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

8 Oct 2018


      On Mon, 8 Oct 2018 16:00:10 -0400 (EDT)
Aditya Mahajan  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"  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?
\startluacode
local f = function(x, y) return 2*x^5  + x*y + y^5 end
local abs = math.abs
contour = { }
function contour.generate(x_min, x_max, y_min, y_max)
   local pts = { }
   local length = 1000
   local eps = 1e-3
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(f(xi,yi)) < eps then
              pts[#pts + 1] = {xi, yi}
           end
       end
   end
return pts
end
contour.data = contour.generate(0, 2, -1, 0.5)
function contour.n()
     mp.print(#contour.data)
end
function contour.point(i)
     mp.pair(contour.data[i])
end
\stopluacode
\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
I get an error:
! Missing argument to lua.
<to be read again>
contour
<*> ...caled .01 ; p := for i = 1 upto lua.contour
.n() : lua.contour.point(i...
That macro has more parameters than you thought.
I'll continue by pretending that each missing argument
is either zero or null.
Thanks,
Aditya
You need to put it into the mp namespace:
(then eps should be made a linear function of xi)
(and, indeed this is much faster than calculating in MP)

Alan


\startluacode
local f = function(x, y) return 2*x^5  + x*y + y^5 end
local abs = math.abs

local contour = { }

function contour.generate(x_min, x_max, y_min, y_max)
   local pts = { }
   local length = 1000
   local eps = 1e-3

   local n = 0
   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(f(xi,yi)) < eps then
              n = n + 1
              pts[n] = {xi, yi}
           end
       end
   end

   return pts
end

contour.data = contour.generate(0, 2, -1, 0.5)

function mp.ContourN()
     mp.print(#contour.data)
end

function mp.ContourPoint(i)
     mp.pair(contour.data[i])
end

function mp.ContourPath()
    mp.path(contour.data)
end

\stopluacode

\starttext
\startMPpage[instance=doublefun]
      draw lua.mp.ContourPath() 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