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This chart was created with MATLAB. 
Description 
Illustration of en:Double torus 
Date 
05:50, 6 September 2007 (UTC) 
Source 
Own work 
Author 
Oleg Alexandrov 
Public domainPublic domainfalsefalse 

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.Public domainPublic domainfalsefalse

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 = (Kbh):h:(3*Kb+h); m = length(X);
Y = (Kbh):h:(Kb+h); n = length(Y);
Z = (rh):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.^2r^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 < Kc
y = x;
else
y = (Kc) + sin((x  (Kc))*(pi/2/c));
end
File usage
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