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We try to adapt these documents to upgrades in the (sub)systems +% that they describe. Using parts of the content otherwise can therefore conflict +% with existing functionality and we cannot be held responsible for that. Many of +% the manuals contain characteristic graphics and personal notes or examples that +% make no sense when used out-of-context. + +\usemodule[magazine-basic,abr-02] + +\usemodule[scite] + +\startbuffer[abstract] + As part of the \CONTEXT\ \LMTX\ project, we experiment with new ways to + interface subsystems and \METAPOST\ makes a good candidate. Here I wrap up some + experiments. It's not a manual or a recipe, just food for thought. All you see + here might change and|/|or evolve. +\stopbuffer + +\setuplayout + [backspace=20mm, + topspace=10mm] + +\startdocument + [title={New interfacing in \METAFUN, a preview}, + author={Hans Hagen & Alan Braslau}, + %affiliation=PRAGMA ADE, + date=July 2019, + number=1104 LMTX] + +As we move to \CONTEXT\ \LMTX, some decisions need to be made. For instance, how +shall we introduce new functionality while not affecting the \MKIV\ code base too +much with engine related tests, messy and performance sapping. Of course we +remain downward compatible but the \LUAMETATEX\ engine sometimes permits multiple +solutions. As this is something new, for a while we can use experimental features +that may change or later disappear depending on experience. It is not a big deal +to adapt to these new possibilites and users shouldn't notice, unless of course +they currently employ (yet undocumented) low|-|level features. Part of the +solution is to have separate files for \MKIV\ and \LMTX, although that will +mostly concern low level support modules; even then differences will be subtle +and should not affect users. I must admit that some of those changes are mostly +aesthetic and often don't improve performance, although better performance +sometimes may be the case, in particular concerning \quote {extreme} usage. + +But, that said, there are areas where \LMTX\ will offer entirely new +functionality. One of the areas where we are making interesting developments is +in \METAFUN, which means \METAPOST. Now, it is not to be said that some of the +core functionality needed for this will migrate from \LUAMETATEX\ (used by \LMTX) +to \LUATEX\ (used by \MKIV). But, because (due to external pressure), the later +engine is now considered stable and its functionality frozen, it is not likely to +be quickly backported or at least only will happen when this has been throughly +tested in \CONTEXT|/|\LMTX. + +Over the years there have been (small) improvements in the interface but while +Alan Braslau and I experiment with new graphic abilities, we also are coming up +with (graphic) interfaces that suit \CONTEXT\ much better. Below, I will show +some examples. \footnote {These optional argument handlers themselves are +\emphasize {not} part of \METAPOST\ but implemented in \CONTEXT\ using some +experimental parsing related extensions to a version of \MPLIB\ used in +\LUAMETATEX.} + +\startbuffer +\startMPcode{doublefun} + draw lmt_grid [ + nx = 20, ny = 10, + dx = 5, dy = 2, + tx = 10, ty = 10, + ] ysized 5cm withpen pencircle scaled 1mm withcolor "red" ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +What we see here is an key|/|value driven interface that has been one of the +unique core properties of \CONTEXT\ since it was created. \footnote {Note the use +of the color string \type {"red"} rather then the \METAPOST\ color variable \type +{red := (1,0,0)}. This is a small detail but here imports the color definition +from \CONTEXT, which might be a bit special.} Of course parameters can be +optional as demonstrated in: + +\startbuffer +\startMPcode{doublefun} + draw lmt_grid [ + nx = 10, ny = 10, + dx = 1, dy = 1 + ] ysized 3cm + withpen pencircle scaled 1mm + withcolor "darkblue" ; + + draw lmt_grid [ + nx = 10, ny = 10 + ] ysized 3cm shifted (4cm,0) + withpen pencircle scaled .3mm + withcolor "darkgreen" ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +This syntax means that we can also use the already used interface documentation +system. + +We can actually go quite far in what we provide. It's not so much that these +things were not possible before, but the more concise user interface is something +new indeed. Let's start with drawing some simple axis: + +\startbuffer +\startMPcode{doublefun} + draw lmt_axis [ + nx = 20, ny = 10, + dx = 5, dy = 2, + ] ysized 4cm + withpen pencircle scaled 1mm + withcolor "darkcyan" ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +This \quote {article} is not meant as tutorial but more as a teaser about what is +possible and hopefully it triggers users in coming up with useful demands. As the +previous axis example is not that interesting we move on to a more complex one: + +\startbuffer +\startMPcode{doublefun} + draw lmt_axis [ + sx = 5mm, sy = 5mm, + nx = 20, ny = 10, + dx = 5, dy = 2, + tx = 10, ty = 10, + ] withpen pencircle scaled 1mm withcolor "darkblue" ; + + draw lmt_connected ( + for i = 1 step 2 until 20 : + -- (i, 1 randomized 8) * 5mm + endfor + ) + withpen pencircle scaled 2mm withcolor "darkyellow" ; + + draw lmt_connected ( + for i = 1 step 2 until 20 : + lmt_connection (i, 1 randomized 8) * 5mm + endfor + ) + withpen pencircle scaled 2mm withcolor "darkgreen" ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +These examples are made as part of exploring how to best interface with +\METAPOST, to be used by the upcoming luagraph module, a flexible and high +performance set of macros aimed at drawing graphs and to visualize data. On the +one hand, we want to free the user from dealing with details such as scales to +get the graphics right, but on the other hand it should be possible to +fine|-|tune when needed. + +Again we draw an axis. Using strings as color names, mentioned in the footnote +earlier, is not new, but already present for a while. It will use the colors +defined at the \TEX\ end and is more convenient and natural than using the older +\type {\MPcolor}. The \type {lmt_connected} macro is sort of a gimmick: if you +look closely you will see that it has to start with a point (coordinate) but that +one is discarded silently. Again this is something we need to deal with. + +% This is obscure, and silly. I'm sure that we can do better. Sure, but so is the +% HIDE related alternative trrickery. We probably need something getparameterpath. + +The next variant uses a list of samples. Watch the use of braces, this is +something normally not part of \METAPOST\ syntax, and it signals a \LUA|-|like +list. This is a choice of interfacing. There are subtle and somewhat complicated +aspects involved here as \METAPOST\ parsing involves primaries, secondaries, +tertiaries and expressions, symbols, strings, tags and other specialities. + +% Why does samples = {} require a second pair of brackets? Wouldn't a +% comma-separated list be enough in Lua? Because it's \METAPOST\ which has its own +% ideas about where expressions start and end. + +\startbuffer +\startMPcode{doublefun} + draw lmt_axis [ + sx = 5mm, sy = 5mm, + nx = 20, ny = 10, + dx = 5, dy = 2, + tx = 5, ty = 2, + startx = 1, starty = 0, + + connect = true, + samples = { + { + 4, 2, 4, 9, 3, 0, 8, 9, 10, 1, + 5, 3, 0, 8, 5, 6, 10, 2, 3, 5 + } + }, + axiscolor = "darkgreen", + textcolor = "darkred", + samplecolors = { + "darkblue" + }, + ] withpen pencircle scaled 1mm ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +We can have multiple sample lists. But of course dealing with that is really up +to the underlying code, which itself is not that much related to \METAPOST\ but +has been delegated to \LUA. + +\startbuffer +\definecolor[tdarkred] [r=.6,a=1,t=.5] +\definecolor[tdarkgreen][g=.6,a=1,t=.5] +\definecolor[tdarkblue] [b=.6,a=1,t=.5] + +\startMPcode{doublefun} + save u ; let u = uniformdeviate ; + draw lmt_axis [ + sx = 5mm, sy = 5mm, + nx = 20, ny = 10, + dx = 5, dy = 2, + tx = 10, ty = 2, + samples = { + { + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10 + }, + { + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10 + }, + { + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10, + u10, u10, u10, u10, u10 + } + }, + startx = 1, + starty = 0, + connect = true, + axiscolor = "darkgray", + textcolor = "darkyellow", + samplecolors = { + "tdarkred", + "tdarkgreen", + "tdarkblue" + }, + ] withpen pencircle scaled 1mm ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +Yet another interesting variant might be this: + +\startbuffer +\startluacode + documentdata["lmx-sample-1"] = { + { + 4, 2, 4, 9, 3, 0, 8, 9, 10, 1, + 5, 3, 0, 8, 5, 6, 10, 2, 3, 5 + } + } +\stopluacode +\stopbuffer + +\typebuffer[option=TEX] \getbuffer + +\startbuffer +\startMPcode{doublefun} + draw lmt_axis [ + sx = 5mm, sy = 5mm, + nx = 20, ny = 10, + dx = 5, dy = 2, + tx = 5, ty = 2, + startx = 1, starty = 0, + + samples = "lmx-sample-1", + axiscolor = "darkgreen", + textcolor = "darkred", + samplecolors = { "darkblue" }, + ] withpen pencircle scaled 1mm ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +% OOPS, doesn't work! + +Adding more tricks is not that complex, take, for example: + +\startbuffer +\startMPcode{doublefun} +draw lmt_axis [ + sx = 5mm, sy = 5mm, + nx = 20, ny = 10, + dx = 5, dy = 2, + tx = 10, ty = 10, + + list = { + [ + connect = true, + color = "darkred", + close = true, + points = { (1, 1), (15, 8), (2, 10) }, + texts = { "segment 1", "segment 2", "segment 3" } + ], + [ + connect = true, + color = "darkgreen", + points = { (2, 2), (4, 1), (10, 3), (16, 8), (19, 2) }, + labels = { "a", "b", "c", "d", "e" } + ], + [ + connect = true, + color = "darkblue", + close = true, + points = { (5, 3), (8, 8), (16, 1) }, + labels = { "1", "2", "3" } + ] + }, + +] withpen pencircle scaled 1mm ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +yielding + +\startlinecorrection +\getbuffer +\stoplinecorrection + +but this is experimentation, work in progress, not to be taken as settled. + +\blank + +A variant on this one is the following: + +\startbuffer +\startMPcode{doublefun} +draw lmt_function [ + + xmin = 0, xmax = 10, xstep = .05, + ymin = -2, ymax = 2, + + xticks = "bottom", xsmall = 80, xlarge = 20, + yticks = "left", ysmall = 40, ylarge = 4, + + code = "1.5 * math.cosd(240 * math.sqrt(x))", + + xlabels = "yes", + ylabels = "yes", + + ycaption = "\strut\tfd \rotate[rotation=90]{vertical}", + xcaption = "\strut\tfd horizontal", + + pointsymbol = "dot", pointsize = 4, pointcolor = "orange", + + sx = 2mm, sy = 4mm, linewidth = .025mm, offset = .1mm, +] + xsized 8cm +; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +A valid question is if this should be combined with the previous but having +distinctive variants is less likely to complicate the settings, as these can +depend on the application: + +\startlinecorrection +\getbuffer +\stoplinecorrection + +A more complex usage (still under exploration) is demonstrated next: + +\startbuffer +\definecolor[MyColorR][r=.5,t=.5,a=1] +\definecolor[MyColorG][g=.5,t=.5,a=1] +\definecolor[MyColorB][b=.5,t=.5,a=1] +\definecolor[MyColorY][r=.5,g=.5,t=.5,a=1] + +\startMPcode{doublefun} +draw lmt_function [ + sx = 1mm, sy = 4mm, linewidth = .025mm, offset = .1mm, + + xmin = 0, xmax = 20, xstep = .1, + ymin = -2, ymax = 2, + + xticks = "bottom", xsmall = 80, xlarge = 20, xlabels = "nolimits", + yticks = "left", ysmall = 40, ylarge = 4, ylabels = "yes", + + code = "1.5 * math.sind (50 * x - 150)", + + frame = "sticks", % "ticks" + + functions = { + [ + xmin = 1.0, + xmax = 7.0, + close = true, + fillcolor = "MyColorR" + ], + [ + xmin = 7.0, + xmax = 12.0, + close = true, + fillcolor = "MyColorG" + ], + [ + xmin = 12.0, + xmax = 19.0, + close = true, + fillcolor = "MyColorB" + ], + [ + drawcolor = "darkyellow", + drawsize = 2, + ], + [ + xmin = 4, + xmax = 17, + xstep = .25, + drawcolor = "darkmagenta", + shape = "steps", + code = "0.5 * math.random(-2,2)", + ], + [ + xmin = 5.0, + xmax = 15.0, + close = true, + fillcolor = "MyColorY" + code = "1.75 * math.cosd (50 * x - 150)", + ] + }, + ycaption = "\rotate[rotation=90]{\tfd\strut a mix of drawings}", + xcaption = "\framed[foregroundstyle=\tfd]{a mixture of $\sin(x), \cos(x), \sqrt{x}$ etc.}", +] + xsized 8cm +; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +Of course calling the same command multiple times with different code snippets +will also work. + +\startlinecorrection +\getbuffer +\stoplinecorrection + +The previous examples used new code but how about improving existing features? +Let's look at outlines. + +\startbuffer +\startMPcode{doublefun} + save h ; h = 12mm ; + + draw lmt_outline [ + content = "hello" + kind = "draw", + drawcolor = "darkblue", + ] ysized h ; + + draw lmt_outline [ + content = "hello", + kind = "fill", + fillcolor = "darkred", + ] ysized h shifted (3.75h,0) ; + + draw lmt_outline [ + content = "hello", + kind = "both", + fillcolor = "darkred", + ] ysized h shifted (7.5h,0mm) ; + + draw lmt_outline [ + content = "hello", + kind = "both", + fillcolor = "darkred", + drawcolor = "darkblue", + rulethickness = 1/5, + ] ysized h shifted (0,-1.25h) ; + + draw lmt_outline [ + content = "hello", + kind = "reverse", + fillcolor = "darkred", + drawcolor = "darkblue", + rulethickness = 1/2, + ] ysized h shifted (3.75h,-1.25h) ; + + draw lmt_outline [ + content = "hello", + kind = "u", + fillcolor = "darkgreen", + rulethickness = 0, + ] ysized h shifted (7.5h,-1.25h) ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +This interface is much nicer than the one where each variant (the parameter \type +{kind} above) had its own macro due to the need to group properties of the +outline and fill. Let's show some more: + +\startbuffer +\startMPcode{doublefun} + draw lmt_outline [ + content = "\obeydiscretionaries\samplefile{tufte}", + align = "normal", + kind = "draw", + drawcolor = "darkblue", + ] xsized TextWidth ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +\startbuffer +\startMPcode{doublefun} + draw lmt_outline [ + content = "\obeydiscretionaries\samplefile{ward}", + align = "normal,tolerant", + width = 10cm, + kind = "draw", + drawcolor = "darkblue", + ] xsized TextWidth ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +\startbuffer +\startMPcode{doublefun} + draw lmt_outline [ + content = "\obeydiscretionaries\samplefile{sapolsky}", + align = "normal,tolerant", + style = "bold", + width = 10cm, + kind = "draw", + rulethickness = 1/5, + drawcolor = "darkred", + ] xsized TextWidth ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +Another \METAFUN\ text related mechanism deals with following a specific path. +That interface has evolved over time, also due to more advanced possibilities in +\MKIV. But, it's again time for a upgrade, for example: + +\startbuffer +\startMPcode{doublefun} + draw lmt_followtext [ + content = "How well does it work {\bf 1}! ", + path = (fullcircle scaled 4cm), + trace = true, + spread = true, + ] ysized 5cm ; + + draw lmt_followtext [ + content = "How well does it work {\bf 2}! ", + path = fullcircle scaled 4cm, + trace = true, + spread = false, + reverse = true, + ] ysized 5cm shifted (0,-6cm) ; + + draw lmt_followtext [ + content = "How well does it work {\bf 3}! ", + trace = true, + autoscaleup = "yes" + ] ysized 5cm shifted (6cm,0) ; + + draw lmt_followtext [ + content = "How well does it work {\bf 4}! ", + path = fullcircle scaled 2cm, + trace = true, + autoscaleup = "max" + ] ysized 5cm shifted (6cm,-6cm) ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +Although \METAPOST\ can draw arrows a bit more code is involved than one would +have expected. As a consequence, influencing the way an arrowhead is drawn as +currently using variables is somewhat cumbersome. Here is an alternative: + +\startbuffer +\startMPcode{doublefun} + draw lmt_arrow [ + path = fullcircle + scaled 3cm + shifted (0,0cm), + ] withcolor "darkred" ; + + draw lmt_arrow [ + location = "both" + path = fullcircle + scaled 3cm + rotated 90 + shifted (0,-3.5cm), + ] withcolor "darkgreen" ; + + draw lmt_arrow [ + kind = "draw", + location = "middle", + alternative = "curved", + path = fullcircle + scaled 3cm + shifted (3.5cm,0cm), + ] withcolor "darkblue" ; + + for i = 0 step 5 until 100 : + draw lmt_arrow [ + alternative = "dimpled", + location = "percentage", + percentage = i, + dimple = (1/5 + i/200), + headonly = (i = 0), + path = fullcircle + scaled 3cm + shifted (3.5cm,-3.5cm), + ] withcolor "darkyellow" ; + endfor ; +\stopMPcode +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +These new interfaces for outlines, following text and arrows certainly will make +it in some form to be permanent \METAFUN\ extensions. Some will also be used in +macros at the \TEX\ end, for instance, when you load the dummy library: + +\startbuffer +\useMPlibrary[dum] +\stopbuffer + +\typebuffer[option=TEX] \getbuffer + +You can do this: + +\startbuffer +\startcombination + {\externalfigure[crap-001]} {one} + {\externalfigure[crap-004][alternative=triangle]} {two} +\stopcombination +\stopbuffer + +\typebuffer[option=TEX] + +and get: + +\startlinecorrection +\getbuffer +\stoplinecorrection + +This placeholder now also can be accessed directly: + +\startbuffer +\useMPmacro + [minifun] + [placeholder] + [width=10cm, + height=3cm, + reduction=.2, + alternative=triangle, + color=orange] +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +The \type {\useMPmacro} is an entirely new interface to \METAFUN\ code. Although +it is still experimental, we show an example. Of course, as needed, you can throw +in some \LUA\ magic. + +\startbuffer +\startMPcalculation + presetparameters "demo" [ + n = 5, + s = 1cm, + ] ; + + def lmt_demo = applyparameters "demo" "lmt_do_demo" enddef ; + + vardef lmt_do_demo = + for i=1 upto getparameter "demo" "n" : + draw fullcircle scaled (i*getparameter "demo" "s"); + endfor ; + enddef ; +\stopMPcalculation +\stopbuffer + +\typebuffer[option=TEX] + +The calculation wrapper makes this code be processed immediately, which is needed +because we don't use a module. + +\getbuffer + +A the \TEX\ end we do this: + +\startbuffer +\defineMPparameterset[demo][n=integer,s=dimension] +\stopbuffer + +\typebuffer[option=TEX] + +\getbuffer + +We can now let the macro do its work: + +\startbuffer +\startcombination[nx=4,location=middle] + {\useMPmacro[demo][n=8,s=2mm]} {Demo 1} + {\useMPmacro[demo][n=4,s=4mm]} {Demo 2} + {\useMPmacro[demo][n=4,s=5\exheight]} {Demo 3} + {\useMPmacro[demo]} {Demo 4} +\stopcombination +\stopbuffer + +\typebuffer[option=TEX] + +\startlinecorrection +\getbuffer +\stoplinecorrection + +You can also set the parameters separately. There is one catch: there is no +grouping so in this case you need to reset the parameters afterwards. + +\starttyping +\presetMPparameters[demo][n=8] \useMPmacro[demo]\blank +\presetMPparameters[demo][n=4] \useMPmacro[demo]\blank +\resetMPparameters [demo] \useMPmacro[demo]\blank +\stoptyping + +These examples demonstrate that we can make \METAPOST\ a bit friendlier for users +who are not that fluent with the language. It remains to be seen to what extent +additional modules will be written, but the possibilities are there. + +\stopdocument |