Image:Double torus illustration.png

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Description

Illustration of en:Double torus

Source

self-made

Date

05:50, 6 September 2007 (UTC)

Author

Oleg Alexandrov

Permission
( Reusing this image)

see below



Public domain
I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


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Source code

% illustration of a double torus, obtained as an isosurface
function main()
 
   % big and small radii of the torus
   R = 3; r = 1; 
 
   % c controls the transition from one ring to the other
   c = 1.3*pi/2;
 
   Kb = R+r;
 
   h = 0.1; % h is the grid size. Smaller h means prettier picture.
 
   X = (-Kb-h):h:(3*Kb+h); m = length(X);
   Y = (-Kb-h):h:(Kb+h);   n = length(Y);
   Z = (-r-h):h:(r+h);     k = length(Z);
 
   W = zeros(m, n, k); % the zero level set of this function will be the desired shape
 
   for i=1:m
      for j=1:n
         x = X(i); x = my_map(x, Kb, c);   % map from two torii to one torus
         y = Y(j); 
         W(i, j, :) = (sqrt(x^2+y^2)-R)^2 + Z.^2-r^2; % torus eqn, vectorize in Z
      end
   end
 
   figure(4); clf; hold on; axis equal; axis off;
 
   H = patch(isosurface(W, 0));
   isonormals(W, H);
 
   light_green=[184, 224, 98]/256;
 
   % set some propeties
   set(H, 'FaceColor', light_green, 'EdgeColor','none', 'FaceAlpha', 1);
   set(H, 'SpecularColorReflectance', 0.1, 'DiffuseStrength', 0.8);
   set(H, 'FaceLighting', 'phong', 'AmbientStrength', 0.3);
   set(H, 'SpecularExponent', 108);
 
   daspect([1 1 1]);
   axis tight;
   colormap(prism(28))
 
% viewing angle
   view(-165, 42);
 
% add in a source of light
   camlight (-50, 54); lighting phong;
 
% save as png
  print('-dpng', '-r500', sprintf('Double_torus_illustration.png'));
 
% This function constructs the second ring in the double torus
% by mapping from the first one.
function y=my_map(x, K, c)
 
   if x > K
      x = 2*K - x;
   end
 
   if x < K-c
      y = x;
   else
      y = (K-c) + sin((x - (K-c))*(pi/2/c));
   end

File history

Click on a date/time to view the file as it appeared at that time.

Date/Time Dimensions User Comment
current 04:32, 12 July 2008 985×1,077 (260 KB) Oleg Alexandrov (Higher quality version, using isosurface instead of patches. Same license and all that.)
05:49, 6 September 2007 1,176×1,240 (350 KB) Oleg Alexandrov ({{Information |Description= |Source=self-made |Date=Illustration of en:Double torus |Author= Oleg Alexandrov }} {{PD-self}} Category:Differential geometry Category:Files by User:Oleg Alexandrov from en.wikipedia)
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