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

8 Oct 2018


      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  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?
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


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