Beginner's help for a graphic for a free physics textbook

[Matthias Brennwald]

On 31.03.2009, at 19:03, help-octave-request at octave.org wrote:

> Date: Tue, 31 Mar 2009 17:33:15 +0200
> From: Christoph Schiller <cs at motionmountain.net>
> Subject: Beginner's help for a graphic for a free physics textbook
> To: help-octave at octave.org
> Message-ID: <309EE733-D2B3-452B-8A40-60FE746F4AFE at motionmountain.net>
> Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes
>
> With permission form the original author I would like to produce an
> improved version of the animated graphic shown at
> http://en.wikipedia.org/wiki/File:Snells_law_wavefronts.gif
>
> I'd like to add the animation to my 1600 page physics textbook in pdf
> format
> that I offer on the internet for free.
> The original graphics was made in MATLAB (the code is given below.)
>
> I have Mac OSX 10.5.6 and downloaded and installed Octave
> just to produce this graphic. So I have a few questions (I have never
> used either Octave nor MATLAB):
>
> 1 - Does the code shown below run on Octave?
> 2 - How do I input a command file in Octave? (I did not find this in
> the help files)
> 3 - Will I be able to produce and save the gif on OSX or do I need
> other packages?
>
> (Here is what I plan to change in the graphics of Snell's law:
> - introduce a shaded region in blue to show where the water is
> - take out the grey line (becomes unnecessary)
> - make the blue lines green (to contrast with the blue water)
> - make the wave front lines half the thickness they are now (will be
> more pretty)
> )
>
> Any help will be appreciated by the readers world-wide - thank you in
> advance!
>
> Best regards
>
> Christoph Schiller
> The free physics textbook
> www.motionmountain.net
>
>
> P.S. Here is the original, unmodified code:
>
>
> % Illustration of Snell's law
> function main()
>
>   % indexes of refraction
>   n1=1.0;
>   n2=1.5;
>
>   sign = -1;% is the source up or down?
>   O=[0, -1*sign];
>   k=500;
>
>
> % KSmrq's colors
>   red    = [0.867 0.06 0.14];
>   blue   = [0, 129, 205]/256;
>   green  = [0, 200,  70]/256;
>   yellow = [254, 194,   0]/256;
>   white = 0.99*[1, 1, 1];
>   black = [0, 0, 0];
>   gray = 0.5*white;
>
>   color1=red;
>   color2=blue;
>   color3=gray;
>   lw = 3;
>
>   plot_line=0;
>   Theta=linspace(0, 2*pi, k);
>   V=0*Theta; W=0*Theta;
>   S0=7;
>   spacing=0.45;
>   p=floor(S0/spacing);
>   S=linspace(0, S0, p+1);
>   spacing=S(2)-S(1);
>
>   num_frames = 10;
>   for frame_iter=1:num_frames
>
>      figure(1); clf; hold on; axis equal; axis off;
>
>      % plot the interface between diellectrics
>      L=1.2*S0;
>      plot([-L, L], [0, 0], 'color', color3, 'linewidth', lw);
>
>
>      % plot a ray
>      plot_line=1;
>      s=L;
>      theta=pi/3; wfr(s, theta, n1, n2, O, sign, plot_line, color1,  
> lw);
>
>      % plot the wafefronts
>      plot_line=0;
>      for i=1:p
>
>         s=S(i)+spacing*(frame_iter-1)/num_frames;
>
>         for j=1:k
>            theta=Theta(j);
>            [V(j), W(j)]=wfr(s, theta, n1, n2, O, sign, plot_line,
> color1,
> lw);
>         end
>         plot(V, W, 'color', color2, 'linewidth', lw);
>      end
>
>
>      %  dummy points to enlarge the bounding box
>      plot(0, S0+2.5*spacing, '*', 'color', white);
>      plot(0, -(S0+2.5*spacing)/n2, '*', 'color', white);
>
>      % to know where to crop later
>      Lx=3.2; Ly=Lx; shift = 1;
>      plot([-Lx, Lx, Lx, -Lx -Lx], ...
>           [-Ly, -Ly, Ly, Ly, -Ly]+shift);
>
>      file = sprintf('Frame%d.eps', 1000+frame_iter);
>      disp(file);
>      saveas(gcf, file, 'psc2')
>   end
>
> % Converted to gif with the UNIX command
> % convert -density 100 -antialias Frame10* Snell_animation.gif
> % then cropped in Gimp
>
> function [a, b]=wfr(s, theta, n1, n2, O, sign, plot_line, color1, lw);
>
>   X=O+s*[sin(theta), sign*cos(theta)];
>
>  if( sign*X(2) > 0 )
>    t=-sign*O(2)/cos(theta);
>    X0=O+t*[sin(theta), sign*cos(theta)];
>
>    if (plot_line == 1)
>      plot([O(1), X0(1)], [O(2), X0(2)], 'color', color1, 'linewidth',
> lw,
> 'linestyle', '--');
>    end
>
>    d = norm(O-X0);
>    r = (s-d)*(n2/n1)^(sign);
>
>    theta2=asin(n1*sin(theta)/n2);
>    XE=X0+r*[sin(theta2), sign*cos(theta2)];
>  else
>    XE = X;
>  end
>  a = XE(1);
>  b = XE(2);
>
>  if (plot_line==1)
>    plot([X0(1), XE(1)], [X0(2), XE(2)], 'color', color1, 'linewidth',
> lw,
> 'linestyle', '--');
>  end


Dear Christoph

I tried your script, and it seems to work with Octave with a minor  
modification. I replaced the line

    saveas(gcf, file, 'psc2')

by

    print (file,'-depsc');

To save the frames to eps files, which you may then convert to gif  
files. Alternatively, to save to gif files directly, replace

      file = sprintf('Frame%d.eps', 1000+frame_iter);
      disp(file);
      saveas(gcf, file, 'psc2')

by

      file = sprintf('Frame%d.gif', 1000+frame_iter);
      disp(file);
      print (file,'-dgif');

to save the frames to gif files directly. This worked for me on Mac OS  
X (but I may have non-standard stuff installed that allowed me to  
produce gifs from Octave/gnuplot directly).

To run your script, save it to an m file (e.g. snell.m, in ASCII  
format), run Octave, cd to the path where the script file lives and  
run it by typing the file name without the extension (snell in my  
example) to the Octave prompt.

IHTH,
Matthias

--
Matthias Brennwald
Käferholzstrasse 173
CH 8046 Zürich
+41 364 17 03