎$ and $𝑏$. It is not shown here because I +don't want to mess up my goodie file. + +\stopsection + +\stopchapter + +\stopcomponent |