OT: looking for metapost/fun examples

OT: looking for metapost/fun examples

[Gerben Wierda]

I am trying to learn metapost/fun, inline in ConTeXt source. Some basic 
things are clear, but now the issue is metapost itself.

For instance, I would like to plot a Fourier approximation of a block 
function.

For instance, I would like to plot a gaussian spread.

I am looking for examples on how to do this. I need to do a bit of 
programming here and these are my initial projects.

Thanks in advance,

G

Re: OT: looking for metapost/fun examples

[David Arnold]

Gerben,

I am so happy I can contribute as a way of thanking you for all the 
work that you've done for us. Thanks. Here, try this one, which uses an 
RK4 routine. I just tried it out in Texshop, so I know they both 
compile.

%This file creates two figures associated with the
%system x'=f(x,y), y'=g(x,y)
%1. Plots the graphs of x(t) and y(t)
%2. Plots the graph of (x(t),y(t)) in the phase plane.

%verbatimtex
%\input mtplain
%etex

%Generate standard eps
prologues:=2;

beginfig(0);

%Place RHS of x'=f(t,x,y) here
  def fxy(expr t, x, y)=
   (0.4-0.01*y)*x
  enddef;

%Place RHS of y'=g(t,x,y) here
  def gxy(expr t, x, y)=
   (-0.3+0.005*x)*y
  enddef;

%Declare some variables
  path q, trajx, trajy;
  pair L, R, B, T, xt, yt;
  numeric sx[], sy[];

%Initialize clipping window
  a:=0; b:=40;   %left and right of viewing rectangle
  c:=0; d:=150;  %bottom and top of viewing rectangle

%Initialize timespan
  tstart:=a;
  tstop:=b;

%Initialize number of points to be plotted
  N:=500;

%Calculate time increment dt for Euler's method
  dt:=(tstop-tstart)/N;

%Scaling factors for horizontal and vertical axes. Note that this 
produces
%an image that is 2 inches by 2 inches.
  (b-a)*ux=1.75in;
  (d-c)*uy=1.75in;

%Clipping boundary
  q=(a,c)--(b,c)--(b,d)--(a,d)--cycle;

%Use Runge-Kutta4 to create path (t,x(t))

%Choose initial condition
  t:=tstart;
  x:=40;
  y:=20;
  trajx:=(t,x);
  forever:
   sx1:=fxy(t,x,y);
   sy1:=gxy(t,x,y);
   sx2:=fxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
   sy2:=gxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
   sx3:=fxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
   sy3:=gxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
   sx4:=fxy((t+dt),(x+dt*sx3),(y+dt*sy3));
   sy4:=gxy((t+dt),(x+dt*sx3),(y+dt*sy3));
   x:=x+dt*(sx1+2*sx2+2*sx3+sx4)/6;
   y:=y+dt*(sy1+2*sy2+2*sy3+sy4)/6;
   t:=t+dt;
   trajx:=trajx..(t,x);
   exitif ((t>tstop) or (t>b) or (x<c) or (x>d));
  endfor;

%Use Runge-Kutta4 to create path (t,y(t))

%Choose initial condition
  t:=tstart;
  x:=40;
  y:=20;
  trajy:=(t,y);
  forever:
   sx1:=fxy(t,x,y);
   sy1:=gxy(t,x,y);
   sx2:=fxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
   sy2:=gxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
   sx3:=fxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
   sy3:=gxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
   sx4:=fxy((t+dt),(x+dt*sx3),(y+dt*sy3));
   sy4:=gxy((t+dt),(x+dt*sx3),(y+dt*sy3));
   x:=x+dt*(sx1+2*sx2+2*sx3+sx4)/6;
   y:=y+dt*(sy1+2*sy2+2*sy3+sy4)/6;
   t:=t+dt;
   trajy:=trajy..(t,y);
   exitif ((t>tstop) or (t>b) or (y<c) or (y>d));
  endfor;

%Draw the paths x(t) and y(t) and clip them to bounding box
  draw trajx xscaled ux yscaled uy withcolor red;
  draw trajy xscaled ux yscaled uy withcolor red dashed evenly;
  clip currentpicture to (q xscaled ux yscaled uy);

%Label graph x(t) and initial condition
  len:= 0.65*(length trajx);
  xt:=point len of trajx;
  label.urt(btex $\scriptstyle x(t)$ etex, (xt xscaled ux yscaled uy));

%Label graph y(t) and initial condition
  len:= 0.5*(length trajy);
  yt:=point len of trajy;
  label.lrt(btex $\scriptstyle y(t)$ etex, (yt xscaled ux yscaled uy));


%Initialize left and right endpoints on time-axis
  L=(a*ux,0);R=(b*ux,0);

%Draw and label t-axis
  drawarrow L--R;
  label.rt(btex $\scriptstyle t$ etex,(b*ux,0));

%Initialize bottom and top endpoints on time-axis
  B=(0,c*uy);T=(0,d*uy);

%Draw and label vertical axis
  drawarrow B--T;
  label.lft(btex $\scriptstyle 0$ etex, B);
  label.lft(btex $\scriptstyle 150$ etex, T);

endfig;


beginfig(2);

%Make some variables local
  save ux, uy;

%Place RHS of x'=f(t,x,y) here
  def fxy(expr t, x, y)=
   (0.4-0.01*y)*x
  enddef;

%Place RHS of y'=g(t,x,y) here
  def gxy(expr t, x, y)=
   (-0.3+0.005*x)*y
  enddef;

%Declare some variables
  path q, trajxy;
  pair L, R, B, T;

%Initialize clipping window
  a:=0; b:=150;   %left and right of viewing rectangle
  c:=0; d:=100;  %bottom and top of viewing rectangle

%Initialize timespan
  tstart:=a;
  tstop:=b;

%Initialize number of points to be plotted
  N:=500;

%Calculate time increment dt for Euler's method
  dt:=(tstop-tstart)/N;

%Scaling factors for horizontal and vertical axes. Note that this 
produces
%an image that is 2 inches by 2 inches.
  (b-a)*ux=1.75in;
  (d-c)*uy=1.75in;

%Clipping boundary
  q=(a,c)--(b,c)--(b,d)--(a,d)--cycle;

%Use Runge-Kutta4 to create path (x(t),y(t))

%Choose initial condition
  t:=tstart;
  x:=40;
  y:=20;
  trajxy:=(x,y);
  forever:
   sx1:=fxy(t,x,y);
   sy1:=gxy(t,x,y);
   sx2:=fxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
   sy2:=gxy((t+dt/2),(x+dt*sx1/2),(y+dt*sy1/2));
   sx3:=fxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
   sy3:=gxy((t+dt/2),(x+dt*sx2/2),(y+dt*sy2/2));
   sx4:=fxy((t+dt),(x+dt*sx3),(y+dt*sy3));
   sy4:=gxy((t+dt),(x+dt*sx3),(y+dt*sy3));
   x:=x+dt*(sx1+2*sx2+2*sx3+sx4)/6;
   y:=y+dt*(sy1+2*sy2+2*sy3+sy4)/6;
   t:=t+dt;
   trajxy:=trajxy..(x,y);
   exitif ((t>tstop) or (t>b) or (x<a) or (x>b) or (y<c) or (y>d));
  endfor;


%Draw the paths x(t) and y(t) and clip them to bounding box
  draw trajxy xscaled ux yscaled uy withcolor red;
  clip currentpicture to (q xscaled ux yscaled uy);

%Initialize left and right endpoints on x-axis
  L=(a*ux,0);R=(b*ux,0);

%Draw and label x-axis
  drawarrow L--R;
  label.rt(btex $\scriptstyle x$ etex,(b*ux,0));
  label.bot(btex $\scriptstyle 0$ etex,L);
  label.bot(btex $\scriptstyle 150$ etex,R);

%Initialize bottom and top endpoints on y-axis
  B=(0,c*uy);T=(0,d*uy);

%Draw and label vertical axis
  drawarrow B--T;
  label.rt(btex $\scriptstyle y$ etex,(0,d*uy));
  label.lft(btex $\scriptstyle 0$ etex, B);
  label.lft(btex $\scriptstyle 100$ etex, T);

endfig;

end;


On Mar 26, 2005, at 3:19 PM, Gerben Wierda wrote:

> I am trying to learn metapost/fun, inline in ConTeXt source. Some 
> basic things are clear, but now the issue is metapost itself.
>
> For instance, I would like to plot a Fourier approximation of a block 
> function.
>
> For instance, I would like to plot a gaussian spread.
>
> I am looking for examples on how to do this. I need to do a bit of 
> programming here and these are my initial projects.
>
> Thanks in advance,
>
> G
>
> _______________________________________________
> ntg-context mailing list
> ntg-context@ntg.nl
> http://www.ntg.nl/mailman/listinfo/ntg-context
>

Re: OT: looking for metapost/fun examples

[David Arnold]

Gerben, Again, thanks for all you do. Here's a Fourier approximation of 
a square wave. Again, I compiled this in Texshop so I know it works.

%verbatimtex
% \input mtplain
% \MTMI{8pt}{6pt}{5pt}
% \MTSY{8pt}{6pt}{5pt}
% \MTEX{8pt}
% \MathRoman{tir}{8pt}{6pt}{5pt}
% \MathBold{tib}{8pt}{6pt}{5pt}
%etex

%Input Context macros
input mp-tool

%define ytick
  vardef ytick(expr pos)=
   path p;
   p:=(-2,0)--(2,0);
   draw p shifted pos;
  enddef;

%define xtick
  vardef xtick(expr pos)=
   path p;
   p:=(0,-2)--(0,2);
   draw p shifted pos;
  enddef;

%define pi
  pi:=3.14159;

%define cosine in radians
  vardef cos(expr x)=
   cosd(x*180/pi)
  enddef;

%define sine in radians
  vardef sin(expr x)=
   sind(x*180/pi)
  enddef;

%hyperbolic sine
  vardef sinh(expr x)=
   (exp(x)-exp(-x))/2
  enddef;

beginfig(1);

%enter number of terms
  numeric N;
  N=6;

%define L
  numeric L;
  L:=pi;

%define a_0
  ao:=1;

%define a_n
  vardef a(expr n)=
   2*sin(n*pi/2)/(n*pi)
  enddef;

%define b_n
  vardef b(expr n)=
   0
  enddef;

%initialize scale
  numeric ux, uy;
  pi*ux=2in; 1.5*uy=2in;

%draw axes
  drawarrow (0,0)--(3.5ux,0);
  drawarrow (0,0)--(0,1.5uy);

%label axes
  label.rt(btex $x$ etex, (3.5ux,0));

%tick marks
  xtick((pi*ux,0));
  label.bot(btex $\pi$ etex, (pi*ux,0));
  ytick((0,1*uy));
  label.lft(btex $1$ etex, (0,1*uy));

%draw the function in black
  draw (0,1uy)--((pi/2)*ux,1uy);

%draw Fourier approximation in cyan
  path p;
  numeric x, y;
  x:=0;
  y:=ao/2;
  for k=1 step 1 until N:
   y:=y+a(k)*cos(k*pi*x/L)+b(k)*sin(k*pi*x/L);
  endfor;
  p:=(x,y);
  for x=0 step .1 until pi:
   y:=ao/2;
   for k=1 step 1 until N:
    y:=y+a(k)*cos(k*pi*x/L)+b(k)*sin(k*pi*x/L);
   endfor;
   p:=p--(x,y);
  endfor;
  x:=pi;
  y:=ao/2;
  for k=1 step 1 until N:
   y:=y+a(k)*cos(k*pi*x/L)+b(k)*sin(k*pi*x/L);
  endfor;
  p:=p--(x,y);
  p:=p xyscaled(ux,uy);
  draw p withcolor cyan;

endfig;


beginfig(0);

%enter number of terms
  numeric N;
  N=6;

%define L
  numeric L;
  L:=pi;

%define a_0
  ao:=1;

%define a_n
  vardef a(expr n)=
   2*sin(n*pi/2)/(n*pi)
  enddef;

%define b_n
  vardef b(expr n)=
   0
  enddef;

%initialize scale
  numeric ux, uy;
  6*pi*ux=2in; 1.5*uy=2in;

%draw axes
  drawdblarrow (-3.5*pi*ux,0)--(3.5*pi*ux,0);
  drawarrow (0,0)--(0,1.5uy);

%label axes
  label.rt(btex $x$ etex, (3.5*pi*ux,0));

%tick marks
  xtick((pi*ux,0));
  xtick((2*pi*ux,0));
  xtick((3*pi*ux,0));
  label.bot(btex $3\pi$ etex, (3*pi*ux,0));
  xtick((-pi*ux,0));
  xtick((-2*pi*ux,0));
  xtick((-3*pi*ux,0));
  label.bot(btex $-3\pi$ etex, (-3*pi*ux,0));
  ytick((0,1*uy));
  label.lft(btex $1$ etex, (0,1*uy));

%draw the function in black
  path q;
  q:=(-pi/2,1)--(pi/2,1);
  q:=q xyscaled(ux,uy);
  draw q;
  draw q shifted (2*pi*ux,0);
  draw q shifted (-2*pi*ux,0);

%draw Fourier approximation in cyan
  path p;
  numeric x, y;
  x:=-3*pi;
  y:=ao/2;
  for k=1 step 1 until N:
   y:=y+a(k)*cos(k*pi*x/L)+b(k)*sin(k*pi*x/L);
  endfor;
  p:=(x,y);
  for x=-3*pi step .1 until 3*pi:
   y:=ao/2;
   for k=1 step 1 until N:
    y:=y+a(k)*cos(k*pi*x/L)+b(k)*sin(k*pi*x/L);
   endfor;
   p:=p--(x,y);
  endfor;
  x:=3*pi;
  y:=ao/2;
  for k=1 step 1 until N:
   y:=y+a(k)*cos(k*pi*x/L)+b(k)*sin(k*pi*x/L);
  endfor;
  p:=p--(x,y);
  p:=p xyscaled(ux,uy);
  draw p withcolor cyan;

endfig;
end;


On Mar 26, 2005, at 3:19 PM, Gerben Wierda wrote:

> I am trying to learn metapost/fun, inline in ConTeXt source. Some 
> basic things are clear, but now the issue is metapost itself.
>
> For instance, I would like to plot a Fourier approximation of a block 
> function.
>
> For instance, I would like to plot a gaussian spread.
>
> I am looking for examples on how to do this. I need to do a bit of 
> programming here and these are my initial projects.
>
> Thanks in advance,
>
> G
>
> _______________________________________________
> ntg-context mailing list
> ntg-context@ntg.nl
> http://www.ntg.nl/mailman/listinfo/ntg-context
>

Re: OT: looking for metapost/fun examples

[Thomas A.Schmitz]

Gerben,

I assume you already know about the wonderful metafun manual 
(http://www.pragma-ade.com/general/manuals/metafun-s.pdf). I also found 
this website extremely useful: 
http://tex.loria.fr/prod-graph/zoonekynd/metapost/metapost.html

HTH

Thomas
On Mar 27, 2005, at 12:19 AM, Gerben Wierda wrote:

> I am trying to learn metapost/fun, inline in ConTeXt source. Some 
> basic things are clear, but now the issue is metapost itself.
>
> For instance, I would like to plot a Fourier approximation of a block 
> function.
>
> For instance, I would like to plot a gaussian spread.
>
> I am looking for examples on how to do this. I need to do a bit of 
> programming here and these are my initial projects.
>
> Thanks in advance,
>
> G
>
> _______________________________________________
> ntg-context mailing list
> ntg-context@ntg.nl
> http://www.ntg.nl/mailman/listinfo/ntg-context
>