[NTG-context] Implicit plots/level curves possible?

Aditya Mahajan adityam at umich.edu
Mon Oct 8 23:56:24 CEST 2018


On Mon, 8 Oct 2018, Aditya Mahajan wrote:

> On Mon, 8 Oct 2018, Alan Braslau wrote:
>
>> On Mon, 8 Oct 2018 16:00:10 -0400 (EDT)
>> Aditya Mahajan <adityam at umich.edu> wrote:
>>
>>> On Sun, 7 Oct 2018, Hans Hagen wrote:
>>>
>>>> On 10/7/2018 7:14 PM, Alan Braslau wrote:
>>>>> On Sun, 7 Oct 2018 17:25:35 +0200
>>>>> "Mikael P. Sundqvist" <mickep at gmail.com> wrote:
>>>>>
>>>>>> ContourPlot[2 x^5 + x y + y^5 == 0, {x, 0, 2}, {y, -2, 1/2}]

Here is a proof of concept implementation in Lua + MP so that you can use:

\ContourPlot
   [
     function=2*x^5 + x*y + y^5,
     x={0, 2},
     y={-2, 0.5},
     n=1000, % Number of discretization points
   ]

The code is fairly fast. But be careful. As with all ConTeXt key-value 
assignment, `x = { ...}` is different from `x={...}`. I am being a bit 
lazy here, and haven't adapted the metapost code to draw the axes to adapt 
to the function.

\define\ContourPlot
     {\dosingleargument\doContourPlot}

\def\doContourPlot[#1]%
     {\setvariables[ContourPlot][#1]%
      \ctxlua{userdata.contourplot(
         function(x,y) return \getvariable{ContourPlot}{function} end,
         {\getvariable{ContourPlot}{x}},
         {\getvariable{ContourPlot}{y}},
          \getvariable{ContourPlot}{n})}%
     \useMPgraphic{doublefun::ContourPlot}}

\startluacode
   userdata = userdata or { }
   local abs = math.abs
   local data = { }
   local eps  = 1e-3

   function userdata.contourplot(f, xlim, ylim, length)
       local n = 0
       data    = { }
       for x = xlim[1], xlim[2], (xlim[2] - xlim[1])/length do
           for y = ylim[1], ylim[2], (ylim[2] - ylim[1])/length do
               if abs(f(x,y)) < eps*x then
                  n = n + 1
                  data[n] = {x, y}
               end
           end
       end
   end

   function mp.ContourPath()
       mp.path(data)
   end
\stopluacode

\startuseMPgraphic{doublefun::ContourPlot}
      draw lua.mp.ContourPath() withpen pencircle scaled .01 ;

      % This needs to be fixed to adapt to the function.
       setbounds currentpicture to (0,-2)--(2,-2)--(2,.5)--(0,.5)--cycle ;
       currentpicture := currentpicture xsized 5cm ;

       picture pic ; pic := currentpicture ;
       drawarrow llcorner pic--lrcorner pic ;
       drawarrow llcorner pic--ulcorner pic ;
       label.rt ("$x$", lrcorner pic) ;
       label.top("$y$", ulcorner pic) ;
       for x=0 step .5 until 2 :
           label.bot(decimal x,(x/2)[llcorner pic,lrcorner pic]) ;
       endfor ;
       for y=0 step .5 until 2.5 :
           label.lft(decimal (y-2),(y/2.5)[llcorner pic,ulcorner pic]) ;
       endfor ;
\stopuseMPgraphic

\starttext
\ContourPlot
   [
     function=2*x^5 + x*y + y^5,
     x={0, 2},
     y={-2, 0.5},
     n=1000,
   ]
\stoptext


\endinput


\starttext
\startMPpage[instance=doublefun]
      pen savedpen ; savedpen := currentpen ;
      pickup pencircle scaled .01 ;

      p := for i = 1 upto lua.contour.n() :
           lua.contour.point(i) ..
      endfor cycle;

      draw subpath (0,length p - 1) of p ;
      setbounds currentpicture to (0,-2)--(2,-2)--(2,.5)--(0,.5)--cycle ;
      currentpicture := currentpicture xsized 5cm ;
      pickup savedpen ;
      picture pic ; pic := currentpicture ;
      drawarrow llcorner pic--lrcorner pic ;
      drawarrow llcorner pic--ulcorner pic ;
      label.rt ("$x$", lrcorner pic) ;
      label.top("$y$", ulcorner pic) ;
      for x=0 step .5 until 2 :
          label.bot(decimal x,(x/2)[llcorner pic,lrcorner pic]) ;
      endfor ;
      for y=0 step .5 until 2.5 :
          label.lft(decimal (y-2),(y/2.5)[llcorner pic,ulcorner pic]) ;
      endfor ;
\stopMPpage
\stoptext


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