Numerical Calculations

Numerical Calculations

[Troy Henderson]

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Is there a way to for ConTeXt to do basic arithmetic operations?  For
example,

\calc{1+2} and have it return 3 or

\calc{1/3.8} and have it return 0.263157894736842 (or rounded)

Troy

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Re: Numerical Calculations

[Thomas A. Schmitz]

On 12/19/2012 07:09 PM, Troy Henderson wrote:
> Is there a way to for ConTeXt to do basic arithmetic operations?  For
> example,
>
> \calc{1+2} and have it return 3 or
>
> \calc{1/3.8} and have it return 0.263157894736842 (or rounded)
>
> Troy

http://wiki.contextgarden.net/Programming_in_LuaTeX#Examples

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Re: Numerical Calculations

[Hans Hagen]

On 12/19/2012 7:09 PM, Troy Henderson wrote:
> Is there a way to for ConTeXt to do basic arithmetic operations?  For
> example,
>
> \calc{1+2} and have it return 3 or
>
> \calc{1/3.8} and have it return 0.263157894736842 (or rounded)

\luaexpr{1+2}

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Re: Numerical Calculations

[Hans Hagen]

On 12/19/2012 7:09 PM, Troy Henderson wrote:

> \calc{1/3.8} and have it return 0.263157894736842 (or rounded)

\ctxcommand{format("@0.3f",1/3.8)}

@ as well as % ... just lua format but @ is more tex friendly

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Re: Numerical Calculations

[Troy Henderson]

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Do \luaexpr{1/3.8} and \ctxcommand{format("@0.3f",1/3.8)} return numbers or
strings?  That is, I would like to use these results in a \if or \ifnum
command to exit a \doloop.

Troy

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Re: Numerical Calculations

[Roland Thiers]

Le 20 déc. 12 à 05:43, Troy Henderson a écrit :

> Do \luaexpr{1/3.8} and \ctxcommand{format("@0.3f",1/3.8)} return  
> numbers or strings?  That is, I would like to use these results in a  
> \if or \ifnum command to exit a \doloop.
>
> Troy
  Bonjour,
\ctxlua{context(type(\luaexpr{1/3.8}))} gives : number
Roland


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Re: Numerical Calculations

[Hans Hagen]

On 12/19/2012 7:43 PM, Troy Henderson wrote:
> Do \luaexpr{1/3.8} and \ctxcommand{format("@0.3f",1/3.8)} return numbers
> or strings?  That is, I would like to use these results in a \if or
> \ifnum command to exit a \doloop.

they return tokens i.e.

\ifnum\luaexpr{math.round(1/3.8)}>1\relax

should work ok; it all depends on what you do, but you could also set a 
counter ans use that:

\ctxlua{tex.count.scratchcounter=math.round(1/3.8)}

\ifnum\scratchcounter>0




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Re: Numerical Calculations

[Hans Hagen]

On 12/19/2012 8:19 PM, Roland Thiers wrote:
>
> Le 20 déc. 12 à 05:43, Troy Henderson a écrit :
>
>> Do \luaexpr{1/3.8} and \ctxcommand{format("@0.3f",1/3.8)} return
>> numbers or strings?  That is, I would like to use these results in a
>> \if or \ifnum command to exit a \doloop.
>>
>> Troy
>   Bonjour,
> \ctxlua{context(type(\luaexpr{1/3.8}))} gives : number

sure, but the context command pipes it back to tex as characters that 
get tokenized

Hans

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Re: Numerical Calculations

[Philipp Gesang]

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···<date: 2012-12-19, Wednesday>···<from: Troy Henderson>···

> Do \luaexpr{1/3.8} and \ctxcommand{format("@0.3f",1/3.8)} return numbers or
> strings?  That is, I would like to use these results in a \if or \ifnum
> command to exit a \doloop.

Fwiw there are Lua-side conditionals available as well:

  http://www.ntg.nl/pipermail/ntg-context/2012/068673.html

with these maybe you won’t need TeX for the tests.

Regards
Philipp


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Re: Numerical Calculations

[Hans Hagen]

On 12/19/2012 9:13 PM, Troy Henderson wrote:
> I got this to work.  There's probably a better method though ;)
>
> \edef\r{\luaexpr{1/3.8}}
> \edef\q{1}\doloop{\ctxlua{commands.doifelse(math.abs(\q*\r -
> math.floor(\q*\r+0.5))<0.000001)}{\exitloop}{\edef\q{\luaexpr{\q+1}}}}

Yes, you need to think more hybrid .. two variants:

\startluacode
     local r = 1 / 3.8
     local q = 1
     while true do
         if math.abs(q*r - math.floor(q*r+0.5)) < 0.000001 then
             break
         else
             q = q + 1
         end
     end
     context.setvalue("MyQ",q)
\stopluacode

\startluacode
     userdata = userdata or { }
     function userdata.CalculateQ(r)
         local q = 1
         while true do
             if math.abs(q*r - math.floor(q*r+0.5)) < 0.000001 then
                 break
             else
                 q = q + 1
             end
         end
         context(q)
     end
\stopluacode

\edef\MyOtherQ{\ctxlua{userdata.CalculateQ(1/3.8)}}

\starttext

     q: \MyQ

     q: \MyOtherQ

\stoptext



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Re: Numerical Calculations

[Troy Henderson]

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In case anyone cares, here is the "finished" product which is a
frame-by-frame animation of a hypocycloid.  The following code will produce
a 190 page PDF where each page is an individual frame of the animation.

Troy

\edef\r{\luaexpr{1/3.8}} % Radius of smaller circle (larger circle has
radius 1)
\edef\N{10} % Number of frames in animation per hypocycloid "branch"

\edef\K{1}\doloop{\ctxlua{commands.doifelse(math.abs(\K*\r -
math.floor(\K*\r+0.5))<0.000001)}{\exitloop}{\edef\K{\luaexpr{\K+1}}}}
\startMPinclusions[+]
    r:=\r; % Radius of smaller circle (larger circle has radius 1)
    u:=70; % Scaling factor for the graphics
    K:=\K; % Number of "branches" per period (computed automatically)
    M:=8; % Number of points in the Bezier curve for each "branch"
    N:=\N; % Number of frames in animation per hypocycloid "bran
    path p; % p is the "first branch" of the hypocycloid
    p:=(1,0) for m=1 upto (M-1): ..
(r*cosd(360*(r-1)/(M-1)*m)-(r-1)*cosd(360*r/(M-1)*m),r*sind(360*(r-1)/(M-1)*m)-(r-1)*sind(360*r/(M-1)*m))
endfor;
    W:=ceiling(u/32*65); % Width of each figure's bounding box
    H:=W; % Height of each figure's bounding box
    path q;
\stopMPinclusions
\starttext
    \dorecurse{\luaexpr{\K*\N}}{
        \startMPpage
            m:=floor((\recurselevel-1)/N);
            n:=\recurselevel-m*N-1;
            numeric s[];
            t:=n/N;

q:=(((1-r)*cosd(360*r*t),(1-r)*sind(360*r*t))--((1+r)*cosd(360*(r-1)*t)-(r-1)*cosd(360*r*t),(1+r)*sind(360*(r-1)*t)-(r-1)*sind(360*r*t)));
            (s1,s2) = p intersectiontimes reverse q;
            for j=0 upto (m-1): draw p scaled u rotated (360*r*j) withcolor
red; endfor;
            draw subpath (0,s1) of p scaled u rotated (360*r*m) withcolor
red;
            draw fullcircle scaled (2*u);
            draw fullcircle scaled (2*r*u) shifted
((1-r)*u*cosd(360*r*t),(1-r)*u*sind(360*r*t)) rotated (360*r*m);
            draw subpath (s2,length q) of (reverse q) scaled u rotated
(360*r*m);
            setbounds currentpicture to
(-W/2,-H/2)--(W/2,-H/2)--(W/2,H/2)--(-W/2,H/2)--cycle;
        \stopMPpage
    }
\stoptext

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Re: Numerical Calculations

[Marco Patzer]

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On 2012–12–19 Troy Henderson wrote:

> In case anyone cares, here is the "finished" product which is a
> frame-by-frame animation of a hypocycloid.  The following code will produce
> a 190 page PDF where each page is an individual frame of the animation.
> 
> […]

Very nice work, indeed. It reminds me of a drawing toy I had when I
was a kid. Thanks a lot for sharing.

Marco

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Re: Numerical Calculations

[Troy Henderson]

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>
> Very nice work, indeed. It reminds me of a drawing toy I had when I
> was a kid. Thanks a lot for sharing.
>

Spirograph?

http://en.wikipedia.org/wiki/Spirograph

Troy

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Re: Numerical Calculations

[Troy Henderson]

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Here's the animated (video) version.

http://www.youtube.com/watch?v=2_OZ-yKMd7g

Troy

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Re: Numerical Calculations

[Marco Patzer]

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On 2012–12–19 Troy Henderson wrote:

> >
> > Very nice work, indeed. It reminds me of a drawing toy I had when I
> > was a kid. Thanks a lot for sharing.
> >
> 
> Spirograph?
> 
> http://en.wikipedia.org/wiki/Spirograph

Exactly, that's it.

Plenty of beautiful patterns with just small change in parameters.
Maybe this can be adapted for (non-circular) ornaments as well,
which could be used for text decorations. It would make for a nice
module.

Marco

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Re: Numerical Calculations

[Andre Caldas]

> Here's the animated (video) version.
>
> http://www.youtube.com/watch?v=2_OZ-yKMd7g

How did you produce a video out of the PDF?
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Re: Numerical Calculations

[Troy Henderson]

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>
> How did you produce a video out of the PDF?
>

I wrote a BASH script to automate this process, but essentially it involves
converting each "frame"/page of the PDF to JPG and then combining the JPG
sequence into a MP4 movie.

The hypocycloid example has 191 frames, and so I did something like:

let n=0;
while [ $n -lt 191 ]
do
   convert -density 720 hypocycloid.pdf[$n] -resize "x720" -flatten
-gravity center -extent "1280x720" -quality 100 hypocycloid-$n.jpg
done
ffmpeg -r 13 -i hypocycloid-%d.jpg -b 5000k -vcodec libx264 -y
hypocycloid.mp4

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