Re: [NTG-context] Implicit plots/level curves possible?
On Tue, 9 Oct 2018, Alan Braslau wrote:
On Mon, 8 Oct 2018 17:56:24 -0400 (EDT)
Aditya Mahajan wrote:
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.
Hans and I played with Aditya's demonstration, to complete the example.
It demonstrates some fun lua+MP+ConTeXt tricks:
Looking at lua-mplib.mpvi, isn't it better to use MP namespace (instead of
mp) for user defined functions?
The metafun manual says that one can omit the prefix `lua` and simply use
`mp` or `MP`. That does not seem to work.
Aditya
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Re: [NTG-context] Implicit plots/level curves possible?
On Mon, 8 Oct 2018 17:56:24 -0400 (EDT)
Aditya Mahajan wrote:
> 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.
Hans and I played with Aditya's demonstration, to complete the example.
It demonstrates some fun lua+MP+ConTeXt tricks:
Alan
\startluacode
userdata = userdata or { }
userdata.contour = { }
userdata.xlim= { 0, 0 }
userdata.ylim= { 0, 0 }
function userdata.contourplot(f, xlim, ylim, length, ef)
local xmin, xmax = xlim[1], xlim[2]
local ymin, ymax = ylim[1], ylim[2]
local t = { }
local n = 0
for x = xmin, xmax, (xmax - xmin)/length do
for y = ymin, ymax, (ymax - ymin)/length do
local e = ef(x,y)
local z = f(x,y)
if z < e and z > -e then
n = n + 1
t[n] = { x, y }
end
end
end
userdata.xlim= xlim
userdata.ylim= ylim
userdata.contour = t
end
function mp.ContourPath()
mp.path(userdata.contour)
end
function mp.ContourX()
mp.pair(userdata.xlim)
end
function mp.ContourY()
mp.pair(userdata.ylim)
end
\stopluacode
\startuseMPgraphic{doublefun::ContourPlot}{width}
save xmin, xmax, ymin, ymax ;
(xmin, xmax) = lua.mp.ContourX() ;
(ymin, ymax) = lua.mp.ContourY() ;
draw lua.mp.ContourPath() withpen pencircle scaled ((xmax-xmin)/200) ;
setbounds currentpicture to boundingbox ((xmin,ymin)--(xmax,ymax));
currentpicture := currentpicture xsized \MPvar{width} ;
save pic ; picture pic ; pic := currentpicture ;
drawarrow llcorner pic--lrcorner pic ;
drawarrow llcorner pic--ulcorner pic ;
label.rt ("$x$", lrcorner pic) ;
label.top("$y$", ulcorner pic) ;
label.bot(decimal xmin,llcorner pic) ;
label.bot(decimal xmax,lrcorner pic) ;
label.lft(decimal ymin,llcorner pic) ;
label.lft(decimal ymax,ulcorner pic) ;
\stopuseMPgraphic
\unexpanded\def\ContourPlot
{\dosingleempty\doContourPlot}
\def\doContourPlot[#1]%
{\setvariables
[ContourPlot]
[x={0,0},
y={0,0},
w=10cm,
n=1000,
e=1e-2,
#1]%
\ctxlua{userdata.contourplot(
function(x,y) return \getvariable{ContourPlot}{function} end,
{\getvariable{ContourPlot}{x}},{\getvariable{ContourPlot}{y}},
\getvariable{ContourPlot}{n},
function(x,y) return \getvariable{ContourPlot}{e} end
)}%
\useMPgraphic{doublefun::ContourPlot}{width=\getvariable{ContourPlot}{w}}}
\starttext
\ContourPlot
[function={2*x^5 + x*y + y^5},
x={0,2},y={-2,0.5},
n=1000,e={x/1000},w=5cm]
\stoptext
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Re: [NTG-context] Implicit plots/level curves possible?
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 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 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
>
>
> -
>Hans Hagen | PRAGMA ADE
>Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
> tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
> -
>
> ___
> If your question is of interest to others as well, please add an entry to
> the Wiki!
>
> maillist : ntg-context@ntg.nl /
> http://www.ntg.nl/mailman/listinfo/ntg-context
> webpage : http://www.pragma-ade.nl / http://context.aanhet.net
> archive :
Re: [NTG-context] Implicit plots/level curves possible?
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
-
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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Re: [NTG-context] Implicit plots/level curves possible?
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 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}]
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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Re: [NTG-context] Implicit plots/level curves possible?
On Mon, 8 Oct 2018 17:25:24 -0400 (EDT) Aditya Mahajan wrote: > > (then eps should be made a linear function of xi) > > Oh, I missed that. Thanks. This is because the function is O(xy) for small x so one will get oscillations in the curve (multiple hits in the grid search) otherwise. Alan ___ If your question is of interest to others as well, please add an entry to the Wiki! maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context webpage : http://www.pragma-ade.nl / http://context.aanhet.net archive : https://bitbucket.org/phg/context-mirror/commits/ wiki : http://contextgarden.net ___
Re: [NTG-context] Implicit plots/level curves possible?
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
1ms in any reasonable programming language. Metapost for loops work with
macro expansion, which can be very expensive for large loops.
Aditya
___
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___
Re: [NTG-context] Implicit plots/level curves possible?
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.
>
> 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
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Re: [NTG-context] Implicit plots/level curves possible?
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.
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
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Re: [NTG-context] Implicit plots/level curves possible?
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:
\startTEXpage
\startMPcode {doublefun}
pen savedpen ; savedpen := currentpen ;
pickup pencircle scaled .01 ;
path p ;
p := for i=0 upto 1000 :
for j=0 upto 1000 :
hide(x := 2i/1000 ; y := 2.5j/1000 - 2 ;)
if abs(2*(x**5)+x*y+y**5) < .002i/1000 : (x,y) .. fi
endfor
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
\stopMPcode
\stopTEXpage
as this takes some time here's a cheat:
\starttext
\startbuffer[demo]
% when an environment is used, load it here
\startMPcode {doublefun}
pen savedpen ; savedpen := currentpen ;
pickup pencircle scaled .01 ;
numeric stp ; stp := 1 ;
path p ;
p := for i=0 step stp until 1000 :
for j=0 step stp until 1000 :
hide(x := 2i/1000 ; y := 2.5j/1000 - 2 ;)
if abs(2*(x**5)+x*y+y**5) < .002i/1000 : (x,y) .. fi
endfor
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 ;
\stopMPcode
\stopbuffer
\startTEXpage
\typesetbuffer[demo]
\stopTEXpage
\stoptext
a next run the already prepared buffer will be taken unles it has been
changed.
Hans
-
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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Re: [NTG-context] Implicit plots/level curves possible?
On Sun, Oct 7, 2018 at 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:
>
> \startTEXpage
> \startMPcode {doublefun}
> pen savedpen ; savedpen := currentpen ;
> pickup pencircle scaled .01 ;
> path p ;
> p := for i=0 upto 1000 :
>for j=0 upto 1000 :
> hide(x := 2i/1000 ; y := 2.5j/1000 - 2 ;)
> if abs(2*(x**5)+x*y+y**5) < .002i/1000 : (x,y) .. fi
>endfor
> 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
> \stopMPcode
> \stopTEXpage
>
>
> Alan
Thanks both to luigi and to Alan! I'm impressed by your brute force
method, Alan! In particular it learned me the "hide" command.
I feel a bit ashamed. Earlier today I answered something else giving a
reference to the metafun manual. Now I'm here not reading it carefully
enough myself. In the helpers section it is clearly written how to
import and plot data. Thus, I exported the data from the Mathematica
plot (that file is pasted below in case anyone wants to try this
themselves, sorry in advance for the big amount of text it generates
in this email) and then importing it just worked fine. I like Alan's
method very much, but it takes some time during compilation, so I will
probably stick with importing. Working code below (where one can see
that Alan's method is indeed working fine, at least with this
example).
Again, thanks to both luigi and Alan!
\starttext
\startTEXpage[offset=2bp]
\startMPcode{doublefun}
pen savedpen ; savedpen := currentpen ;
pickup pencircle scaled .01 ;
lua("MP = { } MP.data = table.load('mmadata.txt')") ;
numeric n ;
lua("mp.print('n := ',\#MP.data)") ;
path mycurve;
mycurve :=
lua("mp.pair(MP.data[1])")
for i=2 upto n :
.. lua("mp.pair(MP.data[" & decimal i & "])")
endfor;
draw mycurve withcolor darkred withpen pencircle scaled 0.04;
path p ;
p := for i=0 upto 1000 :
for j=0 upto 1000 :
hide(x := 2i/1000 ; y := 2.5j/1000 - 2 ;)
if abs(2*(x**5)+x*y+y**5) < .002i/1000 : (x,y) .. fi
endfor
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
\stopMPcode
\stopTEXpage
\stoptext
%%% mmadata.txt %%%
return {{1.7781332646374535, -2.0}, {1.7768209908069152,
-1.9983615165933983}, {1.775510204081634, -1.9967215415115265},
{1.7664030082433901, -1.985873790716172}, {1.756875567501,
-1.9744897959183674}, {1.7559890220139953, -1.973381069421283},
{1.7551020408163278, -1.9722667987462739}, {1.7455791311458495,
-1.9608832289248324}, {1.7356495451060165, -1.9489795918367347},
{1.7351734376993888, -1.9483801416512756}, {1.7346938775510217,
-1.9477751961654046}, {1.7247720468786834, -1.9358716760955252},
{1.714463398255413, -1.9234693877551021}, {1.7142857142857155,
-1.9232445076564075}, {1.7093814232165505, -1.9173390239186459},
{1.7039827159442558, -1.910837931600294}, {1.6938775510204094,
-1.8986359463002893}, {1.6935950869756253, -1.8983122637294494},
{1.6932881048717179, -1.8979591836734695}, {1.683212201778606,
-1.8857806661440912}, {1.6734693877551032, -1.8739731304347957},
{1.6728341829160982, -1.873242985640593}, {1.6721459415303699,
-1.8724489795918369}, {1.6624611568740721, -1.8606990641114929},
{1.653061224489797, -1.8492648538255463}, {1.6520932542108602,
-1.8481487383588753}, {1.6510476808879386, -1.8469387755102042},
{1.6417306097129987, -1.8355918398995696}, {1.632653061224491,
-1.824508389583349}, {1.6313733625579403, -1.82302819476176},
{1.6299953447379028, -1.8214285714285716}, {1.621021656483979,
-1.8104576232725786}, {1.6122448979591848, -1.7997008180397196},
{1.6106756399677442, -1.7978799398362397}, {1.6089910811705357,
-1.795918367346939}, {1.6003354664096425, -1.7852949527022344},
{1.5918367346938787, -1.7748390113411368}, {1.5900012943276478,
-1.7727024637230948}, {1.5880371747643334, -1.7704081632653064},
{1.5796732875598591, -1.760102268101198}, {1.5714285714285725,
Re: [NTG-context] Implicit plots/level curves possible?
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:
\startTEXpage
\startMPcode {doublefun}
pen savedpen ; savedpen := currentpen ;
pickup pencircle scaled .01 ;
path p ;
p := for i=0 upto 1000 :
for j=0 upto 1000 :
hide(x := 2i/1000 ; y := 2.5j/1000 - 2 ;)
if abs(2*(x**5)+x*y+y**5) < .002i/1000 : (x,y) .. fi
endfor
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
\stopMPcode
\stopTEXpage
Alan
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Re: [NTG-context] Implicit plots/level curves possible?
On Sun, Oct 7, 2018 at 5:26 PM Mikael P. Sundqvist wrote:
> Dear list,
>
> Is it possiblet to make implicit plots (i.e. ploting the curves
> described by equations) in MetaFun? I cannot find anything about them
> in the MetaFun manual.
>
> For example, in Mathematica I can write something like
>
> ContourPlot[2 x^5 + x y + y^5 == 0, {x, 0, 2}, {y, -2, 1/2}]
>
you need some " Groebner basis computation " kernel to do this kind of
computations.
Have a look at https://www-fourier.ujf-grenoble.fr/~parisse/giac.html
--
luigi
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[NTG-context] Implicit plots/level curves possible?
Dear list,
Is it possiblet to make implicit plots (i.e. ploting the curves
described by equations) in MetaFun? I cannot find anything about them
in the MetaFun manual.
For example, in Mathematica I can write something like
ContourPlot[2 x^5 + x y + y^5 == 0, {x, 0, 2}, {y, -2, 1/2}]
to get the attached figure.
The closest I have found which is something MetaPost-like, is the
levelcurve command in mfpic (see for example this answer
https://tex.stackexchange.com/a/405527/52406).
If this is not currently possible in MetaFun, what is the simplest way
to proceed (I want the same style of the plots as the other ones in my
doc)? Is it to
1) somehow run mfpic from within ConTeXt?
2) export points from Mathematica and plot them in ConTeXt (how could
that be done?). In the latter case, say I have the points (0,0),
(0.4,1), and (0.8,2) exported to a file. What format should it be in
to be easily imported and plot in MetaFun?
3) some other way?
/Mikael
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