Jump to content

File:Triple torus array.png

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (1,123 × 990 pixels, file size: 250 KB, MIME type: image/png)

Description Illustration of a triple torus
Date Oleg Alexandrov (talk) 23:48, 12 July 2008 (UTC)
Source Own work
 
This diagram was created with MATLAB.
Author Oleg Alexandrov
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code (MATLAB)

% illustration of a triple 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:(5*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(-146, 42);

% add in a source of light
   camlight (-50, 54); lighting phong;

% save as png
  print('-dpng', '-r500', sprintf('Triple_torus_illustration.png'));
   
% This function constructs the second and third rings in the triple torus
% by mapping from the first one.
function y=my_map(x, K, c)

   if x > 2*K
      y = -my_map(4*K - x, K, c);
   else

      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
      
   end
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “Triple torus array.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

File history

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

Date/TimeThumbnailDimensionsUserComment
current23:47, 12 July 2008Thumbnail for version as of 23:47, 12 July 20081,123 × 990 (250 KB)Oleg Alexandrov{{Information |Description={{en|1=x}} |Source=Own work by uploader |Author=Oleg Alexandrov |Date=x |Permission=x |other_versions=x }} x {{ImageUpload|full}} Category:x

The following page uses this file:

Global file usage

The following other wikis use this file: