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| -rw-r--r-- | doc/context/presentations/bachotex/2010/bachotex-2010-clash.tex | 1 | ||||
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diff --git a/doc/context/documents/general/manuals/math-tweaks.pdf b/doc/context/documents/general/manuals/math-tweaks.pdf Binary files differnew file mode 100644 index 000000000..a6e3e57fd --- /dev/null +++ b/doc/context/documents/general/manuals/math-tweaks.pdf diff --git a/doc/context/presentations/bachotex/2010/bachotex-2010-clash.tex b/doc/context/presentations/bachotex/2010/bachotex-2010-clash.tex index bda1934e9..6b30ff083 100644 --- a/doc/context/presentations/bachotex/2010/bachotex-2010-clash.tex +++ b/doc/context/presentations/bachotex/2010/bachotex-2010-clash.tex @@ -1,6 +1,7 @@ % \enablemode[paper] \usemodule[present-stepwise,present-wobbling,abr-02] +% \usemodule[present-wobbling,abr-02] \setuppapersize[S6][S6] \setupbodyfont[10pt] \def\METAPOST{MetaPost} diff --git a/doc/context/sources/general/manuals/math/math-tweaks.tex b/doc/context/sources/general/manuals/math/math-tweaks.tex new file mode 100644 index 000000000..cf3ffaa0e --- /dev/null +++ b/doc/context/sources/general/manuals/math/math-tweaks.tex @@ -0,0 +1,1912 @@ +% language=us runpath=texruns:manuals/math macros=mkvi + +% \enabletrackers[math.tweaks] + +% \mapfontsize[pagella][script] [.30] % a test +% \mapfontsize[pagella][scriptscript][.45] % a test + +\hyphenation{ere-whon} + +\enableexperiments[fonts.compact] % gives different sized outline ! + +% \definefontfeature[stixtwo:mathextra][kern=yes,script=dflt,language=dflt] + +\startluacode +local list = { + { "cambria", "cambria-math" }, + { "modern", "modern-math" }, + { "pagella", "pagella-math" }, + { "termes", "termes-math" }, + { "schola", "schola-math" }, + { "bonum", "bonum-math" }, + { "dejavu", "dejavu-math" }, + { "erewhon", "erewhon-math" }, + { "concrete", "concrete-math" }, + { "kpfonts", "kpfonts-math" }, + { "lucida", "lucida-math" }, + { "stixtwo", "stixtwo-math" }, + { "ebgaramond", "ebgaramond-math" }, + { "libertinus", "libertinus-math" }, + { "xcharter", "xcharter-math" }, +} + +local loaded = { } +local used = table.setmetatableindex("table") + +local function identify(fontname,filename) + local g = fonts.goodies.load(filename) + if g then + local tweaks = g.mathematics.tweaks + if tweaks then + local after = tweaks.aftercopying + if after then + local sequence = { } + local usage = { } + local bigslots = false + for i=1,#after do + local tweak = after[i].tweak + if tweak then + sequence[#sequence+1] = tweak + usage[tweak] = true + used[tweak][fontname] = true + if tweak == "bigslots" then + bigslots = bigslots + end + end + end + local t = { + sequence = sequence, + usage = usage, + goodies = g.mathematics, + bigslots = bigslots, + } + loaded[fontname] = t + end + else + print("no tweaks",filename) + end + else + print("no goodie file",filename) + end +end + +for i=1,#list do + local l = list[i] + identify(l[1],l[2]) + context.usebodyfont { l[1] } + context.usebodyfont { l[1] .. "-nt" } +end + +document.usedfonts = list -- order +document.usedgoodies = loaded +document.usedtweaks = used + +function document.gettweakusage(name) + local list = table.sortedkeys(document.usedtweaks[name]) + if #list > 0 then + context("This tweak is used in: %, t.",list) + else + context("This tweak is used \\emphasized{nowhere}.") + end +end + +function document.showsomething(name) + for i=1,#document.usedfonts do + context[name](document.usedfonts[i][1]) + end +end + +-- inspect(loaded) + +\stopluacode + +\def\ShowTweakUsage#1{\ctxlua{document.gettweakusage("#1")}} +\def\ShowSomething #1{\ctxlua{document.showsomething("#1")}} + +\setupbodyfont[bonum] + +\usemodule[abbreviations-logos] + +\setuplayout + [height=middle, + width=middle, + footer=0pt] + +\setupwhitespace + [big] + +\setuphead + [chapter] + [header=high] + +\starttext + +% A riddle. Maybe use the path and the path randomizer. + +\startMPpage + fill Page enlarged 1mm withcolor darkred ; + + picture p ; p := lmt_outline [ text = "\textdollar" ] ; + picture q ; q := lmt_outline [ text = "\texteuro" ] ; + + p := (p shifted - center p) randomized .7 ; + q := (q shifted - center q) randomized .7 ; + + draw image ( draw p ; draw q ; ) + xysized (PaperWidth -4cm, PaperHeight -10cm) + shifted center Page + shifted (0,4cm) + withcolor yellow + withpen pencircle scaled 5mm ; + + draw textext ("tweaking") + xsized (PaperWidth -4cm) + shifted center bottomboundary Page + shifted (0,5.5cm) + withcolor white ; + + draw textext ("math fonts") + xsized (PaperWidth -4cm) + shifted center bottomboundary Page + shifted (0,2.25cm) + withcolor white ; + + setbounds currentpicture to Page ; +\stopMPpage + +\starttitle[title=Contents] + \startcolumns + \placelist[chapter][before=,after=,alternative=a] + \stopcolumns +\stoptitle + +\startchapter[title=What is there to tweak] + +We have written about our struggle to \OPENTYPE\ render math fonts well before, +but here we will do it from the perspective of \LUAMETATEX\ and \CONTEXT\ \LMTX\ +combined with the fonts available in 2022. So what is the state of these fonts? +The answer to this question is that now the landscape has settled we have a +curious mix of old and new style fonts that has to be dealt with. Our answer to +this is an updated math engine combined with (in \CONTEXT) tweaking font +properties that we can (or will not) deal with in the engine: think of adapting +dimensions, adding missing shapes, variants and extensibles, normalizing anchors +and kerns. Before we discuss these in details let us look at what fonts we +have. + +In 2022 we can distinguish several groups of math fonts. The first contains only +one font: Cambria by \MICROSOFT. This is the reference font that more or less +defines the standard and indicates how an \OPENTYPE\ math font is to be +constructed. It has been stable for a long time and we don't see any development +in it. In the meantime the specification has been improved but there is still +room for interpretation. + +The second group consists if Latin Modern, Pagella, Termes, Bonum, Schola and +Dejavu. These are the outcome of the \TEX Gyre project funded by user groups and +conducted by the GUST foundation (Jerzy, Jacko and friends). In this project some +choices were made that are reflected in todays versions. It is a mix between old +school \TEX\ fonts (that were the starting point) and interpretation of the +\quote {standard} that at that time to some extend had to be deduced from +observing Cambria usage in MSWord. + +The third group started with the release of the \TYPEONE\ \STIX\ fonts that had +been announced several times as the reference \UNICODE\ math coverage font. In +order to check its promises those fonts were quickly converted into a useable +\XITS\ \OPENTYPE\ math font by Khaled Hosny. It took a while before an official +\STIX\ (two) showed up. In principle that font can replace \XITS\ now because +\XITS\ is no longer maintained (but it remain useful as it is a good benchmark +for \STIX). We also inherit some bidirectional elements of \XITS\ that we can +inject into other fonts. + +A fourth group contains Erewhon, Kepler, XCharter, Concrete and Euler. These are +existing fonts repackaged and fine-tuned by Daniel Flippo. At the time of writing +this they are a bit in flux and getting better by the day. + +Then there are the commercial fonts. Most noticeable is Lucida by Biggelow and +Holmes which is font expanded, maintained and distributed by \TUG\ derived from +the original \TYPEONE\ fonts. When we were upgrading the math engine we were +happy to be awarded the opportunity to improve the metrics (and some minor) +details in order to bring down the quite extensive number of runtime tweaks +needed. As a commercial font it stands out because there is an update policy, so +we can trust fixes to be available to users. The complete \OPENTYPE\ Lucida font +family is also dirt cheap compared to fonts with such a broad coverage. Another +commercial math font is Minion Math by Johannes Küstler but we have limited +possibilities to tweak that because one needs the font as well as the text +minions. It doesn't make sense to spend much time on fonts that one can't use in +(sample) documents and one cannot expect us to invest in fonts we can't use +anyway, right? So where Lucida is extensively supported for other commercial +fonts we just apply default tweaks to those fonts which is probably good enough. + +Group six contains the left-overs: Garamond and Libertinus. We also expect a Plex +Math companion. Originally Asana was in this group but eventually we decided that +it is unusable in practice, so we dropped support for that weird and visually +inconsistent mix of fonts. We have to see how Computer Modern Book will fit in +but as we can use Latin Modern with effects instead there is no hurry with that +one. The mentioned Garamond (that is meant to be combined with EBGaramond) is a +bit outlier in the sense that it has excessive amounts of variants and some +shapes that might look okay in text but not so in math, but thereby it makes a +good test case for tweaks. + +There are some other setups that we take into account, like Euler over Pagella and +Pagella over Euler but these just use the tweaks that apply to either of them. + +\stopchapter + +\startchapter[title=Math fonts in \CONTEXT] + +In \MKII\ math fonts are set up in the traditional way and because all available +fonts \TYPEONE\ are modelled after Computer Modern quite some definitions were +needed to populate the math families: the basic foursome: roman, italic, symbol, +extensible, as well as additional families that deal with additional alphabets. + +In \MKIV\ it became simpler: we went \UNICODE. Traditional fonts can be assembled +into a virtual \UNICODE\ font at runtime. Loading now came down to just one font, +or two when bold math is required. Because \XITS\ introduced right-to-left math +we actually can kick in a a few more instances but it doesn't change the +principles. + +In \LMTX\ we integrated bidirectional math in such a way that we now only need +one instance and the new \LUAMETATEX\ engine also provides an alternative to the +triple family model where text, script and scriptscript share the same font +instance which further limits loading time, which in turn means that we can waste +some runtime on tweaking. + +So indeed in \MKIV\ and \LMTX\ we can tweak fonts runtime: we patch them before +passing them to the engine. What was still experimental in \MKIV\ has matured in +\LMTX, also because now considerable time was spent on trying out and configuring +tweaks. This made sense because by now we can consider the math fonts to be sort +of frozen: we have to accept that and have to rely on these patches. That we +divert a bit from the \quote {official} \OPENTYPE\ math approach doesn't bother +us much because after all, \TEX\ is still sort of setting the quality standard. + +We start with showing some usage tables. When defining a typeface one or more +goodie files can be specified. This is what we set up by default: + +\startluacode + +context.starttabulate { "|l|l|" } + context.NC() context("bodyfont") + context.NC() context("goodie file") + context.NC() context.NR() + for i=1,#document.usedfonts do + local name = document.usedfonts[i][1] + local goodie = document.usedfonts[i][2] + context.NC() context(name) + context.NC() context(goodie) + context.NC() context.NR() + end +context.stoptabulate() +\stopluacode + +Tweaks are applied in a specific order and sometimes a tweak is applied several +times with different character lists and|/|or directives: + +\startluacode +context.starttabulate { "|l|lp|" } + context.NC() context("bodyfont") + context.NC() context("tweak order") + context.NC() context.NR() + for i=1,#document.usedfonts do + local name = document.usedfonts[i][1] + local goodie = document.usedfonts[i][2] + local sequence = document.usedgoodies[name].sequence + context.NC() context(name) + context.NC() context("% t",sequence) + context.NC() context.NR() + end +context.stoptabulate() +\stopluacode + +Keep in mind that some of these steps are driven by optional features or specific +versions of the font, so there are likely less applied than seen here. We can +condense this list to usage only: + +\startluacode +context.starttabulate { "|l|lp|" } + context.NC() context("bodyfont") + context.NC() context("tweak usage") + context.NC() context.NR() + for i=1,#document.usedfonts do + local name = document.usedfonts[i][1] + local goodie = document.usedfonts[i][2] + local usage = table.sortedkeys(document.usedgoodies[name].usage) + context.NC() context(name) + context.NC() context("% t",usage) + context.NC() context.NR() + end +context.stoptabulate() +\stopluacode + +Finally we show what tweaks are actually applied. We have some more but these are +either experimental, diagnostic or in the meantime sort of obsolete. + +\startluacode +context.starttabulate { "|l|lp|" } + context.NC() context("tweak") + context.NC() context("usage") + context.NC() context.NR() + for tweak, detail in table.sortedhash(document.usedtweaks) do + context.NC() context(tweak) + context.NC() context("% t",table.sortedkeys(detail)) + context.NC() context.NR() + end +context.stoptabulate() +-- inspect(table.sortedkeys(mathematics.tweaks)) +\stopluacode + +In the next chapters we will discuss the possible tweaks where roughly group them. Tweaks +that are no longer used will be left out (even if they are still in \LMTX). One reason +for orphaning tweaks is that we (finally) decided to get rid of all italics. + +(This is work in progress: we don't want to waste time on tweaks that became unused.) + +\stopchapter + +\startchapter[title=Math constants] + +A math goodie file looks like this" + +\starttyping +return { + name = "pagella-math", + version = "1.00", + comment = "Goodies that complement pagella.", + author = "Hans Hagen & Mikael Sundqvist", + copyright = "ConTeXt development team", + mathematics = { + parameters = { + AccentTopShiftUp = 10, + FlattenedAccentTopShiftUp = 10, + AccentBaseDepth = 80, + DelimiterPercent = 90, + DelimiterShortfall = 400, + DisplayOperatorMinHeight = 1800, -- 1500 in font + PrimeRaisePercent = 75, -- 50 default + PrimeRaiseComposedPercent = 10, -- 25 default + }, + tweaks = { + -- Here we have a list of tweaks. Just have a look at the file! + }, + } +} +\stoptyping + +In following chapters we discuss the entries in the tweaks subtable, here we spend some +words on the parameters. In \OPENTYPE\ speak these are called constants, which is also the +term we use when passing a font from \LUA\ to the engine. + +\definedescription[MathFP][alternative=serried,width=fit,headstyle=\bf\tt,align={flushleft}] + +These are the mandate font parameters with their description straight from the specification: + +\startMathFP {ScriptPercentScaleDown} Percentage of scaling down for level 1 superscripts and subscripts. Suggested value: 80 pct. \stopMathFP +\startMathFP {ScriptScriptPercentScaleDown} Percentage of scaling down for level 2 (scriptscript) superscripts and subscripts. Suggested value: 60 pct. \stopMathFP +\startMathFP {DelimitedSubFormulaMinHeight} Minimum height required for a delimited expression (contained within parentheses, etc.) to be treated as a sub-formula. Suggested value: normal line height times 1.5. \stopMathFP +\startMathFP {DisplayOperatorMinHeight} Minimum height of n-ary operators (such as integral and summation) for formulas in display mode (that is, appearing as standalone page elements, not embedded inline within text). \stopMathFP +\startMathFP {MathLeading} White space to be left between math formulas to ensure proper line spacing. For example, for applications that treat line gap as a part of line ascender, formulas with ink going above (\typ {os2.sTypoAscender} + \typ {os2.sTypoLineGap} - \typ {MathLeading}) or with ink going below \typ {os2.sTypoDescender} will result in increasing line height. \stopMathFP +\startMathFP {AxisHeight} Axis height of the font. In math typesetting, the term axis refers to a horizontal reference line used for positioning elements in a formula. The math axis is similar to but distinct from the baseline for regular text layout. For example, in a simple equation, a minus symbol or fraction rule would be on the axis, but a string for a variable name would be set on a baseline that is offset from the axis. The axisHeight value determines the amount of that offset. \stopMathFP +\startMathFP {AccentBaseHeight} Maximum (ink) height of accent base that does not require raising the accents. Suggested: x‑height of the font (\typ {os2.sxHeight}) plus any possible overshots. \stopMathFP +\startMathFP {FlattenedAccentBaseHeight} Maximum (ink) height of accent base that does not require flattening the accents. Suggested: cap height of the font (\typ {os2.sCapHeight}). \stopMathFP +\startMathFP {SubscriptShiftDown} The standard shift down applied to subscript elements. Positive for moving in the downward direction. Suggested: \typ {os2.ySubscriptYOffset}. \stopMathFP +\startMathFP {SubscriptTopMax} Maximum allowed height of the (ink) top of subscripts that does not require moving subscripts further down. Suggested: 4/5 \typ {xheigh}t. \stopMathFP +\startMathFP {SubscriptBaselineDropMin} Minimum allowed drop of the baseline of subscripts relative to the (ink) bottom of the base. Checked for bases that are treated as a box or extended shape. Positive for subscript baseline dropped below the base bottom. \stopMathFP +\startMathFP {SuperscriptShiftUp} Standard shift up applied to superscript elements. Suggested: \typ {os2.ySuperscriptYOffset}. \stopMathFP +\startMathFP {SuperscriptShiftUpCramped} Standard shift of superscripts relative to the base, in cramped style. \stopMathFP +\startMathFP {SuperscriptBottomMin} Minimum allowed height of the (ink) bottom of superscripts that does not require moving subscripts further up. Suggested: 1/4 times \typ {xheight}. \stopMathFP +\startMathFP {SuperscriptBaselineDropMax} Maximum allowed drop of the baseline of superscripts relative to the (ink) top of the base. Checked for bases that are treated as a box or extended shape. Positive for superscript baseline below the base top. \stopMathFP +\startMathFP {SubSuperscriptGapMin} Minimum gap between the superscript and subscript ink. Suggested: 4 times default rule thickness. \stopMathFP +\startMathFP {SuperscriptBottomMaxWithSubscript} The maximum level to which the (ink) bottom of superscript can be pushed to increase the gap between superscript and subscript, before subscript starts being moved down. Suggested: 4/5 times \typ {xheigh}t. \stopMathFP +\startMathFP {SpaceAfterScript} Extra white space to be added after each subscript and superscript. Suggested: 0.5 pt for a 12 pt font. (Note that, in some math layout implementations, a constant value, such as 0.5 pt, may be used for all text sizes. Some implementations may use a constant ratio of text size, such as 1/24 of \typ {emwidth}.) \stopMathFP +\startMathFP {UpperLimitGapMin} Minimum gap between the (ink) bottom of the upper limit, and the (ink) top of the base operator. \stopMathFP +\startMathFP {UpperLimitBaselineRiseMin} Minimum distance between baseline of upper limit and (ink) top of the base operator. \stopMathFP +\startMathFP {LowerLimitGapMin} Minimum gap between (ink) top of the lower limit, and (ink) bottom of the base operator. \stopMathFP +\startMathFP {LowerLimitBaselineDropMin} Minimum distance between baseline of the lower limit and (ink) bottom of the base operator. \stopMathFP +\startMathFP {StackTopShiftUp} Standard shift up applied to the top element of a stack. \stopMathFP +\startMathFP {StackTopDisplayStyleShiftUp} Standard shift up applied to the top element of a stack in display style. \stopMathFP +\startMathFP {StackBottomShiftDown} Standard shift down applied to the bottom element of a stack. Positive for moving in the downward direction. \stopMathFP +\startMathFP {StackBottomDisplayStyleShiftDown} Standard shift down applied to the bottom element of a stack in display style. Positive for moving in the downward direction. \stopMathFP +\startMathFP {StackGapMin} Minimum gap between (ink) bottom of the top element of a stack, and the (ink) top of the bottom element. Suggested: 3 times default rule thickness. \stopMathFP +\startMathFP {StackDisplayStyleGapMin} Minimum gap between (ink) bottom of the top element of a stack, and the (ink) top of the bottom element in display style. Suggested: 7 times default rule thickness. \stopMathFP +\startMathFP {StretchStackTopShiftUp} Standard shift up applied to the top element of the stretch stack. \stopMathFP +\startMathFP {StretchStackBottomShiftDown} Standard shift down applied to the bottom element of the stretch stack. Positive for moving in the downward direction. \stopMathFP +\startMathFP {StretchStackGapAboveMin} Minimum gap between the ink of the stretched element, and the (ink) bottom of the element above. Suggested: same value as \typ {UpperLimitGapMin}. \stopMathFP +\startMathFP {StretchStackGapBelowMin} Minimum gap between the ink of the stretched element, and the (ink) top of the element below. Suggested: same value as \typ {LowerLimitGapMin}. \stopMathFP +\startMathFP {FractionNumeratorShiftUp} Standard shift up applied to the numerator. \stopMathFP +\startMathFP {FractionNumeratorDisplayStyleShiftUp} Standard shift up applied to the numerator in display style. Suggested: same value as \typ {StackTopDisplayStyleShiftUp}. \stopMathFP +\startMathFP {FractionDenominatorShiftDown} Standard shift down applied to the denominator. Positive for moving in the downward direction. \stopMathFP +\startMathFP {FractionDenominatorDisplayStyleShiftDown} Standard shift down applied to the denominator in display style. Positive for moving in the downward direction. Suggested: same value as \typ {StackBottomDisplayStyleShiftDown}. \stopMathFP +\startMathFP {FractionNumeratorGapMin} Minimum tolerated gap between the (ink) bottom of the numerator and the ink of the fraction bar. Suggested: default rule thickness. \stopMathFP +\startMathFP {FractionNumDisplayStyleGapMin} Minimum tolerated gap between the (ink) bottom of the numerator and the ink of the fraction bar in display style. Suggested: 3 times default rule thickness. \stopMathFP +\startMathFP {FractionRuleThickness} Thickness of the fraction bar. Suggested: default rule thickness. \stopMathFP +\startMathFP {FractionDenominatorGapMin} Minimum tolerated gap between the (ink) top of the denominator and the ink of the fraction bar. Suggested: default rule thickness. \stopMathFP +\startMathFP {FractionDenomDisplayStyleGapMin} Minimum tolerated gap between the (ink) top of the denominator and the ink of the fraction bar in display style. Suggested: 3 times default rule thickness. \stopMathFP +\startMathFP {SkewedFractionHorizontalGap} Horizontal distance between the top and bottom elements of a skewed fraction. \stopMathFP +\startMathFP {SkewedFractionVerticalGap} Vertical distance between the ink of the top and bottom elements of a skewed fraction. \stopMathFP +\startMathFP {OverbarVerticalGap} Distance between the overbar and the (ink) top of he base. Suggested: 3 times default rule thickness. \stopMathFP +\startMathFP {OverbarRuleThickness} Thickness of overbar. Suggested: default rule thickness. \stopMathFP +\startMathFP {OverbarExtraAscender} Extra white space reserved above the overbar. Suggested: default rule thickness. \stopMathFP +\startMathFP {UnderbarVerticalGap} Distance between underbar and (ink) bottom of the base. Suggested: 3 times default rule thickness. \stopMathFP +\startMathFP {UnderbarRuleThickness} Thickness of underbar. Suggested: default rule thickness. \stopMathFP +\startMathFP {UnderbarExtraDescender} Extra white space reserved below the underbar. Always positive. Suggested: default rule thickness. \stopMathFP +\startMathFP {RadicalVerticalGap} Space between the (ink) top of the expression and the bar over it. Suggested: 5/4 times default rule thickness. \stopMathFP +\startMathFP {RadicalDisplayStyleVerticalGap} Space between the (ink) top of the expression and the bar over it. Suggested: default rule thickness + 1/2 timss \typ {xheight}. \stopMathFP +\startMathFP {RadicalRuleThickness} Thickness of the radical rule. This is the thickness of the rule in designed or constructed radical signs. Suggested: default rule thickness. \stopMathFP +\startMathFP {RadicalExtraAscender} Extra white space reserved above the radical. Suggested: same value as \typ {RadicalRuleThickness}. \stopMathFP +\startMathFP {RadicalKernBeforeDegree} Extra horizontal kern before the degree of a radical, if such is present. Suggested: 5/18 of \typ {emwidth}. \stopMathFP +\startMathFP {RadicalKernAfterDegree} Negative kern after the degree of a radical, if such is present. Suggested: −10/18 of \typ {emwidth}. \stopMathFP +\startMathFP {RadicalDegreeBottomRaisePercent} Height of the bottom of the radical degree, if such is present, in proportion to the ascender of the radical sign. Suggested: 60 pct. \stopMathFP + +All these parameters can be set in the goodie file and will then overload the +ones that are set already in the font. During \LUATEX\ and \LUAMETATEX\ development some +additional parameters have been added: + +\startMathFP {MinConnectorOverlap} to be described \stopMathFP +\startMathFP {SubscriptShiftDownWithSuperscript} to be described \stopMathFP +\startMathFP {FractionDelimiterSize} to be described \stopMathFP +\startMathFP {FractionDelimiterDisplayStyleSize} to be described \stopMathFP +\startMathFP {NoLimitSubFactor} to be described \stopMathFP +\startMathFP {NoLimitSupFactor} to be described \stopMathFP +\startMathFP {AccentBaseDepth} to be described \stopMathFP +\startMathFP {FlattenedAccentBaseDepth} to be described \stopMathFP +\startMathFP {SpaceBeforeScript} to be described \stopMathFP +\startMathFP {PrimeRaisePercent} to be described \stopMathFP +\startMathFP {PrimeShiftUp} to be described \stopMathFP +\startMathFP {PrimeShiftUpCramped} to be described \stopMathFP +\startMathFP {PrimeSpaceAfter} to be described \stopMathFP +\startMathFP {PrimeBaselineDropMax} to be described \stopMathFP +\startMathFP {PrimeWidthPercent} to be described \stopMathFP +\startMathFP {SkewedDelimiterTolerance} to be described \stopMathFP +\startMathFP {AccentTopShiftUp} to be described \stopMathFP +\startMathFP {AccentBottomShiftDown} to be described \stopMathFP +\startMathFP {AccentTopOvershoot} to be described \stopMathFP +\startMathFP {AccentBottomOvershoot} to be described \stopMathFP +\startMathFP {AccentSuperscriptDrop} to be described \stopMathFP +\startMathFP {AccentSuperscriptPercent} to be described \stopMathFP +\startMathFP {FlattenedAccentTopShiftUp} to be described \stopMathFP +\startMathFP {FlattenedAccentBottomShiftDown} to be described \stopMathFP +\startMathFP {DelimiterPercent} to be described \stopMathFP +\startMathFP {DelimiterShortfall} to be described \stopMathFP + +Whenever we thought that we should have some control we added a variable to play +with. There are more variables that control the engine and some are set in +\CONTEXT. Often a parameter can be set per style. We don't set them all. + +\stopchapter + +\startchapter[title=Font sizes] + +For quite a while \CONTEXT\ \MKIV\ and \LMTX\ have been set up to use the script +and scriptscript scales from the \OPENTYPE\ fonts. However, the method used +didn't always work as expected with the configured sizes in bodyfont environments +that were based on initial usage of Computer Modern. That in itself is no big +problem but as we defined the smaller sizes of for instance five point to be that +value too, a conflict of namespace surfaced. It's a side effect of race +condition: we want fast loading for which we need a namespace (at every size) but +when the size in the \OPENTYPE\ file is non standard (read: the 10pt, 7pt, 5pt +ratio) we get the wrong scales from the hash. We need to know the scale before we +initialize the font. But as we don't want to consult the font data each time we +check a scale we have now moved the ratios to the typescripts. This also makes it +possible to overload them easier. + +The following table shows the values as configured and you will notice that there +are differences. By moving them into the typescript we can also assure that +updates to the font have no side effects. As with most math parameters in the +font, these are not then well defined|/|explored anyway. + +\def\MappedScriptSize {\cldcontext{fonts.hashes.mathparameters[\the\fontid\scriptscriptfont0].ScriptPercentScaleDown}} +\def\MappedScriptScriptSize{\cldcontext{fonts.hashes.mathparameters[\the\fontid\scriptscriptfont0].ScriptScriptPercentScaleDown}} + +\starttexdefinition ShowMappedFontSize #1 + \NC #1 + \NC \mappedfontsize{#1}{script} + \NC \mappedfontsize{#1}{scriptscript} + \NC \bgroup\switchtobodyfont[#1]\normalexpanded{\egroup\MappedScriptSize} + \NC \bgroup\switchtobodyfont[#1]\normalexpanded{\egroup\MappedScriptScriptSize} + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|c|c|] + \FL + \NC + \NS[1][c] user or typescript + \NS[1][c] font parameter + \NC \NR + \NC bodyfont + \NC script + \NC scriptscript + \NC script + \NC scriptscript + \NC \NR + \ML + \ShowSomething{ShowMappedFontSize} + \LL +\stoptabulate + +A user can do the following: + +\starttyping +\mapfontsize[pagella][script] [.75] +\mapfontsize[pagella][scriptscript][.65] +\stoptyping + +before defining a typeface. In that case the definition in the typescript is +ignored. + +Below we show the script and scriptscript shapes as available in the font. We +just show overlayed shaped, so this is not a formula with proper spacing. + +\definecolor[tred] [r=1,t=.5,a=1] +\definecolor[tgreen][g=1,t=.5,a=1] +\definecolor[tblue] [b=1,t=.5,a=1] + +\starttexdefinition ShowSizes #1 + \startoverlay + {\tred \definedfont[MathRoman*math]#1} + {\tgreen\definedfont[MathRoman*math-script]#1} + {\tblue \definedfont[MathRoman*math-scriptscript]#1} + \stopoverlay +\stoptexdefinition + +\starttexdefinition ShowMathSizes #1 + \NC #1 \NC \scale [s=4] {\inframed[frame=off] + {\switchtobodyfont[#1]\showglyphs% + \dontleavehmode \strut + \ShowSizes{2}\ShowSizes{+} + \ShowSizes{𝐴}\ShowSizes{=} + \ShowSizes{𝑔}\ShowSizes{−} + \ShowSizes{𝜋}\ShowSizes{)}}} + \NR \NR +\stoptexdefinition + +\starttabulate[|l|l|] + \ShowSomething{ShowMathSizes} +\stoptabulate + +\stopchapter + +\startchapter[title=Data structure] + +A traditional \TEX\ engine only needs metrics, that is: the shape is not +relevant. The only measure that somewhat reflect the shape is the italic +correction but it actually is not so much a correction and more the anchor of the +subscript. This is also true for an engine that can deal with \OPENTYPE\ math. +However, there the shape is reflected in the staircase kern tables that define +the kerning at the corners. + +In \LUAMETATEX\ each character has the following numeric properties (there cna be +more at the \LUA\ end: width, height, depth, italic, expansion, leftprotrusion +and rightprotrusion. An \OPENTYPE\ font only provides the width and boundingbox +so the later defines the height and depth. We have an status field that tells +what we're dealing with and some special treatments is needed and a pointer +(index) to a follow up glyph (the next in size in math.) There are an optional +kerning table and ligature table (pointers to allocated arrays) as well as an +optional pointer to a math specific table. At the \LUA\ end we have more fields +and some play a role in tweaks. For instance, we can redefine dimensions and +shift the shape around. These are \CONTEXT\ specific. + +The optional math (sub)table of a character has many fields. Here we only mention +them because some will be referred to in later chapters: smaller, mirror, {\em +flat accent}, top anchor, bottom anchor, {\em four optional corner math kerns +arrays (with their size)}, {\em optional horizontal and vertical extensible +recipes}, four simple corner kerns, four edge margins, a top and bottom accent +overshoot, {\em italics for vertical and horizontal extensibles}, and an inner +location, x offset and y offset for e.g. degree anchoring. The cursive fields +come from \OPENTYPE\ MATH. + +This means that a math character has more data in the engine and therefore uses +more memory. However, there are only a few math fonts loaded and not all +characters need the math information. One reason for splitting the data in +\LUAMETATEX\ is that we could save a lot of memory when huge e.g. \CJK\ fonts are +used: there we want to occupy as little memory as possible. + +When reading the next chapters keep in mind that quite a bit fo the +implementation of tweaks is \CONTEXT\ specific. The engine should be able to do a +proper job without tweaks in which case one just has to live with the limitations +of and artifacts in fonts. + +When making a manual like this a complication is that one has to load many math +fonts and also find a way to show both the tweaked and non-tweaked version. We +only demonstrate the core set of tweaked files so here is an example: + +\starttexdefinition TweakTest #1 + \NC #1 + \NC \switchtobodyfont[#1] $\showglyphs\showfontitalics f^2_2 + x + 1$ + \NC \switchtobodyfont[#1-nt] $\showglyphs\showfontitalics f^2_2 + x + 1$ + \NC \switchtobodyfont[#1] $\showglyphs\showfontitalics\showmakeup[mathglue] f^2_2 + x + 1$ + \NC \switchtobodyfont[#1-nt] $\showglyphs\showfontitalics\showmakeup[mathglue] f^2_2 + x + 1$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|c|c|] + \NC \NC tweaked \NC original \NC tweaked \NC original \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB() + end + context.TweakTest(document.usedfonts[i][1]) + end + } +\stoptabulate + +You will notice that in the tweaked version we have no kerns that compensate for the +width. We will come to that later because these examples are more meant as calibrating +the loading. + +\stopchapter + +\startchapter[title=Tweak: dimensions] \ShowTweakUsage{dimensions} + +Usage of this tweak can best be observed (and experimented) in the goodie files +because there are many parameters. Most are fractions, for instance of the width. +It is important to realize than when you mess with the \type {width} and \type +{xoffset}, you need to set the \type {advance} to (most likely) the old width +when it hasn't yet be set. This tells the backend what the natural glyph +progression is. + +\stopchapter + +\startchapter[title=Tweak: topanchors] \ShowTweakUsage{topanchors} + +\startbuffer +\im{\hat{f}+\widehat{f}} +\stopbuffer + +\starttabulate[|l|c|c|] + \NC \NC tweaked \NC original \NC \NR + \NC ebgaramond + \NC \switchtobodyfont[ebgaramond] \getbuffer + \NC \switchtobodyfont[ebgaramond-nt] \getbuffer \NR +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: moveitalics] \ShowTweakUsage{moveitalics} + +By now we have written plenty about italic correction in math fonts. To summarize +it: in traditional \TEX\ fonts the width of characters is such that the subscript +sits nicely against the shape, and the italic correction determines where the +superscript ends up or when that is absent where the next item starts. It is also +used for positioning the limits on n-ary operators. In \OPENTYPE\ fonts kerning +happens with staircase kerns and italic correction is supposedly only used after +a run of italic shapes. There positioning the limits is also driven by that +correction. + +The dual purpose is confusing. In traditional fonts the italic correction is +actually a kern and that is why we decided to just add it to the width and use +the same value for a negative bottom kern. An exception is the integral where as +mentioned the correction determines the limits. + +With the fonts being some mix for old and new we also have to deal with the left +end of the shapes, especially in relation to the positioning of top accents which +can be somewhat erratic. + +All this head lead us to a tweak that does several things at once: get rid of +weird left side bearings (so that for instance a math italic \type {f} doesn't +stick out in a way that makes it unusable), correct the advance width with the +italic correction, turn top accent values into top and bottom anchors, add top +and bottom right and left kerns based on all this. Finally we wipe the old italic +and top accent values and end up with a clean glyph that we can deal with properly +in several circumstances. + +In the goodie files you can find these lines: + +\starttyping +presets.moveitalics { correct = true }, +presets.moveitalics { correct = true, letters = true }, +\stoptyping + +In the file \type {common-math.lfg} you can find how these are defined. The first +one does the alphabets and the second one all the letters. That second one is +sort of redundant but one can now comment the line in order to check for +left-overs. Because we do this for all fonts, we have defined these operations as +presets. so it makes sense to study this file. These lines are in fact function +calls that return a regular tweak table entry. + +\stopchapter + +\startchapter[title=Tweak: movelimits] \ShowTweakUsage{movelimits} + +This tweak turns the italic correction of integrals into anchors and right kerns, +something that the engine can deal with in a more advanced way than just some +fuzzy italic correction because kerns permeable through the renderer. Again we +have a preset: + +\starttyping +presets.moveintegrals { factor = 1.5 } +\stoptyping + +This is defined as: + +\starttyping +moveintegrals = function(parameters) + return { + tweak = "movelimits", + factor = parameters.factor or 1, + list = mathematics.tweaks.subsets.integrals, + } +end +\stoptyping + +Watch how we pas a factor that does an extra shift on the top and bottom anchors. +For the list we use a predefined list of integrals (and there are plenty in +\UNICODE). + +\stopchapter + +\startchapter[title=Tweak: wipeanchors] \ShowTweakUsage{wipeanchors} + +This tweak wipes the top anchors (top accents) for the given (ranges) of +characters. There are fonts out there with weird ones and when wiped the centered +positioning that kicks in when no anchor is defined works better. In practice +only a few very sloped characters benefit from anchors. Interesting is that the +math italic f is sensitive for bad dimensions and anchors and as that character +is used a lot the impression can be that a whole font is bad if that one is. + +\stopchapter + +\startchapter[title=Tweak: wipeitalics] \ShowTweakUsage{wipeitalics} + +This tweak wipes the \quote {italic correction} fields that are left over after +applying \type {moveitalics} and \type {movelimits}. For instance some symbols +can have italic corrections that make no sense but might have resulted from some +automatic font generation workflow. + +\stopchapter + +\startchapter[title=Tweak: checkspacing] \ShowTweakUsage{checkspacing} + +This is a rather harmless but still useful tweak. There are plenty of spacing characters +in \UNICODE\ and although in math mode spacing is handled automatically users might be +tempted to inject their own. Normally that happens with commands but using these direct +characters can be an option. + +\starttexdefinition CheckSpacingA #1 + \start + \switchtobodyfont[#1] + \normalexpanded{\stop\ttx\withoutpt\emwidth}% +\stoptexdefinition + +\starttexdefinition CheckSpacingB #1#2 + \vrule height 1.5\exheight depth 0.5\exheight width 1pt + \start + \switchtobodyfont[#1]% + \char#2\relax + \stop + \vrule height 1.5\exheight depth 0.5\exheight width 1pt +\stoptexdefinition + +\startluacode + local list = mathematics.tweaks.datasets.checkspacing + context.starttabulate { "|l|l|" .. string.rep("c|",#list) } + context.NC() context.NC() + for i=1,#list do + context.NC() context.rotate( { rotation = "90" }, string.formatters["\\ttx %U"](list[i][1]) ) + end + context.NC() context.NR() + context.NC() context.NC() + for i=1,#list do + context.NC() context("\\ttx %s",list[i][2]) -- space quad char + end + context.NC() context.NR() + for i=1,#document.usedfonts do + local font = document.usedfonts[i][1] + context.NC() + context(font) + context.NC() + context.CheckSpacingA(font) + for i=1,#list do + context.NC() + context.CheckSpacingB(font,list[i][1]) + end + context.NC() + context.NR() + end + context.stoptabulate() +\stopluacode + +In this table the \type {s} indicates that the value is a spacer, like a \quote +{non breakable space}, the \type {q} that the value is derived from a quad, like +\quote {four per em space}, and the \type {c} means that we have a character +driven quantity, like a \quote {punctuation space}. + +\stopchapter + +\startchapter[title=Tweak: setovershoots] \ShowTweakUsage{setovershoots} + +This tweak add some tolerance to characters which will make accents on top of +them look a bit better. + +\starttyping +{ + tweak = "setovershoots", + list = { + { + target = "uppercasescript", + topovershoot = 0.05, + }, + { + target = "uppercaseboldscript", + topovershoot = 0.05, + }, + }, +} +\stoptyping + +\stopchapter + +\startchapter[title=Tweak: simplifykerns] \ShowTweakUsage{simplifykerns} + +The native kerning mechanism in \OPENTYPE\ math fonts uses staircase kerns for +positioning scripts at each corner. When we looked into fonts in more detail we +noticed that when the first step was normally okay, the second of third was such +that the shape was actually touched. This made us add this tweak, where the +extremes of staircase kerns (first top and last bottom) are used instead. This is +possible because in \LUAMETATEX\ we have additional kerning features. + +One can argue that this degrades the quality but one has to keep in mind that +\TEX\ will move script up and down anyway, so one seldom ends up in the more +dangerous zones. So it's best to just catch it and throw out the few that we +could benefit from. + +\stopchapter + +\startchapter[title=Tweak: kernpairs] \ShowTweakUsage{kernpairs} + +We use this tweak to optimize kerning between successive characters. Here are +some examples for bonum: + +\startlines +{\showglyphs\switchtobodyfont [bonum]$aj$\quad $fj$\quad $ij$} +{\showglyphs\switchtobodyfont[bonum-nt]$aj$\quad $fj$\quad $ij$} +\stoplines + +It might take while before we have set them up; fortunately we can use +categories to set up a lot at the same time. + +Some fonts have kerns, for instance \STIX\ but not for math. Borrowing the +default latin ones is no real option because it looks too inconsistent for use in +math. This is why for now we keep it explicit. + +% \startlines +% {\showglyphs\switchtobodyfont [stixtwo]$aj$\quad $fj$\quad $ij$\quad \char65 \char67} +% {\showglyphs\switchtobodyfont[stixtwo-nt]$aj$\quad $fj$\quad $ij$\quad \char65 \char67} +% \stoplines + +\stopchapter + +\startchapter[title=Tweak: kerns] \ShowTweakUsage{kerns} + +This tweak can be used to set the (simple) corner kerns. + +\starttyping +{ + tweak = "kerns", + list = { + [0x002F] = { topleft = -0.2, bottomright = -0.2 }, + } +} +\stoptyping + +The numbers are a fraction of the width and valid fields are \typ {topleft}, \typ +{topright}, \typ {bottomleft} and \typ {bottomright}. These kerns are used in pre +and postscripts. + +\starttexdefinition KernsTest #1 + \NC #1 + \NC \switchtobodyfont[#1] $\showglyphs x^2/2$ + \NC \switchtobodyfont[#1-nt] $\showglyphs x^2/2$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|] + \NC \NC tweaked \NC original \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB { "medium" } + end + context.KernsTest(document.usedfonts[i][1]) + end + } +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: margins] \ShowTweakUsage{margins} + +This tweak is similar to the kerns tweak but adds margins instead. it is a trick to +enforce larger and|/|or smaller accents (like for instance \type {\widetilde}. + +\starttyping +{ + tweak = "margins", + list = { + [0x1D7DC] = { left = -.1, right = -.1 }, -- doublestruck 4 + } +} +\stoptyping + +The relevant fields are \type {left} and \type {right}, they specify the margins +as fraction of the width, and \type {top} and \type {bottom}, those specify +margins as fraction of the combined height and depth. + +Keep in mind that these are not \OPENTYPE\ math properties but specific (and +native) to \LUAMETATEX. + +\stopchapter + +\startchapter[title=Tweak: staircase] \ShowTweakUsage{staircase} + +{\em This tweak is kind of obsolete and might go away some day.} + +\stopchapter + +\startchapter[title=Tweak: fixintegrals] \ShowTweakUsage{fixintegrals} + +In the Computer Modern font there are only a few sizes for the integral sign +\type {U+222B} and they are very sloped. Nowadays fonts also have an extensible +in which case the shape is upright. In \UNICODE\ there are quite some characters +that can be used to construct extensibles (like braces) and there are also +snippets for constructing integrals: \type {0x2320}, \type {0x23AE} and \type +{0x2321}. The fact that these are there and that fonts then provide them also +makes it easy to provide extensibles: you just stack them: + +\starttexdefinition TestIntegralSnippets #1 + \NC #1 + \NC \showglyphs \switchtobodyfont[#1-nt]% + $ \displaystyle \integral { \quad \vcenter\bgroup + \darkred + \offinterlineskip + \hpack{$\char"2320$} + \hpack{$\char"23AE$} + \hpack{$\char"2321$} + \egroup } $ + \NC \showglyphs \switchtobodyfont[#1-nt]$\char"2320$ + \NC \showglyphs \switchtobodyfont[#1-nt]$\char"23AE$ + \NC \showglyphs \switchtobodyfont[#1-nt]$\char"2321$ + \NC \NR +\stoptexdefinition + +\starttabulate[|||c|c|c|] + \ShowSomething{TestIntegralSnippets} +\stoptabulate + +This tweak can use these snippets to provide an extensible in case it is not part +of the integral glyph definition. In these examples we show the untweaked +integral that is choosen when we provide the one made from three snippets. The +red one is the constructed variant. Keep in mind that an extensible works best +when there is some overlap possible. + +\stopchapter + +\startchapter[title=Tweak: accentdimensions] \ShowTweakUsage{accentdimensions} + +Positioning of accents is driven by \typ {AccentBaseHeight} and \typ +{AccentBaseDepth} combined with the height of what goes under an accent as we ll +as the height of the accent. Unfortunately the height of the accents is not +always consistent across the repertoire and within a variant list starting with +the initial character. + +\starttexdefinition TestAccentDimension #1#2#3 + \NC \ifnum#3=1 #1\fi + \NC \tttf U+\ifnum#2<"FFF 0\fi\tohexadecimal#2 + \NC \switchtobodyfont [#1]\showglyphs$\char#2$ + \NC \switchtobodyfont [#1]\showglyphs$\dorecurse{3}{\char\mathvariantcode #2 ##1\quad}\unskip$ + \NC \switchtobodyfont[#1-nt]\showglyphs$\char#2$ + \NC \switchtobodyfont[#1-nt]\showglyphs$\dorecurse{3}{\char\mathvariantcode #2 ##1\quad}\unskip$ + \NC \NR +\stoptexdefinition + +\startluacode + function document.TestAccentDimension(list) + context.starttabulate { "|l|c|c|c|c|c|" } + context.FL() + context.NC() context("bodyfont") + context.NC() context("unicode") + context.NC() context("tweaked") + context.NC() + context.NC() context("original") + context.NC() + context.NC() context.NR() + for i=1,#document.usedfonts do + context.ML() + local n = 0 + for k, v in table.sortedhash(mathematics.tweaks.datasets.accentdimensions[list]) do + n = n + 1 + context.TestAccentDimension(document.usedfonts[i][1],k,n) + end + end + context.LL() + context.stoptabulate() + end +\stopluacode + +The over and under accents are not always present so other tweaks fill in these gaps. + +\ctxlua{document.TestAccentDimension("over")} +\ctxlua{document.TestAccentDimension("under")} + +We can specify what accents get processed but here we show the default set. In most cases o +treatment is needed. + +\ctxlua{document.TestAccentDimension("accent")} + +The specification can be simple, just the tweak name, but you can also specify +a detailed list: + +\starttyping +{ + tweak = "accentdimensions", + list = { "over", "under" }, -- "accent" +} +\stoptyping + +or even: + +\starttyping +{ + tweak = "accentdimensions", + list = { + [0x203E] = { factor = "over" }, -- overbar + [0x203E] = { factor = "under" }, -- underbar + [0x23DE] = { factor = "over" }, -- overbrace + [0x23DF] = { factor = "under" }, -- underbrace + [0x23DC] = { factor = "over" }, -- overparent + [0x23DD] = { factor = "under" }, -- underparent + [0x23B4] = { factor = "over" }, -- overbracket + [0x23B5] = { factor = "under" }, -- underbracket + } +} +\stoptyping + +Instead of a named factor you can pass a number to be applied to the height or +depth. As with all tweaks, they are normally not applied at the user level so if +you have to you'd better check the source code to see what really happens in this +tweak (this is true for more tweaks). + +\stopchapter + +\startchapter[title=Tweak: copyaccents] \ShowTweakUsage{copyaccents} + +This tweak deals with a mixup of combining accents and wide accents where +recipes can be on the \quote {wrong} code point. + +\startluacode +context.starttabulate { "|T|T|c|c|" } +context.FL() +context.NC() context("base") +context.NC() context("accent") +context.NC() context("scale") +context.NC() context.NR() +context.ML() +for k, v in table.sortedhash(mathematics.tweaks.datasets.copyaccents) do + context.NC() context("%U",k) + context.NC() context("%U",v[1]) + context.NC() context(v[2] and "yes" or "no") + context.NC() context("$\\char %i$",v[1]) + context.NC() context.NR() +end +context.LL() +context.stoptabulate() +\stopluacode + +\stopchapter + +\startchapter[title=Tweak: fixaccents] \ShowTweakUsage{fixaccents} + +When the width of an accent is zero but it has an top (accent) anchor defined we +can fix the its width, which is what this somewhat obscure tweak does. It belongs +to the repertoire of weird tweaks that we came up with when trying to make +suboptimal fonts work well. + +\stopchapter + +\startchapter[title=Tweak: extendaccents] \ShowTweakUsage{extendaccents} + +When a wide accent is used the engine will try to find a best match from a +sequence of variants. When there are no more variants it will use an extensible +(recipe) when present. When that is not the case, one can decide to stretch the +last variant to fit, but that only works for a few accents: the scale column in +the table in the chapter about copying accents shows them. This tweak takes a few +optional parameters: \type{all} that is either \type {true} or a number +indicating after which variant stretching starts, and \type {force} that forces +stretch on all variants. + +\stopchapter + +% \startchapter[title=Tweak: fixanchors] \ShowTweakUsage{fixanchors} +% obsolete +% \stopchapter + +\startchapter[title=Tweak: flattenaccents] \ShowTweakUsage{flattenaccents} + +An \OPENTYPE\ math font can have a flat variant of an accent that can kick in when we +run out of space. This feature will flatten regular accents. The same list is used as +for copying accents. There are optional parameters to control the flattening: + +\starttabulate[||||] +\FL +\NC parameter \NC type \NC default \NC \NR +\ML +\NC force \NC boolean \NC false \NC \NR +\NC height \NC factor \NC 0.8 \NC \NR +\NC offset \NC factor \NC 0.9 or calculated \NC \NR +\NC squeeze \NC factor \NC 0.1 or calculated \NC \NR +\LL +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: bigslots] \ShowTweakUsage{bigslots} + +This tweak can be applied as tweak or at a higher level in the mathematics goodie +table. When defined as tweak it is under font version control. + +\starttexdefinition CheckBigSlotA #1#2 + \start + \switchtobodyfont[#1]% + \im{\char\mathvariantcode "7B #2}% + \stop + \hss +\stoptexdefinition + +\starttexdefinition CheckBigSlotB #1#2 + \start + \switchtobodyfont[#1]% + \setbox\scratchbox\hbox{\im{\char\mathvariantcode "7B #2}}% + \normalexpanded{\stop{\ttxx + \cldcontext{"\letterpercent.3f",\number\htdp\scratchbox/\number\exheight}% + }}\quad +\stoptexdefinition + +\starttexdefinition CheckBigSlotC #1 + \start + \switchtobodyfont[#1]% + \normalexpanded{\stop{\ttxx\withoutpt\exheight}}% +\stoptexdefinition + +\startluacode +context.starttabulate { "|l|l|l|l|l|" } + context.NC() context("font") + -- context.NC() context("tweak") + -- context.NC() context("global") + context.NC() context("sequence") + context.NC() context("ex-height") + context.NC() context("rendering") + context.NC() context("ratio to ex") + context.NC() context.NR() + for i=1,#document.usedfonts do + local font = document.usedfonts[i][1] + local goodies = document.usedgoodies[font] + local llist = goodies.bigslots + local glist = goodies.goodies.bigslots + local list = glist or llist + context.NC() context(font) + -- context.NC() context("% t",llist) + -- context.NC() context("% t",glist) + context.NC() if list then context("\\ttxx % t",list) else context("unset") end + context.NC() + if list then + context.CheckBigSlotC(font) + end + context.NC() + if list then + -- context.switchtobodyfont { font } + -- for i=1,#list do + -- context(function() + -- context.im(utf.char(mathematics.variantcode(0x7B,list[i]))) context.quad() + -- context.im(utf.char(mathematics.variantcode(0x5D,list[i]))) context.quad() + -- end) + -- end + context.hss() + for i=1,#list do + context.CheckBigSlotA(font,list[i]) + end + end + context.NC() + if list then + for i=1,#list do + context.CheckBigSlotB(font,list[i]) + end + end + context.NC() context.NR() + end +context.stoptabulate() +\stopluacode + +\stopchapter + +\startchapter[title=Tweak: wipevariants] \ShowTweakUsage{wipevariants} + +When a font has too many variants one can wipe them with this tweak. The entries +in the list specify the last variant. When a \type {*} will wipe all variants. + +\starttyping % [style=\ttx] +{ + tweak = "radicaldegreeanchors", + list = { + [0x221A] = 5, -- becomes last variant + } +} +\stoptyping + +\stopchapter + +\startchapter[title=Tweak: radicaldegreeanchors] \ShowTweakUsage{radicaldegreeanchors} + +The position of the radical degree is determined by some font parameters (todo) +but these are shared among the different sizes as well as the extensible. We +therefore provide a tweak that sets real anchors. These are not officially in +\UNICODE\ math but an engine feature. Here is the experimental setup we made for +Lucida. It demonstrates that we can set the base character, variants and the +extensible. The factors that default to one, are applied to the width and height +plus depth in order to get the coordinates. + +\starttyping[style=\ttx] +{ + tweak = "radicaldegreeanchors", + list = { + -- the base radical: + -- [0x221A] = { hfactor = .05, vfactor = .675 }, + -- all variants: + -- ["0x221A.variants.*"] = { hfactor = .05, vfactor = .6 }, + -- specific variants: + -- ["0x221A.variants.1"] = { hfactor = .05, vfactor = .65 }, + -- ["0x221A.variants.2"] = { hfactor = .1, vfactor = .65 }, + ["0x221A.variants.3"] = { hfactor = 0, vfactor = .55 }, + ["0x221A.variants.4"] = { hfactor = 0, vfactor = .50 }, + -- ["0x221A.variants.5"] = { hfactor = .05, vfactor = .525 }, + -- ["0x221A.variants.5"] = { hfactor = .1, vfactor = .55 }, + -- ["0x221A.variants.6"] = { hfactor = .1, vfactor = .55 }, + -- extensibles where the setting of bottom wins over top: + -- ["0x221A.parts.top"] = { hfactor = .1, vfactor = 5.5 }, + ["0x221A.parts.bottom"] = { hfactor = 0, vfactor = .85 }, + } +} +\stoptyping + +The \type {location} is not set here and defaults to \type {left}; it is +redundant because currently we only have left sided radical degrees (but we do +have right sided radicals). + +\stopchapter + +\startchapter[title=Tweak: fixradicals] \ShowTweakUsage{fixradicals} + +Because there is are limited number of heights and depths available in original +\TFM\ files and variants by their nature differ in height and depth some glyphs +like radicals have interesting dimensions. At the time of writing this only Latin +Modern has this property. + +{\em ff image needed here} + +\starttexdefinition TestFixRadical #1 + \dontleavehmode + \NC {\srule height3ex depth 2ex \relax}#1 + \NC \showglyphs \switchtobodyfont[#1-nt]$\mathaxisbelow \char"221A + x$ + \NC \showglyphs \switchtobodyfont [#1]$\mathaxisbelow \char"221A + x$ + \NC \showglyphs \switchtobodyfont [#1]$\mathaxisbelow \char\mathvariantcode "221A 1 + x$ + \NC \showglyphs \switchtobodyfont [#1]$\mathaxisbelow \sqrt{x}$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|c|c|] + \NC bodyfont \NC untweaked \NC tweaked \NC first variant \NC example \NC \NR + \ShowSomething{TestFixRadical} +\stoptabulate + +% after this: \dorecurse{15}{ Nacht Na de Dam 2021 | Wende - Bloed in mijn Bloed } + +\stopchapter + +\startchapter[title=Tweak: fallbacks] \ShowTweakUsage{fallbacks} + +This tweak is not really a tweak but hooks into the fallbacks that a user +defined. However, when fallbacks are set, they need to be injected at the right +spot in the sequence of tweaks which is why it is defined in the goodie file. + +\stopchapter + +\startchapter[title=Tweak: replacealphabets] \ShowTweakUsage{replacealphabets} + +This tweak is an important one. It is used to add or swap script and calligraphic +alphabets, inject right to left variants and configure replacements based on +features. The following fields can be set: + +\starttabulate[||||] +\NC filename \NC string \NC source file \NC \NR +\NC feature \NC string \NC feature \NC \NR +\NC source \NC string \NC alphabet name \NC \NR +\NC \NC table \NC first source range \NC \NR +\NC target \NC string \NC alphabet name \NC \NR +\NC \NC table \NC first source range \NC \NR +\NC rscale \NC number \NC relative scale \NC \NR +\stoptabulate + +When an effect (like boldening) is used it is also applied to the injected +alphabets. When not given, the target range is the same as the source. An example +of a more extensive specification is: + +\starttyping +{ + tweak = "replacealphabets", + feature = "euleroverpagella", + filename = "euler.otf", + list = { + { source = { first = 0x02100, last = 0x02BFF } }, + { source = { first = 0x1D400, last = 0x1D7FF } }, + { source = { first = 0x1D538, last = 0x1D550 } }, + }, +} +\stoptyping + +The feature at the outer level is a selector that can be set as follows: + +\starttyping +\definefontfeature[lucida:mathextra][euleroverpagella=yes] +\stoptyping + +This feature is not to be confused by the file related one that we access in for +instance for instance Lucida: + +\starttyping +{ + tweak = "replacealphabets", + list = { + { + source = "uppercasescript", + target = "uppercasecalligraphic", + feature = "ss04", + }, + { + source = "lowercasescript", + target = "lowercasecalligraphic", + feature = "ss04", + }, + { + source = "uppercaseboldscript", + target = "uppercaseboldcalligraphic", + feature = "ss04", + }, + -- No lowercase bold calligraphic/script in font + }, +}, +\stoptyping + +The calligraphic alphabets are not official \UNICODE\ but internal \CONTEXT\ ones +that are used to switch between script and calligraphic styles. + +\stopchapter + +\startchapter[title=Tweak: replace] \ShowTweakUsage{replace} + +You can replace a character in a font by another one: + +\starttyping +{ + tweak = "replace", + list = { + [0x123] = 0x125 + }, +}, +\stoptyping + +\stopchapter + +\startchapter[title=Tweak: substitute] \ShowTweakUsage{substitute} + +You can substitute a character in a font by one from a substitution feature: + +\starttyping +{ + tweak = "substitute", + list = { + [0x123] = "ss01" + }, +}, +\stoptyping + +\stopchapter + +\startchapter[title=Tweak: fixprimes] \ShowTweakUsage{fixprimes} + +\starttexdefinition PrimeTest #1 + \NC #1 + \NC \showglyphs \switchtobodyfont[#1] $f'(x)+e^{g'(x)} - a''+ b''' + c''''$ + \NC \showglyphs \switchtobodyfont[#1-nt] $f'(x)+e^{g'(x)} - a''+ b''' + c''''$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|c|c|] + \NC \NC tweaked \NC original \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB() + end + context.PrimeTest(document.usedfonts[i][1]) + end + } +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: fixslashes] \ShowTweakUsage{fixslashes} + +This tweak makes sure that the regular slash \type {U+002F} behaves compatible +with the math one \type {U+2044}. Not all fonts provide the correct variants +chain. + +% There is currently no need to show datasets.fixslashes as there is +% just one entry. + +\stopchapter + +\startchapter[title=Tweak: fixellipses] \ShowTweakUsage{fixellipses} + +\startbuffer +\im{1 + 2+ \cdots + n} \im{1, 2, \ldots, n} +\stopbuffer + +\starttabulate[|l|c|c|] + \NC \NC tweaked \NC original \NC \NR + \NC concrete + \NC \switchtobodyfont[concrete] \getbuffer + \NC \switchtobodyfont[concrete-nt] \getbuffer \NR +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: wipecues] \ShowTweakUsage{wipecues} + +Cues are hidden directives that should not take space so we set their dimensions +to zero: + +\startluacode + local t = mathematics.tweaks.datasets.wipecues + local c = characters.data + context.starttabulate { "|c|c|l|" } + for i=1,#t do + local u = t[i] + context.NC() context("%U",u) + context.NC() context("$\\char %i$",u) + context.NC() context(c[u].description) + context.NC() context.NR() + end + context.stoptabulate() +\stopluacode + +{\em Maybe some day we add tracers in which case they are visible but stil take +no space.} + +\stopchapter + +\startchapter[title=Tweak: addactuarian] \ShowTweakUsage{addactuarian} + +This adds the annuity symbol \type {U+020E7} but as extensible because in itself +this symbol, if present in the font at all, is rather unusable. It uses the same +mechanism as radicals (roots) but from the other edge. + +% {\em todo: realistic example by Mikael} +% From wiki: https://en.wikipedia.org/wiki/Actuarial_notation + +{\red MPS: In the \typ{\rannuity{m}} example, I would like it to be without the top bar, but I cannot find that. Also, maybe the bar over $n$ should also be tighter.} + + +\starttexdefinition ActuarianTest #1 + \NC #1 + \NC \switchtobodyfont[#1] + $\bar{A}^1_{x:\rannuity{n}}^^{2}__{\rannuity{m}}$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|] + \NC \NC tweaked \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB() + end + context.ActuarianTest(document.usedfonts[i][1]) + end + } +\stoptabulate + + + +\stopchapter + +\startchapter[title=Tweak: addarrows] \ShowTweakUsage{addarrows} + +Not all fonts have extensible arrows. Traditionally in \TEX\ these were made +from arrow heads and rules. This tweak makes proper extensibles. + +\startluacode + local t = mathematics.tweaks.datasets.addarrows + local c = characters.data + context.starttabulate { "|c|c|c|l|" } + for i=1,#t do + local u = t[i] + context.NC() context("%U",u) + context.NC() context("$\\char %i$",u) + context.NC() context("$\\Umathaccent 0 0 %i{\\hskip3em}$",u) + context.NC() context(c[u].description) + context.NC() context.NR() + end + context.stoptabulate() +\stopluacode + +\stopchapter + +\startchapter[title=Tweak: addbars] \ShowTweakUsage{addbars} + +There is only one parameter to this tweak: \type {advance} which is a fraction +of the width. + +\starttexdefinition BarTest #1 + \NC #1 + \NC \showglyphs \switchtobodyfont[#1] $\char"007C\quad\char"2016\quad\char"2980$ + \NC \showglyphs \switchtobodyfont[#1-nt] $\char"007C\quad\char"2016\quad\char"2980$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|] + \NC \NC tweaked \NC original \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB() + end + context.BarTest(document.usedfonts[i][1]) + end + } +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: addequals] \ShowTweakUsage{addequals} + +There is only one parameter to this tweak: \type {advance} which is a fraction +of the width. + +\starttexdefinition EqualTest #1 + \NC #1 + \NC \showglyphs \switchtobodyfont[#1] $\char"003D\quad\char"2A75\quad\char"2A76$ + \NC \showglyphs \switchtobodyfont[#1-nt] $\char"003D\quad\char"2A75\quad\char"2A76$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|] + \NC \NC tweaked \NC original \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB() + end + context.EqualTest(document.usedfonts[i][1]) + end + } +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: addfourier] \ShowTweakUsage{addfourier} + +This adds the fourier rendering which uses the radical subsystem but with a right +hand symbol. + +% {\em todo: realistic example by Mikael} +% From Folland - Real analysis: + +\starttexdefinition FourierTest #1 + \NC #1 + \NC \switchtobodyfont[#1] + $\partial^\alpha \hat{f} = \fourier{[(-2\pi i x )^{\alpha} f]}$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|] + \NC \NC tweaked \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB() + end + context.FourierTest(document.usedfonts[i][1]) + end + } +\stoptabulate + + + + +\stopchapter + +\startchapter[title=Tweak: addmirrors] \ShowTweakUsage{addmirrors} + +This adds symbols for right|-|to|-|left math by simply mirroring existing ones. +Deep down the engine doesn't really care about in what direction typesetting +happens (wrt spacing and building structures) , and it is the backend that does +the real work. However, symbols need to be flipped. + +\stopchapter + +\startchapter[title=Tweak: addparts] \ShowTweakUsage{addparts} + +Here is an example of a (probably rarely used) low level extensible definition: + +\starttyping +{ + tweak = "addparts", + list = { + [0x21F4] = { + horizontal = true, + template = 0x2192, + sequence = { + { glyph = "first", factor = 2 }, + { glyph = 0x2218 }, + { glyph = "first", factor = 2 }, + { glyph = "last" }, + } + } + } +}, +\stoptyping + +In this example \type {first} is equivalent to the first part of the template, and +\type {last} to the last one. Like: + +\blank \start \switchtobodyfont[stixtwo] \im { + \char"21F4 \quad + \Umathtopaccent 0 0 "21F4 {\mathtexttf{\strut one two three}} +} \stop \blank + +\stopchapter + +\startchapter[title=Tweak: addprivates] \ShowTweakUsage{addprivates} + +This tweak adds some characters to the repertoire. Currently we have only a few: + +\starttexdefinition PrivatesTest #1 + \NC #1 + \NC \switchtobodyfont[#1] $\um 2$ + \NC \switchtobodyfont[#1] $\up 2$ + \NC \switchtobodyfont[#1] $\ump 2$ + \NC \switchtobodyfont[#1] $\upm 2$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|c|c|] + \NC \NC \type {\um} \NC \type {\up} \NC \type {\ump} \NC \type {\upm} \NC \NR + \ctxlua { + for i=1,#document.usedfonts do +% if i > 1 then +% context.TB { "small" } +% end + context.PrivatesTest(document.usedfonts[i][1]) + end + } +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: addrules] \ShowTweakUsage{addrules} + +This adds a few (missing) rule based shapes to a font: + +\starttexdefinition RulesTest #1 + \NC #1 + \NC \switchtobodyfont[#1] $\Umathaccent top 0 0 "23B4 {\hskip2cm}$ + \NC \switchtobodyfont[#1] $\Umathaccent top 0 0 "203E {\hskip2cm}$ + \NC \switchtobodyfont[#1] $\Umathaccent bottom 0 0 "23B5 {\hskip2cm}$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|c|] + \NC \NC \type {0x23B4} \NC \type {0x203E} \NC \type {0x23B5} \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB { "small" } + end + context.RulesTest(document.usedfonts[i][1]) + end + } +\stoptabulate + +\stopchapter + +\startchapter[title=Tweak: addscripts] \ShowTweakUsage{addscripts} + +This tweak adds high plus and minus shapes (we use them for indicating calculator +input): + +\starttexdefinition ScriptsTest #1 + \NC #1 + \NC \switchtobodyfont[#1] $\char"207A x$ + \NC \switchtobodyfont[#1] $\char"207B x$ + \NC \switchtobodyfont[#1] $\char"208A x$ + \NC \switchtobodyfont[#1] $\char"208B x$ + \NC \NR +\stoptexdefinition + +\starttabulate[|l|c|c|c|c|] + \NC \NC \type {0x207A} \NC \type {0x2037B} \NC \type {0x208A} \NC \type {0x208B} \NC \NR + \ctxlua { + for i=1,#document.usedfonts do + if i > 1 then + context.TB { "small" } + end + context.ScriptsTest(document.usedfonts[i][1]) + end + } +\stoptabulate + +\stopchapter + +\startchapter[title=What we ran into] + +\startsubject[title=Introduction] + +In this chapter we will show some of the characters that triggered adding a tweak +feature. It can be that in the meantime something changed (got fixed) but +nevertheless we think that by collecting some example here can help developers of +math fonts to play safe so that the engine can do a good job even without tweaks. + +\stopsubject + +\startsubject[title=Latin Modern: radical base] + +In traditional \TEX\ fonts, for practical reasons (like implementation limits) +the base radical character sits quite a bit below the baseline. The engine will +automatically compensate for this when it is defined as radical but it makes +usage as stand alone character hard. It also doesn't play well with corner kerns +and degree anchoring. + +\startlinecorrection +\startcombination + {\externalfigure[lm-radical-base.png] [width=.25\textwidth]} {base} + {\externalfigure[lm-radical-variant1.png][width=.25\textwidth]} {variant 1} +\stopcombination +\stoplinecorrection + +\stopsubject + +\startsubject[title=Latin Modern: weird anchors] + +The \TEX Gyre fonts have top accent anchors defined but they are (at least when +we write this) often positioned on the highest point of the shape, which is +probably a side effect of some automated heuristic. However, for some shapes that +works out bad. This is why we can wipe these anchors, just use the middle of the +width and provide our own when it makes sense. + +\startlinecorrection + \externalfigure[lm-7-anchor.png][width=.25\textwidth] +\stoplinecorrection + +\stopsubject + +\startsubject[title=StixTwo] + +When trying to improve font metrics (aka tweaking) we sometimes take a look at +the shapes in FontForge. So for instance when we noticed that the integral mid +segment in StixTwo was too narrow we took that look. Then we also noticed that +the glyph was positioned at the edge instead of in the middle but that the +hinting was such that it ended up in the middle. Intrigued by this we looked into +it in more detail and noticed that the \OPENTYPE\ and \TRUETYPE\ files show up +quite different. So we fetching the source files from the git repository, and +played with the build script. + +The starting point is a \TRUETYPE\ file that seems to provide all kind of tables, +that are then adapted using a dedicated glyph name file (basically many verbose +glyph names are replaced by (in the end sort of redundant) uni names as well as +plenty small glif files (we didn't check if these are different from what is in +the original ttf file). Intermediate files are generated and at some point auto +hinting happens, using different tools for the two formats. + +At some point we figured out that the left side bearing in the head table was +somehow interfering and more experiments (we used for instance Lucida Math as +comparison) if became clear that the lsb bit in the head flags was the culprit. +By (un)setting it we could let \FONTFORGE\ show the \OPENTYPE\ and \TRUETYPE\ +files in the same way of differently. We could also zero the lsb entries in the +hmtx table, which sort of fixed it independent of the bit. For the record we +show the effect here (this document is also a bit our archive). + +\startlinecorrection +\startcombination[nx=3,ny=1] + {\externalfigure[StixTwo23AE-original.png][width=.25\textwidth]} {original otf} + {\externalfigure[StixTwo23AE-fixed.png] [width=.25\textwidth]} {fixed otf} + {\externalfigure[StixTwo23AE-ttf.png] [width=.25\textwidth]} {ttf} +\stopcombination +\stoplinecorrection + +The original variant: + +\starttyping +<CharString name="uni23AE"> +125 21 -21 hstem +301 102 vstem +403 hmoveto +650 -102 -650 vlineto +endchar +</CharString> +\stoptyping + +The fixed version: + +\starttyping +<CharString name="uni23AE"> +125 0 650 -629 -21 hstemhm +301 102 hintmask 01100000 +403 0 rmoveto +hintmask 10100000 +0 650 rlineto +-102 0 rlineto +0 -650 rlineto +endchar +</CharString> +\stoptyping + +It was this character that we looked at because we use it in a demo, but actually +many characters had this visual hinting side effect. So, one solution is to wipe +the hints and let FontForge add new ones, but easier is to just use the +\TRUETYPE\ files instead of the \OPENTYPE\ ones, either fixed or with hints +removed,as in: + +\starttyping +<CharString name="uni23AE"> + 125 403 0 rmoveto + 0 650 rlineto + -102 0 rlineto + 0 -650 rlineto + endchar +</CharString> +\stoptyping + +This is the original \type {uni23A_E_.glif} file: + +\starttyping +<?xml version='1.0' encoding='UTF-8'?> +<glyph name="uni23AE" format="2"> + <advance width="704"/> + <unicode hex="23AE"/> + <outline> + <contour> + <point x="403" y="0" type="line"/> + <point x="403" y="650" type="line"/> + <point x="301" y="650" type="line"/> + <point x="301" y="0" type="line"/> + </contour> + </outline> +</glyph> +\stoptyping + +In case one wonders why all this matters: occasionally we use the shape in +\METAPOST\ and there we don't apply hinting, which means that we don't want to +end up with the glyph positioned wrongly in the bounding box with hints moving +them to the right spot. So that is why we now prefer the \TRUETYPE\ variant +because then at least we can compare different programs visually. \footnote {In +the FontForge preview rendering in the overview, hinting is also not applied so +there glyphs are also positioned somewhat weird. In TypeTool3 the glyph doesn't +show up at all when we enable outline fill so it makes an interesting puzzle.} + +\stopsubject + +\stopchapter + +% \startchapter[title=Left-overs] + +% "action", +% "subsets", +% "parameters", + +% "message", +% "showinfo", +% "setoptions", +% "oldstylemath", +% "fixoldschool", +% "version", + +% \stopchapter + +\stoptext |