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

Mikael P. Sundqvist mickep at gmail.com
Tue Oct 9 13:12:54 CEST 2018


Wow! This is cool!

I must admit I do not get how the connections between MetaPost and Lua
works, but it seem to work fine.

Challenge: To do this for a more complicated closed and self-intersecting
curve like the
Bernoulli lemniscate, say (x^2+y^2)^2=x^2-y^2 (a good domain could be
-1.5<x<1.5 and -1<y<1).

/Mikael (who hopes for some support for these kind of things in MetaFun in
the future)

On Tue, Oct 9, 2018 at 12:03 AM Hans Hagen <j.hagen at xs4all.nl> wrote:

> On 10/8/2018 11:25 PM, 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}]
> >>>>>
> >>>>> Brut force:
> >>>>> [...]
> >>>>>
> >>>> as this takes some time here's a cheat:
> >>>>
> >>>> \starttext
> >>>>
> >>>> \startbuffer[demo]
> >>>> [...]
> >>>> \stopbuffer
> >>>>
> >>>> \startTEXpage
> >>>>     \typesetbuffer[demo]
> >>>> \stopTEXpage
> >>>> \stoptext
> >>>>
> >>>> a next run the already prepared buffer will be taken unles it has been
> >>>> changed.
> >>>
> >>> I thought that this will also be a good usecase of showing Lua+MP
> >>> interaction. I wrote the code below following the metafun manual, but
> >>> I cannot
> >>> get it to compile. What am I missing?
> >>>
> >>>
> >> You need to put it into the mp namespace:
> >
> > Thanks. The metafun manual is confusing in this regard and I got the
> > impression that any lua namespace could be used.
> >
> >> (then eps should be made a linear function of xi)
> >
> > Oh, I missed that. Thanks.
> >
> >> (and, indeed this is much faster than calculating in MP)
> >
> > Yes. Iterating over 10^6 values on a 1GHz computer should roughly take
>
> hm, my 3.4 gig laptop cpu needs 0.18 sec for the slightly more that i
> million steps ... it depends on the function too
>
> > 1ms in any reasonable programming language. Metapost for loops work with
> > macro expansion, which can be very expensive for large loops.
>
> generalized:
>
> \startluacode
> ----- abs = math.abs
>
> local contour = { }
> local data    = { }
> local origin  = { 0, 0 }
> local length  = 0
>
> local function generate(f, x_min, x_max, y_min, y_max)
>     local points = { }
>     local length = 1000
>     local eps    = 1e-3
>     local spe    = -eps
>     local n      = 0
>     local code   = "return function(x,y) return " .. f .. " end"
>     local action = load(code)
>     if action then
>          action = action()
>     end
>     for xi = x_min, x_max, (x_max - x_min)/length do
>         for yi = y_min, y_max, (y_max - y_min)/length do
>           -- if abs(action(xi,yi)) < eps then -- 10% gain with:
>              local v = action(xi,yi)
>              if v < eps and v > spe then
>                  n = n + 1
>                  points[n] = { xi, yi }
>              end
>         end
>     end
>     return points, n
> end
>
> function mp.Countour(...)
>      data, length = generate(...)
> end
>
> function mp.ContourN()
>      mp.print(length)
> end
>
> function mp.ContourPoint(i)
>      mp.pair(data[i] or origin)
> end
>
> function mp.ContourPath(f,...)
>      if f then
>          data, length = generate(f,...)
>      end
>      mp.path(length > 0 and data or origin)
> end
>
> \stopluacode
>
> \starttext
>      \startMPpage[instance=doublefun]
>        % lua.mp.Countour("2*x^5  + x*y + y^5", 0, 2, -1, 0.5) ;
>        % draw lua.mp.ContourPath() withpen pencircle scaled .01 ;
>          draw lua.mp.ContourPath("2*x^5  + x*y + y^5", 0, 2, -1, 0.5)
> withpen pencircle scaled .01 ;
>          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 ;
>      \stopMPpage
> \stoptext
>
>
> -----------------------------------------------------------------
>                                            Hans Hagen | PRAGMA ADE
>                Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
>         tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
> -----------------------------------------------------------------
>
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